diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex.html index f192334d1..0c61993ba 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex.html @@ -1,10 +1,10 @@ - + Complex Number Inverse Trigonometric Functions - - - + + + @@ -20,11 +20,11 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+

- Complex + Complex Number Inverse Trigonometric Functions

@@ -53,7 +53,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -61,7 +61,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acos.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acos.html index e8cb8da74..a360f555c 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acos.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acos.html @@ -1,10 +1,10 @@ - + acos - - - + + + @@ -20,22 +20,22 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+
- - Header: + + Header: 
#include <boost/math/complex/acos.hpp>
- - Synopsis: + + Synopsis: 
template<class T> 
 std::complex<T> acos(const std::complex<T>& z);
@@ -50,7 +50,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -58,7 +58,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acosh.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acosh.html index cbdddd2ac..ab35e0c0c 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acosh.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acosh.html @@ -1,10 +1,10 @@ - + acosh - - - + + + @@ -20,22 +20,22 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+
- - Header: + + Header: 
#include <boost/math/complex/acosh.hpp>
- - Synopsis: + + Synopsis: 
template<class T> 
 std::complex<T> acosh(const std::complex<T>& z);
@@ -50,7 +50,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -58,7 +58,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asin.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asin.html index f7cbe5648..895d8276a 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asin.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asin.html @@ -1,10 +1,10 @@ - + asin - - - + + + @@ -20,22 +20,22 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+
- - Header: + + Header: 
#include <boost/math/complex/asin.hpp>
- - Synopsis: + + Synopsis: 
template<class T> 
 std::complex<T> asin(const std::complex<T>& z);
@@ -50,7 +50,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -58,7 +58,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asinh.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asinh.html index 473179a9d..35742664e 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asinh.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/asinh.html @@ -1,10 +1,10 @@ - + asinh - - - + + + @@ -20,22 +20,22 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+
- - Header: + + Header: 
#include <boost/math/complex/asinh.hpp>
- - Synopsis: + + Synopsis: 
template<class T> 
 std::complex<T> asinh(const std::complex<T>& z);
@@ -50,7 +50,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -58,7 +58,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atan.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atan.html index 2d9900d33..fc3f59c98 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atan.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atan.html @@ -1,10 +1,10 @@ - + atan - - - + + + @@ -20,22 +20,22 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+
- - Header: + + Header: 
#include <boost/math/complex/atan.hpp>
- - Synopsis: + + Synopsis: 
template<class T> 
 std::complex<T> atan(const std::complex<T>& z);
@@ -50,7 +50,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -58,7 +58,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atanh.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atanh.html index a6432ba07..3a59f3f65 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atanh.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/atanh.html @@ -1,10 +1,10 @@ - + atanh - - - + + + @@ -20,22 +20,22 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+
- - Header: + + Header: 
#include <boost/math/complex/atanh.hpp>
- - Synopsis: + + Synopsis: 
template<class T> 
 std::complex<T> atanh(const std::complex<T>& z);
@@ -50,7 +50,7 @@
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -58,7 +58,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/history.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/history.html index 8f22abba9..576087d02 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/history.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/history.html @@ -1,10 +1,10 @@ - + History - - - + + + @@ -19,24 +19,24 @@
-PrevUpHome +PrevUpHome
-
+
-
    -
  • - 2005/12/17: Added support for platforms with no meaningful numeric_limits<>::infinity(). -
    • -
  • - 2005/12/01: Initial version, added as part of the TR1 library. -
    • +
      +
    • + 2005/12/17: Added support for platforms with no meaningful numeric_limits<>::infinity(). +
      • +
    • + 2005/12/01: Initial version, added as part of the TR1 library. +
-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -44,7 +44,7 @@
-PrevUpHome +PrevUpHome
diff --git a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/implementation.html b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/implementation.html index e41e49909..4a7ff8de0 100644 --- a/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/implementation.html +++ b/doc/complex/html/complex_number_tr1_algorithms/inverse_complex/implementation.html @@ -1,10 +1,10 @@ - + Implementation and Accuracy - - - + + + @@ -20,11 +20,11 @@
-PrevUpHomeNext +PrevUpHomeNext
-
+

@@ -47,7 +47,7 @@

-
Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -55,7 +55,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/complex/html/index.html b/doc/complex/html/index.html index 080c36e00..23b5a60f8 100644 --- a/doc/complex/html/index.html +++ b/doc/complex/html/index.html @@ -1,10 +1,10 @@ - + Complex Number TR1 Algorithms - - - + + + @@ -17,8 +17,8 @@ More
-
Next
-
+
Next
+

@@ -26,9 +26,9 @@

John Maddock

-

Copyright © 2005 John Maddock

+

Copyright © 2005 John Maddock

-

+

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -70,6 +70,6 @@
-
Next
+
Next
diff --git a/doc/distexplorer/html/index.html b/doc/distexplorer/html/index.html index 0a21d5ffe..3c5379970 100644 --- a/doc/distexplorer/html/index.html +++ b/doc/distexplorer/html/index.html @@ -1,9 +1,9 @@ - + Statistical Distribution Explorer - - + + @@ -17,7 +17,7 @@
-
+

@@ -30,9 +30,9 @@ John Maddock

-

Copyright © 2008 Paul A. Bristow, John Maddock

+

Copyright © 2008 Paul A. Bristow, John Maddock

-

+

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -47,115 +47,115 @@

The distributions provided are:

-
    -
  • - bernoulli -
    • -
  • - beta_distribution -
    • -
  • - binomial_distribution -
    • -
  • - cauchy -
    • -
  • - chi_squared -
    • -
  • - exponential -
    • -
  • - extreme_value -
    • -
  • - fisher_f -
    • -
  • - gamma_distribution -
    • -
  • - lognormal_distribution -
    • -
  • - negative_binomial_distribution -
    • -
  • - normal_distribution -
    • -
  • - pareto -
    • -
  • - poisson -
    • -
  • - rayleigh -
    • -
  • - students_t -
    • -
  • - triangular -
    • -
  • - uniform -
    • -
  • - weibull -
    • +
      +
    • + bernoulli +
      • +
    • + beta_distribution +
      • +
    • + binomial_distribution +
      • +
    • + cauchy +
      • +
    • + chi_squared +
      • +
    • + exponential +
      • +
    • + extreme_value +
      • +
    • + fisher_f +
      • +
    • + gamma_distribution +
      • +
    • + lognormal_distribution +
      • +
    • + negative_binomial_distribution +
      • +
    • + normal_distribution +
      • +
    • + pareto +
      • +
    • + poisson +
      • +
    • + rayleigh +
      • +
    • + students_t +
      • +
    • + triangular +
      • +
    • + uniform +
      • +
    • + weibull +

    Properties of distributions computed are:

    -
      -
    • - mean -
      • -
    • - mode -
      • -
    • - median -
      • -
    • - variance -
      • -
    • - standard deviation -
      • -
    • - coefficient of variation, -
      • -
    • - skewness -
      • -
    • - kurtosis -
      • -
    • - excess -
      • -
    • - range supported -
      • +
        +
      • + mean +
        • +
      • + mode +
        • +
      • + median +
        • +
      • + variance +
        • +
      • + standard deviation +
        • +
      • + coefficient of variation, +
        • +
      • + skewness +
        • +
      • + kurtosis +
        • +
      • + excess +
        • +
      • + range supported +

      Calculated, from values provided, are:

      -
        -
      • - probability density (or mass) function (PDF) -
        • -
      • - cumulative distribution function (CDF), and complement -
        • -
      • - Quantiles (percentiles) are calculated for typical risk (alpha) probabilities - (0.001, 0.01, 0.5, 0.1, 0.333) and for additional probabilities provided by - the user. -
        • +
          +
        • + probability density (or mass) function (PDF) +
          • +
        • + cumulative distribution function (CDF), and complement +
          • +
        • + Quantiles (percentiles) are calculated for typical risk (alpha) probabilities + (0.001, 0.01, 0.5, 0.1, 0.333) and for additional probabilities provided + by the user. +

        Results can be saved to text files using Save or SaveAs. All the values on the @@ -207,7 +207,7 @@

      - +

      Last revised: February 26, 2009 at 17:08:18 GMT

      Last revised: July 01, 2010 at 21:45:23 GMT
      diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm.html index 1e19f7f93..c3752fb7d 100644 --- a/doc/gcd/html/gcd_and_lcm/gcd_lcm.html +++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm.html @@ -3,7 +3,7 @@ Greatest Common Divisor and Least Common Multiple - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +

      Greatest Common Divisor and Least Common Multiple diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/compile_time.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/compile_time.html index 744ff1f53..d0fbbcd48 100644 --- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/compile_time.html +++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/compile_time.html @@ -3,7 +3,7 @@ Compile time GCD and LCM determination - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +

      Compile time GCD and LCM determination @@ -59,7 +59,7 @@ range of static_gcd_type.

      - + Example 

      #include <boost/math/common_factor.hpp>
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/credits.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/credits.html
index e4054e5c3..fca8975f6 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/credits.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/credits.html
@@ -3,7 +3,7 @@
 
 Credits
 
-
+
 
 
 
@@ -21,7 +21,7 @@
 
      
 PrevUpHome
 
      
-
      
+
      
 
      
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/demo.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/demo.html
index 82132cfdd..910b3862d 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/demo.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/demo.html
@@ -3,7 +3,7 @@
 
 Demonstration Program
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
      
 PrevUpHomeNext
 
      
-
      
+
      
 
      
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/gcd_function_object.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/gcd_function_object.html
index e683bd11b..6f2e5fb7c 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/gcd_function_object.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/gcd_function_object.html
@@ -3,7 +3,7 @@
 
 GCD Function Object
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
      
 PrevUpHomeNext
 
      
-
      
+
      
 
      
 GCD Function
       Object
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/header.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/header.html
index bada0c749..d57c4f2d8 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/header.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/header.html
@@ -3,7 +3,7 @@
 
 Header <boost/math/common_factor.hpp>
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
      
 PrevUpHomeNext
 
      
-
      
+
      
 
      
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/history.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/history.html
index 1176af3e4..77ea90290 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/history.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/history.html
@@ -3,7 +3,7 @@
 
 History
 
-
+
 
 
 
@@ -22,18 +22,18 @@
 
      
 PrevUpHomeNext
 
      
-
      
+
      
 
      
-
        
-
      • 
+
          
+
        • 
             17 Dec 2005: Converted documentation to Quickbook Format.
           
          • 
-
        • 
+
        • 
             2 Jul 2002: Compile-time and run-time items separated to new headers.
           
          • 
-
        • 
+
        • 
             7 Nov 2001: Initial version
           
          • 
 
        
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/introduction.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/introduction.html
index 33429c94a..63f98c485 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/introduction.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/introduction.html
@@ -3,7 +3,7 @@
 
 Introduction
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
        
 PrevUpHomeNext
 
        
-
        
+
        
 
        
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/lcm_function_object.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/lcm_function_object.html
index bae89db02..2f929be86 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/lcm_function_object.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/lcm_function_object.html
@@ -3,7 +3,7 @@
 
 LCM Function Object
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
        
 PrevUpHomeNext
 
        
-
        
+
        
 
        
 LCM Function
       Object
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/rationale.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/rationale.html
index dec9b9642..4de0ed491 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/rationale.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/rationale.html
@@ -3,7 +3,7 @@
 
 Rationale
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
        
 PrevUpHomeNext
 
        
-
        
+
        
 
        
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/run_time.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/run_time.html
index a906db25e..e5c95bf58 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/run_time.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/run_time.html
@@ -3,7 +3,7 @@
 
 Run-time GCD & LCM Determination
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
        
 PrevUpHomeNext
 
        
-
        
+
        
 
        
  Run-time GCD & LCM
       Determination
diff --git a/doc/gcd/html/gcd_and_lcm/gcd_lcm/synopsis.html b/doc/gcd/html/gcd_and_lcm/gcd_lcm/synopsis.html
index 35817d62d..c6f42f123 100644
--- a/doc/gcd/html/gcd_and_lcm/gcd_lcm/synopsis.html
+++ b/doc/gcd/html/gcd_and_lcm/gcd_lcm/synopsis.html
@@ -3,7 +3,7 @@
 
 Synopsis
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
        
 PrevUpHomeNext
 
        
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+
        
 
        
diff --git a/doc/gcd/html/index.html b/doc/gcd/html/index.html
index c60435190..d72fd4d26 100644
--- a/doc/gcd/html/index.html
+++ b/doc/gcd/html/index.html
@@ -3,7 +3,7 @@
 
 GCD and LCM
 
-
+
 
 
 
@@ -18,7 +18,7 @@
 
 
        
 
        Next
        
-
        
+
        
 
        
 
        
 
        
@@ -28,7 +28,7 @@
 
        
 
        Copyright © 2001 -2002 Daryle Walker
        
 
        
-
        
+
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
diff --git a/doc/html/index.html b/doc/html/index.html
index 84e4c7a2f..6fc94d160 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -1,9 +1,9 @@
 
 
-
+
 Boost.Math
-
-
+
+
 
 
 
@@ -17,7 +17,7 @@
 
 
        
 
        
-
        
+
        
 
        
 
        
 
        
@@ -42,7 +42,7 @@
 Bruno Lalande
 
        
 
        
-Johan Råde
+Johan Råde
 
        
 
        
 Gautam Sewani
@@ -51,11 +51,11 @@
 Thijs van den Berg
 
        
 
        
-
        Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Daryle Walker, Xiaogang Zhang, Bruno Lalande, Johan Råde,
+
        Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
+      Hubert Holin, Daryle Walker, Xiaogang Zhang, Bruno Lalande, Johan Råde,
       Gautam Sewani and Thijs van den Berg
        
 
        
-
        
+
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -73,249 +73,254 @@
 
 
 
-          
        
-            Library
-          
        
+            
        
+              Library
+            
        
           
 
-          
        
-            Description
-          
        
+            
        
+              Description
+            
        
           
 
 
 
 
-          
        
-            Complex Number Inverse Trigonometric Functions
-          
        
-          
        
-            HTML Docs
-          
        
-          
        
-            PDF
-            Docs
-          
        
+            
        
+              Complex Number Inverse Trigonometric Functions
+            
        
+            
        
+              HTML Docs
+            
        
+            
        
+              PDF
+              Docs
+            
        
           
 
-          
        
-            These complex number algorithms are the inverses of trigonometric functions
-            currently present in the C++ standard. Equivalents to these functions
-            are part of the C99 standard, and are part of the Technical
-            Report on C++ Library Extensions.
-          
        
+            
        
+              These complex number algorithms are the inverses of trigonometric functions
+              currently present in the C++ standard. Equivalents to these functions
+              are part of the C99 standard, and are part of the Technical
+              Report on C++ Library Extensions.
+            
        
           
 
 
 
-          
        
-            Greatest Common Divisor and Least Common Multiple
-          
        
-          
        
-            HTML Docs
-          
        
-          
        
-            PDF
-            Docs
-          
        
+            
        
+              Greatest Common Divisor and Least Common Multiple
+            
        
+            
        
+              HTML Docs
+            
        
+            
        
+              PDF
+              Docs
+            
        
           
 
-          
        
-            The class and function templates in <boost/math/common_factor.hpp>
-            provide run-time and compile-time evaluation of the greatest common divisor
-            (GCD) or least common multiple (LCM) of two integers. These facilities
-            are useful for many numeric-oriented generic programming problems.
-          
        
+            
        
+              The class and function templates in <boost/math/common_factor.hpp>
+              provide run-time and compile-time evaluation of the greatest common
+              divisor (GCD) or least common multiple (LCM) of two integers. These
+              facilities are useful for many numeric-oriented generic programming
+              problems.
+            
        
           
 
 
 
-          
        
-            Octonions
-          
        
-          
        
-            HTML Docs
-          
        
-          
        
-            PDF
-            Docs
-          
        
+            
        
+              Octonions
+            
        
+            
        
+              HTML Docs
+            
        
+            
        
+              PDF
+              Docs
+            
        
           
 
-          
        
-            Octonions, like quaternions,
-            are a relative of complex numbers.
-          
        
-          
        
-            Octonions see some use in theoretical physics.
-          
        
-          
        
-            In practical terms, an octonion is simply an octuple of real numbers
-            (α,β,γ,δ,ε,ζ,η,θ), which we can write in the form o = α + βi + γj + δk + εe' + ζi' + ηj' + θk',
-            where i, j
-            and k are the same objects as
-            for quaternions, and e', i',
-            j' and k'
-            are distinct objects which play essentially the same kind of role as
-            i (or j
-            or k).
-          
        
-          
        
-            Addition and a multiplication is defined on the set of octonions, which
-            generalize their quaternionic counterparts. The main novelty this time
-            is that the multiplication is not only not commutative,
-            is now not even associative (i.e. there are quaternions x,
-            y and z
-            such that x(yz) ≠ (xy)z). A way
-            of remembering things is by using the following multiplication table:
-          
        
-          
        
-            octonion_blurb17
-          
        
-          
        
-            Octonions (and their kin) are described in far more details in this other
-            document (with errata
-            and addenda).
-          
        
-          
        
-            Some traditional constructs, such as the exponential, carry over without
-            too much change into the realms of octonions, but other, such as taking
-            a square root, do not (the fact that the exponential has a closed form
-            is a result of the author, but the fact that the exponential exists at
-            all for octonions is known since quite a long time ago).
-          
        
+            
        
+              Octonions, like quaternions,
+              are a relative of complex numbers.
+            
        
+            
        
+              Octonions see some use in theoretical physics.
+            
        
+            
        
+              In practical terms, an octonion is simply an octuple of real numbers
+              (α,β,γ,δ,ε,ζ,η,θ), which we can write in the form o = α + βi + γj + δk + εe' + ζi' + ηj' + θk',
+              where i, j
+              and k are the same objects
+              as for quaternions, and e',
+              i', j'
+              and k' are distinct objects
+              which play essentially the same kind of role as i
+              (or j or k).
+            
        
+            
        
+              Addition and a multiplication is defined on the set of octonions, which
+              generalize their quaternionic counterparts. The main novelty this time
+              is that the multiplication is not only not commutative,
+              is now not even associative (i.e. there are quaternions
+              x, y
+              and z such that x(yz)
+              ≠ (xy)z). A way of remembering things is by using
+              the following multiplication table:
+            
        
+            
        
+              octonion_blurb17
+            
        
+            
        
+              Octonions (and their kin) are described in far more details in this
+              other document (with
+              errata and addenda).
+            
        
+            
        
+              Some traditional constructs, such as the exponential, carry over without
+              too much change into the realms of octonions, but other, such as taking
+              a square root, do not (the fact that the exponential has a closed form
+              is a result of the author, but the fact that the exponential exists
+              at all for octonions is known since quite a long time ago).
+            
        
           
 
 
 
-          
        
-            Special Functions
-          
        
-          
        
-            HTML Docs
-          
        
-          
        
-            PDF
-            Docs
-          
        
+            
        
+              Special Functions
+            
        
+            
        
+              HTML Docs
+            
        
+            
        
+              PDF
+              Docs
+            
        
           
 
-          
        
-            Provides a number of high quality special functions, initially these
-            were concentrated on functions used in statistical applications along
-            with those in the Technical Report on C++ Library Extensions.
-          
        
-          
        
-            The function families currently implemented are the gamma, beta &
-            erf functions along with the incomplete gamma and beta functions (four
-            variants of each) and all the possible inverses of these, plus digamma,
-            various factorial functions, Bessel functions, elliptic integrals, sinus
-            cardinals (along with their hyperbolic variants), inverse hyperbolic
-            functions, Legrendre/Laguerre/Hermite polynomials and various special
-            power and logarithmic functions.
-          
        
-          
        
-            All the implementations are fully generic and support the use of arbitrary
-            "real-number" types, although they are optimised for use with
-            types with known-about significand (or mantissa) sizes: typically float,
-            double or long double.
-          
        
+            
        
+              Provides a number of high quality special functions, initially these
+              were concentrated on functions used in statistical applications along
+              with those in the Technical Report on C++ Library Extensions.
+            
        
+            
        
+              The function families currently implemented are the gamma, beta &
+              erf functions along with the incomplete gamma and beta functions (four
+              variants of each) and all the possible inverses of these, plus digamma,
+              various factorial functions, Bessel functions, elliptic integrals,
+              sinus cardinals (along with their hyperbolic variants), inverse hyperbolic
+              functions, Legrendre/Laguerre/Hermite polynomials and various special
+              power and logarithmic functions.
+            
        
+            
        
+              All the implementations are fully generic and support the use of arbitrary
+              "real-number" types, although they are optimised for use
+              with types with known-about significand (or mantissa) sizes: typically
+              float, double or long double.
+            
        
           
 
 
 
-          
        
-            Statistical Distributions
-          
        
-          
        
-            HTML Docs
-          
        
-          
        
-            PDF
-            Docs
-          
        
+            
        
+              Statistical Distributions
+            
        
+            
        
+              HTML Docs
+            
        
+            
        
+              PDF
+              Docs
+            
        
           
 
-          
        
-            Provides a reasonably comprehensive set of statistical distributions,
-            upon which higher level statistical tests can be built.
-          
        
-          
        
-            The initial focus is on the central univariate distributions. Both continuous
-            (like normal & Fisher) and discrete (like binomial & Poisson)
-            distributions are provided.
-          
        
-          
        
-            A comprehensive tutorial is provided, along with a series of worked examples
-            illustrating how the library is used to conduct statistical tests.
-          
        
+            
        
+              Provides a reasonably comprehensive set of statistical distributions,
+              upon which higher level statistical tests can be built.
+            
        
+            
        
+              The initial focus is on the central univariate distributions. Both
+              continuous (like normal & Fisher) and discrete (like binomial &
+              Poisson) distributions are provided.
+            
        
+            
        
+              A comprehensive tutorial is provided, along with a series of worked
+              examples illustrating how the library is used to conduct statistical
+              tests.
+            
        
           
 
 
 
-          
        
-            Quaternions
-          
        
-          
        
-            HTML Docs
-          
        
-          
        
-            PDF
-            Docs
-          
        
+            
        
+              Quaternions
+            
        
+            
        
+              HTML Docs
+            
        
+            
        
+              PDF
+              Docs
+            
        
           
 
-          
        
-            Quaternions are a relative of complex numbers.
-          
        
-          
        
-            Quaternions are in fact part of a small hierarchy of structures built
-            upon the real numbers, which comprise only the set of real numbers (traditionally
-            named R), the set
-            of complex numbers (traditionally named C),
-            the set of quaternions (traditionally named H)
-            and the set of octonions (traditionally named O),
-            which possess interesting mathematical properties (chief among which
-            is the fact that they are division algebras, i.e.
-            where the following property is true: if y
-            is an element of that algebra and is not equal
-            to zero, then yx = yx',
-            where x and x'
-            denote elements of that algebra, implies that x =
-            x'). Each member of the hierarchy is a super-set
-            of the former.
-          
        
-          
        
-            One of the most important aspects of quaternions is that they provide
-            an efficient way to parameterize rotations in R3
-            (the usual three-dimensional space) and R4.
-          
        
-          
        
-            In practical terms, a quaternion is simply a quadruple of real numbers
-            (α,β,γ,δ), which we can write in the form q = α + βi + γj + δk,
-            where i is the same object as
-            for complex numbers, and j and
-            k are distinct objects which
-            play essentially the same kind of role as i.
-          
        
-          
        
-            An addition and a multiplication is defined on the set of quaternions,
-            which generalize their real and complex counterparts. The main novelty
-            here is that the multiplication is not commutative
-            (i.e. there are quaternions x
-            and y such that xy
-            ≠ yx). A good mnemotechnical way of remembering things
-            is by using the formula i*i = j*j = k*k = -1.
-          
        
-          
        
-            Quaternions (and their kin) are described in far more details in this
-            other document (with errata and addenda).
-          
        
-          
        
-            Some traditional constructs, such as the exponential, carry over without
-            too much change into the realms of quaternions, but other, such as taking
-            a square root, do not.
-          
        
+            
        
+              Quaternions are a relative of complex numbers.
+            
        
+            
        
+              Quaternions are in fact part of a small hierarchy of structures built
+              upon the real numbers, which comprise only the set of real numbers
+              (traditionally named R),
+              the set of complex numbers (traditionally named C), the set of quaternions (traditionally
+              named H) and
+              the set of octonions (traditionally named O),
+              which possess interesting mathematical properties (chief among which
+              is the fact that they are division algebras,
+              i.e. where the following property is true: if
+              y is an element of that algebra
+              and is not equal to zero, then yx
+              = yx', where x
+              and x' denote elements of that
+              algebra, implies that x = x').
+              Each member of the hierarchy is a super-set of the former.
+            
        
+            
        
+              One of the most important aspects of quaternions is that they provide
+              an efficient way to parameterize rotations in R3
+              (the usual three-dimensional space) and R4.
+            
        
+            
        
+              In practical terms, a quaternion is simply a quadruple of real numbers
+              (α,β,γ,δ), which we can write in the form q = α + βi + γj + δk,
+              where i is the same object
+              as for complex numbers, and j
+              and k are distinct objects
+              which play essentially the same kind of role as i.
+            
        
+            
        
+              An addition and a multiplication is defined on the set of quaternions,
+              which generalize their real and complex counterparts. The main novelty
+              here is that the multiplication is not commutative
+              (i.e. there are quaternions x
+              and y such that xy
+              ≠ yx). A good mnemotechnical way of remembering
+              things is by using the formula i*i = j*j = k*k =
+              -1.
+            
        
+            
        
+              Quaternions (and their kin) are described in far more details in this
+              other document (with
+              errata and addenda).
+            
        
+            
        
+              Some traditional constructs, such as the exponential, carry over without
+              too much change into the realms of quaternions, but other, such as
+              taking a square root, do not.
+            
        
           
 
 
@@ -330,133 +335,133 @@
 
 
 
-          
        
-            Library
-          
        
+            
        
+              Library
+            
        
           
 
-          
        
-            Description
-          
        
+            
        
+              Description
+            
        
           
 
 
 
 
-          
        
-            Integer
-          
        
+            
        
+              Integer
+            
        
           
 
-          
        
-            Headers to ease dealing with integral types.
-          
        
+            
        
+              Headers to ease dealing with integral types.
+            
        
           
 
 
 
-          
        
-            Interval
-          
        
+            
        
+              Interval
+            
        
           
 
-          
        
-            As implied by its name, this library is intended to help manipulating
-            mathematical intervals. It consists of a single header <boost/numeric/interval.hpp>
-            and principally a type which can be used as interval<T>.
-          
        
+            
        
+              As implied by its name, this library is intended to help manipulating
+              mathematical intervals. It consists of a single header <boost/numeric/interval.hpp>
+              and principally a type which can be used as interval<T>.
+            
        
           
 
 
 
-          
        
-            Multi Array
-          
        
+            
        
+              Multi Array
+            
        
           
 
-          
        
-            Boost.MultiArray provides a generic N-dimensional array concept definition
-            and common implementations of that interface.
-          
        
+            
        
+              Boost.MultiArray provides a generic N-dimensional array concept definition
+              and common implementations of that interface.
+            
        
           
 
 
 
-          
        
-            Numeric.Conversion
-          
        
+            
        
+              Numeric.Conversion
+            
        
           
 
-          
        
-            The Boost Numeric Conversion library is a collection of tools to describe
-            and perform conversions between values of different numeric types.
-          
        
+            
        
+              The Boost Numeric Conversion library is a collection of tools to describe
+              and perform conversions between values of different numeric types.
+            
        
           
 
 
 
-          
        
-            Operators
-          
        
+            
        
+              Operators
+            
        
           
 
-          
        
-            The header <boost/operators.hpp> supplies several sets of class
-            templates (in namespace boost). These templates define operators at namespace
-            scope in terms of a minimal number of fundamental operators provided
-            by the class.
-          
        
+            
        
+              The header <boost/operators.hpp> supplies several sets of class
+              templates (in namespace boost). These templates define operators at
+              namespace scope in terms of a minimal number of fundamental operators
+              provided by the class.
+            
        
           
 
 
 
-          
        
-            Random
-          
        
+            
        
+              Random
+            
        
           
 
-          
        
-            Random numbers are useful in a variety of applications. The Boost Random
-            Number Library (Boost.Random for short) provides a vast variety of generators
-            and distributions to produce random numbers having useful properties,
-            such as uniform distribution.
-          
        
+            
        
+              Random numbers are useful in a variety of applications. The Boost Random
+              Number Library (Boost.Random for short) provides a vast variety of
+              generators and distributions to produce random numbers having useful
+              properties, such as uniform distribution.
+            
        
           
 
 
 
-          
        
-            Rational
-          
        
+            
        
+              Rational
+            
        
           
 
-          
        
-            The header rational.hpp provides an implementation of rational numbers.
-            The implementation is template-based, in a similar manner to the standard
-            complex number class.
-          
        
+            
        
+              The header rational.hpp provides an implementation of rational numbers.
+              The implementation is template-based, in a similar manner to the standard
+              complex number class.
+            
        
           
 
 
 
-          
        
-            uBLAS
-          
        
+            
        
+              uBLAS
+            
        
           
 
-          
        
-            uBLAS is a C++ template class library that provides BLAS level 1, 2,
-            3 functionality for dense, packed and sparse matrices. The design and
-            implementation unify mathematical notation via operator overloading and
-            efficient code generation via expression templates.
-          
        
+            
        
+              uBLAS is a C++ template class library that provides BLAS level 1, 2,
+              3 functionality for dense, packed and sparse matrices. The design and
+              implementation unify mathematical notation via operator overloading
+              and efficient code generation via expression templates.
+            
        
           
 
 
 
        
 
        
 
-
+
        Last revised: May 28, 2008 at 10:39:25 +0100
        Last revised:  ,  at  
        		
 
        		
 
        
 
        
diff --git a/doc/octonion/html/boost_octonions/octonions.html b/doc/octonion/html/boost_octonions/octonions.html
index 1aa060df2..c20b93835 100644
--- a/doc/octonion/html/boost_octonions/octonions.html
+++ b/doc/octonion/html/boost_octonions/octonions.html
@@ -1,10 +1,10 @@
 
 
-
+
 Octonions
-
-
-
+
+
+
 
 
 
@@ -20,11 +20,11 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        
 
        Overview
        
@@ -54,7 +54,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -62,7 +62,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/acknowledgements.html b/doc/octonion/html/boost_octonions/octonions/acknowledgements.html
index b03264f97..6d7234666 100644
--- a/doc/octonion/html/boost_octonions/octonions/acknowledgements.html
+++ b/doc/octonion/html/boost_octonions/octonions/acknowledgements.html
@@ -1,10 +1,10 @@
 
 
-
+
 Acknowledgements
-
-
-
+
+
+
 
 
 
@@ -20,11 +20,11 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        
         The mathematical text has been typeset with Nisus
@@ -36,7 +36,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -44,7 +44,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/header_file.html b/doc/octonion/html/boost_octonions/octonions/header_file.html
index 2d876b78e..ea199cf73 100644
--- a/doc/octonion/html/boost_octonions/octonions/header_file.html
+++ b/doc/octonion/html/boost_octonions/octonions/header_file.html
@@ -1,10 +1,10 @@
 
 
-
+
 Header File
-
-
-
+
+
+
 
 
 
@@ -20,11 +20,11 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        
         The interface and implementation are both supplied by the header file octonion.hpp.
@@ -32,7 +32,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -40,7 +40,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/history.html b/doc/octonion/html/boost_octonions/octonions/history.html
index 359f35664..824ff15e3 100644
--- a/doc/octonion/html/boost_octonions/octonions/history.html
+++ b/doc/octonion/html/boost_octonions/octonions/history.html
@@ -1,10 +1,10 @@
 
 
-
+
 History
-
-
-
+
+
+
 
 
 
@@ -20,78 +20,82 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
-
          
-
        • 
-          1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
-        
          • 
-
        • 
-          1.5.7 - 25/02/2003: transitionned to the unit test framework; <boost/config.hpp>
-          now included by the library header (rather than the test files), via <boost/math/quaternion.hpp>.
-        
          • 
-
        • 
-          1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
-          Evlogimenos (alkis@routescience.com).
-        
          • 
-
        • 
-          1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
-          (michael@acfr.usyd.edu.au); requires the /Za compiler option.
-        
          • 
-
        • 
-          1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
-          translation units); attempt at an improved compatibility with Microsoft
-          compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist;
-          other compatibility fixes.
-        
          • 
-
        • 
-          1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
-          (gregod@cs.rpi.edu).
-        
          • 
-
        • 
-          1.5.2 - 07/07/2001: introduced namespace math.
-        
          • 
-
        • 
-          1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp>
-          and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>;
-          corrected bug in sin (Daryle Walker); removed check for self-assignment
-          (Gary Powel); made converting functions explicit (Gary Powel); added overflow
-          guards for division operators and abs (Peter Schmitteckert); added sup
-          and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code.
-        
          • 
-
        • 
-          1.5.0 - 23/03/2001: boostification, inlining of all operators except input,
-          output and pow, fixed exception safety of some members (template version).
-        
          • 
-
        • 
-          1.4.0 - 09/01/2001: added tan and tanh.
-        
          • 
-
        • 
-          1.3.1 - 08/01/2001: cosmetic fixes.
-        
          • 
-
        • 
-          1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
-          algorithm.
-        
          • 
-
        • 
-          1.2.0 - 25/05/2000: fixed the division operators and output; changed many
-          signatures.
-        
          • 
-
        • 
-          1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh.
-        
          • 
-
        • 
-          1.0.0 - 10/08/1999: first public version.
-        
          • 
+
            
+
          • 
+            1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
+          
            • 
+
          • 
+            1.5.7 - 25/02/2003: transitionned to the unit test framework; <boost/config.hpp>
+            now included by the library header (rather than the test files), via
+            <boost/math/quaternion.hpp>.
+          
            • 
+
          • 
+            1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
+            Evlogimenos (alkis@routescience.com).
+          
            • 
+
          • 
+            1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
+            (michael@acfr.usyd.edu.au); requires the /Za compiler option.
+          
            • 
+
          • 
+            1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
+            translation units); attempt at an improved compatibility with Microsoft
+            compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik
+            Blomqvist; other compatibility fixes.
+          
            • 
+
          • 
+            1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
+            (gregod@cs.rpi.edu).
+          
            • 
+
          • 
+            1.5.2 - 07/07/2001: introduced namespace math.
+          
            • 
+
          • 
+            1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp>
+            and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>;
+            corrected bug in sin (Daryle Walker); removed check for self-assignment
+            (Gary Powel); made converting functions explicit (Gary Powel); added
+            overflow guards for division operators and abs (Peter Schmitteckert);
+            added sup and l1; used Vesa Karvonen's CPP metaprograming technique to
+            simplify code.
+          
            • 
+
          • 
+            1.5.0 - 23/03/2001: boostification, inlining of all operators except
+            input, output and pow, fixed exception safety of some members (template
+            version).
+          
            • 
+
          • 
+            1.4.0 - 09/01/2001: added tan and tanh.
+          
            • 
+
          • 
+            1.3.1 - 08/01/2001: cosmetic fixes.
+          
            • 
+
          • 
+            1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
+            algorithm.
+          
            • 
+
          • 
+            1.2.0 - 25/05/2000: fixed the division operators and output; changed
+            many signatures.
+          
            • 
+
          • 
+            1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh,
+            cosh.
+          
            • 
+
          • 
+            1.0.0 - 10/08/1999: first public version.
+          
            • 
 
          
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -99,7 +103,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/non_mem.html b/doc/octonion/html/boost_octonions/octonions/non_mem.html
index 73a565a1d..468369c0d 100644
--- a/doc/octonion/html/boost_octonions/octonions/non_mem.html
+++ b/doc/octonion/html/boost_octonions/octonions/non_mem.html
@@ -1,10 +1,10 @@
 
 
-
+
 Octonion Non-Member Operators
-
-
-
+
+
+
 
 
 
@@ -20,16 +20,16 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        
-
-        Unary
+
+        Unary
         Plus and Minus Operators
       
        
 
        template<typename T> octonion<T> operator + (octonion<T> const & o);
@@ -43,8 +43,8 @@
         This unary operator returns the opposite of o.
       
        
 
        
-
-        Binary
+
+        Binary
         Addition Operators
       
        
 
        template<typename T> octonion<T> operator + (T const & lhs, octonion<T> const & rhs);
@@ -60,8 +60,8 @@
         rhs.
       
        
 
        
-
-        Binary
+
+        Binary
         Subtraction Operators
       
        
 
        template<typename T> octonion<T> operator - (T const & lhs, octonion<T> const & rhs);
@@ -77,8 +77,8 @@
         rhs.
       
        
 
        
-
-        Binary
+
+        Binary
         Multiplication Operators
       
        
 
        template<typename T> octonion<T> operator * (T const & lhs, octonion<T> const & rhs);
@@ -94,8 +94,8 @@
         rhs.
       
        
 
        
-
-        Binary
+
+        Binary
         Division Operators
       
        
 
        template<typename T> octonion<T> operator / (T const & lhs, octonion<T> const & rhs);
@@ -112,8 +112,8 @@
         to divide by zero...
       
        
 
        
-
-        Binary
+
+        Binary
         Equality Operators
       
        
 
        template<typename T> bool operator == (T const & lhs, octonion<T> const & rhs);
@@ -130,8 +130,8 @@
         with any floating-type entity, this is essentially meaningless.
       
        
 
        
-
-        Binary
+
+        Binary
         Inequality Operators
       
        
 
        template<typename T> bool operator != (T const & lhs, octonion<T> const & rhs);
@@ -148,8 +148,8 @@
         false. As with any floating-type entity, this is essentially meaningless.
       
        
 
        
-
-        Stream
+
+        Stream
         Extractor
       
        
 
        template<typename T, typename charT, class traits>
@@ -170,8 +170,8 @@
         Returns is.
       
        
 
        
-
-        Stream
+
+        Stream
         Inserter
       
        
 
        template<typename T, typename charT, class traits>
@@ -207,7 +207,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -215,7 +215,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/oct_create.html b/doc/octonion/html/boost_octonions/octonions/oct_create.html
index 2f59fd722..70c16abd5 100644
--- a/doc/octonion/html/boost_octonions/octonions/oct_create.html
+++ b/doc/octonion/html/boost_octonions/octonions/oct_create.html
@@ -1,10 +1,10 @@
 
 
-
+
 Octonion Creation Functions
-
-
-
+
+
+
 
 
 
@@ -20,11 +20,11 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        template<typename T> octonion<T> spherical(T const & rho, T const & theta, T const & phi1, T const & phi2, T const & phi3, T const & phi4, T const & phi5, T const & phi6);
@@ -68,7 +68,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -76,7 +76,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/octonion_member_functions.html b/doc/octonion/html/boost_octonions/octonions/octonion_member_functions.html
index e7d240854..f27288d27 100644
--- a/doc/octonion/html/boost_octonions/octonions/octonion_member_functions.html
+++ b/doc/octonion/html/boost_octonions/octonions/octonion_member_functions.html
@@ -1,10 +1,10 @@
 
 
-
+
 Octonion Member Functions
-
-
-
+
+
+
 
 
 
@@ -20,16 +20,16 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        
-
-        Constructors
+
+        Constructors
       
        
 
        
         Template version:
@@ -85,13 +85,13 @@
         function in a "detail" subnamespace.
       
        
 
        
-
-        Other
+
+        Other
         member functions
       
        
 
        
-
-        Real
+
+        Real
         and Unreal Parts
       
        
 
        T            real()   const;
@@ -105,8 +105,8 @@
         These are returned by the first two functions.
       
        
 
        
-
-        Individual
+
+        Individual
         Real Components
       
        
 
        T   R_component_1() const;
@@ -123,8 +123,8 @@
         functions. Hence real and R_component_1 return the same value.
       
        
 
        
-
-        Individual
+
+        Individual
         Complex Components
       
        
 
        ::std::complex<T> C_component_1() const;
@@ -143,8 +143,8 @@
         the basis (1, j, e', j').
       
        
 
        
-
-        Individual
+
+        Individual
         Quaternion Components
       
        
 
        ::boost::math::quaternion<T> H_component_1() const;
@@ -158,13 +158,13 @@
         to build the octonion using the constructor.
       
        
 
        
-
-        Octonion
+
+        Octonion
         Member Operators
       
        
 
        
-
-        Assignment
+
+        Assignment
         Operators
       
        
 
        octonion<T> & operator = (octonion<T> const & a_affecter);
@@ -181,8 +181,8 @@
         base type's assignment operators must not throw.
       
        
 
        
-
-        Other
+
+        Other
         Member Operators
       
        
 
        octonion<T> & operator += (T const & rhs)
@@ -246,7 +246,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -254,7 +254,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/octonion_member_typedefs.html b/doc/octonion/html/boost_octonions/octonions/octonion_member_typedefs.html
index b6590230f..1c5ae40bd 100644
--- a/doc/octonion/html/boost_octonions/octonions/octonion_member_typedefs.html
+++ b/doc/octonion/html/boost_octonions/octonions/octonion_member_typedefs.html
@@ -1,10 +1,10 @@
 
 
-
+
 Octonion Member Typedefs
-
-
-
+
+
+
 
 
 
@@ -20,11 +20,11 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        
@@ -56,7 +56,7 @@
 
        
 
-
        
 
        Copyright © 2001 -2003 Hubert Holin
        
+
        Copyright © 2001 -2003 Hubert Holin
        
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
        
@@ -64,7 +64,7 @@
 
        
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
 
 
diff --git a/doc/octonion/html/boost_octonions/octonions/octonion_specializations.html b/doc/octonion/html/boost_octonions/octonions/octonion_specializations.html
index 5439f3c1f..7eff6c7ff 100644
--- a/doc/octonion/html/boost_octonions/octonions/octonion_specializations.html
+++ b/doc/octonion/html/boost_octonions/octonions/octonion_specializations.html
@@ -1,10 +1,10 @@
 
 
-
+
 Octonion Specializations
-
-
-
+
+
+
 
 
 
@@ -20,11 +20,11 @@
 
 
        
 
        
-PrevUpHomeNext
+PrevUpHomeNext
 
        
-
        
+
        
 
        
 
        namespace boost{ namespace math{
@@ -35,62 +35,62 @@
 public:
    typedef float value_type;
 
-   explicit  octonion(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f, float const & requested_e = 0.0f, float const & requested_f = 0.0f, float const & requested_g = 0.0f, float const & requested_h = 0.0f);
-   explicit  octonion(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>(), ::std::complex<float> const & z2 = ::std::complex<float>(), ::std::complex<float> const & z3 = ::std::complex<float>());
-   explicit  octonion(::boost::math::quaternion<float> const & q0, ::boost::math::quaternion<float> const & q1 = ::boost::math::quaternion<float>());
-   explicit  octonion(octonion<double> const & a_recopier);
-   explicit  octonion(octonion<long double> const & a_recopier);
+   explicit  octonion(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f, float const & requested_e = 0.0f, float const & requested_f = 0.0f, float const & requested_g = 0.0f, float const & requested_h = 0.0f);
+   explicit  octonion(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>(), ::std::complex<float> const & z2 = ::std::complex<float>(), ::std::complex<float> const & z3 = ::std::complex<float>());
+   explicit  octonion(::boost::math::quaternion<float> const & q0, ::boost::math::quaternion<float> const & q1 = ::boost::math::quaternion<float>());
+   explicit  octonion(octonion<double> const & a_recopier);
+   explicit  octonion(octonion<long double> const & a_recopier);
 
-   float                             real() const;
-   octonion<float>                   unreal() const;
+   float                             real() const;
+   octonion<float>                   unreal() const;
 
-   float                             R_component_1() const;
-   float                             R_component_2() const;
-   float                             R_component_3() const;
-   float                             R_component_4() const;
-   float                             R_component_5() const;
-   float                             R_component_6() const;
-   float                             R_component_7() const;
-   float                             R_component_8() const;
+   float                             R_component_1() const;
+   float                             R_component_2() const;
+   float                             R_component_3() const;
+   float                             R_component_4() const;
+   float                             R_component_5() const;
+   float                             R_component_6() const;
+   float                             R_component_7() const;
+   float                             R_component_8() const;
 
-   ::std::complex<float>             C_component_1() const;
-   ::std::complex<float>             C_component_2() const;
-   ::std::complex<float>             C_component_3() const;
-   ::std::complex<float>             C_component_4() const;
+   ::std::complex<float>             C_component_1() const;
+   ::std::complex<float>             C_component_2() const;
+   ::std::complex<float>             C_component_3() const;
+   ::std::complex<float>             C_component_4() const;
 
-   ::boost::math::quaternion<float>  H_component_1() const;
-   ::boost::math::quaternion<float>  H_component_2() const;
+   ::boost::math::quaternion<float>  H_component_1() const;
+   ::boost::math::quaternion<float>  H_component_2() const;
 
-   octonion<float> & operator = (octonion<float> const  & a_affecter);
+   octonion<float> & operator = (octonion<float> const  & a_affecter);
    template<typename X> 
-   octonion<float> & operator = (octonion<X> const  & a_affecter);
-   octonion<float> & operator = (float const  & a_affecter);
-   octonion<float> & operator = (::std::complex<float> const & a_affecter);
-   octonion<float> & operator = (::boost::math::quaternion<float> const & a_affecter);
+   octonion<float> & operator = (octonion<X> const  & a_affecter);
+   octonion<float> & operator = (float const  & a_affecter);
+   octonion<float> & operator = (::std::complex<float> const & a_affecter);
+   octonion<float> & operator = (::boost::math::quaternion<float> const & a_affecter);
 
-   octonion<float> & operator += (float const & rhs);
-   octonion<float> & operator += (::std::complex<float> const & rhs);
-   octonion<float> & operator += (::boost::math::quaternion<float> const & rhs);
+   octonion<float> & operator += (float const & rhs);
+   octonion<float> & operator += (::std::complex<float> const & rhs);
+   octonion<float> & operator += (::boost::math::quaternion<float> const & rhs);
    template<typename X> 
-   octonion<float> & operator += (octonion<X> const & rhs);
+   octonion<float> & operator += (octonion<X> const & rhs);
 
-   octonion<float> & operator -= (float const & rhs);
-   octonion<float> & operator -= (::std::complex<float> const & rhs);
-   octonion<float> & operator -= (::boost::math::quaternion<float> const & rhs);
+   octonion<float> & operator -= (float const & rhs);
+   octonion<float> & operator -= (::std::complex<float> const & rhs);
+   octonion<float> & operator -= (::boost::math::quaternion<float> const & rhs);
    template<typename X> 
-   octonion<float> & operator -= (octonion<X> const & rhs);
+   octonion<float> & operator -= (octonion<X> const & rhs);
 
-   octonion<float> & operator *= (float const & rhs);
-   octonion<float> & operator *= (::std::complex<float> const & rhs);
-   octonion<float> & operator *= (::boost::math::quaternion<float> const & rhs);
+   octonion<float> & operator *= (float const & rhs);
+   octonion<float> & operator *= (::std::complex<float> const & rhs);
+   octonion<float> & operator *= (::boost::math::quaternion<float> const & rhs);
    template<typename X> 
-   octonion<float> & operator *= (octonion<X> const & rhs);
+   octonion<float> & operator *= (octonion<X> const & rhs);
 
-   octonion<float> & operator /= (float const & rhs);
-   octonion<float> & operator /= (::std::complex<float> const & rhs);
-   octonion<float> & operator /= (::boost::math::quaternion<float> const & rhs);
+   octonion<float> & operator /= (float const & rhs);
+   octonion<float> & operator /= (::std::complex<float> const & rhs);
+   octonion<float> & operator /= (::boost::math::quaternion<float> const & rhs);
    template<typename X> 
-   octonion<float> & operator /= (octonion<X> const & rhs);
+   octonion<float> & operator /= (octonion<X> const & rhs);
 };
 
        
 
        
@@ -101,62 +101,62 @@
 public:
    typedef double value_type;
 
-   explicit  octonion(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0, double const & requested_e = 0.0, double const & requested_f = 0.0, double const & requested_g = 0.0, double const & requested_h = 0.0);
-   explicit  octonion(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>(), ::std::complex<double> const & z2 = ::std::complex<double>(), ::std::complex<double> const & z3 = ::std::complex<double>());
-   explicit  octonion(::boost::math::quaternion<double> const & q0, ::boost::math::quaternion<double> const & q1 = ::boost::math::quaternion<double>());
-   explicit  octonion(octonion<float> const & a_recopier);
-   explicit  octonion(octonion<long double> const & a_recopier);
+   explicit  octonion(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0, double const & requested_e = 0.0, double const & requested_f = 0.0, double const & requested_g = 0.0, double const & requested_h = 0.0);
+   explicit  octonion(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>(), ::std::complex<double> const & z2 = ::std::complex<double>(), ::std::complex<double> const & z3 = ::std::complex<double>());
+   explicit  octonion(::boost::math::quaternion<double> const & q0, ::boost::math::quaternion<double> const & q1 = ::boost::math::quaternion<double>());
+   explicit  octonion(octonion<float> const & a_recopier);
+   explicit  octonion(octonion<long double> const & a_recopier);
 
-   double                             real() const;
-   octonion<double>                   unreal() const;
+   double                             real() const;
+   octonion<double>                   unreal() const;
 
-   double                             R_component_1() const;
-   double                             R_component_2() const;
-   double                             R_component_3() const;
-   double                             R_component_4() const;
-   double                             R_component_5() const;
-   double                             R_component_6() const;
-   double                             R_component_7() const;
-   double                             R_component_8() const;
+   double                             R_component_1() const;
+   double                             R_component_2() const;
+   double                             R_component_3() const;
+   double                             R_component_4() const;
+   double                             R_component_5() const;
+   double                             R_component_6() const;
+   double                             R_component_7() const;
+   double                             R_component_8() const;
 
-   ::std::complex<double>             C_component_1() const;
-   ::std::complex<double>             C_component_2() const;
-   ::std::complex<double>             C_component_3() const;
-   ::std::complex<double>             C_component_4() const;
+   ::std::complex<double>             C_component_1() const;
+   ::std::complex<double>             C_component_2() const;
+   ::std::complex<double>             C_component_3() const;
+   ::std::complex<double>             C_component_4() const;
 
-   ::boost::math::quaternion<double>  H_component_1() const;
-   ::boost::math::quaternion<double>  H_component_2() const;
+   ::boost::math::quaternion<double>  H_component_1() const;
+   ::boost::math::quaternion<double>  H_component_2() const;
 
-   octonion<double> & operator = (octonion<double> const  & a_affecter);
+   octonion<double> & operator = (octonion<double> const  & a_affecter);
    template<typename X> 
-   octonion<double> & operator = (octonion<X> const  & a_affecter);
-   octonion<double> & operator = (double const  & a_affecter);
-   octonion<double> & operator = (::std::complex<double> const & a_affecter);
-   octonion<double> & operator = (::boost::math::quaternion<double> const & a_affecter);
+   octonion<double> & operator = (octonion<X> const  & a_affecter);
+   octonion<double> & operator = (double const  & a_affecter);
+   octonion<double> & operator = (::std::complex<double> const & a_affecter);
+   octonion<double> & operator = (::boost::math::quaternion<double> const & a_affecter);
 
-   octonion<double> & operator += (double const & rhs);
-   octonion<double> & operator += (::std::complex<double> const & rhs);
-   octonion<double> & operator += (::boost::math::quaternion<double> const & rhs);
+   octonion<double> & operator += (double const & rhs);
+   octonion<double> & operator += (::std::complex<double> const & rhs);
+   octonion<double> & operator += (::boost::math::quaternion<double> const & rhs);
    template<typename X> 
-   octonion<double> & operator += (octonion<X> const & rhs);
+   octonion<double> & operator += (octonion<X> const & rhs);
 
-   octonion<double> & operator -= (double const & rhs);
-   octonion<double> & operator -= (::std::complex<double> const & rhs);
-   octonion<double> & operator -= (::boost::math::quaternion<double> const & rhs);
+   octonion<double> & operator -= (double const & rhs);
+   octonion<double> & operator -= (::std::complex<double> const & rhs);
+   octonion<double> & operator -= (::boost::math::quaternion<double> const & rhs);
    template<typename X> 
-   octonion<double> & operator -= (octonion<X> const & rhs);
+   octonion<double> & operator -= (octonion<X> const & rhs);
 
-   octonion<double> & operator *= (double const & rhs);
-   octonion<double> & operator *= (::std::complex<double> const & rhs);
-   octonion<double> & operator *= (::boost::math::quaternion<double> const & rhs);
+   octonion<double> & operator *= (double const & rhs);
+   octonion<double> & operator *= (::std::complex<double> const & rhs);
+   octonion<double> & operator *= (::boost::math::quaternion<double> const & rhs);
    template<typename X> 
-   octonion<double> & operator *= (octonion<X> const & rhs);
+   octonion<double> & operator *= (octonion<X> const & rhs);
 
-   octonion<double> & operator /= (double const & rhs);
-   octonion<double> & operator /= (::std::complex<double> const & rhs);
-   octonion<double> & operator /= (::boost::math::quaternion<double> const & rhs);
+   octonion<double> & operator /= (double const & rhs);
+   octonion<double> & operator /= (::std::complex<double> const & rhs);
+   octonion<double> & operator /= (::boost::math::quaternion<double> const & rhs);
    template<typename X> 
-   octonion<double> & operator /= (octonion<X> const & rhs);
+   octonion<double> & operator /= (octonion<X> const & rhs);
 };

      @@ -167,62 +167,62 @@ public: typedef long double value_type; - explicit octonion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L, long double const & requested_e = 0.0L, long double const & requested_f = 0.0L, long double const & requested_g = 0.0L, long double const & requested_h = 0.0L); - explicit octonion( ::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>(), ::std::complex<long double> const & z2 = ::std::complex<long double>(), ::std::complex<long double> const & z3 = ::std::complex<long double>()); - explicit octonion( ::boost::math::quaternion<long double> const & q0, ::boost::math::quaternion<long double> const & z1 = ::boost::math::quaternion<long double>()); - explicit octonion(octonion<float> const & a_recopier); - explicit octonion(octonion<double> const & a_recopier); + explicit octonion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L, long double const & requested_e = 0.0L, long double const & requested_f = 0.0L, long double const & requested_g = 0.0L, long double const & requested_h = 0.0L); + explicit octonion( ::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>(), ::std::complex<long double> const & z2 = ::std::complex<long double>(), ::std::complex<long double> const & z3 = ::std::complex<long double>()); + explicit octonion( ::boost::math::quaternion<long double> const & q0, ::boost::math::quaternion<long double> const & z1 = ::boost::math::quaternion<long double>()); + explicit octonion(octonion<float> const & a_recopier); + explicit octonion(octonion<double> const & a_recopier); - long double real() const; - octonion<long double> unreal() const; + long double real() const; + octonion<long double> unreal() const; - long double R_component_1() const; - long double R_component_2() const; - long double R_component_3() const; - long double R_component_4() const; - long double R_component_5() const; - long double R_component_6() const; - long double R_component_7() const; - long double R_component_8() const; + long double R_component_1() const; + long double R_component_2() const; + long double R_component_3() const; + long double R_component_4() const; + long double R_component_5() const; + long double R_component_6() const; + long double R_component_7() const; + long double R_component_8() const; - ::std::complex<long double> C_component_1() const; - ::std::complex<long double> C_component_2() const; - ::std::complex<long double> C_component_3() const; - ::std::complex<long double> C_component_4() const; + ::std::complex<long double> C_component_1() const; + ::std::complex<long double> C_component_2() const; + ::std::complex<long double> C_component_3() const; + ::std::complex<long double> C_component_4() const; - ::boost::math::quaternion<long double> H_component_1() const; - ::boost::math::quaternion<long double> H_component_2() const; + ::boost::math::quaternion<long double> H_component_1() const; + ::boost::math::quaternion<long double> H_component_2() const; - octonion<long double> & operator = (octonion<long double> const & a_affecter); + octonion<long double> & operator = (octonion<long double> const & a_affecter); template<typename X> - octonion<long double> & operator = (octonion<X> const & a_affecter); - octonion<long double> & operator = (long double const & a_affecter); - octonion<long double> & operator = (::std::complex<long double> const & a_affecter); - octonion<long double> & operator = (::boost::math::quaternion<long double> const & a_affecter); + octonion<long double> & operator = (octonion<X> const & a_affecter); + octonion<long double> & operator = (long double const & a_affecter); + octonion<long double> & operator = (::std::complex<long double> const & a_affecter); + octonion<long double> & operator = (::boost::math::quaternion<long double> const & a_affecter); - octonion<long double> & operator += (long double const & rhs); - octonion<long double> & operator += (::std::complex<long double> const & rhs); - octonion<long double> & operator += (::boost::math::quaternion<long double> const & rhs); + octonion<long double> & operator += (long double const & rhs); + octonion<long double> & operator += (::std::complex<long double> const & rhs); + octonion<long double> & operator += (::boost::math::quaternion<long double> const & rhs); template<typename X> - octonion<long double> & operator += (octonion<X> const & rhs); + octonion<long double> & operator += (octonion<X> const & rhs); - octonion<long double> & operator -= (long double const & rhs); - octonion<long double> & operator -= (::std::complex<long double> const & rhs); - octonion<long double> & operator -= (::boost::math::quaternion<long double> const & rhs); + octonion<long double> & operator -= (long double const & rhs); + octonion<long double> & operator -= (::std::complex<long double> const & rhs); + octonion<long double> & operator -= (::boost::math::quaternion<long double> const & rhs); template<typename X> - octonion<long double> & operator -= (octonion<X> const & rhs); + octonion<long double> & operator -= (octonion<X> const & rhs); - octonion<long double> & operator *= (long double const & rhs); - octonion<long double> & operator *= (::std::complex<long double> const & rhs); - octonion<long double> & operator *= (::boost::math::quaternion<long double> const & rhs); + octonion<long double> & operator *= (long double const & rhs); + octonion<long double> & operator *= (::std::complex<long double> const & rhs); + octonion<long double> & operator *= (::boost::math::quaternion<long double> const & rhs); template<typename X> - octonion<long double> & operator *= (octonion<X> const & rhs); + octonion<long double> & operator *= (octonion<X> const & rhs); - octonion<long double> & operator /= (long double const & rhs); - octonion<long double> & operator /= (::std::complex<long double> const & rhs); - octonion<long double> & operator /= (::boost::math::quaternion<long double> const & rhs); + octonion<long double> & operator /= (long double const & rhs); + octonion<long double> & operator /= (::std::complex<long double> const & rhs); + octonion<long double> & operator /= (::boost::math::quaternion<long double> const & rhs); template<typename X> - octonion<long double> & operator /= (octonion<X> const & rhs); + octonion<long double> & operator /= (octonion<X> const & rhs); }; } } // namespaces @@ -230,7 +230,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -238,7 +238,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/octonion_value_operations.html b/doc/octonion/html/boost_octonions/octonions/octonion_value_operations.html index 981610453..5ff36d577 100644 --- a/doc/octonion/html/boost_octonions/octonions/octonion_value_operations.html +++ b/doc/octonion/html/boost_octonions/octonions/octonion_value_operations.html @@ -1,10 +1,10 @@ - + Octonion Value Operations - - - + + + @@ -20,16 +20,16 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      - - Real + + Real and Unreal 
      template<typename T> T  real(octonion<T> const & o);
@@ -41,8 +41,8 @@
         respectively.
       
      
 
      
-
-        conj
+
+        conj
       
      
 
      template<typename T> octonion<T> conj(octonion<T> const & o);
 
      
@@ -50,8 +50,8 @@
         This returns the conjugate of the octonion.
       
      
 
      
-
-        sup
+
+        sup
       
      
 
      template<typename T> T   sup(octonion<T> const & o);
 
      
@@ -59,8 +59,8 @@
         This return the sup norm (the greatest among abs(o.R_component_1())...abs(o.R_component_8())) of the octonion.
       
      
 
      
-
-        l1
+
+        l1
       
      
 
      template<typename T> T   l1(octonion<T> const & o);
 
      
@@ -68,8 +68,8 @@
         This return the l1 norm (abs(o.R_component_1())+...+abs(o.R_component_8())) of the octonion.
       
      
 
      
-
-        abs
+
+        abs
       
      
 
      template<typename T> T   abs(octonion<T> const & o);
 
      
@@ -77,8 +77,8 @@
         This return the magnitude (Euclidian norm) of the octonion.
       
      
 
      
-
-        norm
+
+        norm
       
      
 
      template<typename T> T  norm(octonion<T>const  & o);
 
      
@@ -92,7 +92,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -100,7 +100,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/octonions_transcendentals.html b/doc/octonion/html/boost_octonions/octonions/octonions_transcendentals.html index 4c4649dc2..ad64d45cf 100644 --- a/doc/octonion/html/boost_octonions/octonions/octonions_transcendentals.html +++ b/doc/octonion/html/boost_octonions/octonions/octonions_transcendentals.html @@ -1,10 +1,10 @@ - + Octonions Transcendentals - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      @@ -53,8 +53,8 @@ headers.

      - - exp + + exp 
      template<typename T> 
 octonion<T> exp(octonion<T> const & o);
@@ -63,8 +63,8 @@
         Computes the exponential of the octonion.
       
      
 
      
-
-        cos
+
+        cos
       
      
 
      template<typename T> 
 octonion<T> cos(octonion<T> const & o);
@@ -73,8 +73,8 @@
         Computes the cosine of the octonion
       
      
 
      
-
-        sin
+
+        sin
       
      
 
      template<typename T> 
 octonion<T> sin(octonion<T> const & o);
@@ -83,8 +83,8 @@
         Computes the sine of the octonion.
       
      
 
      
-
-        tan
+
+        tan
       
      
 
      template<typename T> 
 octonion<T> tan(octonion<T> const & o);
@@ -93,8 +93,8 @@
         Computes the tangent of the octonion.
       
      
 
      
-
-        cosh
+
+        cosh
       
      
 
      template<typename T> 
 octonion<T> cosh(octonion<T> const & o);
@@ -103,8 +103,8 @@
         Computes the hyperbolic cosine of the octonion.
       
      
 
      
-
-        sinh
+
+        sinh
       
      
 
      template<typename T> 
 octonion<T> sinh(octonion<T> const & o);
@@ -113,8 +113,8 @@
         Computes the hyperbolic sine of the octonion.
       
      
 
      
-
-        tanh
+
+        tanh
       
      
 
      template<typename T> 
 octonion<T> tanh(octonion<T> const & o);
@@ -123,8 +123,8 @@
         Computes the hyperbolic tangent of the octonion.
       
      
 
      
-
-        pow
+
+        pow
       
      
 
      template<typename T> 
 octonion<T>  pow(octonion<T> const & o, int n);
@@ -135,7 +135,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -143,7 +143,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/overview.html b/doc/octonion/html/boost_octonions/octonions/overview.html index 3424fc5f5..ee713150f 100644 --- a/doc/octonion/html/boost_octonions/octonions/overview.html +++ b/doc/octonion/html/boost_octonions/octonions/overview.html @@ -1,10 +1,10 @@ - + Overview - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      Octonions, like quaternions, @@ -69,7 +69,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -77,7 +77,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/synopsis.html b/doc/octonion/html/boost_octonions/octonions/synopsis.html index da2757e2a..fa93b69bc 100644 --- a/doc/octonion/html/boost_octonions/octonions/synopsis.html +++ b/doc/octonion/html/boost_octonions/octonions/synopsis.html @@ -1,10 +1,10 @@ - + Synopsis - - - + + + @@ -20,111 +20,111 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      namespace boost{ namespace math{
 
-template<typename T> class octonion;
-template<>           class octonion<float>;
-template<>           class octonion<double>; 
-template<>           class octonion<long double>; 
+template<typename T> class octonion;
+template<>           class octonion<float>;
+template<>           class octonion<double>; 
+template<>           class octonion<long double>; 
 
 // operators
 
-template<typename T> octonion<T> operator + (T const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator + (octonion<T> const & lhs, T const & rhs);
-template<typename T> octonion<T> operator + (::std::complex<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator + (octonion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> octonion<T> operator + (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator + (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
-template<typename T> octonion<T> operator + (octonion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator + (T const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator + (octonion<T> const & lhs, T const & rhs);
+template<typename T> octonion<T> operator + (::std::complex<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator + (octonion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> octonion<T> operator + (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator + (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
+template<typename T> octonion<T> operator + (octonion<T> const & lhs, octonion<T> const & rhs);
 
-template<typename T> octonion<T> operator - (T const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator - (octonion<T> const & lhs, T const & rhs);
-template<typename T> octonion<T> operator - (::std::complex<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator - (octonion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> octonion<T> operator - (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator - (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
-template<typename T> octonion<T> operator - (octonion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator - (T const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator - (octonion<T> const & lhs, T const & rhs);
+template<typename T> octonion<T> operator - (::std::complex<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator - (octonion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> octonion<T> operator - (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator - (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
+template<typename T> octonion<T> operator - (octonion<T> const & lhs, octonion<T> const & rhs);
 
-template<typename T> octonion<T> operator * (T const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator * (octonion<T> const & lhs, T const & rhs);
-template<typename T> octonion<T> operator * (::std::complex<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator * (octonion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> octonion<T> operator * (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator * (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
-template<typename T> octonion<T> operator * (octonion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator * (T const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator * (octonion<T> const & lhs, T const & rhs);
+template<typename T> octonion<T> operator * (::std::complex<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator * (octonion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> octonion<T> operator * (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator * (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
+template<typename T> octonion<T> operator * (octonion<T> const & lhs, octonion<T> const & rhs);
 
-template<typename T> octonion<T> operator / (T const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator / (octonion<T> const & lhs, T const & rhs);
-template<typename T> octonion<T> operator / (::std::complex<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator / (octonion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> octonion<T> operator / (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
-template<typename T> octonion<T> operator / (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
-template<typename T> octonion<T> operator / (octonion<T> const & lhs, octonion<T> const & rhs); 
+template<typename T> octonion<T> operator / (T const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator / (octonion<T> const & lhs, T const & rhs);
+template<typename T> octonion<T> operator / (::std::complex<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator / (octonion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> octonion<T> operator / (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> octonion<T> operator / (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
+template<typename T> octonion<T> operator / (octonion<T> const & lhs, octonion<T> const & rhs); 
 
-template<typename T> octonion<T> operator + (octonion<T> const & o);
-template<typename T> octonion<T> operator - (octonion<T> const & o); 
+template<typename T> octonion<T> operator + (octonion<T> const & o);
+template<typename T> octonion<T> operator - (octonion<T> const & o); 
 
-template<typename T> bool operator == (T const & lhs, octonion<T> const & rhs);
-template<typename T> bool operator == (octonion<T> const & lhs, T const & rhs);
-template<typename T> bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs);
-template<typename T> bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
-template<typename T> bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
-template<typename T> bool operator == (octonion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator == (T const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator == (octonion<T> const & lhs, T const & rhs);
+template<typename T> bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
+template<typename T> bool operator == (octonion<T> const & lhs, octonion<T> const & rhs);
 
-template<typename T> bool operator != (T const & lhs, octonion<T> const & rhs);
-template<typename T> bool operator != (octonion<T> const & lhs, T const & rhs);
-template<typename T> bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs);
-template<typename T> bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
-template<typename T> bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
-template<typename T> bool operator != (octonion<T> const & lhs, octonion<T> const & rhs); 
+template<typename T> bool operator != (T const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator != (octonion<T> const & lhs, T const & rhs);
+template<typename T> bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
+template<typename T> bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
+template<typename T> bool operator != (octonion<T> const & lhs, octonion<T> const & rhs); 
 
 template<typename T, typename charT, class traits>
-::std::basic_istream<charT,traits> & operator >> (::std::basic_istream<charT,traits> & is, octonion<T> & o);
+::std::basic_istream<charT,traits> & operator >> (::std::basic_istream<charT,traits> & is, octonion<T> & o);
 
 template<typename T, typename charT, class traits>
-::std::basic_ostream<charT,traits> & operator << (::std::basic_ostream<charT,traits> & os, octonion<T> const & o);
+::std::basic_ostream<charT,traits> & operator << (::std::basic_ostream<charT,traits> & os, octonion<T> const & o);
 
 // values
 
-template<typename T> T           real(octonion<T> const & o);
-template<typename T> octonion<T> unreal(octonion<T> const & o);
+template<typename T> T           real(octonion<T> const & o);
+template<typename T> octonion<T> unreal(octonion<T> const & o);
 
-template<typename T> T           sup(octonion<T> const & o);
-template<typename T> T           l1(octonion<T>const & o); 
-template<typename T> T           abs(octonion<T> const & o);
-template<typename T> T           norm(octonion<T>const  & o);
-template<typename T> octonion<T> conj(octonion<T> const & o);
+template<typename T> T           sup(octonion<T> const & o);
+template<typename T> T           l1(octonion<T>const & o); 
+template<typename T> T           abs(octonion<T> const & o);
+template<typename T> T           norm(octonion<T>const  & o);
+template<typename T> octonion<T> conj(octonion<T> const & o);
 
-template<typename T> octonion<T> spherical(T const & rho, T const & theta, T const & phi1, T const & phi2, T const & phi3, T const & phi4, T const & phi5, T const & phi6);
-template<typename T> octonion<T> multipolar(T const & rho1, T const & theta1, T const & rho2, T const & theta2, T const & rho3, T const & theta3, T const & rho4, T const & theta4);
-template<typename T> octonion<T> cylindrical(T const & r, T const & angle, T const & h1, T const & h2, T const & h3, T const & h4, T const & h5, T const & h6);
+template<typename T> octonion<T> spherical(T const & rho, T const & theta, T const & phi1, T const & phi2, T const & phi3, T const & phi4, T const & phi5, T const & phi6);
+template<typename T> octonion<T> multipolar(T const & rho1, T const & theta1, T const & rho2, T const & theta2, T const & rho3, T const & theta3, T const & rho4, T const & theta4);
+template<typename T> octonion<T> cylindrical(T const & r, T const & angle, T const & h1, T const & h2, T const & h3, T const & h4, T const & h5, T const & h6);
 
 // transcendentals
 
-template<typename T> octonion<T> exp(octonion<T> const & o);
-template<typename T> octonion<T> cos(octonion<T> const & o);
-template<typename T> octonion<T> sin(octonion<T> const & o);
-template<typename T> octonion<T> tan(octonion<T> const & o);
-template<typename T> octonion<T> cosh(octonion<T> const & o);
-template<typename T> octonion<T> sinh(octonion<T> const & o);
-template<typename T> octonion<T> tanh(octonion<T> const & o);
+template<typename T> octonion<T> exp(octonion<T> const & o);
+template<typename T> octonion<T> cos(octonion<T> const & o);
+template<typename T> octonion<T> sin(octonion<T> const & o);
+template<typename T> octonion<T> tan(octonion<T> const & o);
+template<typename T> octonion<T> cosh(octonion<T> const & o);
+template<typename T> octonion<T> sinh(octonion<T> const & o);
+template<typename T> octonion<T> tanh(octonion<T> const & o);
 
-template<typename T> octonion<T> pow(octonion<T> const & o, int n);
+template<typename T> octonion<T> pow(octonion<T> const & o, int n);
 
 }  } // namespaces
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -132,7 +132,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/template_class_octonion.html b/doc/octonion/html/boost_octonions/octonions/template_class_octonion.html index 97f1e51e9..e757edbd0 100644 --- a/doc/octonion/html/boost_octonions/octonions/template_class_octonion.html +++ b/doc/octonion/html/boost_octonions/octonions/template_class_octonion.html @@ -1,10 +1,10 @@ - + Template Class octonion - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      namespace boost{ namespace math {
@@ -35,62 +35,62 @@
 public:
    typedef T value_type;
 
-   explicit  octonion(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T(), T const & requested_e = T(), T const & requested_f = T(), T const & requested_g = T(), T const & requested_h = T());
-   explicit  octonion(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>(), ::std::complex<T> const & z2 = ::std::complex<T>(), ::std::complex<T> const & z3 = ::std::complex<T>());
-   explicit  octonion(::boost::math::quaternion<T> const & q0, ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>());
+   explicit  octonion(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T(), T const & requested_e = T(), T const & requested_f = T(), T const & requested_g = T(), T const & requested_h = T());
+   explicit  octonion(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>(), ::std::complex<T> const & z2 = ::std::complex<T>(), ::std::complex<T> const & z3 = ::std::complex<T>());
+   explicit  octonion(::boost::math::quaternion<T> const & q0, ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>());
    template<typename X> 
-   explicit  octonion(octonion<X> const & a_recopier);
+   explicit  octonion(octonion<X> const & a_recopier);
 
-   T                             real() const;
-   octonion<T>                   unreal() const;
+   T                             real() const;
+   octonion<T>                   unreal() const;
 
-   T                             R_component_1() const;
-   T                             R_component_2() const;
-   T                             R_component_3() const;
-   T                             R_component_4() const;
-   T                             R_component_5() const;
-   T                             R_component_6() const;
-   T                             R_component_7() const;
-   T                             R_component_8() const;
+   T                             R_component_1() const;
+   T                             R_component_2() const;
+   T                             R_component_3() const;
+   T                             R_component_4() const;
+   T                             R_component_5() const;
+   T                             R_component_6() const;
+   T                             R_component_7() const;
+   T                             R_component_8() const;
 
-   ::std::complex<T>             C_component_1() const;
-   ::std::complex<T>             C_component_2() const;
-   ::std::complex<T>             C_component_3() const;
-   ::std::complex<T>             C_component_4() const;
+   ::std::complex<T>             C_component_1() const;
+   ::std::complex<T>             C_component_2() const;
+   ::std::complex<T>             C_component_3() const;
+   ::std::complex<T>             C_component_4() const;
 
-   ::boost::math::quaternion<T>  H_component_1() const;
-   ::boost::math::quaternion<T>  H_component_2() const;
+   ::boost::math::quaternion<T>  H_component_1() const;
+   ::boost::math::quaternion<T>  H_component_2() const;
 
-   octonion<T> & operator = (octonion<T> const  & a_affecter);
+   octonion<T> & operator = (octonion<T> const  & a_affecter);
    template<typename X> 
-   octonion<T> & operator = (octonion<X> const  & a_affecter);
-   octonion<T> & operator = (T const  & a_affecter);
-   octonion<T> & operator = (::std::complex<T> const & a_affecter);
-   octonion<T> & operator = (::boost::math::quaternion<T> const & a_affecter);
+   octonion<T> & operator = (octonion<X> const  & a_affecter);
+   octonion<T> & operator = (T const  & a_affecter);
+   octonion<T> & operator = (::std::complex<T> const & a_affecter);
+   octonion<T> & operator = (::boost::math::quaternion<T> const & a_affecter);
 
-   octonion<T> & operator += (T const & rhs);
-   octonion<T> & operator += (::std::complex<T> const & rhs);
-   octonion<T> & operator += (::boost::math::quaternion<T> const & rhs);
+   octonion<T> & operator += (T const & rhs);
+   octonion<T> & operator += (::std::complex<T> const & rhs);
+   octonion<T> & operator += (::boost::math::quaternion<T> const & rhs);
    template<typename X> 
-   octonion<T> & operator += (octonion<X> const & rhs);
+   octonion<T> & operator += (octonion<X> const & rhs);
 
-   octonion<T> & operator -= (T const & rhs);
-   octonion<T> & operator -= (::std::complex<T> const & rhs);
-   octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs);
+   octonion<T> & operator -= (T const & rhs);
+   octonion<T> & operator -= (::std::complex<T> const & rhs);
+   octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs);
    template<typename X> 
-   octonion<T> & operator -= (octonion<X> const & rhs);
+   octonion<T> & operator -= (octonion<X> const & rhs);
 
-   octonion<T> & operator *= (T const & rhs);
-   octonion<T> & operator *= (::std::complex<T> const & rhs);
-   octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs);
+   octonion<T> & operator *= (T const & rhs);
+   octonion<T> & operator *= (::std::complex<T> const & rhs);
+   octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs);
    template<typename X> 
-   octonion<T> & operator *= (octonion<X> const & rhs);
+   octonion<T> & operator *= (octonion<X> const & rhs);
 
-   octonion<T> & operator /= (T const & rhs);
-   octonion<T> & operator /= (::std::complex<T> const & rhs);
-   octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs);
+   octonion<T> & operator /= (T const & rhs);
+   octonion<T> & operator /= (::std::complex<T> const & rhs);
+   octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs);
    template<typename X> 
-   octonion<T> & operator /= (octonion<X> const & rhs);
+   octonion<T> & operator /= (octonion<X> const & rhs);
 };
 
 } } // namespaces
@@ -98,7 +98,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -106,7 +106,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/test_program.html b/doc/octonion/html/boost_octonions/octonions/test_program.html index 6fae84a2e..6c8e11e94 100644 --- a/doc/octonion/html/boost_octonions/octonions/test_program.html +++ b/doc/octonion/html/boost_octonions/octonions/test_program.html @@ -1,10 +1,10 @@ - + Test Program - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      The octonion_test.cpp @@ -44,7 +44,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -52,7 +52,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/octonion/html/boost_octonions/octonions/to_do.html b/doc/octonion/html/boost_octonions/octonions/to_do.html index 8131251c6..1dfca0c41 100644 --- a/doc/octonion/html/boost_octonions/octonions/to_do.html +++ b/doc/octonion/html/boost_octonions/octonions/to_do.html @@ -1,10 +1,10 @@ - + To Do - - - + + + @@ -19,27 +19,28 @@
      -PrevUpHome +PrevUpHome
      -
      +
      -
        -
      • - Improve testing. -
        • -
      • - Rewrite input operatore using Spirit (creates a dependency). -
        • -
      • - Put in place an Expression Template mechanism (perhaps borrowing from uBlas). -
        • +
          +
        • + Improve testing. +
          • +
        • + Rewrite input operatore using Spirit (creates a dependency). +
          • +
        • + Put in place an Expression Template mechanism (perhaps borrowing from + uBlas). +
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -47,7 +48,7 @@
      -PrevUpHome +PrevUpHome
      diff --git a/doc/octonion/html/index.html b/doc/octonion/html/index.html index 36763c070..ac98024c9 100644 --- a/doc/octonion/html/index.html +++ b/doc/octonion/html/index.html @@ -1,10 +1,10 @@ - + Boost.Octonions - - - + + + @@ -17,8 +17,8 @@ More
      -
      Next
      -
      +
      Next
      +

      @@ -26,9 +26,9 @@

      Hubert Holin

      -

      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      -

      +

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -77,6 +77,6 @@
      -
      Next
      +
      Next
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions.html b/doc/quaternion/html/boost_quaternions/quaternions.html index 83acaeda6..5c9d38b3c 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions.html +++ b/doc/quaternion/html/boost_quaternions/quaternions.html @@ -1,10 +1,10 @@ - + Quaternions - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      Overview
      @@ -53,7 +53,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -61,7 +61,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/acknowledgements.html b/doc/quaternion/html/boost_quaternions/quaternions/acknowledgements.html index 4d27a9c7c..b60f02bbd 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/acknowledgements.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/acknowledgements.html @@ -1,10 +1,10 @@ - + Acknowledgements - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      The mathematical text has been typeset with Nisus @@ -36,7 +36,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -44,7 +44,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/create.html b/doc/quaternion/html/boost_quaternions/quaternions/create.html index c378f1ba2..6fb401057 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/create.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/create.html @@ -1,10 +1,10 @@ - + Quaternion Creation Functions - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      template<typename T>	quaternion<T>	spherical(T const & rho, T const & theta, T const & phi1, T const & phi2);
@@ -102,7 +102,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -110,7 +110,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/exp.html b/doc/quaternion/html/boost_quaternions/quaternions/exp.html index 348858d33..1d855fa50 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/exp.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/exp.html @@ -1,10 +1,10 @@ - + The Quaternionic Exponential - - - + + + @@ -20,26 +20,30 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      Please refer to the following PDF's:

      -
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -47,7 +51,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/header_file.html b/doc/quaternion/html/boost_quaternions/quaternions/header_file.html index cd1cffaa0..2c5854f98 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/header_file.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/header_file.html @@ -1,10 +1,10 @@ - + Header File - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      The interface and implementation are both supplied by the header file quaternion.hpp. @@ -32,7 +32,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -40,7 +40,7 @@
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      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/history.html b/doc/quaternion/html/boost_quaternions/quaternions/history.html index c919c1e69..5de1a8172 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/history.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/history.html @@ -1,10 +1,10 @@ - + History - - - + + + @@ -20,80 +20,82 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      -
        -
      • - 1.5.8 - 17/12/2005: Converted documentation to Quickbook Format. -
        • -
      • - 1.5.7 - 24/02/2003: transitionned to the unit test framework; <boost/config.hpp> - now included by the library header (rather than the test files). -
        • -
      • - 1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis - Evlogimenos (alkis@routescience.com). -
        • -
      • - 1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens - (michael@acfr.usyd.edu.au); requires the /Za compiler option. -
        • -
      • - 1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different - translation units); attempt at an improved compatibility with Microsoft - compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist; - other compatibility fixes. -
        • -
      • - 1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor - (gregod@cs.rpi.edu). -
        • -
      • - 1.5.2 - 07/07/2001: introduced namespace math. -
        • -
      • - 1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp> - and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>; - corrected bug in sin (Daryle Walker); removed check for self-assignment - (Gary Powel); made converting functions explicit (Gary Powel); added overflow - guards for division operators and abs (Peter Schmitteckert); added sup - and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code. -
        • -
      • - 1.5.0 - 26/03/2001: boostification, inlining of all operators except input, - output and pow, fixed exception safety of some members (template version) - and output operator, added spherical, semipolar, multipolar, cylindrospherical - and cylindrical. -
        • -
      • - 1.4.0 - 09/01/2001: added tan and tanh. -
        • -
      • - 1.3.1 - 08/01/2001: cosmetic fixes. -
        • -
      • - 1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl) - algorithm. -
        • -
      • - 1.2.0 - 25/05/2000: fixed the division operators and output; changed many - signatures. -
        • -
      • - 1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh. -
        • -
      • - 1.0.0 - 10/08/1999: first public version. -
        • +
          +
        • + 1.5.8 - 17/12/2005: Converted documentation to Quickbook Format. +
          • +
        • + 1.5.7 - 24/02/2003: transitionned to the unit test framework; <boost/config.hpp> + now included by the library header (rather than the test files). +
          • +
        • + 1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis + Evlogimenos (alkis@routescience.com). +
          • +
        • + 1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens + (michael@acfr.usyd.edu.au); requires the /Za compiler option. +
          • +
        • + 1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different + translation units); attempt at an improved compatibility with Microsoft + compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik + Blomqvist; other compatibility fixes. +
          • +
        • + 1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor + (gregod@cs.rpi.edu). +
          • +
        • + 1.5.2 - 07/07/2001: introduced namespace math. +
          • +
        • + 1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp> + and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>; + corrected bug in sin (Daryle Walker); removed check for self-assignment + (Gary Powel); made converting functions explicit (Gary Powel); added + overflow guards for division operators and abs (Peter Schmitteckert); + added sup and l1; used Vesa Karvonen's CPP metaprograming technique to + simplify code. +
          • +
        • + 1.5.0 - 26/03/2001: boostification, inlining of all operators except + input, output and pow, fixed exception safety of some members (template + version) and output operator, added spherical, semipolar, multipolar, + cylindrospherical and cylindrical. +
          • +
        • + 1.4.0 - 09/01/2001: added tan and tanh. +
          • +
        • + 1.3.1 - 08/01/2001: cosmetic fixes. +
          • +
        • + 1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl) + algorithm. +
          • +
        • + 1.2.0 - 25/05/2000: fixed the division operators and output; changed + many signatures. +
          • +
        • + 1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, + cosh. +
          • +
        • + 1.0.0 - 10/08/1999: first public version. +
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -101,7 +103,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/mem_fun.html b/doc/quaternion/html/boost_quaternions/quaternions/mem_fun.html index 689ee8d31..91ba2800a 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/mem_fun.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/mem_fun.html @@ -1,10 +1,10 @@ - + Quaternion Member Functions - - - + + + @@ -20,16 +20,16 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      - - Constructors + + Constructors

      Template version: @@ -80,13 +80,13 @@ function in a "detail" subnamespace.

      - - Other + + Other member functions

      - - Real + + Real and Unreal Parts 
      T             real() const;
@@ -100,8 +100,8 @@
         case). These are returned by the first two functions.
       
      
 
      
-
-        Individual
+
+        Individual
         Real Components
       
      
 
      T R_component_1() const;
@@ -114,8 +114,8 @@
         functions. Hence real and R_component_1 return the same value.
       
      
 
      
-
-        Individual
+
+        Individual
         Complex Components
       
      
 
      ::std::complex<T>	C_component_1() const;
@@ -129,13 +129,13 @@
         is the same as q.real().
       
      
 
      
-
-        Quaternion
+
+        Quaternion
         Member Operators
       
      
 
      
-
-        Assignment
+
+        Assignment
         Operators
       
      
 
      quaternion<T>& operator = (quaternion<T> const & a_affecter);
@@ -151,8 +151,8 @@
         base type's assignment operators must not throw.
       
      
 
      
-
-        Addition
+
+        Addition
         Operators
       
      
 
      quaternion<T>& operator += (T const & rhs)
@@ -168,8 +168,8 @@
         base type's assignment operators must not throw.
       
      
 
      
-
-        Subtraction
+
+        Subtraction
         Operators
       
      
 
      quaternion<T>& operator -= (T const & rhs)
@@ -185,8 +185,8 @@
         base type's assignment operators must not throw.
       
      
 
      
-
-        Multiplication
+
+        Multiplication
         Operators
       
      
 
      quaternion<T>& operator *= (T const & rhs)
@@ -203,8 +203,8 @@
         assignment operators must not throw.
       
      
 
      
-
-        Division
+
+        Division
         Operators
       
      
 
      quaternion<T>& operator /= (T const & rhs)
@@ -223,7 +223,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -231,7 +231,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/mem_typedef.html b/doc/quaternion/html/boost_quaternions/quaternions/mem_typedef.html index 00ddd1ffc..cfc5ce79c 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/mem_typedef.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/mem_typedef.html @@ -1,10 +1,10 @@ - + Quaternion Member Typedefs - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      @@ -56,7 +56,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -64,7 +64,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/non_mem.html b/doc/quaternion/html/boost_quaternions/quaternions/non_mem.html index b113e015c..17fca15f2 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/non_mem.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/non_mem.html @@ -1,10 +1,10 @@ - + Quaternion Non-Member Operators - - - + + + @@ -20,16 +20,16 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      - - Unary Plus + + Unary Plus 
      template<typename T>	
 quaternion<T> operator + (quaternion<T> const & q);
@@ -38,8 +38,8 @@
         This unary operator simply returns q.
       
      
 
      
-
-        Unary Minus
+
+        Unary Minus
       
      
 
      template<typename T>
 quaternion<T> operator - (quaternion<T> const & q);
@@ -48,8 +48,8 @@
         This unary operator returns the opposite of q.
       
      
 
      
-
-        Binary
+
+        Binary
         Addition Operators
       
      
 
      template<typename T>	quaternion<T>	operator + (T const & lhs, quaternion<T> const & rhs);
@@ -63,8 +63,8 @@
         rhs.
       
      
 
      
-
-        Binary
+
+        Binary
         Subtraction Operators
       
      
 
      template<typename T>	quaternion<T>	operator - (T const & lhs, quaternion<T> const & rhs);
@@ -78,8 +78,8 @@
         rhs.
       
      
 
      
-
-        Binary
+
+        Binary
         Multiplication Operators
       
      
 
      template<typename T>	quaternion<T>	operator * (T const & lhs, quaternion<T> const & rhs);
@@ -93,8 +93,8 @@
         rhs.
       
      
 
      
-
-        Binary
+
+        Binary
         Division Operators
       
      
 
      template<typename T>	quaternion<T>	operator / (T const & lhs, quaternion<T> const & rhs);
@@ -109,8 +109,8 @@
         to divide by zero...
       
      
 
      
-
-        Equality
+
+        Equality
         Operators
       
      
 
      template<typename T>	bool	operator == (T const & lhs, quaternion<T> const & rhs);
@@ -125,8 +125,8 @@
         with any floating-type entity, this is essentially meaningless.
       
      
 
      
-
-        Inequality
+
+        Inequality
         Operators
       
      
 
      template<typename T>	bool	operator != (T const & lhs, quaternion<T> const & rhs);
@@ -141,8 +141,8 @@
         false. As with any floating-type entity, this is essentially meaningless.
       
      
 
      
-
-        Stream
+
+        Stream
         Extractor
       
      
 
      template<typename T, typename charT, class traits>
@@ -173,8 +173,8 @@
         complex numbers which happen to have imaginary parts equal to zero).
       
      
 
      
-
-        Stream
+
+        Stream
         Inserter
       
      
 
      template<typename T, typename charT, class traits>
@@ -206,7 +206,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -214,7 +214,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/overview.html b/doc/quaternion/html/boost_quaternions/quaternions/overview.html index 40fb3b307..fd320b107 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/overview.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/overview.html @@ -1,10 +1,10 @@ - + Overview - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      Quaternions are a relative of complex numbers. @@ -79,7 +79,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -87,7 +87,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/quat.html b/doc/quaternion/html/boost_quaternions/quaternions/quat.html index 0dd30b479..b8c83180e 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/quat.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/quat.html @@ -1,10 +1,10 @@ - + Template Class quaternion - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      namespace boost{ namespace math{
 
@@ -33,47 +33,47 @@
 {
 public:
 
-   typedef T value_type;
+   typedef T value_type;
 
-   explicit quaternion(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T());
-   explicit quaternion(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>());
+   explicit quaternion(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T());
+   explicit quaternion(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>());
    template<typename X> 
-   explicit quaternion(quaternion<X> const & a_recopier);
+   explicit quaternion(quaternion<X> const & a_recopier);
 
-   T                  real() const;
-   quaternion<T>      unreal() const;
-   T                  R_component_1() const;
-   T                  R_component_2() const;
-   T                  R_component_3() const;
-   T                  R_component_4() const;
-   ::std::complex<T>  C_component_1() const;
-   ::std::complex<T>  C_component_2() const;
+   T                  real() const;
+   quaternion<T>      unreal() const;
+   T                  R_component_1() const;
+   T                  R_component_2() const;
+   T                  R_component_3() const;
+   T                  R_component_4() const;
+   ::std::complex<T>  C_component_1() const;
+   ::std::complex<T>  C_component_2() const;
 
-   quaternion<T>&     operator = (quaternion<T> const  & a_affecter);
+   quaternion<T>&     operator = (quaternion<T> const  & a_affecter);
    template<typename X>	
-   quaternion<T>&     operator = (quaternion<X> const  & a_affecter);
-   quaternion<T>&     operator = (T const  & a_affecter);
-   quaternion<T>&     operator = (::std::complex<T> const & a_affecter);
+   quaternion<T>&     operator = (quaternion<X> const  & a_affecter);
+   quaternion<T>&     operator = (T const  & a_affecter);
+   quaternion<T>&     operator = (::std::complex<T> const & a_affecter);
 
-   quaternion<T>&     operator += (T const & rhs);
-   quaternion<T>&     operator += (::std::complex<T> const & rhs);
+   quaternion<T>&     operator += (T const & rhs);
+   quaternion<T>&     operator += (::std::complex<T> const & rhs);
    template<typename X>
-   quaternion<T>&     operator += (quaternion<X> const & rhs);
+   quaternion<T>&     operator += (quaternion<X> const & rhs);
 
-   quaternion<T>&     operator -= (T const & rhs);
-   quaternion<T>&     operator -= (::std::complex<T> const & rhs);
+   quaternion<T>&     operator -= (T const & rhs);
+   quaternion<T>&     operator -= (::std::complex<T> const & rhs);
    template<typename X>
-   quaternion<T>&     operator -= (quaternion<X> const & rhs);
+   quaternion<T>&     operator -= (quaternion<X> const & rhs);
 
-   quaternion<T>&     operator *= (T const & rhs);
-   quaternion<T>&     operator *= (::std::complex<T> const & rhs);
+   quaternion<T>&     operator *= (T const & rhs);
+   quaternion<T>&     operator *= (::std::complex<T> const & rhs);
    template<typename X>
-   quaternion<T>&     operator *= (quaternion<X> const & rhs);
+   quaternion<T>&     operator *= (quaternion<X> const & rhs);
 
-   quaternion<T>&     operator /= (T const & rhs);
-   quaternion<T>&     operator /= (::std::complex<T> const & rhs);
+   quaternion<T>&     operator /= (T const & rhs);
+   quaternion<T>&     operator /= (::std::complex<T> const & rhs);
    template<typename X>
-   quaternion<T>&     operator /= (quaternion<X> const & rhs);
+   quaternion<T>&     operator /= (quaternion<X> const & rhs);
 };
 
 } // namespace math
@@ -82,7 +82,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -90,7 +90,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/spec.html b/doc/quaternion/html/boost_quaternions/quaternions/spec.html index 7cdb8274e..c0f1983a2 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/spec.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/spec.html @@ -1,10 +1,10 @@ - + Quaternion Specializations - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      namespace boost{ namespace math{
 
@@ -32,47 +32,47 @@
 class quaternion<float>
 {
 public:
-   typedef float value_type;
+   typedef float value_type;
 	
-   explicit quaternion(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f);
-   explicit quaternion(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>());
-   explicit quaternion(quaternion<double> const & a_recopier);
-   explicit quaternion(quaternion<long double> const & a_recopier);
+   explicit quaternion(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f);
+   explicit quaternion(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>());
+   explicit quaternion(quaternion<double> const & a_recopier);
+   explicit quaternion(quaternion<long double> const & a_recopier);
 	
-   float                  real() const;
-   quaternion<float>      unreal() const;
-   float                  R_component_1() const;
-   float                  R_component_2() const;
-   float                  R_component_3() const;
-   float                  R_component_4() const;
-   ::std::complex<float>  C_component_1() const;
-   ::std::complex<float>  C_component_2() const;
+   float                  real() const;
+   quaternion<float>      unreal() const;
+   float                  R_component_1() const;
+   float                  R_component_2() const;
+   float                  R_component_3() const;
+   float                  R_component_4() const;
+   ::std::complex<float>  C_component_1() const;
+   ::std::complex<float>  C_component_2() const;
 
-   quaternion<float>&     operator = (quaternion<float> const  & a_affecter);
+   quaternion<float>&     operator = (quaternion<float> const  & a_affecter);
    template<typename X>	
-   quaternion<float>&     operator = (quaternion<X> const  & a_affecter);
-   quaternion<float>&     operator = (float const  & a_affecter);
-   quaternion<float>&     operator = (::std::complex<float> const & a_affecter);
+   quaternion<float>&     operator = (quaternion<X> const  & a_affecter);
+   quaternion<float>&     operator = (float const  & a_affecter);
+   quaternion<float>&     operator = (::std::complex<float> const & a_affecter);
 
-   quaternion<float>&     operator += (float const & rhs);
-   quaternion<float>&     operator += (::std::complex<float> const & rhs);
+   quaternion<float>&     operator += (float const & rhs);
+   quaternion<float>&     operator += (::std::complex<float> const & rhs);
    template<typename X>
-   quaternion<float>&     operator += (quaternion<X> const & rhs);
+   quaternion<float>&     operator += (quaternion<X> const & rhs);
 
-   quaternion<float>&     operator -= (float const & rhs);
-   quaternion<float>&     operator -= (::std::complex<float> const & rhs);
+   quaternion<float>&     operator -= (float const & rhs);
+   quaternion<float>&     operator -= (::std::complex<float> const & rhs);
    template<typename X>
-   quaternion<float>&     operator -= (quaternion<X> const & rhs);
+   quaternion<float>&     operator -= (quaternion<X> const & rhs);
 
-   quaternion<float>&     operator *= (float const & rhs);
-   quaternion<float>&     operator *= (::std::complex<float> const & rhs);
+   quaternion<float>&     operator *= (float const & rhs);
+   quaternion<float>&     operator *= (::std::complex<float> const & rhs);
    template<typename X>
-   quaternion<float>&     operator *= (quaternion<X> const & rhs);
+   quaternion<float>&     operator *= (quaternion<X> const & rhs);
 
-   quaternion<float>&     operator /= (float const & rhs);
-   quaternion<float>&     operator /= (::std::complex<float> const & rhs);
+   quaternion<float>&     operator /= (float const & rhs);
+   quaternion<float>&     operator /= (::std::complex<float> const & rhs);
    template<typename X>
-   quaternion<float>&     operator /= (quaternion<X> const & rhs);
+   quaternion<float>&     operator /= (quaternion<X> const & rhs);
 };

      @@ -81,47 +81,47 @@ class quaternion<double> { public: - typedef double value_type; + typedef double value_type; - explicit quaternion(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0); - explicit quaternion(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>()); - explicit quaternion(quaternion<float> const & a_recopier); - explicit quaternion(quaternion<long double> const & a_recopier); + explicit quaternion(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0); + explicit quaternion(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>()); + explicit quaternion(quaternion<float> const & a_recopier); + explicit quaternion(quaternion<long double> const & a_recopier); - double real() const; - quaternion<double> unreal() const; - double R_component_1() const; - double R_component_2() const; - double R_component_3() const; - double R_component_4() const; - ::std::complex<double> C_component_1() const; - ::std::complex<double> C_component_2() const; + double real() const; + quaternion<double> unreal() const; + double R_component_1() const; + double R_component_2() const; + double R_component_3() const; + double R_component_4() const; + ::std::complex<double> C_component_1() const; + ::std::complex<double> C_component_2() const; - quaternion<double>& operator = (quaternion<double> const & a_affecter); + quaternion<double>& operator = (quaternion<double> const & a_affecter); template<typename X> - quaternion<double>& operator = (quaternion<X> const & a_affecter); - quaternion<double>& operator = (double const & a_affecter); - quaternion<double>& operator = (::std::complex<double> const & a_affecter); + quaternion<double>& operator = (quaternion<X> const & a_affecter); + quaternion<double>& operator = (double const & a_affecter); + quaternion<double>& operator = (::std::complex<double> const & a_affecter); - quaternion<double>& operator += (double const & rhs); - quaternion<double>& operator += (::std::complex<double> const & rhs); + quaternion<double>& operator += (double const & rhs); + quaternion<double>& operator += (::std::complex<double> const & rhs); template<typename X> - quaternion<double>& operator += (quaternion<X> const & rhs); + quaternion<double>& operator += (quaternion<X> const & rhs); - quaternion<double>& operator -= (double const & rhs); - quaternion<double>& operator -= (::std::complex<double> const & rhs); + quaternion<double>& operator -= (double const & rhs); + quaternion<double>& operator -= (::std::complex<double> const & rhs); template<typename X> - quaternion<double>& operator -= (quaternion<X> const & rhs); + quaternion<double>& operator -= (quaternion<X> const & rhs); - quaternion<double>& operator *= (double const & rhs); - quaternion<double>& operator *= (::std::complex<double> const & rhs); + quaternion<double>& operator *= (double const & rhs); + quaternion<double>& operator *= (::std::complex<double> const & rhs); template<typename X> - quaternion<double>& operator *= (quaternion<X> const & rhs); + quaternion<double>& operator *= (quaternion<X> const & rhs); - quaternion<double>& operator /= (double const & rhs); - quaternion<double>& operator /= (::std::complex<double> const & rhs); + quaternion<double>& operator /= (double const & rhs); + quaternion<double>& operator /= (::std::complex<double> const & rhs); template<typename X> - quaternion<double>& operator /= (quaternion<X> const & rhs); + quaternion<double>& operator /= (quaternion<X> const & rhs); };

      @@ -130,47 +130,47 @@ class quaternion<long double> { public: - typedef long double value_type; + typedef long double value_type; - explicit quaternion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L); - explicit quaternion(::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>()); - explicit quaternion(quaternion<float> const & a_recopier); - explicit quaternion(quaternion<double> const & a_recopier); + explicit quaternion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L); + explicit quaternion(::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>()); + explicit quaternion(quaternion<float> const & a_recopier); + explicit quaternion(quaternion<double> const & a_recopier); - long double real() const; - quaternion<long double> unreal() const; - long double R_component_1() const; - long double R_component_2() const; - long double R_component_3() const; - long double R_component_4() const; - ::std::complex<long double> C_component_1() const; - ::std::complex<long double> C_component_2() const; + long double real() const; + quaternion<long double> unreal() const; + long double R_component_1() const; + long double R_component_2() const; + long double R_component_3() const; + long double R_component_4() const; + ::std::complex<long double> C_component_1() const; + ::std::complex<long double> C_component_2() const; - quaternion<long double>& operator = (quaternion<long double> const & a_affecter); + quaternion<long double>& operator = (quaternion<long double> const & a_affecter); template<typename X> - quaternion<long double>& operator = (quaternion<X> const & a_affecter); - quaternion<long double>& operator = (long double const & a_affecter); - quaternion<long double>& operator = (::std::complex<long double> const & a_affecter); + quaternion<long double>& operator = (quaternion<X> const & a_affecter); + quaternion<long double>& operator = (long double const & a_affecter); + quaternion<long double>& operator = (::std::complex<long double> const & a_affecter); - quaternion<long double>& operator += (long double const & rhs); - quaternion<long double>& operator += (::std::complex<long double> const & rhs); + quaternion<long double>& operator += (long double const & rhs); + quaternion<long double>& operator += (::std::complex<long double> const & rhs); template<typename X> - quaternion<long double>& operator += (quaternion<X> const & rhs); + quaternion<long double>& operator += (quaternion<X> const & rhs); - quaternion<long double>& operator -= (long double const & rhs); - quaternion<long double>& operator -= (::std::complex<long double> const & rhs); + quaternion<long double>& operator -= (long double const & rhs); + quaternion<long double>& operator -= (::std::complex<long double> const & rhs); template<typename X> - quaternion<long double>& operator -= (quaternion<X> const & rhs); + quaternion<long double>& operator -= (quaternion<X> const & rhs); - quaternion<long double>& operator *= (long double const & rhs); - quaternion<long double>& operator *= (::std::complex<long double> const & rhs); + quaternion<long double>& operator *= (long double const & rhs); + quaternion<long double>& operator *= (::std::complex<long double> const & rhs); template<typename X> - quaternion<long double>& operator *= (quaternion<X> const & rhs); + quaternion<long double>& operator *= (quaternion<X> const & rhs); - quaternion<long double>& operator /= (long double const & rhs); - quaternion<long double>& operator /= (::std::complex<long double> const & rhs); + quaternion<long double>& operator /= (long double const & rhs); + quaternion<long double>& operator /= (::std::complex<long double> const & rhs); template<typename X> - quaternion<long double>& operator /= (quaternion<X> const & rhs); + quaternion<long double>& operator /= (quaternion<X> const & rhs); }; } // namespace math @@ -179,7 +179,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -187,7 +187,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/synopsis.html b/doc/quaternion/html/boost_quaternions/quaternions/synopsis.html index f9402fc0f..d2948c107 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/synopsis.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/synopsis.html @@ -1,10 +1,10 @@ - + Synopsis - - - + + + @@ -20,90 +20,90 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      namespace boost{ namespace math{
 
-template<typename T> class quaternion;
-template<>           class quaternion<float>;
-template<>           class quaternion<double>; 
-template<>           class quaternion<long double>; 
+template<typename T> class quaternion;
+template<>           class quaternion<float>;
+template<>           class quaternion<double>; 
+template<>           class quaternion<long double>; 
 
 // operators
-template<typename T> quaternion<T> operator + (T const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, T const & rhs);
-template<typename T> quaternion<T> operator + (::std::complex<T> const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator + (T const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, T const & rhs);
+template<typename T> quaternion<T> operator + (::std::complex<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> quaternion<T> operator + (quaternion<T> const & lhs, quaternion<T> const & rhs);
 
-template<typename T> quaternion<T> operator - (T const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, T const & rhs);
-template<typename T> quaternion<T> operator - (::std::complex<T> const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator - (T const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, T const & rhs);
+template<typename T> quaternion<T> operator - (::std::complex<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> quaternion<T> operator - (quaternion<T> const & lhs, quaternion<T> const & rhs);
 
-template<typename T> quaternion<T> operator * (T const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, T const & rhs);
-template<typename T> quaternion<T> operator * (::std::complex<T> const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator * (T const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, T const & rhs);
+template<typename T> quaternion<T> operator * (::std::complex<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> quaternion<T> operator * (quaternion<T> const & lhs, quaternion<T> const & rhs);
 
-template<typename T> quaternion<T> operator / (T const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, T const & rhs);
-template<typename T> quaternion<T> operator / (::std::complex<T> const & lhs, quaternion<T> const & rhs);
-template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, quaternion<T> const & rhs); 
+template<typename T> quaternion<T> operator / (T const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, T const & rhs);
+template<typename T> quaternion<T> operator / (::std::complex<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> quaternion<T> operator / (quaternion<T> const & lhs, quaternion<T> const & rhs); 
 
-template<typename T> quaternion<T> operator + (quaternion<T> const & q);
-template<typename T> quaternion<T> operator - (quaternion<T> const & q); 
+template<typename T> quaternion<T> operator + (quaternion<T> const & q);
+template<typename T> quaternion<T> operator - (quaternion<T> const & q); 
 
-template<typename T> bool operator == (T const & lhs, quaternion<T> const & rhs);
-template<typename T> bool operator == (quaternion<T> const & lhs, T const & rhs);
-template<typename T> bool operator == (::std::complex<T> const & lhs, quaternion<T> const & rhs);
-template<typename T> bool operator == (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> bool operator == (quaternion<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> bool operator == (T const & lhs, quaternion<T> const & rhs);
+template<typename T> bool operator == (quaternion<T> const & lhs, T const & rhs);
+template<typename T> bool operator == (::std::complex<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> bool operator == (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> bool operator == (quaternion<T> const & lhs, quaternion<T> const & rhs);
 
-template<typename T> bool operator != (T const & lhs, quaternion<T> const & rhs);
-template<typename T> bool operator != (quaternion<T> const & lhs, T const & rhs);
-template<typename T> bool operator != (::std::complex<T> const & lhs, quaternion<T> const & rhs);
-template<typename T> bool operator != (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
-template<typename T> bool operator != (quaternion<T> const & lhs, quaternion<T> const & rhs); 
+template<typename T> bool operator != (T const & lhs, quaternion<T> const & rhs);
+template<typename T> bool operator != (quaternion<T> const & lhs, T const & rhs);
+template<typename T> bool operator != (::std::complex<T> const & lhs, quaternion<T> const & rhs);
+template<typename T> bool operator != (quaternion<T> const & lhs, ::std::complex<T> const & rhs);
+template<typename T> bool operator != (quaternion<T> const & lhs, quaternion<T> const & rhs); 
 
 template<typename T, typename charT, class traits>
-::std::basic_istream<charT,traits>& operator >> (::std::basic_istream<charT,traits> & is, quaternion<T> & q);
+::std::basic_istream<charT,traits>& operator >> (::std::basic_istream<charT,traits> & is, quaternion<T> & q);
 
 template<typename T, typename charT, class traits>
-::std::basic_ostream<charT,traits>& operator operator << (::std::basic_ostream<charT,traits> & os, quaternion<T> const & q);
+::std::basic_ostream<charT,traits>& operator operator << (::std::basic_ostream<charT,traits> & os, quaternion<T> const & q);
 
 // values
-template<typename T>	T              real(quaternion<T> const & q);
-template<typename T>	quaternion<T>  unreal(quaternion<T> const & q);
+template<typename T>	T              real(quaternion<T> const & q);
+template<typename T>	quaternion<T>  unreal(quaternion<T> const & q);
 
-template<typename T>	T              sup(quaternion<T> const & q);
-template<typename T>	T              l1(quaternion<T> const & q);
-template<typename T>	T              abs(quaternion<T> const & q);
-template<typename T>	T              norm(quaternion<T>const  & q);
-template<typename T>	quaternion<T>  conj(quaternion<T> const & q);
+template<typename T>	T              sup(quaternion<T> const & q);
+template<typename T>	T              l1(quaternion<T> const & q);
+template<typename T>	T              abs(quaternion<T> const & q);
+template<typename T>	T              norm(quaternion<T>const  & q);
+template<typename T>	quaternion<T>  conj(quaternion<T> const & q);
 
-template<typename T>	quaternion<T>  spherical(T const & rho, T const & theta, T const & phi1, T const & phi2);
-template<typename T>	quaternion<T>  semipolar(T const & rho, T const & alpha, T const & theta1, T const & theta2);
-template<typename T>	quaternion<T>  multipolar(T const & rho1, T const & theta1, T const & rho2, T const & theta2);
-template<typename T>	quaternion<T>  cylindrospherical(T const & t, T const & radius, T const & longitude, T const & latitude);
-template<typename T>	quaternion<T>  cylindrical(T const & r, T const & angle, T const & h1, T const & h2);
+template<typename T>	quaternion<T>  spherical(T const & rho, T const & theta, T const & phi1, T const & phi2);
+template<typename T>	quaternion<T>  semipolar(T const & rho, T const & alpha, T const & theta1, T const & theta2);
+template<typename T>	quaternion<T>  multipolar(T const & rho1, T const & theta1, T const & rho2, T const & theta2);
+template<typename T>	quaternion<T>  cylindrospherical(T const & t, T const & radius, T const & longitude, T const & latitude);
+template<typename T>	quaternion<T>  cylindrical(T const & r, T const & angle, T const & h1, T const & h2);
 
 // transcendentals
-template<typename T>	quaternion<T>  exp(quaternion<T> const & q);
-template<typename T>	quaternion<T>  cos(quaternion<T> const & q);
-template<typename T>	quaternion<T>  sin(quaternion<T> const & q);
-template<typename T>	quaternion<T>  tan(quaternion<T> const & q);
-template<typename T>	quaternion<T>  cosh(quaternion<T> const & q);
-template<typename T>	quaternion<T>  sinh(quaternion<T> const & q);
-template<typename T>	quaternion<T>  tanh(quaternion<T> const & q);
-template<typename T>	quaternion<T>  pow(quaternion<T> const & q, int n);
+template<typename T>	quaternion<T>  exp(quaternion<T> const & q);
+template<typename T>	quaternion<T>  cos(quaternion<T> const & q);
+template<typename T>	quaternion<T>  sin(quaternion<T> const & q);
+template<typename T>	quaternion<T>  tan(quaternion<T> const & q);
+template<typename T>	quaternion<T>  cosh(quaternion<T> const & q);
+template<typename T>	quaternion<T>  sinh(quaternion<T> const & q);
+template<typename T>	quaternion<T>  tanh(quaternion<T> const & q);
+template<typename T>	quaternion<T>  pow(quaternion<T> const & q, int n);
 
 } // namespace math
 } // namespace boost
@@ -111,7 +111,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -119,7 +119,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/test_program.html b/doc/quaternion/html/boost_quaternions/quaternions/test_program.html index 31d785f1a..db0eb5746 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/test_program.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/test_program.html @@ -1,10 +1,10 @@ - + Test Program - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      The quaternion_test.cpp @@ -45,7 +45,7 @@

      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -53,7 +53,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/to_do.html b/doc/quaternion/html/boost_quaternions/quaternions/to_do.html index ffc581cea..dc3930173 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/to_do.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/to_do.html @@ -1,10 +1,10 @@ - + To Do - - - + + + @@ -19,31 +19,32 @@
      -PrevUpHome +PrevUpHome
      -
      +
      -
        -
      • - Improve testing. -
        • -
      • - Rewrite input operatore using Spirit (creates a dependency). -
        • -
      • - Put in place an Expression Template mechanism (perhaps borrowing from uBlas). -
        • -
      • - Use uBlas for the link with rotations (and move from the example - implementation to an efficient one). -
        • +
          +
        • + Improve testing. +
          • +
        • + Rewrite input operatore using Spirit (creates a dependency). +
          • +
        • + Put in place an Expression Template mechanism (perhaps borrowing from + uBlas). +
          • +
        • + Use uBlas for the link with rotations (and move from the example + implementation to an efficient one). +
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -51,7 +52,7 @@
      -PrevUpHome +PrevUpHome
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/trans.html b/doc/quaternion/html/boost_quaternions/quaternions/trans.html index 33d8d634c..0bc9e9cec 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/trans.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/trans.html @@ -1,10 +1,10 @@ - + Quaternion Transcendentals - - - + + + @@ -20,11 +20,11 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      There is no log or sqrt provided for quaternions in this implementation, @@ -56,8 +56,8 @@ headers.

      - - exp + + exp 
      template<typename T>	quaternion<T> exp(quaternion<T> const & q);
      @@ -65,8 +65,8 @@ Computes the exponential of the quaternion.

      - - cos + + cos 
      template<typename T>	quaternion<T>  cos(quaternion<T> const & q);
      @@ -74,8 +74,8 @@ Computes the cosine of the quaternion

      - - sin + + sin 
      template<typename T>	quaternion<T>  sin(quaternion<T> const & q);
      @@ -83,8 +83,8 @@ Computes the sine of the quaternion.

      - - tan + + tan 
      template<typename T>	quaternion<T>  tan(quaternion<T> const & q);
      @@ -92,8 +92,8 @@ Computes the tangent of the quaternion.

      - - cosh + + cosh 
      template<typename T>	quaternion<T>  cosh(quaternion<T> const & q);
      @@ -101,8 +101,8 @@ Computes the hyperbolic cosine of the quaternion.

      - - sinh + + sinh 
      template<typename T>	quaternion<T>  sinh(quaternion<T> const & q);
      @@ -110,8 +110,8 @@ Computes the hyperbolic sine of the quaternion.

      - - tanh + + tanh 
      template<typename T>	quaternion<T>  tanh(quaternion<T> const & q);
      @@ -119,8 +119,8 @@ Computes the hyperbolic tangent of the quaternion.

      - - pow + + pow 
      template<typename T>	quaternion<T>  pow(quaternion<T> const & q, int n);
      @@ -130,7 +130,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -138,7 +138,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/boost_quaternions/quaternions/value_op.html b/doc/quaternion/html/boost_quaternions/quaternions/value_op.html index 6056c61e5..20ec5db01 100644 --- a/doc/quaternion/html/boost_quaternions/quaternions/value_op.html +++ b/doc/quaternion/html/boost_quaternions/quaternions/value_op.html @@ -1,10 +1,10 @@ - + Quaternion Value Operations - - - + + + @@ -20,16 +20,16 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      - - real + + real and unreal 
      template<typename T>	T              real(quaternion<T> const & q);
@@ -41,8 +41,8 @@
         respectively.
       
      
 
      
-
-        conj
+
+        conj
       
      
 
      template<typename T>	quaternion<T>  conj(quaternion<T> const & q);
 
      
@@ -50,8 +50,8 @@
         This returns the conjugate of the quaternion.
       
      
 
      
-
-        sup
+
+        sup
       
      
 
      
         template<typename T> T sup(quaternion<T> const & q);
@@ -60,8 +60,8 @@
         This return the sup norm (the greatest among abs(q.R_component_1())...abs(q.R_component_4())) of the quaternion.
       
      
 
      
-
-        l1
+
+        l1
       
      
 
      template<typename T>	T  l1(quaternion<T> const & q);
 
      
@@ -69,8 +69,8 @@
         This return the l1 norm (abs(q.R_component_1())+...+abs(q.R_component_4())) of the quaternion.
       
      
 
      
-
-        abs
+
+        abs
       
      
 
      template<typename T>	T  abs(quaternion<T> const & q);
 
      
@@ -78,8 +78,8 @@
         This return the magnitude (Euclidian norm) of the quaternion.
       
      
 
      
-
-        norm
+
+        norm
       
      
 
      template<typename T>	T  norm(quaternion<T>const  & q);
 
      
@@ -93,7 +93,7 @@
      -
      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -101,7 +101,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/quaternion/html/index.html b/doc/quaternion/html/index.html index df47f53e3..307c75d57 100644 --- a/doc/quaternion/html/index.html +++ b/doc/quaternion/html/index.html @@ -1,10 +1,10 @@ - + Boost.Quaternions - - - + + + @@ -17,8 +17,8 @@ More
      -
      Next
      -
      +
      Next
      +

      @@ -26,9 +26,9 @@

      Hubert Holin

      -

      Copyright © 2001 -2003 Hubert Holin

      +

      Copyright © 2001 -2003 Hubert Holin

      -

      +

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -76,6 +76,6 @@
      -
      Next
      +
      Next
      diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 35ca1181d..7a89f407b 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -2,8 +2,8 @@ Math Toolkit - - + + @@ -17,8 +17,8 @@ More
      -
      Next
      -
      +
      Next
      +

      @@ -53,7 +53,7 @@ Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg

      -

      +

      Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

      @@ -488,10 +488,10 @@

      - +

      Last revised: April 13, 2010 at 12:21:17 GMT

      Last revised: July 01, 2010 at 21:46:24 GMT
      -
      Next
      +
      Next
      diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders.html b/doc/sf_and_dist/html/math_toolkit/backgrounders.html index a1eef1c96..d25671c58 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders.html @@ -2,8 +2,8 @@ Backgrounders - - + + @@ -20,9 +20,9 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      @@ -48,7 +48,7 @@
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html index 8897982df..5ee616462 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -2,8 +2,8 @@ Additional Implementation Notes - - + + @@ -20,9 +20,9 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +

      Additional Implementation Notes @@ -33,7 +33,7 @@ and reflect more the general implementation philosophy used.

      - + Implemention philosophy
      @@ -85,7 +85,7 @@ These could still provide sufficient accuracy for some speed-critical applications.

      - + Accuracy and Representation of Test Values
      @@ -130,20 +130,20 @@ binary value).

      - + Tolerance of Tests

      The tolerances need to be set to the maximum of:

      -
        -
      • - Some epsilon value. -
        • -
      • - The accuracy of the data (often only near 64-bit double). -
        • +
          +
        • + Some epsilon value. +
          • +
        • + The accuracy of the data (often only near 64-bit double). +

        Otherwise when long double has more digits than the test data, then no amount @@ -156,7 +156,7 @@ first that the suffix L is present, and then that the tolerance is big enough.

        - + Handling Unsuitable Arguments
        @@ -166,49 +166,31 @@ it is proposed that signalling a domain error is mandatory when the argument would give an mathematically undefined result.

        -
        • - Guideline 1 -
        -
        -

        -

        -

        - A mathematical function is said to be defined at a point a = (a1, a2, - . . .) if the limits as x = (x1, x2, . . .) 'approaches a from all directions - agree'. The defined value may be any number, or +infinity, or -infinity. -

        -

        -

        -
        +
        • + Guideline 1 +
        +

        + A mathematical function is said to be defined at a point a = (a1, a2, . + . .) if the limits as x = (x1, x2, . . .) 'approaches a from all directions + agree'. The defined value may be any number, or +infinity, or -infinity. +

        Put crudely, if the function goes to + infinity and then emerges 'round-the-back' with - infinity, it is NOT defined.

        -
        -

        -

        -

        - The library function which approximates a mathematical function shall - signal a domain error whenever evaluated with argument values for which - the mathematical function is undefined. -

        -

        -

        -
        -
        • - Guideline 2 -
        -
        -

        -

        -

        - The library function which approximates a mathematical function shall - signal a domain error whenever evaluated with argument values for which - the mathematical function obtains a non-real value. -

        -

        -

        -
        +

        + The library function which approximates a mathematical function shall signal + a domain error whenever evaluated with argument values for which the mathematical + function is undefined. +

        +
        • + Guideline 2 +
        +

        + The library function which approximates a mathematical function shall signal + a domain error whenever evaluated with argument values for which the mathematical + function obtains a non-real value. +

        This implementation is believed to follow these proposals and to assist compatibility with ISO/IEC 9899:1999 Programming languages - C and @@ -229,7 +211,7 @@

        - +
        [Caution][Caution] Caution

        @@ -242,7 +224,7 @@

        - + Handling of Functions that are Not Mathematically defined
        @@ -266,7 +248,7 @@

        - +
        [Warning][Warning] Warning

        @@ -276,7 +258,7 @@

        - + Median of distributions
        @@ -309,7 +291,7 @@ Basic Statistics. give more detail, in particular for discrete distributions.

        - + Handling of Floating-Point Infinity
        @@ -353,7 +335,7 @@ handling policies.

        - + Scale, Shape and Location
        @@ -380,19 +362,19 @@ functions, they can be added if required.

        - + Notes on Implementation of Specific Functions & Distributions
        -
        • - Default parameters for the Triangular Distribution. We are uncertain about - the best default parameters. Some sources suggest that the Standard Triangular - Distribution has lower = 0, mode = half and upper = 1. However as a approximation - for the normal distribution, the most common usage, lower = -1, mode = - 0 and upper = 1 would be more suitable. -
        +
        • + Default parameters for the Triangular Distribution. We are uncertain + about the best default parameters. Some sources suggest that the Standard + Triangular Distribution has lower = 0, mode = half and upper = 1. However + as a approximation for the normal distribution, the most common usage, + lower = -1, mode = 0 and upper = 1 would be more suitable. +
        - + Rational Approximations Used
        @@ -435,7 +417,7 @@ to the "true" minimax solution.

        - + Representation of Mathematical Constants
        @@ -496,7 +478,7 @@ double p = boost::math::constants::pi(); // Context does not allow for disambiguation of overloaded function
        - + Thread safety
        @@ -521,7 +503,7 @@ the right thing here at some point.

        - + Sources of Test Data
        @@ -543,18 +525,12 @@ Is a Javascript application that calculates and plots probability distributions, and provides the most complete range of distributions:

        -
        -

        -

        -

        - Bernoulli, Binomial, discrete uniform, geometric, hypergeometric, negative - binomial, Poisson, beta, Cauchy-Lorentz, chi-sequared, Erlang, exponential, - extreme value, Fisher, gamma, Laplace, logistic, lognormal, normal, Parteo, - Student's t, triangular, uniform, and Weibull. -

        -

        -

        -
        +

        + Bernoulli, Binomial, discrete uniform, geometric, hypergeometric, negative + binomial, Poisson, beta, Cauchy-Lorentz, chi-sequared, Erlang, exponential, + extreme value, Fisher, gamma, Laplace, logistic, lognormal, normal, Parteo, + Student's t, triangular, uniform, and Weibull. +

        It calculates pdf, cdf, survivor, log survivor, hazard, tail areas, & critical values for 5 tail values. @@ -565,7 +541,7 @@ the underlying special function is known to be difficult to implement.

        - + Creating and Managing the Equations
        @@ -737,7 +713,7 @@ done HTML: this needs further investigation.

        - + Producing Graphs
        @@ -746,9 +722,9 @@ done same process as the equations.

        - The programs /libs/math/doc/sf_and_dist/graphs/dist_graphs.cpp and /libs/math/doc/sf_and_dist/graphssf_graphs.cpp - generate the SVG's directly using the [@http:/code.google.com/soc/2007/boost/about.html - Google Summer of Code 2007] project of Jacob Voytko (whose work so far is + The programs /libs/math/doc/sf_and_dist/graphs/dist_graphs.cpp and /libs/math/doc/sf_and_dist/graphs/sf_graphs.cpp + generate the SVG's directly using the Google + Summer of Code 2007 project of Jacob Voytko (whose work so far is at .\boost-sandbox\SOC\2007\visualization).

      @@ -764,7 +740,7 @@ done
      -PrevUpHomeNext +PrevUpHomeNext
      diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html index e30671dbb..a67ebb501 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -2,8 +2,8 @@ The Lanczos Approximation - - + + @@ -20,14 +20,14 @@
      -PrevUpHomeNext +PrevUpHomeNext
      -
      +
      - + Motivation

      @@ -45,19 +45,20 @@ Lanczos approximation does have a couple of properties that make it worthy of further consideration:

      -
        -
      • - The approximation has an easy to compute truncation error that holds for - all z > 0. In practice that means we can use the - same approximation for all z > 0, and be certain - that no matter how large or small z is, the truncation - error will at worst be bounded by some finite value. -
        • -
      • - The approximation has a form that is particularly amenable to analytic - manipulation, in particular ratios of gamma or gamma-like functions are - particularly easy to compute without resorting to logarithms. -
        • +
          +
        • + The approximation has an easy to compute truncation error that holds + for all z > 0. In practice that means we can + use the same approximation for all z > 0, and + be certain that no matter how large or small z is, + the truncation error will at worst be bounded by + some finite value. +
          • +
        • + The approximation has a form that is particularly amenable to analytic + manipulation, in particular ratios of gamma or gamma-like functions are + particularly easy to compute without resorting to logarithms. +

        It is the combination of these two properties that make the approximation @@ -98,7 +99,7 @@ functions divided by large powers into single (simpler) expressions.

        - + The Approximation
        @@ -148,7 +149,7 @@

        - +
        [Note][Note] Note

        @@ -160,7 +161,7 @@

        - + Computing the Coefficients
        @@ -204,7 +205,7 @@ multiplied by F as the last step.

        - + Choosing the Right Parameters
        @@ -228,10 +229,10 @@ computing to float precision with double precision arithmetic.

        -

        Table 53. Optimal choices for N and g when computing with - guard digits (source: Pugh)

        -
        +

        Table 53. Optimal choices for N and g when computing with guard digits (source: + Pugh)

        +
        @@ -240,70 +241,70 @@ +

        + Significand Size +

        + +

        + N +

        + +

        + g +

        + +

        + Max Error +

        + +

        + 24 +

        + +

        + 6 +

        + +

        + 5.581 +

        + +

        + 9.51e-12 +

        + +

        + 53 +

        + +

        + 13 +

        + +

        + 13.144565 +

        + +

        + 9.2213e-23 +

        +
        -

        - Significand Size -

        -         		-

        - N -

        -         		-

        - g -

        -         		-

        - Max Error -

        -
        -

        - 24 -

        -         		-

        - 6 -

        -         		-

        - 5.581 -

        -         		-

        - 9.51e-12 -

        -
        -

        - 53 -

        -         		-

        - 13 -

        -         		-

        - 13.144565 -

        -         		-

        - 9.2213e-23 -

        -
        @@ -371,10 +372,8 @@ exactly matches the machine epsilon for the type in question.

        -

        Table 54. Optimum value for N and g when computing at fixed - precision

        -
        +

        Table 54. Optimum value for N and g when computing at fixed precision

        +
        @@ -384,139 +383,139 @@ +

        + Significand Size +

        + +

        + Platform/Compiler Used +

        + +

        + N +

        + +

        + g +

        + +

        + Max Truncation Error +

        + +

        + 24 +

        + +

        + Win32, VC++ 7.1 +

        + +

        + 6 +

        + +

        + 1.428456135094165802001953125 +

        + +

        + 9.41e-007 +

        + +

        + 53 +

        + +

        + Win32, VC++ 7.1 +

        + +

        + 13 +

        + +

        + 6.024680040776729583740234375 +

        + +

        + 3.23e-016 +

        + +

        + 64 +

        + +

        + Suse Linux 9 IA64, gcc-3.3.3 +

        + +

        + 17 +

        + +

        + 12.2252227365970611572265625 +

        + +

        + 2.34e-024 +

        + +

        + 116 +

        + +

        + HP Tru64 Unix 5.1B / Alpha, Compaq C++ V7.1-006 +

        + +

        + 24 +

        + +

        + 20.3209821879863739013671875 +

        + +

        + 4.75e-035 +

        +
        -

        - Significand Size -

        -         		-

        - Platform/Compiler Used -

        -         		-

        - N -

        -         		-

        - g -

        -         		-

        - Max Truncation Error -

        -
        -

        - 24 -

        -         		-

        - Win32, VC++ 7.1 -

        -         		-

        - 6 -

        -         		-

        - 1.428456135094165802001953125 -

        -         		-

        - 9.41e-007 -

        -
        -

        - 53 -

        -         		-

        - Win32, VC++ 7.1 -

        -         		-

        - 13 -

        -         		-

        - 6.024680040776729583740234375 -

        -         		-

        - 3.23e-016 -

        -
        -

        - 64 -

        -         		-

        - Suse Linux 9 IA64, gcc-3.3.3 -

        -         		-

        - 17 -

        -         		-

        - 12.2252227365970611572265625 -

        -         		-

        - 2.34e-024 -

        -
        -

        - 116 -

        -         		-

        - HP Tru64 Unix 5.1B / Alpha, Compaq C++ V7.1-006 -

        -         		-

        - 24 -

        -         		-

        - 20.3209821879863739013671875 -

        -         		-

        - 4.75e-035 -

        -
        @@ -536,27 +535,27 @@ is exact, and so isn't used for the gamma function.

        - + References
        -
          -
        1. - Paul Godfrey, "A note - on the computation of the convergent Lanczos complex Gamma approximation". -
          2. -
        2. - Glendon Ralph Pugh, "An - Analysis of the Lanczos Gamma Approximation", PhD Thesis November - 2004. -
          3. -
        3. - Viktor T. Toth, "Calculators - and the Gamma Function". -
          4. -
        4. - Mathworld, The - Lanczos Approximation. -
          5. +
            +
          1. + Paul Godfrey, "A + note on the computation of the convergent Lanczos complex Gamma approximation". +
            2. +
          2. + Glendon Ralph Pugh, "An + Analysis of the Lanczos Gamma Approximation", PhD Thesis + November 2004. +
            3. +
          3. + Viktor T. Toth, "Calculators + and the Gamma Function". +
            4. +
          4. + Mathworld, The + Lanczos Approximation. +
        @@ -571,7 +570,7 @@
        -PrevUpHomeNext +PrevUpHomeNext
        diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html index af4d4be1e..680bba4a4 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html @@ -2,8 +2,8 @@ References - - + + @@ -20,14 +20,14 @@
        -PrevUpHomeNext +PrevUpHomeNext
        -
        +
        - + General references
        @@ -91,7 +91,7 @@ Library (version 2), Walter E. Brown

        - + Calculators* that we found (and used to cross-check - as far as their widely-varying accuracy allowed). @@ -101,7 +101,7 @@ Binomial Probability Distribution Calculator.

        - + Other Libraries

        @@ -171,7 +171,7 @@

        -PrevUpHomeNext +PrevUpHomeNext
        diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html index a85011296..43833e782 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html @@ -2,8 +2,8 @@ Relative Error - - + + @@ -20,9 +20,9 @@
        -PrevUpHomeNext +PrevUpHomeNext
        -
        +

        Relative Error @@ -81,7 +81,7 @@

        - + The Impossibility of Zero Error
        @@ -119,7 +119,7 @@
        -PrevUpHomeNext +PrevUpHomeNext
        diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html index 586759d56..1a6811424 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -2,8 +2,8 @@ The Remez Method - - + + @@ -20,9 +20,9 @@
        -PrevUpHomeNext +PrevUpHomeNext
        -
        +
        @@ -65,17 +65,17 @@ yields the smallest maximal value of the error function. Chebyshev showed that there is a unique minimax solution for R(x) that has the following properties:

        -
          -
        • - If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1 - coefficients of the polynomial, and maximal value of the error function. -
          • -
        • - The error function has N+1 roots, and N+2 extrema (minima and maxima). -
          • -
        • - The extrema alternate in sign, and all have the same magnitude. -
          • +
            +
          • + If R(x) is a polynomial of degree N, then there are N+2 unknowns: the + N+1 coefficients of the polynomial, and maximal value of the error function. +
            • +
          • + The error function has N+1 roots, and N+2 extrema (minima and maxima). +
            • +
          • + The extrema alternate in sign, and all have the same magnitude. +

          That means that if we know the location of the extrema of the error function @@ -94,7 +94,7 @@ are located!

          - + The Remez Method
          @@ -150,7 +150,7 @@

          - +
          [Note][Note] Note
          @@ -174,7 +174,7 @@
          - + Remez Step 1
          @@ -205,7 +205,7 @@ to 5.6x10-4.

          - + Remez Step 2
          @@ -234,7 +234,7 @@ In our example we perform multi-point exchange.

          - + Iteration

          @@ -250,7 +250,7 @@ remez-4

          - + Rational Approximations
          @@ -299,7 +299,7 @@ number of terms overall.

          - + Practical Considerations
          @@ -407,7 +407,7 @@ desired minimax solution (5x10-4).

          - + Remez Method Checklist
          @@ -416,52 +416,52 @@ wrong, it is by no means an exhaustive list, but is provided in the hopes that it will prove useful.

          -
            -
          • - Is the function smooth enough? Can it be better separated into a rapidly - changing part, and an asymptotic part? -
            • -
          • - Does the function being approximated have any "blips" in it? - Check for problems as the function changes computation method, or if a - root, or an infinity has been divided out. The telltale sign is if there - is a narrow region where the Remez method will not converge. -
            • -
          • - Check you have enough accuracy in your calculations: remember that the - Remez method works on the difference between the approximation and the - function being approximated: so you must have more digits of precision - available than the precision of the approximation being constructed. So - for example at double precision, you shouldn't expect to be able to get - better than a float precision approximation. -
            • -
          • - Try skewing the initial interpolated approximation to minimise the error - before you begin the Remez steps. -
            • -
          • - If the approximation won't converge or is ill-conditioned from one starting - location, try starting from a different location. -
            • -
          • - If a rational function won't converge, one can minimise a polynomial (which - presents no problems), then rotate one term from the numerator to the denominator - and minimise again. In theory one can continue moving terms one at a time - from numerator to denominator, and then re-minimising, retaining the last - set of control points at each stage. -
            • -
          • - Try using a smaller interval. It may also be possible to optimise over - one (small) interval, rescale the control points over a larger interval, - and then re-minimise. -
            • -
          • - Keep absissa values small: use a change of variable to keep the abscissa - over, say [0, b], for some smallish value b. -
            • +
              +
            • + Is the function smooth enough? Can it be better separated into a rapidly + changing part, and an asymptotic part? +
              • +
            • + Does the function being approximated have any "blips" in it? + Check for problems as the function changes computation method, or if + a root, or an infinity has been divided out. The telltale sign is if + there is a narrow region where the Remez method will not converge. +
              • +
            • + Check you have enough accuracy in your calculations: remember that the + Remez method works on the difference between the approximation and the + function being approximated: so you must have more digits of precision + available than the precision of the approximation being constructed. + So for example at double precision, you shouldn't expect to be able to + get better than a float precision approximation. +
              • +
            • + Try skewing the initial interpolated approximation to minimise the error + before you begin the Remez steps. +
              • +
            • + If the approximation won't converge or is ill-conditioned from one starting + location, try starting from a different location. +
              • +
            • + If a rational function won't converge, one can minimise a polynomial + (which presents no problems), then rotate one term from the numerator + to the denominator and minimise again. In theory one can continue moving + terms one at a time from numerator to denominator, and then re-minimising, + retaining the last set of control points at each stage. +
              • +
            • + Try using a smaller interval. It may also be possible to optimise over + one (small) interval, rescale the control points over a larger interval, + and then re-minimise. +
              • +
            • + Keep absissa values small: use a change of variable to keep the abscissa + over, say [0, b], for some smallish value b. +
            - + References

            @@ -537,7 +537,7 @@

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist.html b/doc/sf_and_dist/html/math_toolkit/dist.html index 62ef5d8fc..3b57c4ef2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist.html @@ -2,8 +2,8 @@ Statistical Distributions and Functions - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            @@ -208,7 +208,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html index 351e5629a..d03379368 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html @@ -2,8 +2,8 @@ Statistical Distributions Reference - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +

            Statistical Distributions Reference @@ -99,7 +99,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html index 78e831bc2..f3da099c6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html @@ -2,8 +2,8 @@ Distribution Algorithms - - + + @@ -20,15 +20,15 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            - + Finding the Location and Scale for Normal and similar distributions
            @@ -50,7 +50,7 @@ using boost::math::complement; // Will be needed by users who want to use complements.
            - + find_location function
            @@ -80,7 +80,7 @@ }} // namespaces
            - + find_scale function
            @@ -140,7 +140,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html index 46bcfbe5b..17cee5b58 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html @@ -2,8 +2,8 @@ Distributions - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            @@ -92,7 +92,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html index 230eebe6c..8243c65f6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html @@ -2,8 +2,8 @@ Bernoulli Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Bernoulli Distribution @@ -87,7 +87,7 @@

            - + Member Functions
            @@ -103,7 +103,7 @@ Returns the success_fraction parameter of this distribution.

            - + Non-member Accessors
            @@ -128,7 +128,7 @@ exception and make an error message available.

            - + Accuracy

            @@ -136,7 +136,7 @@ and so should have errors within an epsilon or two.

            - + Implementation

            @@ -146,7 +146,7 @@

            - +
            [Note][Note] Note
            @@ -169,172 +169,176 @@
            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - Supported range -

            +

            + Supported range +

            		-

            - {0, 1} -

            +

            + {0, 1} +

            -

            - pdf -

            +

            + pdf +

            		-

            - Using the relation: pdf = 1 - p for k = 0, else p -

            +

            + Using the relation: pdf = 1 - p for k = 0, else p +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relation: cdf = 1 - p for k = 0, else 1 -

            +

            + Using the relation: cdf = 1 - p for k = 0, else 1 +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - q = 1 - p -

            +

            + q = 1 - p +

            -

            - quantile -

            +

            + quantile +

            		-

            - if x <= (1-p) 0 else 1 -

            +

            + if x <= (1-p) 0 else 1 +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - if x <= (1-p) 1 else 0 -

            +

            + if x <= (1-p) 1 else 0 +

            -

            - mean -

            +

            + mean +

            		-

            - p -

            +

            + p +

            -

            - variance -

            +

            + variance +

            		-

            - p * (1 - p) -

            +

            + p * (1 - p) +

            -

            - mode -

            +

            + mode +

            		-

            - if (p < 0.5) 0 else 1 -

            +

            + if (p < 0.5) 0 else 1 +

            -

            - skewness -

            +

            + skewness +

            		-

            - (1 - 2 * p) / sqrt(p * q) -

            +

            + (1 - 2 * p) / sqrt(p * q) +

            -

            - kurtosis -

            +

            + kurtosis +

            		-

            - 6 * p * p - 6 * p +1/ p * q -

            +

            + 6 * p * p - 6 * p +1/ p * q +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - kurtosis -3 -

            +

            + kurtosis -3 +

            - + References
            -
            @@ -349,7 +353,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html index 2c7480d23..c5c48c30a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html @@ -2,8 +2,8 @@ Beta Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Beta Distribution @@ -133,12 +133,12 @@ from the centre (where x = half).

            - + Member Functions
            - + Constructor 
            beta_distribution(RealType alpha, RealType beta);
@@ -165,7 +165,7 @@
             yellow in the graph above).
           
            
 
            
-
+
             Parameter
             Accessors
           
            
@@ -189,7 +189,7 @@
 assert(mybeta.beta() == 5.);   // mybeta.beta()  returns 5
            - + Parameter Estimators
            @@ -242,7 +242,7 @@ from presumed-known mean and variance. Returns the value of β that gives: cdf(beta_distribution<RealType>(alpha, beta), x) == probability.

            - + Non-member Accessor Functions
            @@ -264,7 +264,7 @@ from presumed-known mean and variance. Mathworld.

            - + Applications

            @@ -277,7 +277,7 @@ from presumed-known mean and variance. statistical inference.

            - + Related distributions
            @@ -303,7 +303,7 @@ from presumed-known mean and variance. Distribution with its p parameter set to x.

            - + Accuracy

            @@ -315,7 +315,7 @@ from presumed-known mean and variance. please refer to these functions for information on accuracy.

            - + Implementation

            @@ -330,274 +330,273 @@ from presumed-known mean and variance. -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - f(x;α,β) = xα - 1 (1 - x)β -1 / B(α, β) -

            -

            - Implemented using ibeta_derivative(a, - b, x). -

            +

            + f(x;α,β) = xα - 1 (1 - x)β -1 / B(α, β) +

            +

            + Implemented using ibeta_derivative(a, + b, x). +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the incomplete beta function ibeta(a, - b, x) -

            +

            + Using the incomplete beta function ibeta(a, + b, x) +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - ibetac(a, - b, x) -

            +

            + ibetac(a, + b, x) +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the inverse incomplete beta function ibeta_inv(a, - b, p) -

            +

            + Using the inverse incomplete beta function ibeta_inv(a, + b, p) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - ibetac_inv(a, - b, q) -

            +

            + ibetac_inv(a, + b, q) +

            -

            - mean -

            +

            + mean +

            -

            - a/(a+b) -

            +

            + a/(a+b) +

            -

            - variance -

            +

            + variance +

            -

            - a * - b / - (a+b)^2 * (a + - b + - 1) -

            +

            + a * + b / + (a+b)^2 + * (a + + b + + 1) +

            -

            - mode -

            +

            + mode +

            -

            - (a-1) / - (a - + b - - 2) -

            +

            + (a-1) / + (a + + b + - 2) +

            -

            - skewness -

            +

            + skewness +

            -

            - 2 (b-a) - sqrt(a+b+1)/(a+b+2) * sqrt(a - * b) -

            +

            + 2 (b-a) + sqrt(a+b+1)/(a+b+2) + * sqrt(a + * b) +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - -

            +

            + +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - kurtosis + - 3 -

            +

            + kurtosis + + 3 +

            -

            - parameter estimation -

            +

            + parameter estimation +

            -

            -

            +

            +

            -

            - alpha -

            -

            - from mean and variance -

            +

            + alpha +

            +

            + from mean and variance +

            -

            - mean * - (( (mean * - (1 - - mean)) / - variance)- - 1) -

            +

            + mean * + (( (mean * + (1 + - mean)) / + variance)- + 1) +

            -

            - beta -

            -

            - from mean and variance -

            +

            + beta +

            +

            + from mean and variance +

            -

            - (1 - - mean) * - (((mean - * (1 - mean)) - /variance)-1) -

            +

            + (1 + - mean) * + (((mean + * (1 - + mean)) + /variance)-1) +

            -

            - The member functions find_alpha - and find_beta -

            -

            - from cdf and probability x -

            -

            - and either alpha - or beta -

            +

            + The member functions find_alpha + and find_beta +

            +

            + from cdf and probability x +

            +

            + and either alpha + or beta +

            -

            - Implemented in terms of the inverse incomplete beta functions -

            -

            - ibeta_inva, - and ibeta_invb - respectively. -

            +

            + Implemented in terms of the inverse incomplete beta functions +

            +

            + ibeta_inva, + and ibeta_invb + respectively. +

            -

            - find_alpha -

            +

            + find_alpha +

            -

            - ibeta_inva(beta, - x, - probability) -

            +

            + ibeta_inva(beta, x, probability) +

            -

            - find_beta -

            +

            + find_beta +

            -

            - ibeta_invb(alpha, - x, - probability) -

            +

            + ibeta_invb(alpha, x, probability) +

            - + References

            @@ -625,7 +624,7 @@ from presumed-known mean and variance.

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index f7e1a1149..11fa519c0 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -2,8 +2,8 @@ Binomial Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Binomial Distribution @@ -96,7 +96,7 @@

            - +
            [Note][Note] Note

            @@ -131,7 +131,7 @@

            - +
            [Caution][Caution] Caution
            @@ -167,12 +167,12 @@

            - + Member Functions
            - + Construct 
            binomial_distribution(RealType n, RealType p);
@@ -189,7 +189,7 @@
             otherwise calls domain_error.
           
            
 
            
-
+
             Accessors
           
            
 
            RealType success_fraction() const;
@@ -205,7 +205,7 @@
             was constructed.
           
            
 
            
-
+
             Lower
             Bound on the Success Fraction
           
            
@@ -223,23 +223,23 @@
 
            
 
            trials
            
 
            
-                The total number of trials conducted.
-              
            
+                  The total number of trials conducted.
+                
            
 
            successes
            
 
            
-                The number of successes that occurred.
-              
            
+                  The number of successes that occurred.
+                
            
 
            alpha
            
 
            
-                The largest acceptable probability that the true value of the success
-                fraction is less than the value
-                returned.
-              
            
+                  The largest acceptable probability that the true value of the success
+                  fraction is less than the value
+                  returned.
+                
            
 
            method
            
 
            
-                An optional parameter that specifies the method to be used to compute
-                the interval (See below).
-              
            
+                  An optional parameter that specifies the method to be used to compute
+                  the interval (See below).
+                
            
 
            
 
 
            
@@ -311,7 +311,7 @@
             limits illustrated in the case of the binomial. Biometrika 26 404-413.
           
            
 
            
-
+
             Upper
             Bound on the Success Fraction
           
            
@@ -329,24 +329,24 @@
 
            
 
            trials
            
 
            
-                The total number of trials conducted.
-              
            
+                  The total number of trials conducted.
+                
            
 
            successes
            
 
            
-                The number of successes that occurred.
-              
            
+                  The number of successes that occurred.
+                
            
 
            alpha
            
 
            
-                The largest acceptable probability that the true value of the success
-                fraction is greater than the value
-                returned.
-              
            
+                  The largest acceptable probability that the true value of the success
+                  fraction is greater than the value
+                  returned.
+                
            
 
            method
            
 
            
-                An optional parameter that specifies the method to be used to compute
-                the interval. Refer to the documentation for find_upper_bound_on_p
-                above for the meaning of the method options.
-              
            
+                  An optional parameter that specifies the method to be used to compute
+                  the interval. Refer to the documentation for find_upper_bound_on_p
+                  above for the meaning of the method options.
+                
            
 
            
 
 
            
@@ -364,7 +364,7 @@
           
            
 
            
-
+
            
 
            [Note][Note]
 Note
 
            
 
            
@@ -389,7 +389,7 @@
 
            
 
            
 
            
-
+
             Estimating
             the Number of Trials Required for a Certain Number of Successes
           
            
@@ -408,17 +408,17 @@
 
            
 
            k
            
 
            
-                The number of success observed.
-              
            
+                  The number of success observed.
+                
            
 
            p
            
 
            
-                The probability of success for each trial.
-              
            
+                  The probability of success for each trial.
+                
            
 
            alpha
            
 
            
-                The maximum acceptable probability that k events or fewer will be
-                observed.
-              
            
+                  The maximum acceptable probability that k events or fewer will
+                  be observed.
+                
            
 
            
 
 
            
@@ -431,7 +431,7 @@
             of seeing 10 events that occur with frequency one half.
           
            
 
            
-
+
             Estimating
             the Maximum Number of Trials to Ensure no more than a Certain Number
             of Successes
@@ -451,17 +451,17 @@
 
            
 
            k
            
 
            
-                The number of success observed.
-              
            
+                  The number of success observed.
+                
            
 
            p
            
 
            
-                The probability of success for each trial.
-              
            
+                  The probability of success for each trial.
+                
            
 
            alpha
            
 
            
-                The maximum acceptable probability that more than k events will be
-                observed.
-              
            
+                  The maximum acceptable probability that more than k events will
+                  be observed.
+                
            
 
            
 
 
            
@@ -479,7 +479,7 @@
             Worked Example.
           
            
 
            
-
+
             Non-member
             Accessors
           
            
@@ -504,7 +504,7 @@
             in the context of this distribution:
           
            
 
            
-
            Table 11. Meaning of the non-member accessors
            
+
            Table 11. Meaning of the non-member accessors
            
 
            @@ -512,122 +512,123 @@
 
+                    
            
+                      Function
+                    
            
+                  
+                    
            
+                      Meaning
+                    
            
+                  
+                    
            
+                      Probability Density Function
+                    
            
+                  
+                    
            
+                      The probability of obtaining exactly
+                      k successes from n trials with success fraction
+                      p. For example:
+                    
            
+                    
            
+                      pdf(binomial(n,
+                      p),
+                      k)
+                    
            
+                  
+                    
            
+                      Cumulative Distribution Function
+                    
            
+                  
+                    
            
+                      The probability of obtaining k successes
+                      or fewer from n trials with success fraction p.
+                      For example:
+                    
            
+                    
            
+                      cdf(binomial(n,
+                      p),
+                      k)
+                    
            
+                  
+                    
            
+                      Complement of the Cumulative
+                      Distribution Function
+                    
            
+                  
+                    
            
+                      The probability of obtaining more than
+                      k successes from n trials with success fraction
+                      p. For example:
+                    
            
+                    
            
+                      cdf(complement(binomial(n,
+                      p),
+                      k))
+                    
            
+                  
+                    
            
+                      Quantile
+                    
            
+                  
+                    
            
+                      The greatest number of successes
+                      that may be observed from n trials with success fraction p,
+                      at probability P. Note that the value returned is a real-number,
+                      and not an integer. Depending on the use case you may want
+                      to take either the floor or ceiling of the result. For example:
+                    
            
+                    
            
+                      quantile(binomial(n,
+                      p),
+                      P)
+                    
            
+                  
+                    
            
+                      Quantile from the complement
+                      of the probability
+                    
            
+                  
+                    
            
+                      The smallest number of successes
+                      that may be observed from n trials with success fraction p,
+                      at probability P. Note that the value returned is a real-number,
+                      and not an integer. Depending on the use case you may want
+                      to take either the floor or ceiling of the result. For example:
+                    
            
+                    
            
+                      quantile(complement(binomial(n,
+                      p),
+                      P))`
+                    
            
+                  
            
 
 

 
            
 
-                
            
-                  Function
-                
            
-                            		
 
-                
            
-                  Meaning
-                
            
-                            		
 
            
 
 
            
 
-                
            
-                  Probability Density Function
-                
            
-                            		
 
-                
            
-                  The probability of obtaining exactly k successes
-                  from n trials with success fraction p. For example:
-                
            
-                
            
-                  pdf(binomial(n,
-                  p),
-                  k)
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Cumulative Distribution Function
-                
            
-                            		
 
-                
            
-                  The probability of obtaining k successes
-                  or fewer from n trials with success fraction p. For
-                  example:
-                
            
-                
            
-                  cdf(binomial(n,
-                  p),
-                  k)
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Complement of the Cumulative Distribution
-                  Function
-                
            
-                            		
 
-                
            
-                  The probability of obtaining more than k
-                  successes from n trials with success fraction p. For
-                  example:
-                
            
-                
            
-                  cdf(complement(binomial(n,
-                  p),
-                  k))
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Quantile
-                
            
-                            		
 
-                
            
-                  The greatest number of successes
-                  that may be observed from n trials with success fraction p, at
-                  probability P. Note that the value returned is a real-number, and
-                  not an integer. Depending on the use case you may want to take
-                  either the floor or ceiling of the result. For example:
-                
            
-                
            
-                  quantile(binomial(n,
-                  p),
-                  P)
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Quantile from the complement
-                  of the probability
-                
            
-                            		
 
-                
            
-                  The smallest number of successes
-                  that may be observed from n trials with success fraction p, at
-                  probability P. Note that the value returned is a real-number, and
-                  not an integer. Depending on the use case you may want to take
-                  either the floor or ceiling of the result. For example:
-                
            
-                
            
-                  quantile(complement(binomial(n,
-                  p),
-                  P))`
-                
            
-                            		
 
            
             
 
            
 
            
 
            
-
+
             Examples
           
            
 
            
@@ -635,7 +636,7 @@
             examples are available illustrating the use of the binomial distribution.
           
            
 
            
-
+
             Accuracy
           
            
 
            
@@ -645,7 +646,7 @@
             please refer to these functions for information on accuracy.
           
            
 
            
-
+
             Implementation
           
            
 
            
@@ -661,248 +662,251 @@
            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            		-

            - Implementation is in terms of ibeta_derivative: - if nCk is the binomial coefficient of a and b, then we have: -

            -

            - -

            -

            - Which can be evaluated as ibeta_derivative(k+1, n-k+1, p) / - (n+1) -

            -

            - The function ibeta_derivative - is used here, since it has already been optimised for the lowest - possible error - indeed this is really just a thin wrapper around - part of the internals of the incomplete beta function. -

            -

            - There are also various special cases: refer to the code for details. -

            +

            + Implementation is in terms of ibeta_derivative: + if nCk is the binomial coefficient of a and b, then we have: +

            +

            + +

            +

            + Which can be evaluated as ibeta_derivative(k+1, n-k+1, p) / + (n+1) +

            +

            + The function ibeta_derivative + is used here, since it has already been optimised for the lowest + possible error - indeed this is really just a thin wrapper + around part of the internals of the incomplete beta function. +

            +

            + There are also various special cases: refer to the code for + details. +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relation: -

            -

            - +

            + Using the relation: +

            +

            + 

            p = I[sub 1-p](n - k, k + 1)
   = 1 - I[sub p](k + 1, n - k)
   = ibetac(k + 1, n - k, p)

            -

            -

            - There are also various special cases: refer to the code for details. -

            +

            +

            + There are also various special cases: refer to the code for + details. +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - Using the relation: q = ibeta(k - + 1, n - k, p) -

            -

            - There are also various special cases: refer to the code for details. -

            +

            + Using the relation: q = ibeta(k + + 1, n - k, p) +

            +

            + There are also various special cases: refer to the code for + details. +

            -

            - quantile -

            +

            + quantile +

            		-

            - Since the cdf is non-linear in variate k - none of the inverse incomplete beta functions can be used here. - Instead the quantile is found numerically using a derivative - free method (TOMS - Algorithm 748). -

            +

            + Since the cdf is non-linear in variate k + none of the inverse incomplete beta functions can be used here. + Instead the quantile is found numerically using a derivative + free method (TOMS + Algorithm 748). +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - Found numerically as above. -

            +

            + Found numerically as above. +

            -

            - mean -

            +

            + mean +

            		-

            - p * - n -

            +

            + p * + n +

            -

            - variance -

            +

            + variance +

            		-

            - p * - n * - (1-p) -

            +

            + p * + n * + (1-p) +

            -

            - mode -

            +

            + mode +

            		-

            - floor(p * - (n - + 1)) -

            +

            + floor(p * + (n + + 1)) +

            -

            - skewness -

            +

            + skewness +

            		-

            - (1 - - 2 - * p) / - sqrt(n * - p * - (1 - - p)) -

            +

            + (1 + - 2 + * p) / + sqrt(n * + p * + (1 + - p)) +

            -

            - kurtosis -

            +

            + kurtosis +

            		-

            - 3 - - (6 - / n) + - (1 - / (n * - p * - (1 - - p))) -

            +

            + 3 - + (6 + / n) + + (1 + / (n * + p * + (1 + - p))) +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - (1 - - 6 - * p - * q) / - (n - * p - * q) -

            +

            + (1 + - 6 + * p + * q) / + (n + * p + * q) +

            -

            - parameter estimation -

            +

            + parameter estimation +

            		-

            - The member functions find_upper_bound_on_p - find_lower_bound_on_p - and find_number_of_trials - are implemented in terms of the inverse incomplete beta functions - ibetac_inv, - ibeta_inv, - and ibetac_invb - respectively -

            +

            + The member functions find_upper_bound_on_p + find_lower_bound_on_p + and find_number_of_trials + are implemented in terms of the inverse incomplete beta functions + ibetac_inv, + ibeta_inv, + and ibetac_invb + respectively +

            - + References
            -
            @@ -917,7 +921,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html index 03a38d040..f66cd5d2b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html @@ -2,8 +2,8 @@ Cauchy-Lorentz Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Cauchy-Lorentz Distribution @@ -88,7 +88,7 @@

            - + Member Functions
            @@ -114,7 +114,7 @@ Returns the scale parameter of the distribution.

            - + Non-member Accessors
            @@ -133,11 +133,8 @@

            Note however that the Cauchy distribution does not have a mean, standard deviation, etc. See mathematically - undefined function -

            -

            - to control whether these should fail to compile with a BOOST_STATIC_ASSERTION_FAILURE, - which is the default. + undefined function to control whether these should fail to compile + with a BOOST_STATIC_ASSERTION_FAILURE, which is the default.

            Alternately, the functions mean, @@ -151,7 +148,7 @@ The domain of the random variable is [-[max_value], +[min_value]].

            - + Accuracy

            @@ -160,7 +157,7 @@ have very low error rates.

            - + Implementation

            @@ -175,118 +172,124 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = 1 / (π * γ * (1 + ((x - x0 ) / γ)2) -

            +

            + Using the relation: pdf = 1 / (π * γ * (1 + ((x - x0 ) / γ)2) +

            -

            - cdf and its complement -

            +

            + cdf and its complement +

            -

            - The cdf is normally given by: -

            -

            - p = 0.5 + atan(x)/π -

            -

            - But that suffers from cancellation error as x -> -∞. So recall - that for x < - 0: -

            -

            - atan(x) = -π/2 - atan(1/x) -

            -

            - Substituting into the above we get: -

            -

            - p = -atan(1/x) ; x < 0 -

            -

            - So the procedure is to calculate the cdf for -fabs(x) using the - above formula. Note that to factor in the location and scale - parameters you must substitute (x - x0 ) / γ for x in the above. -

            -

            - This procedure yields the smaller of p and - q, so the result may need subtracting from - 1 depending on whether we want the complement or not, and whether - x is less than x0 or not. -

            +

            + The cdf is normally given by: +

            +

            + p = 0.5 + atan(x)/π +

            +

            + But that suffers from cancellation error as x -> -∞. So recall + that for x < 0: +

            +

            + atan(x) = -π/2 - atan(1/x) +

            +

            + Substituting into the above we get: +

            +

            + p = -atan(1/x) ; x < 0 +

            +

            + So the procedure is to calculate the cdf for -fabs(x) using + the above formula. Note that to factor in the location and + scale parameters you must substitute (x - x0 ) / γ for x in the + above. +

            +

            + This procedure yields the smaller of p + and q, so the result may need subtracting + from 1 depending on whether we want the complement or not, + and whether x is less than x0 or not. +

            -

            - quantile -

            +

            + quantile +

            -

            - The same procedure is used irrespective of whether we're starting - from the probability or it's complement. First the argument - p is reduced to the range [-0.5, 0.5], then - the relation -

            -

            - x = x0 ± γ / tan(π * p) -

            -

            - is used to obtain the result. Whether we're adding or subtracting - from x0 is determined by whether we're starting from the complement - or not. -

            +

            + The same procedure is used irrespective of whether we're starting + from the probability or it's complement. First the argument + p is reduced to the range [-0.5, 0.5], + then the relation +

            +

            + x = x0 ± γ / tan(π * p) +

            +

            + is used to obtain the result. Whether we're adding or subtracting + from x0 is determined by whether we're starting from the complement + or not. +

            -

            - mode -

            +

            + mode +

            -

            - The location parameter. -

            +

            + The location parameter. +

            - + References
            -
            @@ -301,7 +304,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html index c333476e8..3628c3b04 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html @@ -2,8 +2,8 @@ Chi Squared Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Chi Squared Distribution @@ -87,7 +87,7 @@ independent, normally distributed random

            - + Member Functions
            @@ -122,28 +122,28 @@ independent, normally distributed random
            difference_from_variance

            - The difference from the assumed nominal variance that is to be detected: - Note that the sign of this value is critical, see below. -

            + The difference from the assumed nominal variance that is to be + detected: Note that the sign of this value is critical, see below. +

            alpha

            - The maximum acceptable risk of rejecting the null hypothesis when - it is in fact true. -

            + The maximum acceptable risk of rejecting the null hypothesis when + it is in fact true. +

            beta

            - The maximum acceptable risk of falsely failing to reject the null - hypothesis. -

            + The maximum acceptable risk of falsely failing to reject the null + hypothesis. +

            variance

            - The nominal variance being tested against. -

            + The nominal variance being tested against. +

            hint

            - An optional hint on where to start looking for a result: the current - sample size would be a good choice. -

            + An optional hint on where to start looking for a result: the current + sample size would be a good choice. +

            @@ -170,7 +170,7 @@ independent, normally distributed random NIST Engineering Statistics Handbook, Section 7.2.3.2.

            - + Non-member Accessors
            @@ -196,7 +196,7 @@ independent, normally distributed random The domain of the random variable is [0, +∞].

            - + Examples

            @@ -204,7 +204,7 @@ independent, normally distributed random are available illustrating the use of the Chi Squared Distribution.

            - + Accuracy

            @@ -212,7 +212,7 @@ independent, normally distributed random gamma functions: please refer to the accuracy data for those functions.

            - + Implementation

            @@ -228,168 +228,174 @@ independent, normally distributed random -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = gamma_p_derivative(v - / 2, x / 2) / 2 -

            +

            + Using the relation: pdf = gamma_p_derivative(v + / 2, x / 2) / 2 +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: p = gamma_p(v - / 2, x / 2) -

            +

            + Using the relation: p = gamma_p(v + / 2, x / 2) +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = gamma_q(v - / 2, x / 2) -

            +

            + Using the relation: q = gamma_q(v + / 2, x / 2) +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: x = 2 * gamma_p_inv(v - / 2, p) -

            +

            + Using the relation: x = 2 * gamma_p_inv(v + / 2, p) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: x = 2 * gamma_q_inv(v - / 2, p) -

            +

            + Using the relation: x = 2 * gamma_q_inv(v + / 2, p) +

            -

            - mean -

            +

            + mean +

            -

            - v -

            +

            + v +

            -

            - variance -

            +

            + variance +

            -

            - 2v -

            +

            + 2v +

            -

            - mode -

            +

            + mode +

            -

            - v - 2 (if v >= 2) -

            +

            + v - 2 (if v >= 2) +

            -

            - skewness -

            +

            + skewness +

            -

            - 2 * sqrt(2 / v) == sqrt(8 / v) -

            +

            + 2 * sqrt(2 / v) == sqrt(8 / v) +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - 3 + 12 / v -

            +

            + 3 + 12 / v +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - 12 / v -

            +

            + 12 / v +

            - + References
            -
            @@ -404,7 +410,7 @@ independent, normally distributed random
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html index 1ca209116..18b23c5c3 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html @@ -2,8 +2,8 @@ Exponential Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Exponential Distribution @@ -71,7 +71,7 @@

            - + Member Functions
            @@ -91,7 +91,7 @@ Accessor function returns the lambda parameter of the distribution.

            - + Non-member Accessors
            @@ -111,7 +111,7 @@ The domain of the random variable is [0, +∞].

            - + Accuracy

            @@ -122,7 +122,7 @@ should have very low error rates.

            - + Implementation

            @@ -137,176 +137,184 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = λ * exp(-λ * x) -

            +

            + Using the relation: pdf = λ * exp(-λ * x) +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: p = 1 - exp(-x * λ) = -expm1(-x * λ) -

            +

            + Using the relation: p = 1 - exp(-x * λ) = -expm1(-x * λ) +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = exp(-x * λ) -

            +

            + Using the relation: q = exp(-x * λ) +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: x = -log(1-p) / λ = -log1p(-p) / λ -

            +

            + Using the relation: x = -log(1-p) / λ = -log1p(-p) / λ +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: x = -log(q) / λ -

            +

            + Using the relation: x = -log(q) / λ +

            -

            - mean -

            +

            + mean +

            -

            - 1/λ -

            +

            + 1/λ +

            -

            - standard deviation -

            +

            + standard deviation +

            -

            - 1/λ -

            +

            + 1/λ +

            -

            - mode -

            +

            + mode +

            -

            - 0 -

            +

            + 0 +

            -

            - skewness -

            +

            + skewness +

            -

            - 2 -

            +

            + 2 +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - 9 -

            +

            + 9 +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - 6 -

            +

            + 6 +

            - + references
            -
            @@ -320,7 +328,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html index 7bba8455d..313d6c77a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html @@ -2,8 +2,8 @@ Extreme Value Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Extreme Value Distribution @@ -100,7 +100,7 @@

            - + Member Functions
            @@ -125,7 +125,7 @@ Returns the scale parameter of the distribution.

            - + Non-member Accessors
            @@ -145,7 +145,7 @@ The domain of the random parameter is [-∞, +∞].

            - + Accuracy

            @@ -154,7 +154,7 @@ very low error rates.

            - + Implementation

            @@ -170,149 +170,149 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = exp((a-x)/b) * exp(-exp((a-x)/b)) / - b -

            +

            + Using the relation: pdf = exp((a-x)/b) * exp(-exp((a-x)/b)) + / b +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: p = exp(-exp((a-x)/b)) -

            +

            + Using the relation: p = exp(-exp((a-x)/b)) +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = -expm1(-exp((a-x)/b)) -

            +

            + Using the relation: q = -expm1(-exp((a-x)/b)) +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: a - log(-log(p)) * b -

            +

            + Using the relation: a - log(-log(p)) * b +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: a - log(-log1p(-q)) * b -

            +

            + Using the relation: a - log(-log1p(-q)) * b +

            -

            - mean -

            +

            + mean +

            -

            - a + Euler-Mascheroni-constant - * b -

            +

            + a + Euler-Mascheroni-constant + * b +

            -

            - standard deviation -

            +

            + standard deviation +

            -

            - pi * b / sqrt(6) -

            +

            + pi * b / sqrt(6) +

            -

            - mode -

            +

            + mode +

            -

            - The same as the location parameter a. -

            +

            + The same as the location parameter a. +

            -

            - skewness -

            +

            + skewness +

            -

            - 12 * sqrt(6) * zeta(3) / pi3 -

            +

            + 12 * sqrt(6) * zeta(3) / pi3 +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - 27 / 5 -

            +

            + 27 / 5 +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - kurtosis - 3 or 12 / 5 -

            +

            + kurtosis - 3 or 12 / 5 +

            @@ -330,7 +330,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html index 233b5579c..272d1f458 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html @@ -2,8 +2,8 @@ F Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            @@ -80,7 +80,7 @@

            - + Member Functions
            @@ -106,7 +106,7 @@ Returns the denominator degrees of freedom parameter of the distribution.

            - + Non-member Accessors
            @@ -126,7 +126,7 @@ The domain of the random variable is [0, +∞].

            - + Examples

            @@ -134,7 +134,7 @@ are available illustrating the use of the F Distribution.

            - + Accuracy

            @@ -143,7 +143,7 @@ refer to those functions for accuracy data.

            - + Implementation

            @@ -159,263 +159,267 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - The usual form of the PDF is given by: -

            -

            - -

            -

            - However, that form is hard to evaluate directly without incurring - problems with either accuracy or numeric overflow. -

            -

            - Direct differentiation of the CDF expressed in terms of the incomplete - beta function -

            -

            - led to the following two formulas: -

            -

            - fv1,v2(x) = y * ibeta_derivative(v2 - / 2, v1 / 2, v2 / (v2 + v1 * x)) -

            -

            - with y = (v2 * v1) / ((v2 + v1 * x) * (v2 + v1 * x)) -

            -

            - and -

            -

            - fv1,v2(x) = y * ibeta_derivative(v1 - / 2, v2 / 2, v1 * x / (v2 + v1 * x)) -

            -

            - with y = (z * v1 - x * v1 * v1) / z2 -

            -

            - and z = v2 + v1 * x -

            -

            - The first of these is used for v1 * x > v2, otherwise the - second is used. -

            -

            - The aim is to keep the x argument to ibeta_derivative - away from 1 to avoid rounding error. -

            +

            + The usual form of the PDF is given by: +

            +

            + +

            +

            + However, that form is hard to evaluate directly without incurring + problems with either accuracy or numeric overflow. +

            +

            + Direct differentiation of the CDF expressed in terms of the + incomplete beta function +

            +

            + led to the following two formulas: +

            +

            + fv1,v2(x) = y * ibeta_derivative(v2 + / 2, v1 / 2, v2 / (v2 + v1 * x)) +

            +

            + with y = (v2 * v1) / ((v2 + v1 * x) * (v2 + v1 * x)) +

            +

            + and +

            +

            + fv1,v2(x) = y * ibeta_derivative(v1 + / 2, v2 / 2, v1 * x / (v2 + v1 * x)) +

            +

            + with y = (z * v1 - x * v1 * v1) / z2 +

            +

            + and z = v2 + v1 * x +

            +

            + The first of these is used for v1 * x > v2, otherwise the + second is used. +

            +

            + The aim is to keep the x argument to + ibeta_derivative + away from 1 to avoid rounding error. +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relations: -

            -

            - p = ibeta(v1 - / 2, v2 / 2, v1 * x / (v2 + v1 * x)) -

            -

            - and -

            -

            - p = ibetac(v2 - / 2, v1 / 2, v2 / (v2 + v1 * x)) -

            -

            - The first is used for v1 * x > v2, otherwise the second is - used. -

            -

            - The aim is to keep the x argument to ibeta - well away from 1 to avoid rounding error. -

            +

            + Using the relations: +

            +

            + p = ibeta(v1 + / 2, v2 / 2, v1 * x / (v2 + v1 * x)) +

            +

            + and +

            +

            + p = ibetac(v2 + / 2, v1 / 2, v2 / (v2 + v1 * x)) +

            +

            + The first is used for v1 * x > v2, otherwise the second + is used. +

            +

            + The aim is to keep the x argument to + ibeta + well away from 1 to avoid rounding error. +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relations: -

            -

            - p = ibetac(v1 - / 2, v2 / 2, v1 * x / (v2 + v1 * x)) -

            -

            - and -

            -

            - p = ibeta(v2 - / 2, v1 / 2, v2 / (v2 + v1 * x)) -

            -

            - The first is used for v1 * x < v2, otherwise the second is - used. -

            -

            - The aim is to keep the x argument to ibeta - well away from 1 to avoid rounding error. -

            +

            + Using the relations: +

            +

            + p = ibetac(v1 + / 2, v2 / 2, v1 * x / (v2 + v1 * x)) +

            +

            + and +

            +

            + p = ibeta(v2 + / 2, v1 / 2, v2 / (v2 + v1 * x)) +

            +

            + The first is used for v1 * x < v2, otherwise the second + is used. +

            +

            + The aim is to keep the x argument to + ibeta + well away from 1 to avoid rounding error. +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: -

            -

            - x = v2 * a / (v1 * b) -

            -

            - where: -

            -

            - a = ibeta_inv(v1 - / 2, v2 / 2, p) -

            -

            - and -

            -

            - b = 1 - a -

            -

            - Quantities a and b - are both computed by ibeta_inv - without the subtraction implied above. -

            +

            + Using the relation: +

            +

            + x = v2 * a / (v1 * b) +

            +

            + where: +

            +

            + a = ibeta_inv(v1 + / 2, v2 / 2, p) +

            +

            + and +

            +

            + b = 1 - a +

            +

            + Quantities a and b + are both computed by ibeta_inv + without the subtraction implied above. +

            -

            - quantile -

            -

            - from the complement -

            +

            + quantile +

            +

            + from the complement +

            -

            - Using the relation: -

            -

            - x = v2 * a / (v1 * b) -

            -

            - where -

            -

            - a = ibetac_inv(v1 - / 2, v2 / 2, p) -

            -

            - and -

            -

            - b = 1 - a -

            -

            - Quantities a and b - are both computed by ibetac_inv - without the subtraction implied above. -

            +

            + Using the relation: +

            +

            + x = v2 * a / (v1 * b) +

            +

            + where +

            +

            + a = ibetac_inv(v1 + / 2, v2 / 2, p) +

            +

            + and +

            +

            + b = 1 - a +

            +

            + Quantities a and b + are both computed by ibetac_inv + without the subtraction implied above. +

            -

            - mean -

            +

            + mean +

            -

            - v2 / (v2 - 2) -

            +

            + v2 / (v2 - 2) +

            -

            - variance -

            +

            + variance +

            -

            - 2 * v22 * (v1 + v2 - 2) / (v1 * (v2 - 2) * (v2 - 2) * (v2 - 4)) -

            +

            + 2 * v22 * (v1 + v2 - 2) / (v1 * (v2 - 2) * (v2 - 2) * (v2 - + 4)) +

            -

            - mode -

            +

            + mode +

            -

            - v2 * (v1 - 2) / (v1 * (v2 + 2)) -

            +

            + v2 * (v1 - 2) / (v1 * (v2 + 2)) +

            -

            - skewness -

            +

            + skewness +

            -

            - 2 * (v2 + 2 * v1 - 2) * sqrt((2 * v2 - 8) / (v1 * (v2 + v1 - - 2))) / (v2 - 6) -

            +

            + 2 * (v2 + 2 * v1 - 2) * sqrt((2 * v2 - 8) / (v1 * (v2 + v1 + - 2))) / (v2 - 6) +

            -

            - kurtosis and kurtosis excess -

            +

            + kurtosis and kurtosis excess +

            -

            - Refer to, Weisstein, - Eric W. "F-Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Refer to, Weisstein, + Eric W. "F-Distribution." From MathWorld--A Wolfram + Web Resource. +

            @@ -433,7 +437,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html index 1f144f30a..1edca746e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html @@ -2,8 +2,8 @@ Gamma (and Erlang) Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Gamma (and Erlang) Distribution @@ -65,7 +65,7 @@

            - + @@ -373,7 +373,7 @@
            [Note][Note] Note
            @@ -137,7 +137,7 @@ than a dedicated Erlang Distribution.

            - + Member Functions
            @@ -162,7 +162,7 @@ Returns the scale parameter of this distribution.

            - + Non-member Accessors
            @@ -182,7 +182,7 @@ The domain of the random variable is [0,+∞].

            - + Accuracy

            @@ -194,7 +194,7 @@ refer to the accuracy data for those functions for more information.

            - + Implementation

            @@ -210,152 +210,152 @@

            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            		-

            - Using the relation: pdf = gamma_p_derivative(k, - x / θ) / θ -

            +

            + Using the relation: pdf = gamma_p_derivative(k, + x / θ) / θ +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relation: p = gamma_p(k, - x / θ) -

            +

            + Using the relation: p = gamma_p(k, + x / θ) +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - Using the relation: q = gamma_q(k, - x / θ) -

            +

            + Using the relation: q = gamma_q(k, + x / θ) +

            -

            - quantile -

            +

            + quantile +

            		-

            - Using the relation: x = θ* gamma_p_inv(k, - p) -

            +

            + Using the relation: x = θ* gamma_p_inv(k, + p) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - Using the relation: x = θ* gamma_q_inv(k, - p) -

            +

            + Using the relation: x = θ* gamma_q_inv(k, + p) +

            -

            - mean -

            +

            + mean +

            		-

            - kθ -

            +

            + kθ +

            -

            - variance -

            +

            + variance +

            		-

            - kθ2 -

            +

            + kθ2 +

            -

            - mode -

            +

            + mode +

            		-

            - (k-1)θ for k>1 otherwise a domain_error -

            +

            + (k-1)θ for k>1 otherwise a domain_error +

            -

            - skewness -

            +

            + skewness +

            		-

            - 2 / sqrt(k) -

            +

            + 2 / sqrt(k) +

            -

            - kurtosis -

            +

            + kurtosis +

            		-

            - 3 + 6 / k -

            +

            + 3 + 6 / k +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - 6 / k -

            +

            + 6 / k +

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html index 4b089f988..bb60dd1fc 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html @@ -2,8 +2,8 @@ Hypergeometric Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Hypergeometric Distribution @@ -75,7 +75,7 @@

            - +
            [Note][Note] Note

            @@ -102,7 +102,7 @@

            - + Member Functions
            @@ -131,7 +131,7 @@ from the population N.

            - + Non-member Accessors
            @@ -155,7 +155,7 @@

            - +
            [Caution][Caution] Caution
            @@ -185,7 +185,7 @@
            - + Accuracy

            @@ -211,7 +211,7 @@ meaningless for N >= 1015.

            - + Testing

            @@ -223,7 +223,7 @@ this implementation and NTL::RR.

            - + Implementation

            @@ -338,7 +338,7 @@

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html index 1f69346f7..3f7b0de5e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html @@ -2,8 +2,8 @@ Laplace Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Laplace Distribution @@ -81,7 +81,7 @@

            - + Member Functions
            @@ -113,7 +113,7 @@ Returns the scale parameter of this distribution.

            - + Non-member Accessors
            @@ -133,7 +133,7 @@ The domain of the random variable is [-∞,+∞].

            - + Accuracy

            @@ -141,7 +141,7 @@ log and exp functions and as such should have very small errors.

            - + Implementation

            @@ -157,193 +157,195 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = e-abs(x-μ) / σ / (2 * σ) -

            +

            + Using the relation: pdf = e-abs(x-μ) / σ / (2 * σ) +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relations: -

            -

            - x < μ : p = e(x-μ)/σ / σ -

            -

            - x >= μ : p = 1 - e(μ-x)/σ / σ +

            + Using the relations: +

            +

            + x < μ : p = e(x-μ)/σ / σ +

            +

            + x >= μ : p = 1 - e(μ-x)/σ / σ -

            +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: -

            -

            - -x < μ : q = e(-x-μ)/σ / σ -

            -

            - -x >= μ : q = 1 - e(μ+x)/σ / σ +

            + Using the relation: +

            +

            + -x < μ : q = e(-x-μ)/σ / σ +

            +

            + -x >= μ : q = 1 - e(μ+x)/σ / σ -

            +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relations: -

            -

            - p < 0.5 : x = μ + σ * log(2*p) -

            -

            - p >= 0.5 : x = μ - σ * log(2-2*p) -

            +

            + Using the relations: +

            +

            + p < 0.5 : x = μ + σ * log(2*p) +

            +

            + p >= 0.5 : x = μ - σ * log(2-2*p) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: -

            -

            - q > 0.5: x = μ + σ*log(2-2*q) -

            -

            - q <=0.5: x = μ - σ*log( 2*q ) -

            +

            + Using the relation: +

            +

            + q > 0.5: x = μ + σ*log(2-2*q) +

            +

            + q <=0.5: x = μ - σ*log( 2*q ) +

            -

            - mean -

            +

            + mean +

            -

            - μ -

            +

            + μ +

            -

            - variance -

            +

            + variance +

            -

            - 2 * σ2 -

            +

            + 2 * σ2 +

            -

            - mode -

            +

            + mode +

            -

            - μ -

            +

            + μ +

            -

            - skewness -

            +

            + skewness +

            -

            - 0 -

            +

            + 0 +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - 6 -

            +

            + 6 +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - 3 -

            +

            + 3 +

            - + References
            -
            @@ -358,7 +360,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html index dad5bc394..5867d8a48 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html @@ -2,8 +2,8 @@ Logistic Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Logistic Distribution @@ -72,7 +72,7 @@

            - + Member Functions
            @@ -98,7 +98,7 @@ Returns the scale of this distribution.

            - + Non-member Accessors
            @@ -128,7 +128,7 @@ as special cases if RealType and +overflow_error respectively.

            - + Accuracy

            @@ -140,7 +140,7 @@ as special cases if RealType error can be guarenteed.

            - + Implementation
            @@ -150,135 +150,135 @@ as special cases if RealType @@ -296,7 +296,7 @@ as special cases if RealType
            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            		-

            - Using the relation: pdf = e-(x-u)/s / (s*(1+e-(x-u)/s)2) -

            +

            + Using the relation: pdf = e-(x-u)/s / (s*(1+e-(x-u)/s)2) +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relation: p = 1/(1+e-(x-u)/s) -

            +

            + Using the relation: p = 1/(1+e-(x-u)/s) +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - Using the relation: q = 1/(1+e(x-u)/s) -

            +

            + Using the relation: q = 1/(1+e(x-u)/s) +

            -

            - quantile -

            +

            + quantile +

            		-

            - Using the relation: x = u - s*log(1/p-1) -

            +

            + Using the relation: x = u - s*log(1/p-1) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - Using the relation: x = u + s*log(p/1-p) -

            +

            + Using the relation: x = u + s*log(p/1-p) +

            -

            - mean -

            +

            + mean +

            		-

            - u -

            +

            + u +

            -

            - mode -

            +

            + mode +

            		-

            - The same as the mean. -

            +

            + The same as the mean. +

            -

            - skewness -

            +

            + skewness +

            		-

            - 0 -

            +

            + 0 +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - 6/5 -

            +

            + 6/5 +

            -

            - variance -

            +

            + variance +

            		-

            - (π*s)2 / 3 -

            +

            + (π*s)2 / 3 +

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html index e45b58189..3ecbffa13 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html @@ -2,8 +2,8 @@ Log Normal Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Log Normal Distribution @@ -88,7 +88,7 @@

            - + Member Functions
            @@ -121,7 +121,7 @@ Returns the scale parameter of this distribution.

            - + Non-member Accessors
            @@ -141,7 +141,7 @@ The domain of the random variable is [0,+∞].

            - + Accuracy

            @@ -150,7 +150,7 @@ function, and as such should have very low error rates.

            - + Implementation

            @@ -166,151 +166,151 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = e-(ln(x) - m)2 / 2s2 / (x * s * sqrt(2pi)) -

            +

            + Using the relation: pdf = e-(ln(x) - m)2 / 2s2 / (x * s * sqrt(2pi)) +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: p = cdf(normal_distribtion<RealType>(m, - s), log(x)) -

            +

            + Using the relation: p = cdf(normal_distribtion<RealType>(m, + s), log(x)) +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = cdf(complement(normal_distribtion<RealType>(m, - s), log(x))) -

            +

            + Using the relation: q = cdf(complement(normal_distribtion<RealType>(m, + s), log(x))) +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: x = exp(quantile(normal_distribtion<RealType>(m, - s), p)) -

            +

            + Using the relation: x = exp(quantile(normal_distribtion<RealType>(m, + s), p)) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: x = exp(quantile(complement(normal_distribtion<RealType>(m, - s), q))) -

            +

            + Using the relation: x = exp(quantile(complement(normal_distribtion<RealType>(m, + s), q))) +

            -

            - mean -

            +

            + mean +

            -

            - em + s2 / 2 -

            +

            + em + s2 / 2 +

            -

            - variance -

            +

            + variance +

            -

            - (es2 - 1) * e2m + s2 -

            +

            + (es2 - 1) * e2m + s2 +

            -

            - mode -

            +

            + mode +

            -

            - em + s2 -

            +

            + em + s2 +

            -

            - skewness -

            +

            + skewness +

            -

            - sqrt(es2 - 1) * (2 + es2 ) -

            +

            + sqrt(es2 - 1) * (2 + es2 ) +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - e4s2 + 2e3s2 + 3e2s2 - 3 -

            +

            + e4s2 + 2e3s2 + 3e2s2 - 3 +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - e4s2 + 2e3s2 + 3e2s2 - 6 -

            +

            + e4s2 + 2e3s2 + 3e2s2 - 6 +

            @@ -328,7 +328,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html index 36c357fd9..ab86e2ec4 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html @@ -2,8 +2,8 @@ Noncentral Beta Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Noncentral Beta Distribution @@ -96,7 +96,7 @@ is a central χ2 random variable with

            - + Member Functions
            @@ -128,7 +128,7 @@ is a central χ2 random variable with was constructed.

            - + Non-member Accessors
            @@ -152,7 +152,7 @@ is a central χ2 random variable with The domain of the random variable is [0, 1].

            - + Accuracy

            @@ -168,7 +168,7 @@ is a central χ2 random variable with zero error.

            -

            Table 13. Errors In CDF of the Noncentral Beta

            +

            Table 13. Errors In CDF of the Noncentral Beta

            @@ -178,114 +178,114 @@ is a central χ2 random variable with +

            + Significand Size +

            +             +

            + Platform and Compiler +

            +             +

            + α, β,λ < 200 +

            +             +

            + α,β,λ > 200 +

            +             +

            + 53 +

            +             +

            + Win32, Visual C++ 8 +

            +             +

            + Peak=620 Mean=22 +

            +             +

            + Peak=8670 Mean=1040 +

            +             +

            + 64 +

            +             +

            + RedHat Linux IA32, gcc-4.1.1 +

            +             +

            + Peak=825 Mean=50 +

            +             +

            + Peak=2.5x104 Mean=4000 +

            +             +

            + 64 +

            +             +

            + Redhat Linux IA64, gcc-3.4.4 +

            +             +

            + Peak=825 Mean=30 +

            +             +

            + Peak=1.7x104 Mean=2500 +

            +             +

            + 113 +

            +             +

            + HPUX IA64, aCC A.06.06 +

            +             +

            + Peak=420 Mean=50 +

            +             +

            + Peak=9200 Mean=1200 +

            +
            -

            - Significand Size -

            -             		-

            - Platform and Compiler -

            -             		-

            - α, β,λ < 200 -

            -             		-

            - α,β,λ > 200 -

            -
            -

            - 53 -

            -             		-

            - Win32, Visual C++ 8 -

            -             		-

            - Peak=620 Mean=22 -

            -             		-

            - Peak=8670 Mean=1040 -

            -
            -

            - 64 -

            -             		-

            - RedHat Linux IA32, gcc-4.1.1 -

            -             		-

            - Peak=825 Mean=50 -

            -             		-

            - Peak=2.5x104 Mean=4000 -

            -
            -

            - 64 -

            -             		-

            - Redhat Linux IA64, gcc-3.4.4 -

            -             		-

            - Peak=825 Mean=30 -

            -             		-

            - Peak=1.7x104 Mean=2500 -

            -
            -

            - 113 -

            -             		-

            - HPUX IA64, aCC A.06.06 -

            -             		-

            - Peak=420 Mean=50 -

            -             		-

            - Peak=9200 Mean=1200 -

            -
            @@ -295,7 +295,7 @@ is a central χ2 random variable with functions are broadly similar.

            - + Tests

            @@ -307,7 +307,7 @@ is a central χ2 random variable with tests.

            - + Implementation

            @@ -408,7 +408,7 @@ is a central χ2 random variable with

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html index d3a082421..63c6c8ae9 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html @@ -2,8 +2,8 @@ Noncentral Chi-Squared Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Noncentral Chi-Squared Distribution @@ -110,7 +110,7 @@

            - + Member Functions
            @@ -183,7 +183,7 @@ == q.

            - + Non-member Accessors
            @@ -203,7 +203,7 @@ The domain of the random variable is [0, +∞].

            - + Examples

            @@ -211,7 +211,7 @@ example for the noncentral chi-squared distribution.

            - + Accuracy

            @@ -223,7 +223,7 @@ zero error.

            -

            Table 14. Errors In CDF of the Noncentral Chi-Squared

            +

            Table 14. Errors In CDF of the Noncentral Chi-Squared

            @@ -233,120 +233,120 @@ +

            + Significand Size +

            + +

            + Platform and Compiler +

            + +

            + ν,λ < 200 +

            + +

            + ν,λ > 200 +

            + +

            + 53 +

            + +

            + Win32, Visual C++ 8 +

            + +

            + Peak=50 Mean=9.9 +

            +

            + R Peak=685 Mean=109 +

            + +

            + Peak=9780 Mean=718 +

            +

            + R Peak=3x108 Mean=2x107 +

            + +

            + 64 +

            + +

            + RedHat Linux IA32, gcc-4.1.1 +

            + +

            + Peak=270 Mean=27 +

            + +

            + Peak=7900 Mean=900 +

            + +

            + 64 +

            + +

            + Redhat Linux IA64, gcc-3.4.4 +

            + +

            + Peak=107 Mean=17 +

            + +

            + Peak=5000 Mean=630 +

            + +

            + 113 +

            + +

            + HPUX IA64, aCC A.06.06 +

            + +

            + Peak=270 Mean=20 +

            + +

            + Peak=4600 Mean=560 +

            +
            -

            - Significand Size -

            -             		-

            - Platform and Compiler -

            -             		-

            - ν,λ < 200 -

            -             		-

            - ν,λ > 200 -

            -
            -

            - 53 -

            -             		-

            - Win32, Visual C++ 8 -

            -             		-

            - Peak=50 Mean=9.9 -

            -

            - R Peak=685 Mean=109 -

            -             		-

            - Peak=9780 Mean=718 -

            -

            - R Peak=3x108 Mean=2x107 -

            -
            -

            - 64 -

            -             		-

            - RedHat Linux IA32, gcc-4.1.1 -

            -             		-

            - Peak=270 Mean=27 -

            -             		-

            - Peak=7900 Mean=900 -

            -
            -

            - 64 -

            -             		-

            - Redhat Linux IA64, gcc-3.4.4 -

            -             		-

            - Peak=107 Mean=17 -

            -             		-

            - Peak=5000 Mean=630 -

            -
            -

            - 113 -

            -             		-

            - HPUX IA64, aCC A.06.06 -

            -             		-

            - Peak=270 Mean=20 -

            -             		-

            - Peak=4600 Mean=560 -

            -
            @@ -359,7 +359,7 @@ produce an accuracy greater than the square root of the machine epsilon.

            - + Tests

            @@ -373,7 +373,7 @@ to at least 50 decimal digits - and is the used for our accuracy tests.

            - + Implementation

            @@ -510,7 +510,7 @@

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html index 19543d7d6..e6eac930e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html @@ -2,8 +2,8 @@ Noncentral F Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Noncentral F Distribution @@ -95,7 +95,7 @@ random variable with v1

            - + Member Functions
            @@ -127,7 +127,7 @@ random variable with v1 which this object was constructed.

            - + Non-member Accessors
            @@ -147,7 +147,7 @@ random variable with v1 The domain of the random variable is [0, +∞].

            - + Accuracy

            @@ -155,7 +155,7 @@ random variable with v1 Beta Distribution: refer to that distribution for accuracy data.

            - + Tests

            @@ -164,7 +164,7 @@ random variable with v1 Math library statistical package and its pbeta and dbeta functions.

            - + Implementation

            @@ -182,216 +182,217 @@ is the non-centrality parameter, x is the -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Implemented in terms of the non-central beta PDF using the relation: -

            -

            - f(x;v1,v2;λ) = (v1/v2) / ((1+y)*(1+y)) * g(y/(1+y);v1/2,v2/2;λ) -

            -

            - where g(x; a, b; λ) is the non central beta PDF, and: -

            -

            - y = x * v1 / v2 -

            +

            + Implemented in terms of the non-central beta PDF using the + relation: +

            +

            + f(x;v1,v2;λ) = (v1/v2) / ((1+y)*(1+y)) * g(y/(1+y);v1/2,v2/2;λ) +

            +

            + where g(x; a, b; λ) is the non central beta PDF, and: +

            +

            + y = x * v1 / v2 +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: -

            -

            - p = By(v1/2, v2/2; λ) -

            -

            - where Bx(a, b; λ) is the noncentral beta distribution CDF and -

            -

            - y = x * v1 / v2 -

            -

            -

            +

            + Using the relation: +

            +

            + p = By(v1/2, v2/2; λ) +

            +

            + where Bx(a, b; λ) is the noncentral beta distribution CDF and +

            +

            + y = x * v1 / v2 +

            +

            +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: -

            -

            - q = 1 - By(v1/2, v2/2; λ) -

            -

            - where 1 - Bx(a, b; λ) is the complement of the noncentral beta - distribution CDF and -

            -

            - y = x * v1 / v2 -

            -

            -

            +

            + Using the relation: +

            +

            + q = 1 - By(v1/2, v2/2; λ) +

            +

            + where 1 - Bx(a, b; λ) is the complement of the noncentral beta + distribution CDF and +

            +

            + y = x * v1 / v2 +

            +

            +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: -

            -

            - x = (bx / (1-bx)) * (v1 / v2) -

            -

            - where -

            -

            - bx = Qp-1(v1/2, v2/2; λ) -

            -

            - and -

            -

            - Qp-1(v1/2, v2/2; λ) -

            -

            - is the noncentral beta quantile. -

            -

            -

            +

            + Using the relation: +

            +

            + x = (bx / (1-bx)) * (v1 / v2) +

            +

            + where +

            +

            + bx = Qp-1(v1/2, v2/2; λ) +

            +

            + and +

            +

            + Qp-1(v1/2, v2/2; λ) +

            +

            + is the noncentral beta quantile. +

            +

            +

            -

            - quantile -

            -

            - from the complement -

            +

            + quantile +

            +

            + from the complement +

            -

            - Using the relation: -

            -

            - x = (bx / (1-bx)) * (v1 / v2) -

            -

            - where -

            -

            - bx = QCq-1(v1/2, v2/2; λ) -

            -

            - and -

            -

            - QCq-1(v1/2, v2/2; λ) -

            -

            - is the noncentral beta quantile from the complement. -

            +

            + Using the relation: +

            +

            + x = (bx / (1-bx)) * (v1 / v2) +

            +

            + where +

            +

            + bx = QCq-1(v1/2, v2/2; λ) +

            +

            + and +

            +

            + QCq-1(v1/2, v2/2; λ) +

            +

            + is the noncentral beta quantile from the complement. +

            -

            - mean -

            +

            + mean +

            -

            - v2 * (v1 + l) / (v1 * (v2 - 2)) -

            +

            + v2 * (v1 + l) / (v1 * (v2 - 2)) +

            -

            - mode -

            +

            + mode +

            -

            - By numeric maximalisation of the PDF. -

            +

            + By numeric maximalisation of the PDF. +

            -

            - variance -

            +

            + variance +

            -

            - Refer to, Weisstein, - Eric W. "Noncentral F-Distribution." From MathWorld--A - Wolfram Web Resource. -

            +

            + Refer to, Weisstein, + Eric W. "Noncentral F-Distribution." From MathWorld--A + Wolfram Web Resource. +

            -

            - skewness -

            +

            + skewness +

            -

            - Refer to, Weisstein, - Eric W. "Noncentral F-Distribution." From MathWorld--A - Wolfram Web Resource., and to the Mathematica - documentation -

            +

            + Refer to, Weisstein, + Eric W. "Noncentral F-Distribution." From MathWorld--A + Wolfram Web Resource., and to the Mathematica + documentation +

            -

            - kurtosis and kurtosis excess -

            +

            + kurtosis and kurtosis excess +

            -

            - Refer to, Weisstein, - Eric W. "Noncentral F-Distribution." From MathWorld--A - Wolfram Web Resource., and to the Mathematica - documentation -

            +

            + Refer to, Weisstein, + Eric W. "Noncentral F-Distribution." From MathWorld--A + Wolfram Web Resource., and to the Mathematica + documentation +

            @@ -417,7 +418,7 @@ is the non-centrality parameter, x is the
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html index c070bc014..62e1565f0 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html @@ -2,8 +2,8 @@ Noncentral T Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Noncentral T Distribution @@ -85,7 +85,7 @@

            - + Member Functions
            @@ -111,7 +111,7 @@ which this object was constructed.

            - + Non-member Accessors
            @@ -131,7 +131,7 @@ The domain of the random variable is [-∞, +∞].

            - + Accuracy

            @@ -141,7 +141,7 @@ one shown will have effectively zero error.

            -

            Table 15. Errors In CDF of the Noncentral T Distribution

            +

            Table 15. Errors In CDF of the Noncentral T Distribution

            @@ -150,96 +150,96 @@ +

            + Significand Size +

            + +

            + Platform and Compiler +

            + +

            + ν,δ < 600 +

            + +

            + 53 +

            + +

            + Win32, Visual C++ 8 +

            + +

            + Peak=120 Mean=26 +

            + +

            + 64 +

            + +

            + RedHat Linux IA32, gcc-4.1.1 +

            + +

            + Peak=121 Mean=26 +

            + +

            + 64 +

            + +

            + Redhat Linux IA64, gcc-3.4.4 +

            + +

            + Peak=122 Mean=25 +

            + +

            + 113 +

            + +

            + HPUX IA64, aCC A.06.06 +

            + +

            + Peak=115 Mean=24 +

            +
            -

            - Significand Size -

            -             		-

            - Platform and Compiler -

            -             		-

            - ν,δ < 600 -

            -
            -

            - 53 -

            -             		-

            - Win32, Visual C++ 8 -

            -             		-

            - Peak=120 Mean=26 -

            -
            -

            - 64 -

            -             		-

            - RedHat Linux IA32, gcc-4.1.1 -

            -             		-

            - Peak=121 Mean=26 -

            -
            -

            - 64 -

            -             		-

            - Redhat Linux IA64, gcc-3.4.4 -

            -             		-

            - Peak=122 Mean=25 -

            -
            -

            - 113 -

            -             		-

            - HPUX IA64, aCC A.06.06 -

            -             		-

            - Peak=115 Mean=24 -

            -

            - +
            [Caution][Caution] Caution

            @@ -255,7 +255,7 @@ epsilon.

            - + Tests

            @@ -270,7 +270,7 @@ least 50 decimal places.

            - + Implementation

            @@ -361,7 +361,7 @@

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html index c677c2dc3..195c80aac 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html @@ -2,8 +2,8 @@ Negative Binomial Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Negative Binomial Distribution @@ -92,7 +92,7 @@

            - +
            [Note][Note] Note

            @@ -123,7 +123,7 @@

            - + Related Distributions
            @@ -164,7 +164,7 @@

            - + @@ -879,17 +885,17 @@

            Implementation notes:

            -
              -
            • - The real concept type (that deliberately lacks the Lanczos approximation), - was found to take several minutes to evaluate some extreme test values, - so the test has been disabled for this type. -
              • -
            • - Much greater speed, and perhaps greater accuracy, might be achieved - for extreme values by using a normal approximation. This is NOT been - tested or implemented. -
              • +
                +
              • + The real concept type (that deliberately lacks the Lanczos approximation), + was found to take several minutes to evaluate some extreme test values, + so the test has been disabled for this type. +
                • +
              • + Much greater speed, and perhaps greater accuracy, might be achieved + for extreme values by using a normal approximation. This is NOT been + tested or implemented. +
            [Caution][Caution] Caution
            @@ -200,12 +200,12 @@

            - + Member Functions
            - + Construct 
            negative_binomial_distribution(RealType r, RealType p);
@@ -221,7 +221,7 @@
             <= 1.
           
            
 
            
-
+
             Accessors
           
            
 
            RealType success_fraction() const; // successes / trials (0 <= p <= 1)
@@ -237,7 +237,7 @@
             was constructed.
           
            
 
            
-
+
             Lower
             Bound on Parameter p
           
            
@@ -255,18 +255,18 @@
 
            
 
            failures
            
 
            
-                The total number of failures before the r th success.
-              
            
+                  The total number of failures before the r th success.
+                
            
 
            successes
            
 
            
-                The number of successes required.
-              
            
+                  The number of successes required.
+                
            
 
            alpha
            
 
            
-                The largest acceptable probability that the true value of the success
-                fraction is less than the value
-                returned.
-              
            
+                  The largest acceptable probability that the true value of the success
+                  fraction is less than the value
+                  returned.
+                
            
 
            
 
 
            
@@ -298,7 +298,7 @@
             vol. 48, no3, 605-621.
           
            
 
            
-
+
             Upper
             Bound on Parameter p
           
            
@@ -316,18 +316,18 @@
 
            
 
            trials
            
 
            
-                The total number of trials conducted.
-              
            
+                  The total number of trials conducted.
+                
            
 
            successes
            
 
            
-                The number of successes that occurred.
-              
            
+                  The number of successes that occurred.
+                
            
 
            alpha
            
 
            
-                The largest acceptable probability that the true value of the success
-                fraction is greater than the value
-                returned.
-              
            
+                  The largest acceptable probability that the true value of the success
+                  fraction is greater than the value
+                  returned.
+                
            
 
            
 
 
            
@@ -358,7 +358,7 @@
             vol. 48, no3, 605-621.
           
            
 
            
-
+
             Estimating
             Number of Trials to Ensure at Least a Certain Number of Failures
           
            
@@ -376,17 +376,17 @@
 
            
 
            k
            
 
            
-                The target number of failures to be observed.
-              
            
+                  The target number of failures to be observed.
+                
            
 
            p
            
 
            
-                The probability of success for each trial.
-              
            
+                  The probability of success for each trial.
+                
            
 
            alpha
            
 
            
-                The maximum acceptable risk that only k failures or fewer will be
-                observed.
-              
            
+                  The maximum acceptable risk that only k failures or fewer will
+                  be observed.
+                
            
 
            
 
 
            
@@ -409,7 +409,7 @@
             probability of observing k failures or fewer.
           
            
 
            
-
+
             Estimating
             Number of Trials to Ensure a Maximum Number of Failures or Less
           
            
@@ -428,17 +428,17 @@
 
            
 
            k
            
 
            
-                The maximum number of failures to be observed.
-              
            
+                  The maximum number of failures to be observed.
+                
            
 
            p
            
 
            
-                The probability of success for each trial.
-              
            
+                  The probability of success for each trial.
+                
            
 
            alpha
            
 
            
-                The maximum acceptable risk that more than k
-                failures will be observed.
-              
            
+                  The maximum acceptable risk that more than
+                  k failures will be observed.
+                
            
 
            
 
 
            
@@ -457,7 +457,7 @@
             probability of observing more than k failures.
           
            
 
            
-
+
             Non-member
             Accessors
           
            
@@ -478,7 +478,7 @@
             in the context of this distribution:
           
            
 
            
-
            Table 12. Meaning of the non-member accessors.
            
+
            Table 12. Meaning of the non-member accessors.
            
 
            @@ -486,124 +486,127 @@
 
+                    
            
+                      Function
+                    
            
+                  
+                    
            
+                      Meaning
+                    
            
+                  
+                    
            
+                      Probability Density Function
+                    
            
+                  
+                    
            
+                  
+                    
            
+                      Cumulative Distribution Function
+                    
            
+                  
+                    
            
+                  
+                    
            
+                      Complement of the Cumulative
+                      Distribution Function
+                    
            
+                  
+                    
            
+                  
+                    
            
+                      Quantile
+                    
            
+                  
+                    
            
+                  
+                    
            
+                      Quantile from the complement
+                      of the probability
+                    
            
+                  
+                    
            
+                  
            
 
 

 
            
 
-                
            
-                  Function
-                
            
-                            		
 
-                
            
-                  Meaning
-                
            
-                            		
 
            
 
 
            
 
-                
            
-                  Probability Density Function
-                
            
-                            		
 
-                
            
-                  The probability of obtaining exactly k failures
-                  from k+r trials with success fraction p. For example:
-                
            
-                
            
-                  
+                    
            
+                      The probability of obtaining exactly
+                      k failures from k+r trials with success fraction
+                      p. For example:
+                    
            
+                    
            
+                      
 
            
 
            pdf(negative_binomial(r, p), k)
            
 
            
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Cumulative Distribution Function
-                
            
-                            		
 
-                
            
-                  The probability of obtaining k failures or
-                  fewer from k+r trials with success fraction p and success
-                  on the last trial. For example:
-                
            
-                
            
-                  
+                    
            
+                      The probability of obtaining k failures
+                      or fewer from k+r trials with success fraction p
+                      and success on the last trial. For example:
+                    
            
+                    
            
+                      
 
            
 
            cdf(negative_binomial(r, p), k)
            
 
            
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Complement of the Cumulative Distribution
-                  Function
-                
            
-                            		
 
-                
            
-                  The probability of obtaining more than k
-                  failures from k+r trials with success fraction p and
-                  success on the last trial. For example:
-                
            
-                
            
-                  
+                    
            
+                      The probability of obtaining more than
+                      k failures from k+r trials with success fraction
+                      p and success on the last trial. For example:
+                    
            
+                    
            
+                      
 
            
 
            cdf(complement(negative_binomial(r, p), k))
            
 
            
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Quantile
-                
            
-                            		
 
-                
            
-                  The greatest number of failures
-                  k expected to be observed from k+r trials with success fraction
-                  p, at probability P. Note that the value returned is a real-number,
-                  and not an integer. Depending on the use case you may want to take
-                  either the floor or ceiling of the real result. For example:
-                
            
-                
            
-                  
+                    
            
+                      The greatest number of failures
+                      k expected to be observed from k+r trials with success fraction
+                      p, at probability P. Note that the value returned is a real-number,
+                      and not an integer. Depending on the use case you may want
+                      to take either the floor or ceiling of the real result. For
+                      example:
+                    
            
+                    
            
+                      
 
            
 
            quantile(negative_binomial(r, p), P)
            
 
            
-                
            
-                            		
 
            
 
            
 
-                
            
-                  Quantile from the complement
-                  of the probability
-                
            
-                            		
 
-                
            
-                  The smallest number of failures
-                  k expected to be observed from k+r trials with success fraction
-                  p, at probability P. Note that the value returned is a real-number,
-                  and not an integer. Depending on the use case you may want to take
-                  either the floor or ceiling of the real result. For example: 
+                    
            
+                      The smallest number of failures
+                      k expected to be observed from k+r trials with success fraction
+                      p, at probability P. Note that the value returned is a real-number,
+                      and not an integer. Depending on the use case you may want
+                      to take either the floor or ceiling of the real result. For
+                      example: 
 
            
 
            quantile(complement(negative_binomial(r, p), P))
            
 
            
-                
            
-                            		
 
            
             
 
            
 
            
 
            
-
+
             Accuracy
           
            
 
            
@@ -613,7 +616,7 @@
             please refer to these functions for information on accuracy.
           
            
 
            
-
+
             Implementation
           
            
 
            
@@ -629,249 +632,252 @@
            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            		-

            - pdf = exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, r) - * pow((1-p), k) -

            -

            - Implementation is in terms of ibeta_derivative: -

            -

            - (p/(r + k)) * ibeta_derivative(r, static_cast<RealType>(k+1), - p) The function ibeta_derivative - is used here, since it has already been optimised for the lowest - possible error - indeed this is really just a thin wrapper around - part of the internals of the incomplete beta function. -

            +

            + pdf = exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, + r) * pow((1-p), k) +

            +

            + Implementation is in terms of ibeta_derivative: +

            +

            + (p/(r + k)) * ibeta_derivative(r, static_cast<RealType>(k+1), + p) The function ibeta_derivative + is used here, since it has already been optimised for the lowest + possible error - indeed this is really just a thin wrapper + around part of the internals of the incomplete beta function. +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relation: -

            -

            - cdf = Ip(r, k+1) = ibeta(r, k+1, p) -

            -

            - = ibeta(r, static_cast<RealType>(k+1), p) -

            +

            + Using the relation: +

            +

            + cdf = Ip(r, k+1) = ibeta(r, k+1, p) +

            +

            + = ibeta(r, static_cast<RealType>(k+1), p) +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - Using the relation: -

            -

            - 1 - cdf = Ip(k+1, r) -

            -

            - = ibetac(r, static_cast<RealType>(k+1), p) -

            +

            + Using the relation: +

            +

            + 1 - cdf = Ip(k+1, r) +

            +

            + = ibetac(r, static_cast<RealType>(k+1), p) +

            -

            - quantile -

            +

            + quantile +

            		-

            - ibeta_invb(r, p, P) - 1 -

            +

            + ibeta_invb(r, p, P) - 1 +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - ibetac_invb(r, p, Q) -1) -

            +

            + ibetac_invb(r, p, Q) -1) +

            -

            - mean -

            +

            + mean +

            		-

            - r(1-p)/p -

            +

            + r(1-p)/p +

            -

            - variance -

            +

            + variance +

            		-

            - r (1-p) - / p - * p -

            +

            + r (1-p) + / p + * p +

            -

            - mode -

            +

            + mode +

            		-

            - floor((r-1) * (1 - p)/p) -

            +

            + floor((r-1) + * (1 - + p)/p) +

            -

            - skewness -

            +

            + skewness +

            		-

            - (2 - - p) / - sqrt(r * - (1 - - p)) -

            +

            + (2 + - p) / + sqrt(r * + (1 + - p)) +

            -

            - kurtosis -

            +

            + kurtosis +

            		-

            - 6 / - r + - (p - * p) / - r * - (1 - - p - ) -

            +

            + 6 / + r + + (p + * p) / + r * + (1 + - p + ) +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - 6 / - r + - (p - * p) / - r * - (1 - - p - ) -3 -

            +

            + 6 / + r + + (p + * p) / + r * + (1 + - p + ) -3 +

            -

            - parameter estimation member functions -

            +

            + parameter estimation member functions +

            		-

            -

            +

            +

            -

            - find_lower_bound_on_p -

            +

            + find_lower_bound_on_p +

            		-

            - ibeta_inv(successes, failures + 1, alpha) -

            +

            + ibeta_inv(successes, failures + 1, alpha) +

            -

            - find_upper_bound_on_p -

            +

            + find_upper_bound_on_p +

            		-

            - ibetac_inv(successes, failures, alpha) plus see comments in code. -

            +

            + ibetac_inv(successes, failures, alpha) plus see comments in + code. +

            -

            - find_minimum_number_of_trials -

            +

            + find_minimum_number_of_trials +

            		-

            - ibeta_inva(k + 1, p, alpha) -

            +

            + ibeta_inva(k + 1, p, alpha) +

            -

            - find_maximum_number_of_trials -

            +

            + find_maximum_number_of_trials +

            		-

            - ibetac_inva(k + 1, p, alpha) -

            +

            + ibetac_inva(k + 1, p, alpha) +

            @@ -904,7 +910,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html index 9a49e3aeb..54a973aca 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html @@ -2,8 +2,8 @@ Normal (Gaussian) Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Normal (Gaussian) Distribution @@ -79,7 +79,7 @@

            - + Member Functions
            @@ -109,7 +109,7 @@ be used generically).

            - + Non-member Accessors
            @@ -131,7 +131,7 @@ and complement cdf -∞ = 1 and +∞ = 0, if RealType permits.

            - + Accuracy

            @@ -139,7 +139,7 @@ function, and as such should have very low error rates.

            - + Implementation

            @@ -153,135 +153,135 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = e-(x-m)2/(2s2) / (s * sqrt(2*pi)) -

            +

            + Using the relation: pdf = e-(x-m)2/(2s2) / (s * sqrt(2*pi)) +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: p = 0.5 * erfc(-(x-m)/(s*sqrt(2))) -

            +

            + Using the relation: p = 0.5 * erfc(-(x-m)/(s*sqrt(2))) +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = 0.5 * erfc((x-m)/(s*sqrt(2))) -

            +

            + Using the relation: q = 0.5 * erfc((x-m)/(s*sqrt(2))) +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: x = m - s * sqrt(2) * erfc_inv(2*p) -

            +

            + Using the relation: x = m - s * sqrt(2) * erfc_inv(2*p) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: x = m + s * sqrt(2) * erfc_inv(2*p) -

            +

            + Using the relation: x = m + s * sqrt(2) * erfc_inv(2*p) +

            -

            - mean and standard deviation -

            +

            + mean and standard deviation +

            -

            - The same as dist.mean() and dist.standard_deviation() -

            +

            + The same as dist.mean() and dist.standard_deviation() +

            -

            - mode -

            +

            + mode +

            -

            - The same as the mean. -

            +

            + The same as the mean. +

            -

            - skewness -

            +

            + skewness +

            -

            - 0 -

            +

            + 0 +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - 3 -

            +

            + 3 +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - 0 -

            +

            + 0 +

            @@ -299,7 +299,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html index e2ad02f44..6a00c4878 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html @@ -2,8 +2,8 @@ Pareto Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Pareto Distribution @@ -87,12 +87,12 @@

            - + Related distributions
            - + Member Functions
            @@ -118,7 +118,7 @@ Returns the shape parameter of this distribution.

            - + Non-member Accessors
            @@ -138,7 +138,7 @@ The supported domain of the random variable is [scale, ∞].

            - + Accuracy

            @@ -151,7 +151,7 @@ zero) see also why complements?.

            - + Implementation

            @@ -167,172 +167,176 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf p = αβα/xα +1 -

            +

            + Using the relation: pdf p = αβα/xα +1 +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: cdf p = 1 - (β / x)α -

            +

            + Using the relation: cdf p = 1 - (β / x)α +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = 1 - p = -(β / x)α -

            +

            + Using the relation: q = 1 - p = -(β / x)α +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: x = β / (1 - p)1/α -

            +

            + Using the relation: x = β / (1 - p)1/α +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: x = β / (q)1/α -

            +

            + Using the relation: x = β / (q)1/α +

            -

            - mean -

            +

            + mean +

            -

            - αβ / (β - 1) -

            +

            + αβ / (β - 1) +

            -

            - variance -

            +

            + variance +

            -

            - βα2 / (β - 1)2 (β - 2) -

            +

            + βα2 / (β - 1)2 (β - 2) +

            -

            - mode -

            +

            + mode +

            -

            - α -

            +

            + α +

            -

            - skewness -

            +

            + skewness +

            -

            - Refer to Weisstein, - Eric W. "Pareto Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Refer to Weisstein, + Eric W. "Pareto Distribution." From MathWorld--A + Wolfram Web Resource. +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - Refer to Weisstein, - Eric W. "Pareto Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Refer to Weisstein, + Eric W. "Pareto Distribution." From MathWorld--A + Wolfram Web Resource. +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - Refer to Weisstein, - Eric W. "pareto Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Refer to Weisstein, + Eric W. "pareto Distribution." From MathWorld--A + Wolfram Web Resource. +

            - + References
            -
            @@ -347,7 +351,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html index bf162e454..dbe812dec 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html @@ -2,8 +2,8 @@ Poisson Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Poisson Distribution @@ -86,7 +86,7 @@

            - + @@ -336,7 +336,7 @@
            [Caution][Caution] Caution
            @@ -122,7 +122,7 @@

            - + Member Functions
            @@ -137,7 +137,7 @@ Returns the mean of this distribution.

            - + Non-member Accessors
            @@ -157,7 +157,7 @@ The domain of the random variable is [0, ∞].

            - + Accuracy

            @@ -171,7 +171,7 @@ using an iterative method with a lower tolerance to avoid excessive computation.

            - + Implementation

            @@ -186,139 +186,139 @@

            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            		-

            - Using the relation: pdf = e-λ λk / k! -

            +

            + Using the relation: pdf = e-λ λk / k! +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relation: p = Γ(k+1, λ) / k! = gamma_q(k+1, - λ) -

            +

            + Using the relation: p = Γ(k+1, λ) / k! = gamma_q(k+1, + λ) +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - Using the relation: q = gamma_p(k+1, - λ) -

            +

            + Using the relation: q = gamma_p(k+1, + λ) +

            -

            - quantile -

            +

            + quantile +

            		-

            - Using the relation: k = gamma_q_inva(λ, - p) - 1 -

            +

            + Using the relation: k = gamma_q_inva(λ, + p) - 1 +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - Using the relation: k = gamma_p_inva(λ, - q) - 1 -

            +

            + Using the relation: k = gamma_p_inva(λ, + q) - 1 +

            -

            - mean -

            +

            + mean +

            		-

            - λ -

            +

            + λ +

            -

            - mode -

            +

            + mode +

            		-

            - floor (λ) or ⌊λ⌋ -

            +

            + floor (λ) or ⌊λ⌋ +

            -

            - skewness -

            +

            + skewness +

            		-

            - 1/√λ -

            +

            + 1/√λ +

            -

            - kurtosis -

            +

            + kurtosis +

            		-

            - 3 + 1/λ -

            +

            + 3 + 1/λ +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - 1/λ -

            +

            + 1/λ +

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html index 123390e2d..f620be36e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html @@ -2,8 +2,8 @@ Rayleigh Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Rayleigh Distribution @@ -86,7 +86,7 @@

            - + Related distributions
            @@ -102,7 +102,7 @@ distribution.

            - + Member Functions
            @@ -121,7 +121,7 @@ Returns the sigma parameter of this distribution.

            - + Non-member Accessors
            @@ -141,7 +141,7 @@ The domain of the random variable is [0, max_value].

            - + Accuracy

            @@ -151,7 +151,7 @@ using NTL RR type with 150-bit accuracy, about 50 decimal digits.

            - + Implementation

            @@ -166,168 +166,172 @@ -

            - Function -

            +

            + Function +

            -

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            -

            - Using the relation: pdf = x * exp(-x2)/2 σ2 -

            +

            + Using the relation: pdf = x * exp(-x2)/2 σ2 +

            -

            - cdf -

            +

            + cdf +

            -

            - Using the relation: p = 1 - exp(-x2/2) σ2 = -expm1(-x2/2) - σ2 -

            +

            + Using the relation: p = 1 - exp(-x2/2) σ2 = -expm1(-x2/2) + σ2 +

            -

            - cdf complement -

            +

            + cdf complement +

            -

            - Using the relation: q = exp(-x2/ 2) * σ2 -

            +

            + Using the relation: q = exp(-x2/ 2) * σ2 +

            -

            - quantile -

            +

            + quantile +

            -

            - Using the relation: x = sqrt(-2 * σ 2) * log(1 - p)) = sqrt(-2 - * σ 2) * log1p(-p)) -

            +

            + Using the relation: x = sqrt(-2 * σ 2) * log(1 - p)) = sqrt(-2 + * σ 2) * log1p(-p)) +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            -

            - Using the relation: x = sqrt(-2 * σ 2) * log(q)) -

            +

            + Using the relation: x = sqrt(-2 * σ 2) * log(q)) +

            -

            - mean -

            +

            + mean +

            -

            - σ * sqrt(π/2) -

            +

            + σ * sqrt(π/2) +

            -

            - variance -

            +

            + variance +

            -

            - σ2 * (4 - π/2) -

            +

            + σ2 * (4 - π/2) +

            -

            - mode -

            +

            + mode +

            -

            - σ -

            +

            + σ +

            -

            - skewness -

            +

            + skewness +

            -

            - Constant from Weisstein, - Eric W. "Weibull Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Constant from Weisstein, + Eric W. "Weibull Distribution." From MathWorld--A + Wolfram Web Resource. +

            -

            - kurtosis -

            +

            + kurtosis +

            -

            - Constant from Weisstein, - Eric W. "Weibull Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Constant from Weisstein, + Eric W. "Weibull Distribution." From MathWorld--A + Wolfram Web Resource. +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            -

            - Constant from Weisstein, - Eric W. "Weibull Distribution." From MathWorld--A Wolfram - Web Resource. -

            +

            + Constant from Weisstein, + Eric W. "Weibull Distribution." From MathWorld--A + Wolfram Web Resource. +

            - + References
            -
            @@ -342,7 +346,7 @@
            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html index 364c9a99a..12196e275 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html @@ -2,8 +2,8 @@ Students t Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Students t Distribution @@ -97,7 +97,7 @@

            - + Member Functions
            @@ -134,34 +134,34 @@
            difference_from_mean

            - The difference between the true mean and the sample mean that we - wish to show is significant. -

            + The difference between the true mean and the sample mean that we + wish to show is significant. +

            alpha

            - The maximum acceptable probability of rejecting the null hypothesis - when it is in fact true. -

            + The maximum acceptable probability of rejecting the null hypothesis + when it is in fact true. +

            beta

            - The maximum acceptable probability of failing to reject the null - hypothesis when it is in fact false. -

            + The maximum acceptable probability of failing to reject the null + hypothesis when it is in fact false. +

            sd

            - The sample standard deviation. -

            + The sample standard deviation. +

            hint

            - A hint for the location to start looking for the result, a good choice - for this would be the sample size of a previous borderline Student's - t test. -

            + A hint for the location to start looking for the result, a good + choice for this would be the sample size of a previous borderline + Student's t test. +

            - + @@ -418,7 +418,7 @@
            [Note][Note] Note

            @@ -174,7 +174,7 @@ Engineering Statistics Handbook.

            - + Non-member Accessors
            @@ -194,7 +194,7 @@ The domain of the random variable is [-∞, +∞].

            - + Examples

            @@ -202,7 +202,7 @@ are available illustrating the use of the Student's t distribution.

            - + Accuracy

            @@ -211,7 +211,7 @@ inverses, refer to accuracy data on those functions for more information.

            - + Implementation

            @@ -226,181 +226,181 @@

            -

            - Function -

            +

            + Function +

            		-

            - Implementation Notes -

            +

            + Implementation Notes +

            -

            - pdf -

            +

            + pdf +

            		-

            - Using the relation: pdf = (v / (v + t2))(1+v)/2 / (sqrt(v) * - beta(v/2, - 0.5)) -

            +

            + Using the relation: pdf = (v / (v + t2))(1+v)/2 / (sqrt(v) + * beta(v/2, + 0.5)) +

            -

            - cdf -

            +

            + cdf +

            		-

            - Using the relations: -

            -

            - p = 1 - z iff t > 0 -

            -

            - p = z otherwise -

            -

            - where z is given by: -

            -

            - ibeta(v - / 2, 0.5, v / (v + t2)) / 2 iff v < 2t2 -

            -

            - ibetac(0.5, - v / 2, t2 / (v + t2) / 2 otherwise -

            +

            + Using the relations: +

            +

            + p = 1 - z iff t > 0 +

            +

            + p = z otherwise +

            +

            + where z is given by: +

            +

            + ibeta(v + / 2, 0.5, v / (v + t2)) / 2 iff v < 2t2 +

            +

            + ibetac(0.5, + v / 2, t2 / (v + t2) / 2 otherwise +

            -

            - cdf complement -

            +

            + cdf complement +

            		-

            - Using the relation: q = cdf(-t) -

            +

            + Using the relation: q = cdf(-t) +

            -

            - quantile -

            +

            + quantile +

            		-

            - Using the relation: t = sign(p - 0.5) * sqrt(v * y / x) -

            -

            - where: -

            -

            - x = ibeta_inv(v - / 2, 0.5, 2 * min(p, q)) -

            -

            - y = 1 - x -

            -

            - The quantities x and y - are both returned by ibeta_inv - without the subtraction implied above. -

            +

            + Using the relation: t = sign(p - 0.5) * sqrt(v * y / x) +

            +

            + where: +

            +

            + x = ibeta_inv(v + / 2, 0.5, 2 * min(p, q)) +

            +

            + y = 1 - x +

            +

            + The quantities x and y + are both returned by ibeta_inv + without the subtraction implied above. +

            -

            - quantile from the complement -

            +

            + quantile from the complement +

            		-

            - Using the relation: t = -quantile(q) -

            +

            + Using the relation: t = -quantile(q) +

            -

            - mean -

            +

            + mean +

            		-

            - 0 -

            +

            + 0 +

            -

            - variance -

            +

            + variance +

            		-

            - v / (v - 2) -

            +

            + v / (v - 2) +

            -

            - mode -

            +

            + mode +

            		-

            - 0 -

            +

            + 0 +

            -

            - skewness -

            +

            + skewness +

            		-

            - 0 -

            +

            + 0 +

            -

            - kurtosis -

            +

            + kurtosis +

            		-

            - 3 * (v - 2) / (v - 4) -

            +

            + 3 * (v - 2) / (v - 4) +

            -

            - kurtosis excess -

            +

            + kurtosis excess +

            		-

            - 6 / (df - 4) -

            +

            + 6 / (df - 4) +

            -PrevUpHomeNext +PrevUpHomeNext
            diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html index a74aa8a47..f307e40e2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html @@ -2,8 +2,8 @@ Triangular Distribution - - + + @@ -20,9 +20,9 @@
            -PrevUpHomeNext +PrevUpHomeNext
            -
            +
            Triangular Distribution @@ -81,13 +81,13 @@

            f(x) =

            -
              -
            • - 2(x-a)/(b-a) (c-a) for a <= x <= c -
              • -
            • - 2(b-x)/(b-a)(b-c) for c < x <= b -
              • +
                +
              • + 2(x-a)/(b-a) (c-a) for a <= x <= c +
                • +
              • + 2(b-x)/(b-a)(b-c) for c < x <= b +

              Parameter a (lower) can be any finite value. Parameter b (upper) can @@ -128,7 +128,7 @@

              - + Member Functions
              @@ -163,7 +163,7 @@ (default+1).

              - + Non-member Accessors
              @@ -184,7 +184,7 @@ range is lower <= x <= upper.

              - + Accuracy

              @@ -193,7 +193,7 @@ with arguments nearing the extremes of zero and unity.

              - + Implementation

              @@ -210,165 +210,165 @@ -

              - Function -

              +

              + Function +

              -

              - Implementation Notes -

              +

              + Implementation Notes +

              -

              - pdf -

              +

              + pdf +

              -

              - Using the relation: pdf = 0 for x < mode, 2(x-a)/(b-a)(c-a) - else 2*(b-x)/((b-a)(b-c)) -

              +

              + Using the relation: pdf = 0 for x < mode, 2(x-a)/(b-a)(c-a) + else 2*(b-x)/((b-a)(b-c)) +

              -

              - cdf -

              +

              + cdf +

              -

              - Using the relation: cdf = 0 for x < mode (x-a)2/((b-a)(c-a)) - else 1 - (b-x)2/((b-a)(b-c)) -

              +

              + Using the relation: cdf = 0 for x < mode (x-a)2/((b-a)(c-a)) + else 1 - (b-x)2/((b-a)(b-c)) +

              -

              - cdf complement -

              +

              + cdf complement +

              -

              - Using the relation: q = 1 - p -

              +

              + Using the relation: q = 1 - p +

              -

              - quantile -

              +

              + quantile +

              -

              - let p0 = (c-a)/(b-a) the point of inflection on the cdf, then - given probability p and q = 1-p: -

              -

              - x = sqrt((b-a)(c-a)p) + a ; for p < p0 -

              -

              - x = c ; for p == p0 -

              -

              - x = b - sqrt((b-a)(b-c)q) ; for p > p0 -

              -

              - (See /boost/math/distributions/triangular.hpp - for details.) -

              +

              + let p0 = (c-a)/(b-a) the point of inflection on the cdf, then + given probability p and q = 1-p: +

              +

              + x = sqrt((b-a)(c-a)p) + a ; for p < p0 +

              +

              + x = c ; for p == p0 +

              +

              + x = b - sqrt((b-a)(b-c)q) ; for p > p0 +

              +

              + (See /boost/math/distributions/triangular.hpp + for details.) +

              -

              - quantile from the complement -

              +

              + quantile from the complement +

              -

              - As quantile (See /boost/math/distributions/triangular.hpp - for details.) -

              +

              + As quantile (See /boost/math/distributions/triangular.hpp + for details.) +

              -

              - mean -

              +

              + mean +

              -

              - (a + b + 3) / 3 -

              +

              + (a + b + 3) / 3 +

              -

              - variance -

              +

              + variance +

              -

              - (a2+b2+c2 - ab - ac - bc)/18 -

              +

              + (a2+b2+c2 - ab - ac - bc)/18 +

              -

              - mode -

              +

              + mode +

              -

              - c -

              +

              + c +

              -

              - skewness -

              +

              + skewness +

              -

              - (See /boost/math/distributions/triangular.hpp - for details). -

              +

              + (See /boost/math/distributions/triangular.hpp + for details). +

              -

              - kurtosis -

              +

              + kurtosis +

              -

              - 12/5 -

              +

              + 12/5 +

              -

              - kurtosis excess -

              +

              + kurtosis excess +

              -

              - -3/5 -

              +

              + -3/5 +

              @@ -378,28 +378,38 @@ Calculate and plot probability distributions

              - + References
              -
              @@ -414,7 +424,7 @@
              -PrevUpHomeNext +PrevUpHomeNext
              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html index cd05038a0..878021b5c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html @@ -2,8 +2,8 @@ Uniform Distribution - - + + @@ -20,9 +20,9 @@
              -PrevUpHomeNext +PrevUpHomeNext
              -
              +
              Uniform Distribution @@ -67,20 +67,20 @@

              f(x) =

              -
                -
              • - 1 / (upper - lower) for lower < x < upper -
                • -
              • - zero for x < lower or x > upper -
                • +
                  +
                • + 1 / (upper - lower) for lower < x < upper +
                  • +
                • + zero for x < lower or x > upper +

                and in this implementation:

                -
                • - 1 / (upper - lower) for x = lower or x = upper -
                +
                • + 1 / (upper - lower) for x = lower or x = upper +

                The choice of x = lower or x = upper is made because statistical use of this distribution judged is most likely: the method of maximum likelihood @@ -117,7 +117,7 @@

                - + Member Functions
                @@ -144,7 +144,7 @@ Returns the upper parameter of this distribution.

                - + Non-member Accessors
                @@ -165,7 +165,7 @@ range is only lower <= x <= upper.

                - + Accuracy

                @@ -173,7 +173,7 @@ and so should have errors within an epsilon or two.

                - + Implementation

                @@ -189,164 +189,170 @@ -

                - Function -

                +

                + Function +

                -

                - Implementation Notes -

                +

                + Implementation Notes +

                -

                - pdf -

                +

                + pdf +

                -

                - Using the relation: pdf = 0 for x < a, 1 / (b - a) for a <= - x <= b, 0 for x > b -

                +

                + Using the relation: pdf = 0 for x < a, 1 / (b - a) for a + <= x <= b, 0 for x > b +

                -

                - cdf -

                +

                + cdf +

                -

                - Using the relation: cdf = 0 for x < a, (x - a) / (b - a) for - a <= x <= b, 1 for x > b -

                +

                + Using the relation: cdf = 0 for x < a, (x - a) / (b - a) + for a <= x <= b, 1 for x > b +

                -

                - cdf complement -

                +

                + cdf complement +

                -

                - Using the relation: q = 1 - p, (b - x) / (b - a) -

                +

                + Using the relation: q = 1 - p, (b - x) / (b - a) +

                -

                - quantile -

                +

                + quantile +

                -

                - Using the relation: x = p * (b - a) + a; -

                +

                + Using the relation: x = p * (b - a) + a; +

                -

                - quantile from the complement -

                +

                + quantile from the complement +

                -

                - x = -q * (b - a) + b -

                +

                + x = -q * (b - a) + b +

                -

                - mean -

                +

                + mean +

                -

                - (a + b) / 2 -

                +

                + (a + b) / 2 +

                -

                - variance -

                +

                + variance +

                -

                - (b - a) 2 / 12 -

                +

                + (b - a) 2 / 12 +

                -

                - mode -

                +

                + mode +

                -

                - any value in [a, b] but a is chosen. (Would NaN be better?) -

                +

                + any value in [a, b] but a is chosen. (Would NaN be better?) +

                -

                - skewness -

                +

                + skewness +

                -

                - 0 -

                +

                + 0 +

                -

                - kurtosis excess -

                +

                + kurtosis excess +

                -

                - -6/5 = -1.2 exactly. (kurtosis - 3) -

                +

                + -6/5 = -1.2 exactly. (kurtosis - 3) +

                -

                - kurtosis -

                +

                + kurtosis +

                -

                - 9/5 -

                +

                + 9/5 +

              - + References
              -
              @@ -361,7 +367,7 @@
              -PrevUpHomeNext +PrevUpHomeNext
              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html index 9c4fa98c2..239f5258d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html @@ -2,8 +2,8 @@ Weibull Distribution - - + + @@ -20,9 +20,9 @@
              -PrevUpHomeNext +PrevUpHomeNext
              -
              +
              Weibull Distribution @@ -72,18 +72,18 @@ in particular it can mimic distributions where the failure rate varies over time. If the failure rate is:

              -
              - + References
              -
              @@ -361,7 +367,7 @@
              -PrevUpHomeNext +PrevUpHomeNext
              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html index bc9f249a9..ed71a2753 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html @@ -2,8 +2,8 @@ Non-Member Properties - - + + @@ -20,9 +20,9 @@
              -PrevUpHomeNext +PrevUpHomeNext
              -
              +
              @@ -37,144 +37,152 @@ the function you want if you already know its name.

              - + Function Index
              -
                -
              • -cdf. -
                • -
              • -cdf complement. -
                • -
              • -chf. -
                • -
              • -hazard. -
                • -
              • -kurtosis. -
                • -
              • kurtosis_excess
                • -
              • -mean. -
                • -
              • -median. -
                • -
              • -mode. -
                • -
              • -pdf. -
                • -
              • -range. -
                • -
              • -quantile. -
                • -
              • -quantile from the complement. -
                • -
              • -skewness. -
                • -
              • -standard_deviation. -
                • -
              • -support. -
                • -
              • -variance. -
                • +
                - + Conceptual Index
                -
                  -
                • -Complement of the Cumulative Distribution - Function. -
                  • -
                • -Cumulative Distribution Function. -
                  • -
                • -Cumulative Hazard Function. -
                  • -
                • -Inverse Cumulative Distribution Function. -
                  • -
                • -Inverse Survival Function. -
                  • -
                • Hazard Function
                  • -
                • -Lower Critical Value. -
                  • -
                • -kurtosis. -
                  • -
                • kurtosis_excess
                  • -
                • -mean. -
                  • -
                • -median. -
                  • -
                • -mode. -
                  • -
                • -P. -
                  • -
                • -Percent Point Function. -
                  • -
                • -Probability Density Function. -
                  • -
                • -Probability Mass Function. -
                  • -
                • -range. -
                  • -
                • -Q. -
                  • -
                • -Quantile. -
                  • -
                • -Quantile from the complement of - the probability. -
                  • -
                • -skewness. -
                  • -
                • standard deviation
                  • -
                • -Survival Function. -
                  • -
                • -support. -
                  • -
                • -Upper Critical Value. -
                  • -
                • -variance. -
                  • +
                  - + Cumulative Distribution Function
                  @@ -198,7 +206,7 @@ cdf

                  - + Complement of the Cumulative Distribution Function
                  @@ -239,7 +247,7 @@ complement is useful and when it should be used.

                  - + Hazard Function 
                  template <class RealType, class Policy>
@@ -258,7 +266,7 @@
         
                  
 
                  
-
+
                  
 
                  [Caution][Caution]
 Caution
 
                  
 
                  
@@ -267,7 +275,7 @@
           
                  
 
                  
 
                  
-
+
           Cumulative
           Hazard Function
         
                  
@@ -287,7 +295,7 @@
         
                  
 
                  
-
+
                  
 
                  [Caution][Caution]
 Caution
 
                  
 
                  
@@ -295,7 +303,7 @@
           
                  
 
                  
 
                  
-
+
           mean
         
                  
 
                  template<class RealType, class Policy>
@@ -310,7 +318,7 @@
           distribution).
         
                  
 
                  
-
+
           median
         
                  
 
                  template<class RealType, class Policy>
@@ -320,7 +328,7 @@
           Returns the median of the distribution dist.
         
                  
 
                  
-
+
           mode
         
                  
 
                  template<class RealType, Policy>
@@ -334,7 +342,7 @@
           if the distribution does not have a defined mode.
         
                  
 
                  
-
+
           Probability
           Density Function
         
                  
@@ -363,7 +371,7 @@
           pdf
         
                  
 
                  
-
+
           range
         
                  
 
                  template<class RealType, class Policy>
@@ -373,7 +381,7 @@
           Returns the valid range of the random variable over distribution dist.
         
                  
 
                  
-
+
           Quantile
         
                  
 
                  template <class RealType, class Policy>
@@ -402,7 +410,7 @@
           quantile
         
                  
 
                  
-
+
           Quantile
           from the complement of the probability.
         
                  
@@ -448,7 +456,7 @@
           survival_inv
         
                  
 
                  
-
+
           Standard
           Deviation
         
                  
@@ -463,7 +471,7 @@
           if the distribution does not have a defined standard deviation.
         
                  
 
                  
-
+
           support
         
                  
 
                  template<class RealType, class Policy>
@@ -480,7 +488,7 @@
           where the pdf is zero, and the cdf zero or unity.
         
                  
 
                  
-
+
           Variance
         
                  
 
                  template <class RealType, class Policy>
@@ -494,7 +502,7 @@
           if the distribution does not have a defined variance.
         
                  
 
                  
-
+
           Skewness
         
                  
 
                  template <class RealType, class Policy>
@@ -508,7 +516,7 @@
           if the distribution does not have a defined skewness.
         
                  
 
                  
-
+
           Kurtosis
         
                  
 
                  template <class RealType, class Policy>
@@ -550,7 +558,7 @@
           'Proper' kurtosis can have a value from zero to + infinity.
         
                  
 
                  
-
+
           Kurtosis
           excess
         
                  
@@ -585,7 +593,7 @@
           The kurtosis excess of a normal distribution is zero.
         
                  
 
                  
-
+
           P and Q
         
                  
 
                  
@@ -595,7 +603,7 @@
           returned by these functions.
         
                  
 
                  
-
+
           Percent
           Point Function
         
                  
@@ -604,7 +612,7 @@
           the Quantile.
         
                  
 
                  
-
+
           Inverse
           CDF Function.
         
                  
@@ -613,7 +621,7 @@
           Quantile.
         
                  
 
                  
-
+
           Inverse
           Survival Function.
         
                  
@@ -621,7 +629,7 @@
           The inverse of the survival function, is the same as computing the quantile from the complement of the probability.
         
                  
 
                  
-
+
           Probability
           Mass Function
         
                  
@@ -635,7 +643,7 @@
           applies to continuous distributions.
         
                  
 
                  
-
+
           Lower
           Critical Value.
         
                  
@@ -645,7 +653,7 @@
           the Quantile.
         
                  
 
                  
-
+
           Upper
           Critical Value.
         
                  
@@ -656,7 +664,7 @@
           complement of the probability.
         
                  
 
                  
-
+
           Survival
           Function
         
                  
@@ -677,7 +685,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/future.html b/doc/sf_and_dist/html/math_toolkit/dist/future.html
index c4ef6dcd0..8555d364a 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/future.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/future.html
@@ -2,8 +2,8 @@
 
 
 Extras/Future Directions
-
-
+
+
 
 
 
@@ -20,14 +20,14 @@
 
 
                  
 
                  
-PrevUpHomeNext
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-
                  
+
                  
 
                  
 
                  
-
+
         Adding
         Additional Location and Scale Parameters
       
                  
@@ -55,7 +55,7 @@
         functions.
       
                  
 
                  
-
+
         An
         "any_distribution" class
       
                  
@@ -84,7 +84,7 @@
         use case: this needs more investigation.
       
                  
 
                  
-
+
         Higher
         Level Hypothesis Tests
       
                  
@@ -104,7 +104,7 @@
         expected_mean.
       
                  
 
                  
-
+
         Integration
         With Statistical Accumulators
       
                  
@@ -136,7 +136,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
index 4e0037969..2c140669b 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
@@ -2,8 +2,8 @@
 
 
 Statistical Distributions Tutorial
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
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-
                  
+
                  
 
                  
  Statistical Distributions
       Tutorial
@@ -148,7 +148,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
index 41d4fd1cb..c713fb021 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
@@ -2,8 +2,8 @@
 
 
 Discrete Probability Distributions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
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-
                  
+
                  
 
                  
  Discrete Probability
         Distributions
@@ -56,7 +56,7 @@
         
                  
 
                  
-
+
                  
 
                  [Caution][Caution]
 Caution
 
                  
 
                  
@@ -93,7 +93,7 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
index a118e13d5..0ea7a6b66 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
@@ -2,8 +2,8 @@
 
 
 Overview of Distributions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
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-
                  
+
                  
 
                  
@@ -54,7 +54,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html
index 745605642..c1348aded 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html
@@ -2,8 +2,8 @@
 
 
 Complements are supported too - and when to use them
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
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-
                  
+
                  
 
                  
 
                  
-
+
                  
 
                  [Tip][Tip]
 Tip
 
                  
 
                  
@@ -109,7 +109,7 @@
           
                  
 
                  
-
+
                  
 
                  [Tip][Tip]
 Tip
 
                  
 
                  
@@ -203,7 +203,7 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html
index b1c703fe8..5a8ae0d22 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html
@@ -2,8 +2,8 @@
 
 
 Generic operations common to all distributions are non-member functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
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-
                  
+
                  
 
                  
  Generic
           operations common to all distributions are non-member functions
@@ -54,7 +54,7 @@
           
                  
 
                  
-
+
                  
 
                  [Tip][Tip]
 Tip
 
                  
 
                  
@@ -96,7 +96,7 @@
           
                  
 
                  
-
+
                  
 
                  [Note][Note]
 Note
 
                  
 
                  
@@ -165,7 +165,7 @@
           
                  
 
                  
-
+
                  
 
                  [Note][Note]
 Note
 
                  
 
                  
@@ -233,7 +233,7 @@
 
                  
 
                  
 
                  
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html
index 80796bf5d..5dad9e82e 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html
@@ -2,8 +2,8 @@
 
 
 Headers and Namespaces
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
                  
 
                  
 
                  
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-
                  
+
                  
 
                  
  Headers
           and Namespaces
@@ -52,7 +52,7 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html
index 04da7f5e9..21b9415b3 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html
@@ -2,8 +2,8 @@
 
 
 Distributions are Objects
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
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-
                  
+
                  
 
                  
  Distributions
           are Objects
@@ -38,7 +38,7 @@
           
                  
 
                  
-
+
                  
 
                  [Tip][Tip]
 Tip
 
                  
 
                  
@@ -50,19 +50,19 @@
 
                  
             Making distributions class types does two things:
           
                  
-
                    
-
                  • 
-              It encapsulates the kind of distribution in the C++ type system; so,
-              for example, Students-t distributions are always a different C++ type
-              from Chi-Squared distributions.
-            
                    • 
-
                  • 
-              The distribution objects store any parameters associated with the distribution:
-              for example, the Students-t distribution has a degrees of
-              freedom parameter that controls the shape of the distribution.
-              This degrees of freedom parameter has to be provided
-              to the Students-t object when it is constructed.
-            
                    • 
+
                      
+
                    • 
+                It encapsulates the kind of distribution in the C++ type system;
+                so, for example, Students-t distributions are always a different
+                C++ type from Chi-Squared distributions.
+              
                      • 
+
                    • 
+                The distribution objects store any parameters associated with the
+                distribution: for example, the Students-t distribution has a degrees
+                of freedom parameter that controls the shape of the distribution.
+                This degrees of freedom parameter has to be
+                provided to the Students-t object when it is constructed.
+              
                      • 
 
                    
 
                    
             Although the distribution classes in this library are templates, there
@@ -124,7 +124,7 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html
index 339fadd95..035983464 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html
@@ -2,8 +2,8 @@
 
 
 Parameters can be calculated
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
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-
                  
+
                  
 
                  
 
           Parameters can be calculated
@@ -67,7 +67,7 @@
 
 
                  
 
                  
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html
index e1d90b6d6..c098e42c1 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html
@@ -2,8 +2,8 @@
 
 
 Summary
-
-
+
+
 
 
 
@@ -20,37 +20,37 @@
 
 
                  
 
                  
-PrevUpHomeNext
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-
                  
+
                  
 
                  
-
                    
-
                  • 
-              Distributions are objects, which are constructed from whatever parameters
-              the distribution may have.
-            
                    • 
-
                  • 
-              Member functions allow you to retrieve the parameters of a distribution.
-            
                    • 
-
                  • 
-              Generic non-member functions provide access to the properties that
-              are common to all the distributions (PDF, CDF, quantile etc).
-            
                    • 
-
                  • 
-              Complements of probabilities are calculated by wrapping the function's
-              arguments in a call to complement(...).
-            
                    • 
-
                  • 
-              Functions that accept a probability can accept a complement of the
-              probability as well, by wrapping the function's arguments in a call
-              to complement(...).
-            
                    • 
-
                  • 
-              Static member functions allow the parameters of a distribution to be
-              found from other information.
-            
                    • 
+
                      
+
                    • 
+                Distributions are objects, which are constructed from whatever parameters
+                the distribution may have.
+              
                      • 
+
                    • 
+                Member functions allow you to retrieve the parameters of a distribution.
+              
                      • 
+
                    • 
+                Generic non-member functions provide access to the properties that
+                are common to all the distributions (PDF, CDF, quantile etc).
+              
                      • 
+
                    • 
+                Complements of probabilities are calculated by wrapping the function's
+                arguments in a call to complement(...).
+              
                      • 
+
                    • 
+                Functions that accept a probability can accept a complement of the
+                probability as well, by wrapping the function's arguments in a call
+                to complement(...).
+              
                      • 
+
                    • 
+                Static member functions allow the parameters of a distribution to
+                be found from other information.
+              
                      • 
 
                    
 
                    
             Now that you have the basics, the next section looks at some worked examples.
@@ -68,7 +68,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
index c1d5df741..46f0a43f7 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
@@ -2,8 +2,8 @@
 
 
 Random Variates and Distribution Parameters
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
  Random Variates
         and Distribution Parameters
@@ -69,7 +69,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
index 938e888a7..b8b37b33e 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
@@ -2,8 +2,8 @@
 
 
 Worked Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
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-
                    
+
                    
 
                    
@@ -125,7 +125,7 @@
 
 
                    
 
                    
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
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--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
@@ -2,8 +2,8 @@
 
 
 Binomial Distribution Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
  Binomial
           Distribution Examples
@@ -55,7 +55,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
index a933505c1..712488bd9 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
@@ -2,8 +2,8 @@
 
 
 Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
 
             Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
@@ -104,15 +104,15 @@
               interval. Had we calculate two single-sided intervals each with a risk
               that the true value is outside the interval of α, then:
             
                    
-
                    • 
-                The risk that it is less than the lower bound is α.
-              
                    
+
                    • 
+                  The risk that it is less than the lower bound is α.
+                
                    
 
                    
               and
             
                    
-
                    • 
-                The risk that it is greater than the upper bound is also α.
-              
                    
+
                    • 
+                  The risk that it is greater than the upper bound is also α.
+                
                    
 
                    
               So the risk it is outside upper or lower bound,
               is twice alpha, and the probability
@@ -237,7 +237,7 @@ _______________________________________________________________________
 
 
                    
 
                    
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
index 9b1beb923..8891e165b 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
@@ -2,8 +2,8 @@
 
 
 Estimating Sample Sizes for a Binomial Distribution.
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
 
             Estimating Sample Sizes for a Binomial Distribution.
@@ -153,7 +153,7 @@ ____________________________
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
index e1400c2c8..d67b74221 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
@@ -2,8 +2,8 @@
 
 
 Binomial Coin-Flipping Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
 
             Binomial Coin-Flipping Example
@@ -401,7 +401,7 @@ Probability of getting upto (<) heads
 
 
                    
 
                    
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
index 57a69e4f5..99437ee84 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
@@ -2,8 +2,8 @@
 
 
 Binomial Quiz Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
 
             Binomial Quiz Example
@@ -498,7 +498,7 @@ Probability of getting between 4 and 4 answers right by guessing is 0.2252
               
               
                    
 
                    
-
+
                 Using
                 Binomial distribution moments
               
                    
@@ -535,7 +535,7 @@ Skewness is 0.2887
               
               
                    
 
                    
-
+
                 Quantiles
               
                    
 
                    
@@ -737,7 +737,7 @@ If guessing then percentiles 1 to 99% will get 0 to 7.788 right.
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
index fd078aa5b..877fda9a6 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
@@ -2,8 +2,8 @@
 
 
 Using the Distributions from Within C#
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Using the
           Distributions from Within C#
@@ -52,7 +52,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
index a785e0b15..3574568e1 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
@@ -2,8 +2,8 @@
 
 
 Chi Squared Distribution Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
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-
                    
+
                    
 
                    
  Chi Squared
           Distribution Examples
@@ -49,7 +49,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
index cb6435c46..74af29a35 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
@@ -2,8 +2,8 @@
 
 
 Confidence Intervals on the Standard Deviation
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Confidence Intervals on the Standard Deviation
@@ -139,7 +139,7 @@ _____________________________________________
               is between 0.00551 and 0.00729.
             
                    
 
                    
-
+
               Confidence
               intervals as a function of the number of observations
             
                    
@@ -230,7 +230,7 @@ ________________________________________
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
index 269c3485c..1ec9d7b6f 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
@@ -2,8 +2,8 @@
 
 
 Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
@@ -176,7 +176,7 @@ _______________________________________________________________
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
index bf3e5f5cf..37830c0e1 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
@@ -2,8 +2,8 @@
 
 
 Chi-Square Test for the Standard Deviation
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Chi-Square Test for the Standard Deviation
@@ -86,67 +86,67 @@
 
 
 
-                    
                    
-                      Hypothesis
-                    
                    
+                      
                    
+                        Hypothesis
+                      
                    
                     
 
-                    
                    
-                      Test
-                    
                    
+                      
                    
+                        Test
+                      
                    
                     
 
 
 
 
-                    
                    
-                      The null-hypothesis: there is no difference in standard deviation
-                      from the specified value
-                    
                    
+                      
                    
+                        The null-hypothesis: there is no difference in standard deviation
+                        from the specified value
+                      
                    
                     
 
-                    
                    
-                      Reject if T < χ2(1-alpha/2; N-1) or T > χ2(alpha/2; N-1)
-                    
                    
+                      
                    
+                        Reject if T < χ2(1-alpha/2; N-1) or T > χ2(alpha/2; N-1)
+                      
                    
                     
 
 
 
-                    
                    
-                      The alternative hypothesis: there is a difference in standard
-                      deviation from the specified value
-                    
                    
+                      
                    
+                        The alternative hypothesis: there is a difference in standard
+                        deviation from the specified value
+                      
                    
                     
 
-                    
                    
-                      Reject if χ2(1-alpha/2; N-1) >= T >= χ2(alpha/2; N-1)
-                    
                    
+                      
                    
+                        Reject if χ2(1-alpha/2; N-1) >= T >= χ2(alpha/2; N-1)
+                      
                    
                     
 
 
 
-                    
                    
-                      The alternative hypothesis: the standard deviation is less
-                      than the specified value
-                    
                    
+                      
                    
+                        The alternative hypothesis: the standard deviation is less
+                        than the specified value
+                      
                    
                     
 
-                    
                    
-                      Reject if χ2(1-alpha; N-1) <= T
-                    
                    
+                      
                    
+                        Reject if χ2(1-alpha; N-1) <= T
+                      
                    
                     
 
 
 
-                    
                    
-                      The alternative hypothesis: the standard deviation is greater
-                      than the specified value
-                    
                    
+                      
                    
+                        The alternative hypothesis: the standard deviation is greater
+                        than the specified value
+                      
                    
                     
 
-                    
                    
-                      Reject if χ2(alpha; N-1) >= T
-                    
                    
+                      
                    
+                        Reject if χ2(alpha; N-1) >= T
+                      
                    
                     
 
 
@@ -290,7 +290,7 @@ Standard Deviation  > 10.000            ACCEPTED
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
index eeb45f170..3f6994074 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
@@ -2,8 +2,8 @@
 
 
 Distribution Construction Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
           Distribution Construction Example
@@ -143,7 +143,7 @@
             
                    
 
                    
-
+
                    
 
                    [Caution][Caution]
 Caution
 
                    
 
                    
@@ -332,7 +332,7 @@ error C3861: 'mybetad0': identifier not found
             
             
                    
 
                    
-
+
               Default
               arguments to distribution constructors.
             
                    
@@ -406,7 +406,7 @@ error C3861: 'mybetad0': identifier not found
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
index 51e45ac07..13e39db29 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
@@ -2,8 +2,8 @@
 
 
 Error Handling Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Error Handling
           Example
@@ -230,7 +230,7 @@ errno is set to: 33
           
                    
 
                    
-
+
                    
 
                    [Caution][Caution]
 Caution
 
                    
 
                    
@@ -260,7 +260,7 @@ errno is set to: 33
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
index f1a25f0e2..89cf14349 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
@@ -2,8 +2,8 @@
 
 
 F Distribution Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  F Distribution
           Examples
@@ -104,69 +104,69 @@ is the standard
 
 
 
-                  
                    
-                    Hypothesis
-                  
                    
+                    
                    
+                      Hypothesis
+                    
                    
                   
 
-                  
                    
-                    Test
-                  
                    
+                    
                    
+                      Test
+                    
                    
                   
 
 
 
 
-                  
                    
-                    The null-hypothesis: there is no difference in standard deviations
-                    (two sided test)
-                  
                    
+                    
                    
+                      The null-hypothesis: there is no difference in standard deviations
+                      (two sided test)
+                    
                    
                   
 
-                  
                    
-                    Reject if F <= F(1-alpha/2; N1-1, N2-1) or F >= F(alpha/2;
-                    N1-1, N2-1)
-                  
                    
+                    
                    
+                      Reject if F <= F(1-alpha/2; N1-1, N2-1) or F >= F(alpha/2;
+                      N1-1, N2-1)
+                    
                    
                   
 
 
 
-                  
                    
-                    The alternative hypothesis: there is a difference in means (two
-                    sided test)
-                  
                    
+                    
                    
+                      The alternative hypothesis: there is a difference in means
+                      (two sided test)
+                    
                    
                   
 
-                  
                    
-                    Reject if F(1-alpha/2; N1-1, N2-1) <= F <= F(alpha/2; N1-1,
-                    N2-1)
-                  
                    
+                    
                    
+                      Reject if F(1-alpha/2; N1-1, N2-1) <= F <= F(alpha/2;
+                      N1-1, N2-1)
+                    
                    
                   
 
 
 
-                  
                    
-                    The alternative hypothesis: Standard deviation of sample 1 is
-                    greater than that of sample 2
-                  
                    
+                    
                    
+                      The alternative hypothesis: Standard deviation of sample 1
+                      is greater than that of sample 2
+                    
                    
                   
 
-                  
                    
-                    Reject if F < F(alpha; N1-1, N2-1)
-                  
                    
+                    
                    
+                      Reject if F < F(alpha; N1-1, N2-1)
+                    
                    
                   
 
 
 
-                  
                    
-                    The alternative hypothesis: Standard deviation of sample 1 is
-                    less than that of sample 2
-                  
                    
+                    
                    
+                      The alternative hypothesis: Standard deviation of sample 1
+                      is less than that of sample 2
+                    
                    
                   
 
-                  
                    
-                    Reject if F > F(1-alpha; N1-1, N2-1)
-                  
                    
+                    
                    
+                      Reject if F > F(1-alpha; N1-1, N2-1)
+                    
                    
                   
 
 
@@ -325,7 +325,7 @@ Standard deviation 1 is greater than standard deviation 2 ACCEPTED
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
index 4f0d2d6ef..8e5100619 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
@@ -2,8 +2,8 @@
 
 
 Find Location and Scale Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Find Location
           and Scale Examples
@@ -48,7 +48,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
index e2264a4fb..2ed91e4af 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
@@ -2,8 +2,8 @@
 
 
 Find Location (Mean) Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Find Location (Mean) Example
@@ -177,7 +177,7 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999
               
               
                    
 
                    
-
+
                 Controlling
                 Error Handling from find_location
               
                    
@@ -278,7 +278,7 @@ Normal distribution with mean = 0.355146 has fraction > 2 = 0.05
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
index 7e67913f9..76793d1da 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
@@ -2,8 +2,8 @@
 
 
 Find mean and standard deviation example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Find mean and standard deviation example
@@ -62,7 +62,7 @@
               
               
                    
 
                    
-
+
                 Using
                 find_location and find_scale to meet dispensing and measurement specifications
               
                    
@@ -246,7 +246,7 @@
               
               
                    
 
                    
-
+
                 Using
                 Cauchy-Lorentz instead of normal distribution
               
                    
@@ -397,7 +397,7 @@
               
               
                    
 
                    
-
+
                 Changing
                 the scale or standard deviation
               
                    
@@ -673,10 +673,10 @@
               
                    
 
                    
               
                    
-
                    • 
-                  Do we over-fill to make sure we meet a minimum specification (or
-                  under-fill to avoid an overdose)?
-                
                    
+
                    • 
+                    Do we over-fill to make sure we meet a minimum specification
+                    (or under-fill to avoid an overdose)?
+                  
                    
 
                    
               
                    
 
                    
@@ -684,9 +684,9 @@
               
                    
 
                    
               
                    
-
                    • 
-                  Do we measure better?
-                
                    
+
                    • 
+                    Do we measure better?
+                  
                    
 
                    
               
                    
 
                    
@@ -721,7 +721,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
index 49f1e95a3..842b52c05 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
@@ -2,8 +2,8 @@
 
 
 Find Scale (Standard Deviation) Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Find Scale (Standard Deviation) Example
@@ -179,7 +179,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999
               
               
                    
 
                    
-
+
                 Controlling
                 how Errors from find_scale are handled
               
                    
@@ -301,7 +301,7 @@ Normal distribution with mean = 0.946339 has fraction > -2 = 0.999
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
index 7c27a8257..567cb71ce 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
@@ -2,8 +2,8 @@
 
 
 Comparison with C, R, FORTRAN-style Free Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Comparison
           with C, R, FORTRAN-style Free Functions
@@ -109,7 +109,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html
index ad35a1138..1b472f797 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html
@@ -2,8 +2,8 @@
 
 
 Non Central Chi Squared Example
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Non Central
           Chi Squared Example
@@ -46,7 +46,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html
index f83a50682..c1d468201 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html
@@ -2,8 +2,8 @@
 
 
 Tables of the power function of the χ2 test.
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Tables of the power function of the χ2 test.
@@ -175,1143 +175,1143 @@ test at the 5%
 
 
 
-                      
                    
-                        ν
-                      
                    
+                        
                    
+                          ν
+                        
                    
                       
 
-                      
                    
-                        λ=2
-                      
                    
+                        
                    
+                          λ=2
+                        
                    
                       
 
-                      
                    
-                        λ=4
-                      
                    
+                        
                    
+                          λ=4
+                        
                    
                       
 
-                      
                    
-                        λ=6
-                      
                    
+                        
                    
+                          λ=6
+                        
                    
                       
 
-                      
                    
-                        λ=8
-                      
                    
+                        
                    
+                          λ=8
+                        
                    
                       
 
-                      
                    
-                        λ=10
-                      
                    
+                        
                    
+                          λ=10
+                        
                    
                       
 
-                      
                    
-                        λ=12
-                      
                    
+                        
                    
+                          λ=12
+                        
                    
                       
 
-                      
                    
-                        λ=14
-                      
                    
+                        
                    
+                          λ=14
+                        
                    
                       
 
-                      
                    
-                        λ=16
-                      
                    
+                        
                    
+                          λ=16
+                        
                    
                       
 
-                      
                    
-                        λ=18
-                      
                    
+                        
                    
+                          λ=18
+                        
                    
                       
 
-                      
                    
-                        λ=20
-                      
                    
+                        
                    
+                          λ=20
+                        
                    
                       
 
 
 
 
-                      
                    
-                        2
-                      
                    
+                        
                    
+                          2
+                        
                    
                       
 
-                      
                    
-                        0.226
-                      
                    
+                        
                    
+                          0.226
+                        
                    
                       
 
-                      
                    
-                        0.415
-                      
                    
+                        
                    
+                          0.415
+                        
                    
                       
 
-                      
                    
-                        0.584
-                      
                    
+                        
                    
+                          0.584
+                        
                    
                       
 
-                      
                    
-                        0.718
-                      
                    
+                        
                    
+                          0.718
+                        
                    
                       
 
-                      
                    
-                        0.815
-                      
                    
+                        
                    
+                          0.815
+                        
                    
                       
 
-                      
                    
-                        0.883
-                      
                    
+                        
                    
+                          0.883
+                        
                    
                       
 
-                      
                    
-                        0.928
-                      
                    
+                        
                    
+                          0.928
+                        
                    
                       
 
-                      
                    
-                        0.957
-                      
                    
+                        
                    
+                          0.957
+                        
                    
                       
 
-                      
                    
-                        0.974
-                      
                    
+                        
                    
+                          0.974
+                        
                    
                       
 
-                      
                    
-                        0.985
-                      
                    
+                        
                    
+                          0.985
+                        
                    
                       
 
 
 
-                      
                    
-                        3
-                      
                    
+                        
                    
+                          3
+                        
                    
                       
 
-                      
                    
-                        0.192
-                      
                    
+                        
                    
+                          0.192
+                        
                    
                       
 
-                      
                    
-                        0.359
-                      
                    
+                        
                    
+                          0.359
+                        
                    
                       
 
-                      
                    
-                        0.518
-                      
                    
+                        
                    
+                          0.518
+                        
                    
                       
 
-                      
                    
-                        0.654
-                      
                    
+                        
                    
+                          0.654
+                        
                    
                       
 
-                      
                    
-                        0.761
-                      
                    
+                        
                    
+                          0.761
+                        
                    
                       
 
-                      
                    
-                        0.84
-                      
                    
+                        
                    
+                          0.84
+                        
                    
                       
 
-                      
                    
-                        0.896
-                      
                    
+                        
                    
+                          0.896
+                        
                    
                       
 
-                      
                    
-                        0.934
-                      
                    
+                        
                    
+                          0.934
+                        
                    
                       
 
-                      
                    
-                        0.959
-                      
                    
+                        
                    
+                          0.959
+                        
                    
                       
 
-                      
                    
-                        0.975
-                      
                    
+                        
                    
+                          0.975
+                        
                    
                       
 
 
 
-                      
                    
-                        4
-                      
                    
+                        
                    
+                          4
+                        
                    
                       
 
-                      
                    
-                        0.171
-                      
                    
+                        
                    
+                          0.171
+                        
                    
                       
 
-                      
                    
-                        0.32
-                      
                    
+                        
                    
+                          0.32
+                        
                    
                       
 
-                      
                    
-                        0.47
-                      
                    
+                        
                    
+                          0.47
+                        
                    
                       
 
-                      
                    
-                        0.605
-                      
                    
+                        
                    
+                          0.605
+                        
                    
                       
 
-                      
                    
-                        0.716
-                      
                    
+                        
                    
+                          0.716
+                        
                    
                       
 
-                      
                    
-                        0.802
-                      
                    
+                        
                    
+                          0.802
+                        
                    
                       
 
-                      
                    
-                        0.866
-                      
                    
+                        
                    
+                          0.866
+                        
                    
                       
 
-                      
                    
-                        0.912
-                      
                    
+                        
                    
+                          0.912
+                        
                    
                       
 
-                      
                    
-                        0.943
-                      
                    
+                        
                    
+                          0.943
+                        
                    
                       
 
-                      
                    
-                        0.964
-                      
                    
+                        
                    
+                          0.964
+                        
                    
                       
 
 
 
-                      
                    
-                        5
-                      
                    
+                        
                    
+                          5
+                        
                    
                       
 
-                      
                    
-                        0.157
-                      
                    
+                        
                    
+                          0.157
+                        
                    
                       
 
-                      
                    
-                        0.292
-                      
                    
+                        
                    
+                          0.292
+                        
                    
                       
 
-                      
                    
-                        0.433
-                      
                    
+                        
                    
+                          0.433
+                        
                    
                       
 
-                      
                    
-                        0.564
-                      
                    
+                        
                    
+                          0.564
+                        
                    
                       
 
-                      
                    
-                        0.677
-                      
                    
+                        
                    
+                          0.677
+                        
                    
                       
 
-                      
                    
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-                      
                    
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-                        9
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
-                        17
-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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-                      
                    
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@@ -1337,7 +1337,7 @@ test at the 5%
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
index d545603bd..f05c99637 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
@@ -2,8 +2,8 @@
 
 
 Negative Binomial Distribution Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Negative
           Binomial Distribution Examples
@@ -55,7 +55,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
index c67ea3044..fe0bfd860 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
@@ -2,8 +2,8 @@
 
 
 Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Calculating Confidence Limits on the Frequency of Occurrence for the
@@ -261,7 +261,7 @@ ___________________________________________
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
index ffc2bd673..786e85bd2 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
@@ -2,8 +2,8 @@
 
 
 Estimating Sample Sizes for the Negative Binomial.
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Estimating Sample Sizes for the Negative Binomial.
@@ -161,7 +161,7 @@
             
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -243,7 +243,7 @@ ____________________________
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
index 97c6ee9d8..dfbde0eb5 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
@@ -2,8 +2,8 @@
 
 
 Negative Binomial Sales Quota Example.
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Negative Binomial Sales Quota Example.
@@ -102,7 +102,7 @@
               
                    
 
                    
-
+
                    
 
                    [Caution][Caution]
 Caution
 
                    
 
                    
@@ -801,7 +801,7 @@ If confidence of meeting quota is 0.95, then finishing house is 21
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
index 97afbb3b0..5a9c22e46 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
@@ -2,8 +2,8 @@
 
 
 Negative Binomial Table Printing Example.
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Negative Binomial Table Printing Example.
@@ -145,7 +145,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html
index 806d0c208..72bb6e396 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html
@@ -2,8 +2,8 @@
 
 
 Normal Distribution Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Normal
           Distribution Examples
@@ -46,7 +46,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
index b4bd73919..9e475e1aa 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
@@ -2,8 +2,8 @@
 
 
 Some Miscellaneous Examples of the Normal (Gaussian) Distribution
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Some Miscellaneous Examples of the Normal (Gaussian) Distribution
@@ -32,7 +32,7 @@
               illustrates their use.
             
                    
 
                    
-
+
               Traditional
               Tables
             
                    
@@ -278,7 +278,7 @@
 
                    
             
                    
 
                    
-
+
               Standard
               deviations either side of the Mean
             
                    
@@ -346,12 +346,12 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
                    
             
                    
 
                    
-
+
               Some
               simple examples
             
                    
 
                    
-
+
               Life
               of light bulbs
             
                    
@@ -422,7 +422,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
               
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -435,7 +435,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
                    
             
                    
 
                    
-
+
               How
               many onions?
             
                    
@@ -494,7 +494,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
                    
             
                    
 
                    
-
+
               Packing
               beef
             
                    
@@ -703,7 +703,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
                    
             
                    
 
                    
-
+
               Length
               of bolts
             
                    
@@ -754,7 +754,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html
index 6ee898fba..7499a0eb9 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html
@@ -2,8 +2,8 @@
 
 
 Student's t Distribution Examples
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Student's
           t Distribution Examples
@@ -53,7 +53,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html
index ef16158c0..ac5e365d3 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html
@@ -2,8 +2,8 @@
 
 
 Comparing two paired samples with the Student's t distribution
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Comparing two paired samples with the Student's t distribution
@@ -42,24 +42,24 @@
 
                    
               That means we can:
             
                    
-
                    
 
@@ -74,7 +74,7 @@
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html
index 71afc94d8..a11b6597f 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html
@@ -2,8 +2,8 @@
 
 
 Calculating confidence intervals on the mean with the Students-t distribution
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Calculating confidence intervals on the mean with the Students-t distribution
@@ -52,7 +52,7 @@
             
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -72,7 +72,7 @@
 
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -84,22 +84,22 @@
 
                    
               From the formula, it should be clear that:
             
                    
-
                      
-
                    • 
-                The width of the confidence interval decreases as the sample size
-                increases.
-              
                      • 
-
                    • 
-                The width increases as the standard deviation increases.
-              
                      • 
-
                    • 
-                The width increases as the confidence level increases
-                (0.5 towards 0.99999 - stronger).
-              
                      • 
-
                    • 
-                The width increases as the significance level decreases
-                (0.5 towards 0.00000...01 - stronger).
-              
                      • 
+
                        
+
                      • 
+                  The width of the confidence interval decreases as the sample size
+                  increases.
+                
                        • 
+
                      • 
+                  The width increases as the standard deviation increases.
+                
                        • 
+
                      • 
+                  The width increases as the confidence level increases
+                  (0.5 towards 0.99999 - stronger).
+                
                        • 
+
                      • 
+                  The width increases as the significance level decreases
+                  (0.5 towards 0.00000...01 - stronger).
+                
                        • 
 
                      
 
                      
               The following example code is taken from the example program students_t_single_sample.cpp.
@@ -263,7 +263,7 @@
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html
index dc2595e3e..b117bbb97 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html
@@ -2,8 +2,8 @@
 
 
 Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Estimating how large a sample size would have to become in order to give
@@ -174,7 +174,7 @@ _______________________________________________________________
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html
index 3f1c09b0c..9062fb3db 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html
@@ -2,8 +2,8 @@
 
 
 Testing a sample mean for difference from a "true" mean
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Testing a sample mean for difference from a "true" mean
@@ -50,7 +50,7 @@
             
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -112,98 +112,98 @@
 
 
                    
 
-                    
                    
-                      Hypothesis
-                    
                    
+                      
                    
+                        Hypothesis
+                      
                    
                                         		
 
-                    
                    
-                      Test
-                    
                    
+                      
                    
+                        Test
+                      
                    
                                         		
 
                    
 
 
                    
 
-                    
                    
-                      The Null-hypothesis: there is no difference
-                      in means
-                    
                    
+                      
                    
+                        The Null-hypothesis: there is no difference
+                        in means
+                      
                    
                                         		
 
-                    
                    
-                      Reject if complement of CDF for |t| < significance level
-                      / 2:
-                    
                    
-                    
                    
-                      cdf(complement(dist,
-                      fabs(t)))
-                      < alpha
-                      / 2
-                    
                    
+                      
                    
+                        Reject if complement of CDF for |t| < significance level
+                        / 2:
+                      
                    
+                      
                    
+                        cdf(complement(dist,
+                        fabs(t)))
+                        < alpha
+                        / 2
+                      
                    
                                         		
 
                    
 
                    
 
-                    
                    
-                      The Alternative-hypothesis: there is
-                      difference in means
-                    
                    
+                      
                    
+                        The Alternative-hypothesis: there is
+                        difference in means
+                      
                    
                                         		
 
-                    
                    
-                      Reject if complement of CDF for |t| > significance level
-                      / 2:
-                    
                    
-                    
                    
-                      cdf(complement(dist,
-                      fabs(t)))
-                      > alpha
-                      / 2
-                    
                    
+                      
                    
+                        Reject if complement of CDF for |t| > significance level
+                        / 2:
+                      
                    
+                      
                    
+                        cdf(complement(dist,
+                        fabs(t)))
+                        > alpha
+                        / 2
+                      
                    
                                         		
 
                    
 
                    
 
-                    
                    
-                      The Alternative-hypothesis: the sample mean is
-                      less than the true mean.
-                    
                    
+                      
                    
+                        The Alternative-hypothesis: the sample mean is
+                        less than the true mean.
+                      
                    
                                         		
 
-                    
                    
-                      Reject if CDF of t > significance level:
-                    
                    
-                    
                    
-                      cdf(dist,
-                      t)
-                      > alpha
-                    
                    
+                      
                    
+                        Reject if CDF of t > significance level:
+                      
                    
+                      
                    
+                        cdf(dist,
+                        t)
+                        > alpha
+                      
                    
                                         		
 
                    
 
                    
 
-                    
                    
-                      The Alternative-hypothesis: the sample mean is
-                      greater than the true mean.
-                    
                    
+                      
                    
+                        The Alternative-hypothesis: the sample mean is
+                        greater than the true mean.
+                      
                    
                                         		
 
-                    
                    
-                      Reject if complement of CDF of t > significance level:
-                    
                    
-                    
                    
-                      cdf(complement(dist,
-                      t))
-                      > alpha
-                    
                    
+                      
                    
+                        Reject if complement of CDF of t > significance level:
+                      
                    
+                      
                    
+                        cdf(complement(dist,
+                        t))
+                        > alpha
+                      
                    
                                         		
 
                    
                     
 
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -329,7 +329,7 @@ Mean  > 38.900            REJECTED
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
index 87aef7541..bffb392f5 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
@@ -2,8 +2,8 @@
 
 
 Comparing the means of two samples with the Students-t test
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
             Comparing the means of two samples with the Students-t test
@@ -117,98 +117,98 @@
 
 
 
-                    
                    
-                      Hypothesis
-                    
                    
+                      
                    
+                        Hypothesis
+                      
                    
                     
 
-                    
                    
-                      Test
-                    
                    
+                      
                    
+                        Test
+                      
                    
                     
 
 
 
 
-                    
                    
-                      The Null-hypothesis: there is no difference
-                      in means
-                    
                    
+                      
                    
+                        The Null-hypothesis: there is no difference
+                        in means
+                      
                    
                     
 
-                    
                    
-                      Reject if complement of CDF for |t| < significance level
-                      / 2:
-                    
                    
-                    
                    
-                      cdf(complement(dist,
-                      fabs(t)))
-                      < alpha
-                      / 2
-                    
                    
+                      
                    
+                        Reject if complement of CDF for |t| < significance level
+                        / 2:
+                      
                    
+                      
                    
+                        cdf(complement(dist,
+                        fabs(t)))
+                        < alpha
+                        / 2
+                      
                    
                     
 
 
 
-                    
                    
-                      The Alternative-hypothesis: there is a difference
-                      in means
-                    
                    
+                      
                    
+                        The Alternative-hypothesis: there is a difference
+                        in means
+                      
                    
                     
 
-                    
                    
-                      Reject if complement of CDF for |t| > significance level
-                      / 2:
-                    
                    
-                    
                    
-                      cdf(complement(dist,
-                      fabs(t)))
-                      < alpha
-                      / 2
-                    
                    
+                      
                    
+                        Reject if complement of CDF for |t| > significance level
+                        / 2:
+                      
                    
+                      
                    
+                        cdf(complement(dist,
+                        fabs(t)))
+                        < alpha
+                        / 2
+                      
                    
                     
 
 
 
-                    
                    
-                      The Alternative-hypothesis: Sample 1 Mean is less
-                      than Sample 2 Mean.
-                    
                    
+                      
                    
+                        The Alternative-hypothesis: Sample 1 Mean is less
+                        than Sample 2 Mean.
+                      
                    
                     
 
-                    
                    
-                      Reject if CDF of t > significance level:
-                    
                    
-                    
                    
-                      cdf(dist,
-                      t)
-                      > alpha
-                    
                    
+                      
                    
+                        Reject if CDF of t > significance level:
+                      
                    
+                      
                    
+                        cdf(dist,
+                        t)
+                        > alpha
+                      
                    
                     
 
 
 
-                    
                    
-                      The Alternative-hypothesis: Sample 1 Mean is greater
-                      than Sample 2 Mean.
-                    
                    
+                      
                    
+                        The Alternative-hypothesis: Sample 1 Mean is greater
+                        than Sample 2 Mean.
+                      
                    
                     
 
-                    
                    
-                      Reject if complement of CDF of t > significance level:
-                    
                    
-                    
                    
-                      cdf(complement(dist,
-                      t))
-                      > alpha
-                    
                    
+                      
                    
+                        Reject if complement of CDF of t > significance level:
+                      
                    
+                      
                    
+                        cdf(complement(dist,
+                        t))
+                        > alpha
+                      
                    
                     
 
 
 
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -278,7 +278,7 @@
             
                    
 
                    
-
+
                    
 
                    [Note][Note]
 Note
 
                    
 
                    
@@ -353,7 +353,7 @@
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c.html b/doc/sf_and_dist/html/math_toolkit/extern_c.html
index 7e36b2eed..33279a8e5 100644
--- a/doc/sf_and_dist/html/math_toolkit/extern_c.html
+++ b/doc/sf_and_dist/html/math_toolkit/extern_c.html
@@ -2,8 +2,8 @@
 
 
 TR1 and C99 external "C" Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
                    
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  TR1 and C99 external "C"
     Functions
@@ -46,7 +46,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html
index b5aadb36e..85dbca46b 100644
--- a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html
+++ b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html
@@ -2,8 +2,8 @@
 
 
 C99 C Functions
-
-
+
+
 
 
 
@@ -20,14 +20,14 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
                    
-
+
         Supported
         C99 Functions
       
                    
@@ -138,7 +138,7 @@
 acosh(2);      // integer argument is treated as a double, returns double.
 
                  
 
                  
-
+
         Quick Reference
       
                  
 
                  
@@ -162,71 +162,71 @@
 
 
 
-              
                  
-                FLT_EVAL_METHOD
-              
                  
+                
                  
+                  FLT_EVAL_METHOD
+                
                  
               
 
-              
                  
-                float_t
-              
                  
+                
                  
+                  float_t
+                
                  
               
 
-              
                  
-                double_t
-              
                  
+                
                  
+                  double_t
+                
                  
               
 
 
 
 
-              
                  
-                0
-              
                  
+                
                  
+                  0
+                
                  
               
 
-              
                  
-                float
-              
                  
+                
                  
+                  float
+                
                  
               
 
-              
                  
-                double
-              
                  
+                
                  
+                  double
+                
                  
               
 
 
 
-              
                  
-                1
-              
                  
+                
                  
+                  1
+                
                  
               
 
-              
                  
-                double
-              
                  
+                
                  
+                  double
+                
                  
               
 
-              
                  
-                double
-              
                  
+                
                  
+                  double
+                
                  
               
 
 
 
-              
                  
-                2
-              
                  
+                
                  
+                  2
+                
                  
               
 
-              
                  
-                long double
-              
                  
+                
                  
+                  long double
+                
                  
               
 
-              
                  
-                long double
-              
                  
+                
                  
+                  long double
+                
                  
               
 
 
@@ -471,7 +471,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html
index c2de63268..f03df8a60 100644
--- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html
+++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html
@@ -2,8 +2,8 @@
 
 
 C99 and TR1 C Functions Overview
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
@@ -48,17 +48,17 @@
         
                  
 
                  
         
                  
-
                    
-
                  • 
-            The header to include is lightweight (i.e. fast to compile).
-          
                    • 
-
                  • 
-            The functions have extern "C" linkage, and so are usable from
-            other languages (not just C and C++).
-          
                    • 
-
                  • 
-            C99 and C++ TR1 Standard compatibility.
-          
                    • 
+
                      
+
                    • 
+              The header to include is lightweight (i.e. fast to compile).
+            
                      • 
+
                    • 
+              The functions have extern "C" linkage, and so are usable
+              from other languages (not just C and C++).
+            
                      • 
+
                    • 
+              C99 and C++ TR1 Standard compatibility.
+            
                      • 
 
                    
 
                    
         
                    
@@ -67,24 +67,24 @@
         
                    
 
                    
         
                    
-
                      
-
                    • 
-            You will need to compile and link to the external Boost.Math libraries.
-          
                      • 
-
                    • 
-            Limited to support for the types, float,
-            double and long double.
-          
                      • 
-
                    • 
-            Error handling is handled via setting ::errno and returning NaN's and
-            infinities: this may be less flexible than an C++ exception based approach.
-          
                      • 
+
                        
+
                      • 
+              You will need to compile and link to the external Boost.Math libraries.
+            
                        • 
+
                      • 
+              Limited to support for the types, float,
+              double and long double.
+            
                        • 
+
                      • 
+              Error handling is handled via setting ::errno and returning NaN's and
+              infinities: this may be less flexible than an C++ exception based approach.
+            
                        • 
 
                      
 
                      
         
                      
 
                      
-
+
@@ -248,7 +248,7 @@
         
                      
 
                      [Note][Note]
 Note
 
                      
 
                      
@@ -112,122 +112,122 @@
 
 
                      
 
-                
                      
-                  Name
-                
                      
+                  
                      
+                    Name
+                  
                      
                                       		
 
-                
                      
-                  Type
-                
                      
+                  
                      
+                    Type
+                  
                      
                                       		
 
-                
                      
-                  Functions
-                
                      
+                  
                      
+                    Functions
+                  
                      
                                       		
 
                      
 
 
                      
 
-                
                      
-                  boost_math_c99f-<suffix>
-                
                      
+                  
                      
+                    boost_math_c99f-<suffix>
+                  
                      
                                       		
 
-                
                      
-                  float
-                
                      
+                  
                      
+                    float
+                  
                      
                                       		
 
-                
                      
-                  C99 Functions
-                
                      
+                  
                      
+                    C99 Functions
+                  
                      
                                       		
 
                      
 
                      
 
-                
                      
-                  boost_math_c99-<suffix>
-                
                      
+                  
                      
+                    boost_math_c99-<suffix>
+                  
                      
                                       		
 
-                
                      
-                  double
-                
                      
+                  
                      
+                    double
+                  
                      
                                       		
 
-                
                      
-                  C99 Functions
-                
                      
+                  
                      
+                    C99 Functions
+                  
                      
                                       		
 
                      
 
                      
 
-                
                      
-                  boost_math_c99l-<suffix>
-                
                      
+                  
                      
+                    boost_math_c99l-<suffix>
+                  
                      
                                       		
 
-                
                      
-                  long double
-                
                      
+                  
                      
+                    long double
+                  
                      
                                       		
 
-                
                      
-                  C99 Functions
-                
                      
+                  
                      
+                    C99 Functions
+                  
                      
                                       		
 
                      
 
                      
 
-                
                      
-                  boost_math_tr1f-<suffix>
-                
                      
+                  
                      
+                    boost_math_tr1f-<suffix>
+                  
                      
                                       		
 
-                
                      
-                  float
-                
                      
+                  
                      
+                    float
+                  
                      
                                       		
 
-                
                      
-                  TR1 Functions
-                
                      
+                  
                      
+                    TR1 Functions
+                  
                      
                                       		
 
                      
 
                      
 
-                
                      
-                  boost_math_tr1-<suffix>
-                
                      
+                  
                      
+                    boost_math_tr1-<suffix>
+                  
                      
                                       		
 
-                
                      
-                  double
-                
                      
+                  
                      
+                    double
+                  
                      
                                       		
 
-                
                      
-                  TR1 Functions
-                
                      
+                  
                      
+                    TR1 Functions
+                  
                      
                                       		
 
                      
 
                      
 
-                
                      
-                  boost_math_tr1l-<suffix>
-                
                      
+                  
                      
+                    boost_math_tr1l-<suffix>
+                  
                      
                                       		
 
-                
                      
-                  long double
-                
                      
+                  
                      
+                    long double
+                  
                      
                                       		
 
-                
                      
-                  TR1 Functions
-                
                      
+                  
                      
+                    TR1 Functions
+                  
                      
                                       		
 
                      
                       
 
                      
-
+
                      
 
                      [Note][Note]
 Note
 
                      
 
                      
@@ -273,7 +273,7 @@
         
                      
 
                      
-
+
                      
 
                      [Note][Note]
 Note
 
                      
 
                      
@@ -285,7 +285,7 @@
         
         
                      
 
                      
-
+
           Usage Recomendations
         
                      
 
                      
@@ -295,14 +295,14 @@
         
                      
 
                      
         
                      
-
                        
-
                      • 
-            To include the header only versions of the functions and have an easier
-            time linking, but a longer compile time.
-          
                        • 
-
                      • 
-            To include the TR1 headers and link against an external library.
-          
                        • 
+
                          
+
                        • 
+              To include the header only versions of the functions and have an easier
+              time linking, but a longer compile time.
+            
                          • 
+
                        • 
+              To include the TR1 headers and link against an external library.
+            
                          • 
 
                        
 
                        
         
                        
@@ -336,7 +336,7 @@
         
         
                        
 
                        
-
+
           Supported
           C99 Functions
         
                        
@@ -440,7 +440,7 @@
         
         
                        
 
                        
-
+
           Supported
           TR1 Functions
         
                        
@@ -579,7 +579,7 @@
         
         
                        
 
                        
-
+
           Currently
           Unsupported C99 Functions
         
                        
@@ -650,7 +650,7 @@
         
         
                        
 
                        
-
+
           Currently
           Unsupported TR1 Functions
         
                        
@@ -683,7 +683,7 @@
 
                      
 
                      
 
                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html
index 9b6447ed3..43d362c01 100644
--- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html
@@ -2,8 +2,8 @@
 
 
 TR1 C Functions Quick Reference
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
                      
 
                      
 
                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                      
-
                      
+
                      
 
                      
 
                      
-
+
         Supported
         TR1 Functions
       
                      
@@ -163,7 +163,7 @@
 expint(2);      // integer argument is treated as a double, returns double.
 
                  
 
                  
-
+
         Quick Reference
       
                  
 
                  // [5.2.1.1] associated Laguerre polynomials:
@@ -494,7 +494,7 @@
         for the full template (header only) version of this function.
       
                  
 
                  
-
+
         Currently
         Unsupported TR1 Functions
       
                  
@@ -511,7 +511,7 @@
 
                  
 
                  
-
+
                  
 
                  [Note][Note]
 Note
 
                  
 
                  
@@ -532,7 +532,7 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview.html
index b0168c85c..d9c24dc1b 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview.html
@@ -2,8 +2,8 @@
 
 
 Overview
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
@@ -66,7 +66,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html
index 56f6a6b26..c933c6bf4 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html
@@ -2,8 +2,8 @@
 
 
 If and How to Build the Library and its Examples and Tests
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
 
                  
-
+
         Building
         the Library
       
                  
@@ -71,7 +71,7 @@
       
                  
 
                  
-
+
                  
 
                  [Note][Note]
 Note
 
                  
 
                  
@@ -93,7 +93,7 @@
         building the sources. Boost.Build will do this automatically when appropriate.
       
                  
 
                  
-
+
         Building
         the Examples
       
                  
@@ -104,7 +104,7 @@
         the Boost headers are in your compilers #include search path.
       
                  
 
                  
-
+
         Building
         the Tests
       
                  
@@ -150,7 +150,7 @@
 
                  
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html
index a446e183d..58413ad45 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html
@@ -2,8 +2,8 @@
 
 
 Compilers
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
@@ -37,7 +37,7 @@
 
                  
         
                  
 
                  
-
                  Table 9. Supported/Tested Compilers
                  
+
                  Table 9. Supported/Tested Compilers
                  
 
                  @@ -47,500 +47,509 @@
 
+                  
                  
+                    Platform
+                  
                  
+                
+                  
                  
+                    Compiler
+                  
                  
+                
+                  
                  
+                    Has long double support
+                  
                  
+                
+                  
                  
+                    Notes
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    MSVC 7.1 and later
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free at level 4 with this
+                    compiler.
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    Intel 8.1 and later
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free at level 4 with this
+                    compiler. However, The tests cases tend to generate a lot of
+                    warnings relating to numeric underflow of the test data: these
+                    are harmless.
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    GNU Mingw32 C++
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    GNU Cygwin C++
+                  
                  
+                
+                  
                  
+                    No
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                  
+                  
                  
+                    Long double support has been disabled because there are no native
+                    long double C std library functions available.
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    Borland C++ 5.8.2 (Developer studio 2006)
+                  
                  
+                
+                  
                  
+                    No
+                  
                  
+                
+                  
                  
+                    We have only partial compatability with this compiler:
+                  
                  
+                  
                  
+                    Long double support has been disabled because the native long
+                    double C standard library functions really only forward to the
+                    double versions. This can result in unpredictable behaviour when
+                    using the long double overloads: for example sqrtl
+                    applied to a finite value, can result in an infinite result.
+                  
                  
+                  
                  
+                    Some functions still fail to compile, there are no known workarounds
+                    at present.
+                  
                  
+                
+                  
                  
+                    Linux
+                  
                  
+                
+                  
                  
+                    GNU C++ 3.4 and later
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                  
+                
+                  
                  
+                    Linux
+                  
                  
+                
+                  
                  
+                    Intel C++ 10.0 and later
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler. However, The tests cases tend to generate a lot of
+                    warnings relating to numeric underflow of the test data: these
+                    are harmless.
+                  
                  
+                
+                  
                  
+                    Linux
+                  
                  
+                
+                  
                  
+                    Intel C++ 8.1 and 9.1
+                  
                  
+                
+                  
                  
+                    No
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    Long double support has been disabled with these compiler releases
+                    because calling the standard library long double math functions
+                    can result in a segfault. The issue is Linux distribution and
+                    glibc version specific and is Intel bug report #409291. Fully
+                    up to date releases of Intel 9.1 (post version l_cc_c_9.1.046)
+                    shouldn't have this problem. If you need long double support
+                    with this compiler, then comment out the define of BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+                    at line 55 of boost/math/tools/config.hpp.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler. However, The tests cases tend to generate a lot of
+                    warnings relating to numeric underflow of the test data: these
+                    are harmless.
+                  
                  
+                
+                  
                  
+                    Linux
+                  
                  
+                
+                  
                  
+                    QLogic PathScale 3.0
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    Some tests involving conceptual checks fail to build, otherwise
+                    there appear to be no issues.
+                  
                  
+                
+                  
                  
+                    Linux
+                  
                  
+                
+                  
                  
+                    Sun Studio 12
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    Some tests involving function overload resolution fail to build,
+                    these issues should be rairly encountered in practice.
+                  
                  
+                
+                  
                  
+                    Solaris
+                  
                  
+                
+                  
                  
+                    Sun Studio 12
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    Some tests involving function overload resolution fail to build,
+                    these issues should be rairly encountered in practice.
+                  
                  
+                
+                  
                  
+                    Solaris
+                  
                  
+                
+                  
                  
+                    GNU C++ 4.x
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                  
+                
+                  
                  
+                    HP Tru64
+                  
                  
+                
+                  
                  
+                    Compaq C++ 7.1
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                
+                  
                  
+                    HP-UX Itanium
+                  
                  
+                
+                  
                  
+                    HP aCC 6.x
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    Unfortunately this compiler emits quite a few warnings from libraries
+                    upon which we depend (TR1, Array etc).
+                  
                  
+                
+                  
                  
+                    HP-UX PA-RISC
+                  
                  
+                
+                  
                  
+                    GNU C++ 3.4
+                  
                  
+                
+                  
                  
+                    No
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                
+                  
                  
+                    Apple Mac OS X, Intel
+                  
                  
+                
+                  
                  
+                    Darwin/GNU C++ 4.x
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                
+                  
                  
+                    Apple Mac OS X, PowerPC
+                  
                  
+                
+                  
                  
+                    Darwin/GNU C++ 4.x
+                  
                  
+                
+                  
                  
+                    No
+                  
                  
+                
+                  
                  
+                    All tests OK.
+                  
                  
+                  
                  
+                    Long double support has been disabled on this platform due to
+                    the rather strange nature of Darwin's 106-bit long double implementation.
+                    It should be possible to make this work if someone is prepared
+                    to offer assistance.
+                  
                  
+                
+                  
                  
+                    IMB AIX
+                  
                  
+                
+                  
                  
+                    IBM xlc 5.3
+                  
                  
+                
+                  
                  
+                    Yes
+                  
                  
+                
+                  
                  
+                    All tests pass except for our fpclassify tests which fail due
+                    to a bug in std::numeric_limits,
+                    the bug effects the test code, not fpclassify itself. The IBM
+                    compiler group are aware of the problem.
+                  
                  
+                
                  
 
 

 
                  
 
-              
                  
-                Platform
-              
                  
-                                		
 
-              
                  
-                Compiler
-              
                  
-                                		
 
-              
                  
-                Has long double support
-              
                  
-                                		
 
-              
                  
-                Notes
-              
                  
-                                		
 
                  
 
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                MSVC 7.1 and later
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free at level 4 with this compiler.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                Intel 8.1 and later
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free at level 4 with this compiler.
-                However, The tests cases tend to generate a lot of warnings relating
-                to numeric underflow of the test data: these are harmless.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                GNU Mingw32 C++
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                GNU Cygwin C++
-              
                  
-                                		
 
-              
                  
-                No
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                  
-              
                  
-                Long double support has been disabled because there are no native
-                long double C std library functions available.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                Borland C++ 5.8.2 (Developer studio 2006)
-              
                  
-                                		
 
-              
                  
-                No
-              
                  
-                                		
 
-              
                  
-                We have only partial compatability with this compiler:
-              
                  
-              
                  
-                Long double support has been disabled because the native long double
-                C standard library functions really only forward to the double versions.
-                This can result in unpredictable behaviour when using the long double
-                overloads: for example sqrtl
-                applied to a finite value, can result in an infinite result.
-              
                  
-              
                  
-                Some functions still fail to compile, there are no known workarounds
-                at present.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Linux
-              
                  
-                                		
 
-              
                  
-                GNU C++ 3.4 and later
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Linux
-              
                  
-                                		
 
-              
                  
-                Intel C++ 10.0 and later
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free with -Wall with this compiler.
-                However, The tests cases tend to generate a lot of warnings relating
-                to numeric underflow of the test data: these are harmless.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Linux
-              
                  
-                                		
 
-              
                  
-                Intel C++ 8.1 and 9.1
-              
                  
-                                		
 
-              
                  
-                No
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                Long double support has been disabled with these compiler releases
-                because calling the standard library long double math functions can
-                result in a segfault. The issue is Linux distribution and glibc version
-                specific and is Intel bug report #409291. Fully up to date releases
-                of Intel 9.1 (post version l_cc_c_9.1.046) shouldn't have this problem.
-                If you need long double support with this compiler, then comment
-                out the define of BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS at line
-                55 of boost/math/tools/config.hpp.
-              
                  
-              
                  
-                We aim to keep our headers warning free with -Wall with this compiler.
-                However, The tests cases tend to generate a lot of warnings relating
-                to numeric underflow of the test data: these are harmless.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Linux
-              
                  
-                                		
 
-              
                  
-                QLogic PathScale 3.0
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                Some tests involving conceptual checks fail to build, otherwise there
-                appear to be no issues.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Linux
-              
                  
-                                		
 
-              
                  
-                Sun Studio 12
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                Some tests involving function overload resolution fail to build,
-                these issues should be rairly encountered in practice.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Solaris
-              
                  
-                                		
 
-              
                  
-                Sun Studio 12
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                Some tests involving function overload resolution fail to build,
-                these issues should be rairly encountered in practice.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Solaris
-              
                  
-                                		
 
-              
                  
-                GNU C++ 4.x
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                HP Tru64
-              
                  
-                                		
 
-              
                  
-                Compaq C++ 7.1
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                HP-UX Itanium
-              
                  
-                                		
 
-              
                  
-                HP aCC 6.x
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                Unfortunately this compiler emits quite a few warnings from libraries
-                upon which we depend (TR1, Array etc).
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                HP-UX PA-RISC
-              
                  
-                                		
 
-              
                  
-                GNU C++ 3.4
-              
                  
-                                		
 
-              
                  
-                No
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Apple Mac OS X, Intel
-              
                  
-                                		
 
-              
                  
-                Darwin/GNU C++ 4.x
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Apple Mac OS X, PowerPC
-              
                  
-                                		
 
-              
                  
-                Darwin/GNU C++ 4.x
-              
                  
-                                		
 
-              
                  
-                No
-              
                  
-                                		
 
-              
                  
-                All tests OK.
-              
                  
-              
                  
-                Long double support has been disabled on this platform due to the
-                rather strange nature of Darwin's 106-bit long double implementation.
-                It should be possible to make this work if someone is prepared to
-                offer assistance.
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                IMB AIX
-              
                  
-                                		
 
-              
                  
-                IBM xlc 5.3
-              
                  
-                                		
 
-              
                  
-                Yes
-              
                  
-                                		
 
-              
                  
-                All tests pass except for our fpclassify tests which fail due to
-                a bug in std::numeric_limits, the bug effects
-                the test code, not fpclassify itself. The IBM compiler group are
-                aware of the problem.
-              
                  
-                                		
 
                  
                   
 
                  
 
                  
-

                   
                  
+

                  
+        
                  
 
                  
-
                  Table 10. Unsupported Compilers
                  
+
                  Table 10. Unsupported Compilers
                  
 
                  @@ -548,40 +557,40 @@
 
+                  
                  
+                    Platform
+                  
                  
+                
+                  
                  
+                    Compiler
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    Borland C++ 5.9.2 (Borland Developer Studio 2007)
+                  
                  
+                
+                  
                  
+                    Windows
+                  
                  
+                
+                  
                  
+                    MSVC 6 and 7
+                  
                  
+                
                  
 
 

 
                  
 
-              
                  
-                Platform
-              
                  
-                                		
 
-              
                  
-                Compiler
-              
                  
-                                		
 
                  
 
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                Borland C++ 5.9.2 (Borland Developer Studio 2007)
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                Windows
-              
                  
-                                		
 
-              
                  
-                MSVC 6 and 7
-              
                  
-                                		
 
                  
                   
 
                  
@@ -624,7 +633,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
index 85b81b40e..3c2b46b79 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
@@ -2,8 +2,8 @@
 
 
 Contact Info and Support
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
  Contact Info and
       Support
@@ -30,15 +30,16 @@
 
                  
         The main support for this library is via the Boost mailing lists:
       
                  
-
                    
-
                  • 
-          Use the boost-user
-          list for general support questions.
-        
                    • 
-
                  • 
-          Use the boost-developer
-          list for discussion about implementation and or submission of extensions.
-        
                    • 
+
                    
 
                    
         You can also find JM at john - at - johnmaddock.co.uk and PAB at pbristow
@@ -57,7 +58,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
index 6292fa6f4..828f5dca1 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
@@ -2,8 +2,8 @@
 
 
 Directory and File Structure
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
                    
-
+
         boost/math
       
                    
 
                    
@@ -36,44 +36,44 @@
 
                    
 
                    /concepts/
                    
 
                    
-            Prototype defining the essential features
-            of a RealType class (see real_concept.hpp). Most applications will use
-            double as the RealType (and
-            short typedef names of distributions
-            are reserved for this type where possible), a few will use float or long
-            double, but it is also possible
-            to use higher precision types like NTL::RR
-            that conform to the requirements specified by real_concept.
-          
                    
+              Prototype defining the essential features
+              of a RealType class (see real_concept.hpp). Most applications will
+              use double as the RealType
+              (and short typedef names
+              of distributions are reserved for this type where possible), a few
+              will use float or long double,
+              but it is also possible to use higher precision types like NTL::RR
+              that conform to the requirements specified by real_concept.
+            
                    
 
                    /constants/
                    
 
                    
-            Templated definition of some highly accurate math constants (in constants.hpp).
-          
                    
+              Templated definition of some highly accurate math constants (in constants.hpp).
+            
                    
 
                    /distributions/
                    
 
                    
-            Distributions used in mathematics and, especially, statistics: Gaussian,
-            Students-t, Fisher, Binomial etc
-          
                    
+              Distributions used in mathematics and, especially, statistics: Gaussian,
+              Students-t, Fisher, Binomial etc
+            
                    
 
                    /policies/
                    
 
                    
-            Policy framework, for handling user requested behaviour modifications.
-          
                    
+              Policy framework, for handling user requested behaviour modifications.
+            
                    
 
                    /special_functions/
                    
 
                    
-            Math functions generally regarded as 'special', like beta, cbrt, erf,
-            gamma, lgamma, tgamma ... (Some of these are specified in C++, and C99/TR1,
-            and perhaps TR2).
-          
                    
+              Math functions generally regarded as 'special', like beta, cbrt, erf,
+              gamma, lgamma, tgamma ... (Some of these are specified in C++, and
+              C99/TR1, and perhaps TR2).
+            
                    
 
                    /tools/
                    
 
                    
-            Tools used by functions, like evaluating polynomials, continued fractions,
-            root finding, precision and limits, and by tests. Some will find application
-            outside this package.
-          
                    
+              Tools used by functions, like evaluating polynomials, continued fractions,
+              root finding, precision and limits, and by tests. Some will find application
+              outside this package.
+            
                    
 
                    
 
                    
 
                    
-
+
         boost/libs
       
                    
 
                    
@@ -81,29 +81,29 @@
 
                    
 
                    /doc/
                    
 
                    
-            Documentation source files in Quickbook format processed into html and
-            pdf formats.
-          
                    
+              Documentation source files in Quickbook format processed into html
+              and pdf formats.
+            
                    
 
                    /examples/
                    
 
                    
-            Examples and demos of using math functions and distributions.
-          
                    
+              Examples and demos of using math functions and distributions.
+            
                    
 
                    /performance/
                    
 
                    
-            Performance testing and tuning program.
-          
                    
+              Performance testing and tuning program.
+            
                    
 
                    /test/
                    
 
                    
-            Test files, in various .cpp files, most using Boost.Test (some with test
-            data as .ipp files, usually generated using NTL RR type with ample precision
-            for the type, often for precisions suitable for up to 256-bit significand
-            real types).
-          
                    
+              Test files, in various .cpp files, most using Boost.Test (some with
+              test data as .ipp files, usually generated using NTL RR type with ample
+              precision for the type, often for precisions suitable for up to 256-bit
+              significand real types).
+            
                    
 
                    /tools/
                    
 
                    
-            Programs used to generate test data. Also changes to the NTL
-            released package to provide a few additional (and vital) extra features.
-          
                    
+              Programs used to generate test data. Also changes to the NTL
+              released package to provide a few additional (and vital) extra features.
+            
                    
 
                    
 
                    
 
                    
@@ -119,7 +119,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
index f57c579b3..a1b5bffab 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
@@ -2,8 +2,8 @@
 
 
 Error Handling
-
-
+
+
 
 
 
@@ -20,27 +20,27 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
                    
-
+
         Quick
         Reference
       
                    
 
                    
         Handling of errors by this library is split into two orthogonal parts:
       
                    
-
                      
-
                    • 
-          What kind of error has been raised?
-        
                      • 
-
                    • 
-          What should be done when the error is raised?
-        
                      • 
+
                        
+
                      • 
+            What kind of error has been raised?
+          
                        • 
+
                      • 
+            What should be done when the error is raised?
+          
                        • 
 
                      
 
                      
         The kinds of errors that can be raised are:
@@ -50,48 +50,50 @@
 
                      
 
                      Domain Error
                      
 
                      
-            Occurs when one or more arguments to a function are out of range.
-          
                      
+              Occurs when one or more arguments to a function are out of range.
+            
                      
 
                      Pole Error
                      
 
                      
-            Occurs when the particular arguments cause the function to be evaluated
-            at a pole with no well defined residual value. For example if tgamma
-            is evaluated at exactly -2, the function approaches different limiting
-            values depending upon whether you approach from just above or just below
-            -2. Hence the function has no well defined value at this point and a
-            Pole Error will be raised.
-          
                      
+              Occurs when the particular arguments cause the function to be evaluated
+              at a pole with no well defined residual value. For example if tgamma is evaluated
+              at exactly -2, the function approaches different limiting values depending
+              upon whether you approach from just above or just below -2. Hence the
+              function has no well defined value at this point and a Pole Error will
+              be raised.
+            
                      
 
                      Overflow Error
                      
 
                      
-            Occurs when the result is either infinite, or too large to represent
-            in the numeric type being returned by the function.
-          
                      
+              Occurs when the result is either infinite, or too large to represent
+              in the numeric type being returned by the function.
+            
                      
 
                      Underflow Error
                      
 
                      
-            Occurs when the result is not zero, but is too small to be represented
-            by any other value in the type being returned by the function.
-          
                      
+              Occurs when the result is not zero, but is too small to be represented
+              by any other value in the type being returned by the function.
+            
                      
 
                      Denormalisation Error
                      
 
                      
-            Occurs when the returned result would be a denormalised value.
-          
                      
+              Occurs when the returned result would be a denormalised value.
+            
                      
 
                      Rounding Error
                      
 
                      
-            Occurs when the argument to one of the rounding functions trunc,
-            round and modf can not be represented
-            as an integer type, is is outide the range of the result type.
-          
                      
+              Occurs when the argument to one of the rounding functions trunc,
+              round and
+              modf can not
+              be represented as an integer type, is is outide the range of the result
+              type.
+            
                      
 
                      Evaluation Error
                      
 
                      
-            Occurs when an internal error occured that prevented the result from
-            being evaluated: this should never occur, but if it does, then it's likely
-            to be due to an iterative method not converging fast enough.
-          
                      
+              Occurs when an internal error occured that prevented the result from
+              being evaluated: this should never occur, but if it does, then it's
+              likely to be due to an iterative method not converging fast enough.
+            
                      
 
                      Indeterminate Result Error
                      
 
                      
-            Occurs when the result of a function is not defined for the values that
-            were passed to it.
-          
                      
+              Occurs when the result of a function is not defined for the values
+              that were passed to it.
+            
                      
 
                      
 
                    
 
                    
@@ -109,22 +111,22 @@
 
                    
 
                    throw_on_error
                    
 
                    
-            Throws the exception most appropriate to the error condition.
-          
                    
+              Throws the exception most appropriate to the error condition.
+            
                    
 
                    errno_on_error
                    
 
                    
-            Sets ::errno to an appropriate value, and then returns the most appropriate
-            result
-          
                    
+              Sets ::errno to an appropriate value, and then returns the most appropriate
+              result
+            
                    
 
                    ignore_error
                    
 
                    
-            Ignores the error and simply the returns the most appropriate result.
-          
                    
+              Ignores the error and simply the returns the most appropriate result.
+            
                    
 
                    user_error
                    
 
                    
-            Calls a user-supplied
-            error handler.
-          
                    
+              Calls a user-supplied
+              error handler.
+            
                    
 
                    
 
                    
 
                    
@@ -132,7 +134,7 @@
         the default action for each error shown in bold:
       
                    
 
                    
-
                    Table 1. Possible Actions for Domain Errors
                    
+
                    Table 1. Possible Actions for Domain Errors
                    
 
                    @@ -140,74 +142,74 @@
 
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws std::domain_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to EDOM and returns
+                  std::numeric_limits<T>::quiet_NaN()
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns std::numeric_limits<T>::quiet_NaN()
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_domain_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 

 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws std::domain_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to EDOM and returns
-              std::numeric_limits<T>::quiet_NaN()
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns std::numeric_limits<T>::quiet_NaN()
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_domain_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 2. Possible Actions for Pole Errors
                    
+
                    Table 2. Possible Actions for Pole Errors
                    
 
                    @@ -215,74 +217,74 @@
 
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws std::domain_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to EDOM and returns
+                  std::numeric_limits<T>::quiet_NaN()
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns std::numeric_limits<T>::quiet_NaN()
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_pole_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 

 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws std::domain_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to EDOM and returns
-              std::numeric_limits<T>::quiet_NaN()
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns std::numeric_limits<T>::quiet_NaN()
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_pole_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 3. Possible Actions for Overflow Errors
                    
+
                    Table 3. Possible Actions for Overflow Errors
                    
 
                    @@ -290,74 +292,74 @@
 
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws std::overflow_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to ERANGE and returns
+                  std::numeric_limits<T>::infinity()
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns std::numeric_limits<T>::infinity()
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_overflow_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 

 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws std::overflow_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to ERANGE and returns
-              std::numeric_limits<T>::infinity()
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns std::numeric_limits<T>::infinity()
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_overflow_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 4. Possible Actions for Underflow Errors
                    
+
                    Table 4. Possible Actions for Underflow Errors
                    
 
                    @@ -365,74 +367,74 @@
 
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws std::underflow_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to ERANGE and returns
+                  0.
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns 0
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_underflow_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 

 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws std::underflow_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to ERANGE and returns
-              0.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns 0
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_underflow_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 5. Possible Actions for Denorm Errors
                    
+
                    Table 5. Possible Actions for Denorm Errors
                    
 
                    @@ -440,74 +442,74 @@
 
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws std::underflow_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to ERANGE and returns
+                  the denormalised value.
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns the denormalised value.
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_denorm_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 

 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws std::underflow_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to ERANGE and returns
-              the denormalised value.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns the denormalised value.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_denorm_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 6. Possible Actions for Rounding Errors
                    
+
                    Table 6. Possible Actions for Rounding Errors
                    
 
                    @@ -515,229 +517,225 @@
 
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws boost::math::rounding_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to ERANGE and returns
+                  an unspecified value.
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns the an unspecified value.
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_rounding_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 

 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws boost::math::rounding_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to ERANGE and returns
-              an unspecified value.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns the an unspecified value.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_rounding_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 7. Possible Actions for Internal Evaluation
-      Errors
                    
-
                    
+
                    Table 7. Possible Actions for Internal Evaluation Errors
                    
+
                    
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws boost::math::evaluation_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to EDOM and returns
+                  the closest approximation found.
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns the closest approximation found.
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_evaluation_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 
 
 
 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws boost::math::evaluation_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to EDOM and returns
-              the closest approximation found.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns the closest approximation found.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_evaluation_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
                    Table 8. Possible Actions for Indeterminate Result
-      Errors
                    
-
                    
+
                    Table 8. Possible Actions for Indeterminate Result Errors
                    
+
                    
+                
                    
+                  Action
+                
                    
+              
+                
                    
+                  Behaviour
+                
                    
+              
+                
                    
+                  throw_on_error
+                
                    
+              
+                
                    
+                  Throws std::domain_error
+                
                    
+              
+                
                    
+                  errno_on_error
+                
                    
+              
+                
                    
+                  Sets ::errno
+                  to EDOM and returns
+                  the same value as ignore_error.
+                
                    
+              
+                
                    
+                  ignore_error
+                
                    
+              
+                
                    
+                  Returns a default result that depends on
+                  the function where the error occurred.
+                
                    
+              
+                
                    
+                  user_error
+                
                    
+              
+                
                    
+                  Returns the result of boost::math::policies::user_indeterminate_result_error:
+                  this
+                  function must be defined by the user.
+                
                    
+              
                    
 
 
 
 
 
                    
 
-            
                    
-              Action
-            
                    
-                                		
 
-            
                    
-              Behaviour
-            
                    
-                                		
 
                    
 
 
                    
 
-            
                    
-              throw_on_error
-            
                    
-                                		
 
-            
                    
-              Throws std::domain_error
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              errno_on_error
-            
                    
-                                		
 
-            
                    
-              Sets ::errno
-              to EDOM and returns
-              the same value as ignore_error.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              ignore_error
-            
                    
-                                		
 
-            
                    
-              Returns a default result that depends on the
-              function where the error occurred.
-            
                    
-                                		
 
                    
 
                    
 
-            
                    
-              user_error
-            
                    
-                                		
 
-            
                    
-              Returns the result of boost::math::policies::user_indeterminate_result_error:
-              this
-              function must be defined by the user.
-            
                    
-                                		
 
                    
                     
 
                    
 
                    
 
                    
-
+
         Rationale
       
                    
 
                    
@@ -745,18 +743,18 @@
         the default behaviours were chosen based on feedback during the formal review
         of this library. It was felt that:
       
                    
-
                      
-
                    • 
-          Genuine errors should be flagged with exceptions rather than following
-          C-compatible behaviour and setting ::errno.
-        
                      • 
-
                    • 
-          Numeric underflow and denormalised results were not considered to be fatal
-          errors in most cases, so it was felt that these should be ignored.
-        
                      • 
+
                        
+
                      • 
+            Genuine errors should be flagged with exceptions rather than following
+            C-compatible behaviour and setting ::errno.
+          
                        • 
+
                      • 
+            Numeric underflow and denormalised results were not considered to be
+            fatal errors in most cases, so it was felt that these should be ignored.
+          
                        • 
 
                      
 
                      
-
+
         Finding
         More Information
       
                      
@@ -778,7 +776,7 @@
         The various kind of errors are described in more detail below.
       
                      
 
                      
-
+
         Domain
         Errors
       
                      
@@ -808,53 +806,32 @@
         Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
         6:
       
                      
+
                      
+          "Each of the functions declared above shall return a NaN
+          (Not a Number) if any argument value is a NaN, but it shall not report
+          a domain error. Otherwise, each of the functions declared above shall report
+          a domain error for just those argument values for which:
+        
                      
 
                      
 
                      
-          
                      
+          "the function description's Returns clause explicitly specifies
+          a domain, and those arguments fall outside the specified domain; or
+        
                      
 
                      
-            "Each of the functions declared above shall return a NaN
-            (Not a Number) if any argument value is a NaN, but it shall not report
-            a domain error. Otherwise, each of the functions declared above shall
-            report a domain error for just those argument values for which:
-          
                      
-
                      
-        
                      
-
                      
-
                      
-
                      
-          
                      
-
                      
-            "the function description's Returns clause explicitly
-            specifies a domain, and those arguments fall outside the specified domain;
-            or
-          
                      
-
                      
-          
                      
-
                      
-            "the corresponding mathematical function value has a non-zero
-            imaginary component; or
-          
                      
-
                      
-          
                      
-
                      
-            "the corresponding mathematical function is not mathematically
-            defined.
-          
                      
-
                      
-        
                      
-
                      
-
                      
-
                      
-          
                      
-
                      
-            "Note 2: A mathematical function is mathematically defined
-            for a given set of argument values if it is explicitly defined for that
-            set of argument values or if its limiting value exists and does not depend
-            on the direction of approach."
-          
                      
+          "the corresponding mathematical function value has a non-zero
+          imaginary component; or
+        
                      
 
                      
+          "the corresponding mathematical function is not mathematically
+          defined.
         
                      
 
                      
+
                      
+          "Note 2: A mathematical function is mathematically defined
+          for a given set of argument values if it is explicitly defined for that
+          set of argument values or if its limiting value exists and does not depend
+          on the direction of approach."
+        
                      
 
                      
         Note that in order to support information-rich error messages when throwing
         exceptions, Message must
@@ -871,7 +848,7 @@
         for more details.
       
                      
 
                      
-
+
         Evaluation
         at a pole
       
                      
@@ -910,7 +887,7 @@
         for more details.
       
                      
 
                      
-
+
         Numeric
         Overflow
       
                      
@@ -935,7 +912,7 @@
         doesn't support infinities, the maximum value for the type is returned.
       
                      
 
                      
-
+
         Numeric
         Underflow
       
                      
@@ -958,7 +935,7 @@
         an std::underflow_error C++ exception.
       
                      
 
                      
-
+
         Denormalisation
         Errors
       
                      
@@ -981,7 +958,7 @@
         throws an std::underflow_error C++ exception.
       
                      
 
                      
-
+
         Evaluation
         Errors
       
                      
@@ -1018,7 +995,7 @@
         for more details.
       
                      
 
                      
-
+
         Indeterminate
         Result Errors
       
                      
@@ -1045,7 +1022,7 @@
         the result of 00 is 1, even though the result is actually mathematically indeterminate.
       
                      
 
                      
-
+
         Rounding
         Errors
       
                      
@@ -1085,7 +1062,7 @@
         for more details.
       
                      
 
                      
-
+
         Errors
         from typecasts
       
                      
@@ -1118,7 +1095,7 @@
 
 
                      
 
                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
index 7be03d37b..be338ed3b 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
@@ -2,8 +2,8 @@
 
 
 History and What's New
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                      
 
                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                      
-
                      
+
                      
 
                      
  History and What's
       New
@@ -31,284 +31,286 @@
         
         
                      
 
                      
-
+
           Boost-1.41.0
         
                      
 
                      
         
                      
-
                      • 
-            Significantly improved performance for the incomplete gamma function
-            and it's inverse.
-          
                      
+
                      • 
+              Significantly improved performance for the incomplete gamma function
+              and it's inverse.
+            
                      
 
                      
         
         
                      
 
                      
-
+
           Boost-1.40.0
         
                      
 
                      
         
                      
-
                        
-
                      • 
-            Added support for MPFR as a bignum type.
-          
                        • 
-
                      • 
-            Added some full specializations of the policy classes to reduce compile
-            times.
-          
                        • 
-
                      • 
-            Added logistic and hypergeometric distributions, from Gautam Sewani's
-            Google Summer of Code project.
-          
                        • 
-
                      • 
-            Added Laplace distribution submitted by Thijs van den Berg.
-          
                        • 
-
                      • 
-            Updated performance test code to include new distributions, and improved
-            the performance of the non-central distributions.
-          
                        • 
-
                      • 
-            Added SSE2 optimised Lanczos
-            approximation code, from Gautam Sewani's Google Summer of Code
-            project.
-          
                        • 
-
                      • 
-            Fixed bug in cyl_bessel_i that used an incorrect approximation for ν =
-            0.5, also effects the non-central Chi Square Distribution when ν = 3, see
-            bug report #2877.
-          
                        • 
-
                      • 
-            Fixed minor bugs #2873.
-          
                        • 
+
                          
+
                        • 
+              Added support for MPFR as a bignum type.
+            
                          • 
+
                        • 
+              Added some full specializations of the policy classes to reduce compile
+              times.
+            
                          • 
+
                        • 
+              Added logistic and hypergeometric distributions, from Gautam Sewani's
+              Google Summer of Code project.
+            
                          • 
+
                        • 
+              Added Laplace distribution submitted by Thijs van den Berg.
+            
                          • 
+
                        • 
+              Updated performance test code to include new distributions, and improved
+              the performance of the non-central distributions.
+            
                          • 
+
                        • 
+              Added SSE2 optimised Lanczos
+              approximation code, from Gautam Sewani's Google Summer of Code
+              project.
+            
                          • 
+
                        • 
+              Fixed bug in cyl_bessel_i that used an incorrect approximation for
+              ν = 0.5, also effects the non-central Chi Square Distribution when ν =
+              3, see bug report #2877.
+            
                          • 
+
                        • 
+              Fixed minor bugs #2873.
+            
                          • 
 
                        
 
                        
         
         
                        
 
                        
-
+
           Boost-1.38.0
         
                        
 
                        
         
                        
-
                          
-
                        • 
-            Added Johan Råde's optimised floating point classification routines.
-          
                          • 
-
                        • 
-            Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
-          
                          • 
+
                            
+
                          • 
+              Added Johan Råde's optimised floating point classification routines.
+            
                            • 
+
                          • 
+              Fixed code so that it compiles in GCC's -pedantic mode (bug report
+              #1451).
+            
                            • 
 
                          
 
                          
         
         
                          
 
                          
-
+
           Boost-1.37.0
         
                          
 
                          
         
                          
-
                          • 
-            Improved accuracy and testing of the inverse hypergeometric functions.
-          
                          
+
                          • 
+              Improved accuracy and testing of the inverse hypergeometric functions.
+            
                          
 
                          
         
         
                          
 
                          
-
+
           Boost-1.36.0
         
                          
 
                          
         
                          
-
                            
-
                          • 
-            Added Noncentral Chi Squared Distribution.
-          
                            • 
-
                          • 
-            Added Noncentral Beta Distribution.
-          
                            • 
-
                          • 
-            Added Noncentral F Distribution.
-          
                            • 
-
                          • 
-            Added Noncentral T Distribution.
-          
                            • 
-
                          • 
-            Added Exponential Integral Functions.
-          
                            • 
-
                          • 
-            Added Zeta Function.
-          
                            • 
-
                          • 
-            Added Rounding and Truncation functions.
-          
                            • 
-
                          • 
-            Added Compile time powers of runtime bases.
-          
                            • 
-
                          • 
-            Added SSE2 optimizations for Lanczos evaluation.
-          
                            • 
+
                              
+
                            • 
+              Added Noncentral Chi Squared Distribution.
+            
                              • 
+
                            • 
+              Added Noncentral Beta Distribution.
+            
                              • 
+
                            • 
+              Added Noncentral F Distribution.
+            
                              • 
+
                            • 
+              Added Noncentral T Distribution.
+            
                              • 
+
                            • 
+              Added Exponential Integral Functions.
+            
                              • 
+
                            • 
+              Added Zeta Function.
+            
                              • 
+
                            • 
+              Added Rounding and Truncation functions.
+            
                              • 
+
                            • 
+              Added Compile time powers of runtime bases.
+            
                              • 
+
                            • 
+              Added SSE2 optimizations for Lanczos evaluation.
+            
                              • 
 
                            
 
                            
         
         
                            
 
                            
-
+
           Boost-1.35.0:
           Post Review First Official Release
         
                            
 
                            
         
                            
-
                              
-
                            • 
-            Added Policy based framework that allows fine grained control over function
-            behaviour.
-          
                              • 
-
                            • 
-Breaking change: Changed default behaviour
-            for domain, pole and overflow errors to throw an exception (based on
-            review feedback), this behaviour can be customised using Policy's.
-          
                              • 
-
                            • 
-Breaking change: Changed exception thrown
-            when an internal evaluation error occurs to boost::math::evaluation_error.
-          
                              • 
-
                            • 
-Breaking change: Changed discrete quantiles
-            to return an integer result: this is anything up to 20 times faster than
-            finding the true root, this behaviour can be customised using Policy's.
-          
                              • 
-
                            • 
-            Polynomial/rational function evaluation is now customisable and hopefully
-            faster than before.
-          
                              • 
-
                            • 
-            Added performance test program.
-          
                              • 
+
                                
+
                              • 
+              Added Policy based framework that allows fine grained control over
+              function behaviour.
+            
                                • 
+
                              • 
+              Breaking change: Changed default behaviour
+              for domain, pole and overflow errors to throw an exception (based on
+              review feedback), this behaviour can be customised using Policy's.
+            
                                • 
+
                              • 
+              Breaking change: Changed exception
+              thrown when an internal evaluation error occurs to boost::math::evaluation_error.
+            
                                • 
+
                              • 
+              Breaking change: Changed discrete
+              quantiles to return an integer result: this is anything up to 20 times
+              faster than finding the true root, this behaviour can be customised
+              using Policy's.
+            
                                • 
+
                              • 
+              Polynomial/rational function evaluation is now customisable and hopefully
+              faster than before.
+            
                                • 
+
                              • 
+              Added performance test program.
+            
                                • 
 
                              
 
                              
         
         
                              
 
                              
-
+
           Milestone
           4: Second Review Candidate (1st March 2007)
         
                              
 
                              
         
                              
-
                                
-
                              • 
-            Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
-            them into line with the rest of the code.
-          
                                • 
-
                              • 
-            Added C# "Distribution Explorer" demo application.
-          
                                • 
+
                                  
+
                                • 
+              Moved Xiaogang Zhang's Bessel Functions code into the library, and
+              brought them into line with the rest of the code.
+            
                                  • 
+
                                • 
+              Added C# "Distribution Explorer" demo application.
+            
                                  • 
 
                                
 
                                
         
         
                                
 
                                
-
+
           Milestone
           3: First Review Candidate (31st Dec 2006)
         
                                
 
                                
         
                                
-
                                  
-
                                • 
-            Implemented the main probability distribution and density functions.
-          
                                  • 
-
                                • 
-            Implemented digamma.
-          
                                  • 
-
                                • 
-            Added more factorial functions.
-          
                                  • 
-
                                • 
-            Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
-            harmonic functions from TR1.
-          
                                  • 
-
                                • 
-            Moved Xiaogang Zhang's elliptic integral code into the library, and brought
-            them into line with the rest of the code.
-          
                                  • 
-
                                • 
-            Moved Hubert Holin's existing Boost.Math special functions into this
-            library and brought them into line with the rest of the code.
-          
                                  • 
+
                                    
+
                                  • 
+              Implemented the main probability distribution and density functions.
+            
                                    • 
+
                                  • 
+              Implemented digamma.
+            
                                    • 
+
                                  • 
+              Added more factorial functions.
+            
                                    • 
+
                                  • 
+              Implemented the Hermite, Legendre and Laguerre polynomials plus the
+              spherical harmonic functions from TR1.
+            
                                    • 
+
                                  • 
+              Moved Xiaogang Zhang's elliptic integral code into the library, and
+              brought them into line with the rest of the code.
+            
                                    • 
+
                                  • 
+              Moved Hubert Holin's existing Boost.Math special functions into this
+              library and brought them into line with the rest of the code.
+            
                                    • 
 
                                  
 
                                  
         
         
                                  
 
                                  
-
+
           Milestone
           2: Released September 10th 2006
         
                                  
 
                                  
         
                                  
-
                                    
-
                                  • 
-            Implement preview release of the statistical distributions.
-          
                                    • 
-
                                  • 
-            Added statistical distributions tutorial.
-          
                                    • 
-
                                  • 
-            Implemented root finding algorithms.
-          
                                    • 
-
                                  • 
-            Implemented the inverses of the incomplete gamma and beta functions.
-          
                                    • 
-
                                  • 
-            Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
-          
                                    • 
-
                                  • 
-            Integrated the statistical results generated from the test data with
-            Boost.Test: uses a database of expected results, indexed by test, floating
-            point type, platform, and compiler.
-          
                                    • 
-
                                  • 
-            Improved lgamma near 1 and 2 (rational approximations).
-          
                                    • 
-
                                  • 
-            Improved erf/erfc inverses (rational approximations).
-          
                                    • 
-
                                  • 
-            Implemented Rational function generation (the Remez method).
-          
                                    • 
+
                                      
+
                                    • 
+              Implement preview release of the statistical distributions.
+            
                                      • 
+
                                    • 
+              Added statistical distributions tutorial.
+            
                                      • 
+
                                    • 
+              Implemented root finding algorithms.
+            
                                      • 
+
                                    • 
+              Implemented the inverses of the incomplete gamma and beta functions.
+            
                                      • 
+
                                    • 
+              Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
+            
                                      • 
+
                                    • 
+              Integrated the statistical results generated from the test data with
+              Boost.Test: uses a database of expected results, indexed by test, floating
+              point type, platform, and compiler.
+            
                                      • 
+
                                    • 
+              Improved lgamma near 1 and 2 (rational approximations).
+            
                                      • 
+
                                    • 
+              Improved erf/erfc inverses (rational approximations).
+            
                                      • 
+
                                    • 
+              Implemented Rational function generation (the Remez method).
+            
                                      • 
 
                                    
 
                                    
         
         
                                    
 
                                    
-
+
           Milestone
           1: Released March 31st 2006
         
                                    
 
                                    
         
                                    
-
                                      
-
                                    • 
-            Implement gamma/beta/erf functions along with their incomplete counterparts.
-          
                                      • 
-
                                    • 
-            Generate high quality test data, against which future improvements can
-            be judged.
-          
                                      • 
-
                                    • 
-            Provide tools for the evaluation of infinite series, continued fractions,
-            and rational functions.
-          
                                      • 
-
                                    • 
-            Provide tools for testing against tabulated test data, and collecting
-            statistics on error rates.
-          
                                      • 
-
                                    • 
-            Provide sufficient docs for people to be able to find their way around
-            the library.
-          
                                      • 
+
                                        
+
                                      • 
+              Implement gamma/beta/erf functions along with their incomplete counterparts.
+            
                                        • 
+
                                      • 
+              Generate high quality test data, against which future improvements
+              can be judged.
+            
                                        • 
+
                                      • 
+              Provide tools for the evaluation of infinite series, continued fractions,
+              and rational functions.
+            
                                        • 
+
                                      • 
+              Provide tools for testing against tabulated test data, and collecting
+              statistics on error rates.
+            
                                        • 
+
                                      • 
+              Provide sufficient docs for people to be able to find their way around
+              the library.
+            
                                        • 
 
                                      
 
                                      
         
                                      
@@ -335,7 +337,7 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
index 2e97f2c59..cfd68d5bb 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
@@ -2,8 +2,8 @@
 
 
 About the Math Toolkit
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
-
                                      
+
                                      
 
                                      
@@ -30,7 +30,7 @@
         This library is divided into three interconnected parts:
       
                                      
 
                                      
-
+
         Statistical
         Distributions
       
                                      
@@ -56,7 +56,7 @@
         tests.
       
                                      
 
                                      
-
+
         Mathematical
         Special Functions
       
                                      
@@ -83,7 +83,7 @@
         double.
       
                                      
 
                                      
-
+
         Implementation
         Toolkit
       
                                      
@@ -129,7 +129,7 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
index 98930634f..76f8d84d1 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
@@ -2,8 +2,8 @@
 
 
 Namespaces
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
-
                                      
+
                                      
 
                                      
@@ -69,7 +69,7 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
index de04b6fb3..1a7681952 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
@@ -2,8 +2,8 @@
 
 
 Navigation
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
-
                                      
+
                                      
 
                                      
@@ -31,31 +31,21 @@
         as handy shortcuts for common navigation tasks.
       
                                      
 
                                      
-
+
         Shortcuts
       
                                      
 
                                      
 
                                      
-          
                                      
+          p - Previous page
+        
                                      
 
                                      
-            p - Previous page
-          
                                      
+          n - Next page
+        
                                      
 
                                      
-          
                                      
-
                                      
-            n - Next page
-          
                                      
-
                                      
-          
                                      
-
                                      
-            h - home
-          
                                      
-
                                      
-          
                                      
-
                                      
-            u - Up
-          
                                      
+          h - home
+        
                                      
 
                                      
+          u - Up
         
                                      
 
                                      
 
                                      
@@ -68,65 +58,65 @@
 
 
 
-              
                                      
-                Browser
-              
                                      
+                
                                      
+                  Browser
+                
                                      
               
 
-              
                                      
-                Access Method
-              
                                      
+                
                                      
+                  Access Method
+                
                                      
               
 
 
 
 
-              
                                      
-                Internet Explorer
-              
                                      
+                
                                      
+                  Internet Explorer
+                
                                      
               
 
-              
                                      
-                Alt+Key highlights the link only, so for example to move to the next
-                topic you would need "Alt+n" followed by "Enter".
-              
                                      
+                
                                      
+                  Alt+Key highlights the link only, so for example to move to the
+                  next topic you would need "Alt+n" followed by "Enter".
+                
                                      
               
 
 
 
-              
                                      
-                Firefox 2.0 and later
-              
                                      
+                
                                      
+                  Firefox 2.0 and later
+                
                                      
               
 
-              
                                      
-                Alt+Shift+Key follows the link, so for example "Alt+Shift+n"
-                will take you to the next topic.
-              
                                      
+                
                                      
+                  Alt+Shift+Key follows the link, so for example "Alt+Shift+n"
+                  will take you to the next topic.
+                
                                      
               
 
 
 
-              
                                      
-                Opera
-              
                                      
+                
                                      
+                  Opera
+                
                                      
               
 
-              
                                      
-                Press Shift+Esc followed by the access key.
-              
                                      
+                
                                      
+                  Press Shift+Esc followed by the access key.
+                
                                      
               
 
 
 
-              
                                      
-                Konqueror
-              
                                      
+                
                                      
+                  Konqueror
+                
                                      
               
 
-              
                                      
-                Press and release the Ctrl key, followed by the access key
-              
                                      
+                
                                      
+                  Press and release the Ctrl key, followed by the access key
+                
                                      
               
 
 
@@ -149,7 +139,7 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
index c6a942081..b60b759d4 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
@@ -2,8 +2,8 @@
 
 
 Performance
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                      
 
                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                      
-
                                      
+
                                      
 
                                      
@@ -54,17 +54,17 @@
         
                                      
 
                                      
         
                                      
-
                                        
-
                                      1. 
-            Turn on your compilers optimisations: the difference between "release"
-            and "debug" builds can easily be a factor
-            of 20.
-          
                                        2. 
-
                                      2. 
-            Pick your compiler carefully: performance
-            differences of up to 8 fold have been found between some windows
-            compilers for example.
-          
                                        3. 
+
                                          
+
                                        1. 
+              Turn on your compilers optimisations: the difference between "release"
+              and "debug" builds can easily be a factor
+              of 20.
+            
                                          2. 
+
                                        2. 
+              Pick your compiler carefully: performance
+              differences of up to 8 fold have been found between some windows
+              compilers for example.
+            
                                          3. 
 
                                        
 
                                        
         
                                        
@@ -88,7 +88,7 @@
 
 
                                        
 
                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                        
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
index c2091bbe9..3c7d812a2 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
@@ -2,8 +2,8 @@
 
 
 Configuration and Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                        
 
                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                        
-
                                        
+
                                        
 
                                        
  Configuration
       and Policies
@@ -62,35 +62,35 @@
         
                                        
 
                                        
         
                                        
-
                                          
-
                                        • 
-How
-            results from 'bad' arguments are handled, including those that
-            cannot be fully evaluated.
-          
                                          • 
-
                                        • 
-            How accuracy
-            is controlled by internal promotion to use more precise types.
-          
                                          • 
-
                                        • 
-            What working precision
-            should be used to calculate results.
-          
                                          • 
-
                                        • 
-            What to do when a mathematically
-            undefined function is used: Should this raise a run-time or compile-time
-            error?
-          
                                          • 
-
                                        • 
-            Whether discrete
-            functions, like the binomial, should return real or only integral
-            values, and how they are rounded.
-          
                                          • 
-
                                        • 
-            How many iterations a special function is permitted to perform in a series
-            evaluation or root finding algorithm before it gives up and raises an
-            evaluation_error.
-          
                                          • 
+
                                          
 
                                          
         
                                          
@@ -99,22 +99,22 @@
         
                                          
 
                                          
         
                                          
-
                                            
-
                                          • 
-            Using macros
-            to change any default policy: the is the prefered method for installation
-            wide policies.
-          
                                            • 
-
                                          • 
-            At your chosen namespace
-            scope for distributions and/or functions: this is the prefered
-            method for project, namespace, or translation unit scope policies.
-          
                                            • 
-
                                          • 
-            In an ad-hoc manner by
-            passing a specific policy to a special function, or to a statistical
-            distribution.
-          
                                            • 
+
                                            
 
                                            
       
                                            
@@ -131,7 +131,7 @@
 
 
                                            
 
                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
index 986880373..4b65e99e3 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
@@ -2,8 +2,8 @@
 
 
 Calculation of the Type of the Result
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                            
 
                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
  Calculation
       of the Type of the Result
@@ -53,33 +53,33 @@
 
                                            
         Otherwise, the type of the result is computed using the following logic:
       
                                            
-
                                              
-
                                            1. 
-          Any arguments that are not template arguments are disregarded from further
-          analysis.
-        
                                              2. 
-
                                            2. 
-          For each type in the argument list, if that type is an integer type then
-          it is treated as if it were of type double for the purposes of further
-          analysis.
-        
                                              3. 
-
                                            3. 
-          If any of the arguments is a user-defined class type, then the result type
-          is the first such class type that is constructible from all of the other
-          argument types.
-        
                                              4. 
-
                                            4. 
-          If any of the arguments is of type long
-          double, then the result is of type
-          long double.
-        
                                              5. 
-
                                            5. 
-          If any of the arguments is of type double,
-          then the result is of type double.
-        
                                              6. 
-
                                            6. 
-          Otherwise the result is of type float.
-        
                                              7. 
+
                                                
+
                                              1. 
+            Any arguments that are not template arguments are disregarded from further
+            analysis.
+          
                                                2. 
+
                                              2. 
+            For each type in the argument list, if that type is an integer type then
+            it is treated as if it were of type double for the purposes of further
+            analysis.
+          
                                                3. 
+
                                              3. 
+            If any of the arguments is a user-defined class type, then the result
+            type is the first such class type that is constructible from all of the
+            other argument types.
+          
                                                4. 
+
                                              4. 
+            If any of the arguments is of type long
+            double, then the result is of
+            type long double.
+          
                                                5. 
+
                                              5. 
+            If any of the arguments is of type double,
+            then the result is of type double.
+          
                                                6. 
+
                                              6. 
+            Otherwise the result is of type float.
+          
                                                7. 
 
                                              
 
                                              
         For example:
@@ -143,7 +143,7 @@
 
 
                                              
 
                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                              
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html b/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
index cbfb5d28c..1de79ab97 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
@@ -2,8 +2,8 @@
 
 
 Thread Safety
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                              
 
                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                              
-
                                              
+
                                              
 
                                              
@@ -64,7 +64,7 @@
 
 
                                              
 
                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                              
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html
index 9057293cf..3146dd773 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html
@@ -2,8 +2,8 @@
 
 
 C99 and C++ TR1 C-style Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                              
 
                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                              
-
                                              
+
                                              
 
                                              
  C99 and C++ TR1 C-style
       Functions
@@ -49,17 +49,17 @@
         
                                              
 
                                              
         
                                              
-
                                                
-
                                              • 
-            The header to include is lightweight (i.e. fast to compile).
-          
                                                • 
-
                                              • 
-            The functions have extern "C" linkage, and so are usable from
-            other languages (not just C and C++).
-          
                                                • 
-
                                              • 
-            C99 and C++ TR1 Standard compatibility.
-          
                                                • 
+
                                                  
+
                                                • 
+              The header to include is lightweight (i.e. fast to compile).
+            
                                                  • 
+
                                                • 
+              The functions have extern "C" linkage, and so are usable
+              from other languages (not just C and C++).
+            
                                                  • 
+
                                                • 
+              C99 and C++ TR1 Standard compatibility.
+            
                                                  • 
 
                                                
 
                                                
         
                                                
@@ -68,24 +68,24 @@
         
                                                
 
                                                
         
                                                
-
                                                  
-
                                                • 
-            You will need to compile and link to the external Boost.Math libraries.
-          
                                                  • 
-
                                                • 
-            Limited to support for the types, float,
-            double and long double.
-          
                                                  • 
-
                                                • 
-            Error handling is handled via setting ::errno and returning NaN's and
-            infinities: this may be less flexible than an C++ exception based approach.
-          
                                                  • 
+
                                                    
+
                                                  • 
+              You will need to compile and link to the external Boost.Math libraries.
+            
                                                    • 
+
                                                  • 
+              Limited to support for the types, float,
+              double and long double.
+            
                                                    • 
+
                                                  • 
+              Error handling is handled via setting ::errno and returning NaN's and
+              infinities: this may be less flexible than an C++ exception based approach.
+            
                                                    • 
 
                                                  
 
                                                  
         
                                                  
 
                                                  
-
+
@@ -249,7 +249,7 @@
         
                                                  
 
                                                  [Note][Note]
 Note
 
                                                  
 
                                                  
@@ -113,122 +113,122 @@
 
 
                                                  
 
-                
                                                  
-                  Name
-                
                                                  
+                  
                                                  
+                    Name
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  Type
-                
                                                  
+                  
                                                  
+                    Type
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  Functions
-                
                                                  
+                  
                                                  
+                    Functions
+                  
                                                  
                                                                   		
 
                                                  
 
 
                                                  
 
-                
                                                  
-                  boost_math_c99f-<suffix>
-                
                                                  
+                  
                                                  
+                    boost_math_c99f-<suffix>
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  float
-                
                                                  
+                  
                                                  
+                    float
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  C99 Functions
-                
                                                  
+                  
                                                  
+                    C99 Functions
+                  
                                                  
                                                                   		
 
                                                  
 
                                                  
 
-                
                                                  
-                  boost_math_c99-<suffix>
-                
                                                  
+                  
                                                  
+                    boost_math_c99-<suffix>
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  double
-                
                                                  
+                  
                                                  
+                    double
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  C99 Functions
-                
                                                  
+                  
                                                  
+                    C99 Functions
+                  
                                                  
                                                                   		
 
                                                  
 
                                                  
 
-                
                                                  
-                  boost_math_c99l-<suffix>
-                
                                                  
+                  
                                                  
+                    boost_math_c99l-<suffix>
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  long double
-                
                                                  
+                  
                                                  
+                    long double
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  C99 Functions
-                
                                                  
+                  
                                                  
+                    C99 Functions
+                  
                                                  
                                                                   		
 
                                                  
 
                                                  
 
-                
                                                  
-                  boost_math_tr1f-<suffix>
-                
                                                  
+                  
                                                  
+                    boost_math_tr1f-<suffix>
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  float
-                
                                                  
+                  
                                                  
+                    float
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  TR1 Functions
-                
                                                  
+                  
                                                  
+                    TR1 Functions
+                  
                                                  
                                                                   		
 
                                                  
 
                                                  
 
-                
                                                  
-                  boost_math_tr1-<suffix>
-                
                                                  
+                  
                                                  
+                    boost_math_tr1-<suffix>
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  double
-                
                                                  
+                  
                                                  
+                    double
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  TR1 Functions
-                
                                                  
+                  
                                                  
+                    TR1 Functions
+                  
                                                  
                                                                   		
 
                                                  
 
                                                  
 
-                
                                                  
-                  boost_math_tr1l-<suffix>
-                
                                                  
+                  
                                                  
+                    boost_math_tr1l-<suffix>
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  long double
-                
                                                  
+                  
                                                  
+                    long double
+                  
                                                  
                                                                   		
 
-                
                                                  
-                  TR1 Functions
-                
                                                  
+                  
                                                  
+                    TR1 Functions
+                  
                                                  
                                                                   		
 
                                                  
                                                   
 
                                                  
-
+
                                                  
 
                                                  [Note][Note]
 Note
 
                                                  
 
                                                  
@@ -274,7 +274,7 @@
         
                                                  
 
                                                  
-
+
                                                  
 
                                                  [Note][Note]
 Note
 
                                                  
 
                                                  
@@ -286,7 +286,7 @@
         
         
                                                  
 
                                                  
-
+
           Usage
           Recomendations
         
                                                  
@@ -297,14 +297,14 @@
         
                                                  
 
                                                  
         
                                                  
-
                                                    
-
                                                  • 
-            To include the header only versions of the functions and have an easier
-            time linking, but a longer compile time.
-          
                                                    • 
-
                                                  • 
-            To include the TR1 headers and link against an external library.
-          
                                                    • 
+
                                                      
+
                                                    • 
+              To include the header only versions of the functions and have an easier
+              time linking, but a longer compile time.
+            
                                                      • 
+
                                                    • 
+              To include the TR1 headers and link against an external library.
+            
                                                      • 
 
                                                    
 
                                                    
         
                                                    
@@ -338,7 +338,7 @@
         
         
                                                    
 
                                                    
-
+
           Supported
           C99 Functions
         
                                                    
@@ -442,7 +442,7 @@
         
         
                                                    
 
                                                    
-
+
           Supported
           TR1 Functions
         
                                                    
@@ -581,7 +581,7 @@
         
         
                                                    
 
                                                    
-
+
           Currently
           Unsupported C99 Functions
         
                                                    
@@ -652,7 +652,7 @@
         
         
                                                    
 
                                                    
-
+
           Currently
           Unsupported TR1 Functions
         
                                                    
@@ -685,7 +685,7 @@
 
                                                  
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf.html b/doc/sf_and_dist/html/math_toolkit/perf.html
index bab84069b..ef08dd71b 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf.html
@@ -2,8 +2,8 @@
 
 
 Performance
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
                                                  
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
-
                                                  
+
                                                  
 
                                                  
@@ -51,7 +51,7 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
index 4990de9b0..7aacd6f82 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
@@ -2,8 +2,8 @@
 
 
 Comparing Compilers
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
-
                                                  
+
                                                  
 
                                                  
@@ -35,7 +35,7 @@
         in this respect).
       
                                                  
 
                                                  
-
                                                  Table 48. Performance Comparison of Various Windows Compilers
                                                  
+
                                                  Table 48. Performance Comparison of Various Windows Compilers
                                                  
 
                                                  @@ -45,315 +45,315 @@
 
+                
                                                  
+                  Function
+                
                                                  
+              
+                
                                                  
+                  Intel C++ 10.0
+                
                                                  
+                
                                                  
+                  ( /Ox /Qipo /QxN )
+                
                                                  
+              
+                
                                                  
+                  Microsoft Visual C++ 8.0
+                
                                                  
+                
                                                  
+                  ( /Ox /arch:SSE2 )
+                
                                                  
+              
+                
                                                  
+                  Cygwin G++ 3.4
+                
                                                  
+                
                                                  
+                  ( /O3 )
+                
                                                  
+              
+                
                                                  
+                  erf
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  erf_inv
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  ibeta
+                  and ibetac
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  ibeta_inv
+                  and ibetac_inv
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  ibeta_inva,
+                  ibetac_inva,
+                  ibeta_invb
+                  and ibetac_invb
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  gamma_p
+                  and gamma_q
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  gamma_p_inv
+                  and gamma_q_inv
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  gamma_p_inva
+                  and gamma_q_inva
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
                                                  
 
 

 
                                                  
 
-            
                                                  
-              Function
-            
                                                  
-                                                              		
 
-            
                                                  
-              Intel C++ 10.0
-            
                                                  
-            
                                                  
-              ( /Ox /Qipo /QxN )
-            
                                                  
-                                                              		
 
-            
                                                  
-              Microsoft Visual C++ 8.0
-            
                                                  
-            
                                                  
-              ( /Ox /arch:SSE2 )
-            
                                                  
-                                                              		
 
-            
                                                  
-              Cygwin G++ 3.4
-            
                                                  
-            
                                                  
-              ( /O3 )
-            
                                                  
-                                                              		
 
                                                  
 
 
                                                  
 
-            
                                                  
-              erf
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.118e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.483e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.24
                                                  
 
                                                   
                                                  
 
                                                  (1.336e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              erf_inv
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.439e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.888e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  7.88
                                                  
 
                                                   
                                                  
 
                                                  (3.500e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              ibeta
-              and ibetac
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.631e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.14
                                                  
 
                                                   
                                                  
 
                                                  (1.852e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.05
                                                  
 
                                                   
                                                  
 
                                                  (4.975e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              ibeta_inv
-              and ibetac_inv
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.133e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.19
                                                  
 
                                                   
                                                  
 
                                                  (7.311e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.60
                                                  
 
                                                   
                                                  
 
                                                  (1.597e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              ibeta_inva,
-              ibetac_inva,
-              ibeta_invb
-              and ibetac_invb
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.453e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.16
                                                  
 
                                                   
                                                  
 
                                                  (2.847e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.83
                                                  
 
                                                   
                                                  
 
                                                  (6.947e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              gamma_p
-              and gamma_q
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.735e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.41
                                                  
 
                                                   
                                                  
 
                                                  (9.504e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.78
                                                  
 
                                                   
                                                  
 
                                                  (1.872e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              gamma_p_inv
-              and gamma_q_inv
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.637e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.38
                                                  
 
                                                   
                                                  
 
                                                  (3.631e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.31
                                                  
 
                                                   
                                                  
 
                                                  (8.736e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              gamma_p_inva
-              and gamma_q_inva
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (7.716e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.29
                                                  
 
                                                   
                                                  
 
                                                  (9.982e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.56
                                                  
 
                                                   
                                                  
 
                                                  (1.974e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
                                                   
 
                                                  
@@ -372,7 +372,7 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
index 31abb1476..577f22a0e 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
@@ -2,8 +2,8 @@
 
 
 Comparisons to Other Open Source Libraries
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
-
                                                  
+
                                                  
 
                                                  
  Comparisons to Other
       Open Source Libraries
@@ -34,7 +34,7 @@
       
                                                  
 
                                                  
-
+
                                                  
 
                                                  [Caution][Caution]
 Caution
 
                                                  
 
                                                  
@@ -46,7 +46,7 @@
         
                                                  
 
                                                  
 
                                                  
-
+
         Comparison
         to GSL-1.13 and Cephes
       
                                                  
@@ -64,498 +64,495 @@
 
 
 
-              
                                                  
-                Function
-              
                                                  
+                
                                                  
+                  Function
+                
                                                  
               
 
-              
                                                  
-                Boost
-              
                                                  
+                
                                                  
+                  Boost
+                
                                                  
               
 
-              
                                                  
-                GSL-1.9
-              
                                                  
+                
                                                  
+                  GSL-1.9
+                
                                                  
               
 
-              
                                                  
-                Cephes
-              
                                                  
+                
                                                  
+                  Cephes
+                
                                                  
               
 
 
 
 
-              
                                                  
-                cbrt
-              
                                                  
+                
                                                  
+                  cbrt
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.873e-007s)
                                                  
 
                                                  
-              
                                                  
-              
-
-              
                                                  
-                N/A
-              
                                                  
-              
-
-              
                                                  
                 
                                                  
+              
+
+                
                                                  
+                  N/A
+                
                                                  
+              
+
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.699e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                log1p
-              
                                                  
+                
                                                  
+                  log1p
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.664e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.677e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.189e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                expm1
-              
                                                  
+                
                                                  
+                  expm1
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.760e-008s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.248e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.169e-008s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                tgamma
-              
                                                  
+                
                                                  
+                  tgamma
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.80
                                                  
 
                                                   
                                                  
 
                                                  (2.997e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.54
                                                  
 
                                                   
                                                  
 
                                                  (2.569e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.666e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                lgamma
-              
                                                  
+                
                                                  
+                  lgamma
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.20
                                                  
 
                                                   
                                                  
 
                                                  (3.045e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.14
                                                  
 
                                                   
                                                  
 
                                                  (5.713e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.381e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                erf
-                and erfc
-              
                                                  
+                
                                                  
+                  erf
+                  and erfc
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.483e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (7.052e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.722e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                gamma_p
-                and gamma_q
-              
                                                  
+                
                                                  
+                  gamma_p
+                  and gamma_q
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.182e-007s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.57
                                                  
 
                                                   
                                                  
 
                                                  (2.209e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.29
                                                  
 
                                                   
                                                  
 
                                                  (2.651e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                gamma_p_inv
-                and gamma_q_inv
-              
                                                  
+                
                                                  
+                  gamma_p_inv
+                  and gamma_q_inv
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.943e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                N/A
-              
                                                  
+                
                                                  
+                  N/A
+                
                                                  
               
 
-              
                                                  
-                +INF
-                [1]
-              
                                                  
+                
                                                  
+                  +INF [1]
+                
                                                  
               
 
 
 
-              
                                                  
-                ibeta
-                and ibetac
-              
                                                  
+                
                                                  
+                  ibeta
+                  and ibetac
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.670e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.16
                                                  
 
                                                   
                                                  
 
                                                  (1.935e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.16
                                                  
 
                                                   
                                                  
 
                                                  (1.935e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                ibeta_inv
-                and ibetac_inv
-              
                                                  
+                
                                                  
+                  ibeta_inv
+                  and ibetac_inv
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.075e-006s)
                                                  
 
                                                  
-              
                                                  
-              
-
-              
                                                  
-                N/A
-              
                                                  
-              
-
-              
                                                  
                 
                                                  
+              
+
+                
                                                  
+                  N/A
+                
                                                  
+              
+
+                
                                                  
+                  
                                                  
 
                                                  2.45
                                                  
 
                                                   
                                                  
 
                                                  (1.489e-005s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                cyl_bessel_j
-              
                                                  
+                
                                                  
+                  cyl_bessel_j
+                
                                                  
               
 
-              
                                                  
-                
                                                  
-
                                                  17.89
-                [2]
-                
                                                  
+                
                                                  
+                  
                                                  
+
                                                  17.89[2]
                                                  
 
                                                   
                                                  
 
                                                  (4.248e-005s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.214e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.374e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                cyl_bessel_i
-              
                                                  
+                
                                                  
+                  cyl_bessel_i
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.924e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.487e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.823e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-              
                                                  
-                cyl_bessel_k
-              
                                                  
+                
                                                  
+                  cyl_bessel_k
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.783e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.927e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                N/A
-              
                                                  
+                
                                                  
+                  N/A
+                
                                                  
               
 
 
 
-              
                                                  
-                cyl_neumann
-              
                                                  
+                
                                                  
+                  cyl_neumann
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.465e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.230e-005s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
-              
                                                  
-                
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.977e-006s)
                                                  
 
                                                  
-              
                                                  
+                
                                                  
               
 
 
 
-
                                                  [1] 
+
                                                  [1] 
                     Cephes gets stuck in an infinite loop while trying to execute
                     our test cases.
                   
                                                  
-
                                                  [2] 
+
                                                  [2] 
                     The performance here is dominated by a few cases where the parameters
                     grow very large: faster asymptotic expansions are available,
                     but are of limited (or even frankly terrible) precision. The
@@ -566,7 +563,7 @@
 
 
                                                  
 
                                                  
-
+
         Comparison
         to the R and DCDFLIB Statistical Libraries on Windows
       
                                                  
@@ -577,10 +574,8 @@
         (R-2.9.2 appears not to be buildable with Visual C++).
       
                                                  
 
                                                  
-
                                                  Table 51. A Comparison to the R Statistical Library on Windows
-      XP
                                                  
-
                                                  
+
                                                  Table 51. A Comparison to the R Statistical Library on Windows XP
                                                  
+
                                                  @@ -589,1274 +584,1264 @@
 
+                
                                                  
+                  Statistical Function
+                
                                                  
+              
+                
                                                  
+                  Boost
+                
                                                  
+              
+                
                                                  
+                  R
+                
                                                  
+              
+                
                                                  
+                  DCDFLIB
+                
                                                  
+              
+                
                                                  
+                  Beta
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Beta
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Binomial
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Binomial
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Cauchy
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Cauchy
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Chi
+                  Squared Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Chi
+                  Squared Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Exponential
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Exponential
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Fisher
+                  F Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Fisher
+                  F Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Gamma
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Gamma
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Hypergeometric
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Hypergeometric
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Logistic
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Logistic
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Log-normal
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Log-normal
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Negative
+                  Binomial Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Negative
+                  Binomial Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  Chi Squared Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  Chi Squared Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  F Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  F Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  noncentral
+                  T distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  noncentral
+                  T distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Normal
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Normal
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Poisson
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Poisson
+                  Distribution
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Students
+                  t Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Students
+                  t Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Weibull
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Weibull
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
                                                  
 
 
 

 
                                                  
 
-            
                                                  
-              Statistical Function
-            
                                                  
-                                                              		
 
-            
                                                  
-              Boost
-            
                                                  
-                                                              		
 
-            
                                                  
-              R
-            
                                                  
-                                                              		
 
-            
                                                  
-              DCDFLIB
-            
                                                  
-                                                              		
 
                                                  
 
 
                                                  
 
-            
                                                  
-              Beta Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.08
                                                  
 
                                                   
                                                  
 
                                                  (1.385e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.278e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.06
                                                  
 
                                                   
                                                  
 
                                                  (1.349e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Beta Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.975e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  67.66
-              [1]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  67.66[1]
                                                  
 
                                                   
                                                  
 
                                                  (3.366e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.23
                                                  
 
                                                   
                                                  
 
                                                  (2.103e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Binomial
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.06
                                                  
 
                                                   
                                                  
 
                                                  (4.503e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.81
                                                  
 
                                                   
                                                  
 
                                                  (7.680e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.239e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Binomial
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.254e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.15
                                                  
 
                                                   
                                                  
 
                                                  (3.746e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  7.25
                                                  
 
                                                   
                                                  
 
                                                  (2.358e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Cauchy
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.134e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.08
                                                  
 
                                                   
                                                  
 
                                                  (1.227e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Cauchy
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.203e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.203e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Chi
-              Squared Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.21
                                                  
 
                                                   
                                                  
 
                                                  (5.021e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.83
                                                  
 
                                                   
                                                  
 
                                                  (1.176e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.155e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Chi
-              Squared Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.930e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.72
                                                  
 
                                                   
                                                  
 
                                                  (5.243e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.73
                                                  
 
                                                   
                                                  
 
                                                  (1.106e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Exponential
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.798e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.89
                                                  
 
                                                   
                                                  
 
                                                  (2.236e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Exponential
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.41
                                                  
 
                                                   
                                                  
 
                                                  (9.006e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.380e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Fisher F Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.556e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.34
                                                  
 
                                                   
                                                  
 
                                                  (1.283e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.24
                                                  
 
                                                   
                                                  
 
                                                  (1.183e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Fisher F Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.987e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.33
                                                  
 
                                                   
                                                  
 
                                                  (9.325e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.16
                                                  
 
                                                   
                                                  
 
                                                  (2.205e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Gamma Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.52
                                                  
 
                                                   
                                                  
 
                                                  (6.240e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.11
                                                  
 
                                                   
                                                  
 
                                                  (1.279e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.111e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Gamma Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.24
                                                  
 
                                                   
                                                  
 
                                                  (2.179e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  6.25
                                                  
 
                                                   
                                                  
 
                                                  (1.102e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.764e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Hypergeometric
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  3.60
-              [2]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  3.60[2]
                                                  
 
                                                   
                                                  
 
                                                  (5.987e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.665e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Hypergeometric
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.684e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.53
                                                  
 
                                                   
                                                  
 
                                                  (2.004e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Logistic
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.714e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.24
                                                  
 
                                                   
                                                  
 
                                                  (8.984e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Logistic
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.02
                                                  
 
                                                   
                                                  
 
                                                  (2.084e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.043e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Log-normal
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.579e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.49
                                                  
 
                                                   
                                                  
 
                                                  (5.332e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Log-normal
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.622e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.57
                                                  
 
                                                   
                                                  
 
                                                  (1.507e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Negative
-              Binomial Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.227e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.25
                                                  
 
                                                   
                                                  
 
                                                  (1.403e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.21
                                                  
 
                                                   
                                                  
 
                                                  (1.378e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Negative
-              Binomial Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.594e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  43.43
-              [3]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  43.43[3]
                                                  
 
                                                   
                                                  
 
                                                  (3.732e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.48
                                                  
 
                                                   
                                                  
 
                                                  (2.994e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              Chi Squared Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.16
                                                  
 
                                                   
                                                  
 
                                                  (3.926e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  79.93
                                                  
 
                                                   
                                                  
 
                                                  (1.450e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.814e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              Chi Squared Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.00
                                                  
 
                                                   
                                                  
 
                                                  (3.393e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  393.90
-              [4]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  393.90[4]
                                                  
 
                                                   
                                                  
 
                                                  (2.673e-002s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.786e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              F Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.59
                                                  
 
                                                   
                                                  
 
                                                  (1.128e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (7.087e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.274e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              F Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.750e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.62
                                                  
 
                                                   
                                                  
 
                                                  (7.681e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.274e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              noncentral
-              T distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.41
                                                  
 
                                                   
                                                  
 
                                                  (1.852e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.436e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              noncentral
-              T distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.31
                                                  
 
                                                   
                                                  
 
                                                  (5.768e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  1.00
-              [5]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  1.00[5]
                                                  
 
                                                   
                                                  
 
                                                  (4.411e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Normal
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.373e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.68
                                                  
 
                                                   
                                                  
 
                                                  (1.409e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  6.01
                                                  
 
                                                   
                                                  
 
                                                  (5.029e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Normal
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.29
                                                  
 
                                                   
                                                  
 
                                                  (1.521e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.182e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  10.85
                                                  
 
                                                   
                                                  
 
                                                  (1.283e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Poisson
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.18
                                                  
 
                                                   
                                                  
 
                                                  (5.193e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.98
                                                  
 
                                                   
                                                  
 
                                                  (1.314e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.410e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Poisson
-              Distribution
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.203e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.20
                                                  
 
                                                   
                                                  
 
                                                  (2.642e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  7.86
                                                  
 
                                                   
                                                  
 
                                                  (9.457e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Students
-              t Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.655e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.06
                                                  
 
                                                   
                                                  
 
                                                  (9.166e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.04
                                                  
 
                                                   
                                                  
 
                                                  (8.999e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Students
-              t Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.294e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.36
                                                  
 
                                                   
                                                  
 
                                                  (3.131e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.82
                                                  
 
                                                   
                                                  
 
                                                  (1.106e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Weibull Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.865e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.33
                                                  
 
                                                   
                                                  
 
                                                  (4.341e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Weibull Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.608e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.22
                                                  
 
                                                   
                                                  
 
                                                  (4.410e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
                                                   
 
                                                  
-
                                                  [1] 
-                  There are a small number of our test cases where the R library
-                  fails to converge on a result: these tend to dominate the performance
-                  result.
-                
                                                  
-
                                                  [2] 
-                  This result is somewhat misleading: for small values of the parameters
-                  there is virtually no difference between the two libraries, but
-                  for large values the Boost implementation is much
-                  slower, albeit with much improved precision.
-                
                                                  
-
                                                  [3] 
-                  The R library appears to use a linear-search strategy, that can
-                  perform very badly in a small number of pathological cases, but
-                  may or may not be more efficient in "typical" cases
-                
                                                  
-
                                                  [4] 
-                  There are a small number of our test cases where the R library
-                  fails to converge on a result: these tend to dominate the performance
-                  result.
-                
                                                  
-
                                                  [5] 
-                  There are a small number of our test cases where the R library
-                  fails to converge on a result: these tend to dominate the performance
-                  result.
-                
                                                  
+
                                                  [1] 
+                    There are a small number of our test cases where the R library
+                    fails to converge on a result: these tend to dominate the performance
+                    result.
+                  
                                                  
+
                                                  [2] 
+                    This result is somewhat misleading: for small values of the parameters
+                    there is virtually no difference between the two libraries, but
+                    for large values the Boost implementation is much
+                    slower, albeit with much improved precision.
+                  
                                                  
+
                                                  [3] 
+                    The R library appears to use a linear-search strategy, that can
+                    perform very badly in a small number of pathological cases, but
+                    may or may not be more efficient in "typical" cases
+                  
                                                  
+
                                                  [4] 
+                    There are a small number of our test cases where the R library
+                    fails to converge on a result: these tend to dominate the performance
+                    result.
+                  
                                                  
+
                                                  [5] 
+                    There are a small number of our test cases where the R library
+                    fails to converge on a result: these tend to dominate the performance
+                    result.
+                  
                                                  
 
                                                  
 
                                                  
 
                                                  
 
                                                  
-
+
         Comparison
         to the R Statistical Library on Linux
       
                                                  
@@ -1866,7 +1851,7 @@
         G++ 4.3.3 using -O3 -DNDEBUG=1.
       
                                                  
 
                                                  
-
                                                  Table 52. A Comparison to the R Statistical Library on Linux
                                                  
+
                                                  Table 52. A Comparison to the R Statistical Library on Linux
                                                  
 
                                                  @@ -1876,1269 +1861,1259 @@
 
+                
                                                  
+                  Statistical Function
+                
                                                  
+              
+                
                                                  
+                  Boost
+                
                                                  
+              
+                
                                                  
+                  R
+                
                                                  
+              
+                
                                                  
+                  DCDFLIB
+                
                                                  
+              
+                
                                                  
+                  Beta
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Beta
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Binomial
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Binomial
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Cauchy
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Cauchy
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Chi
+                  Squared Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Chi
+                  Squared Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Exponential
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Exponential
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Fisher
+                  F Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Fisher
+                  F Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Gamma
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Gamma
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Hypergeometric
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Hypergeometric
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Logistic
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Logistic
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Log-normal
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Log-normal
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Negative
+                  Binomial Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Negative
+                  Binomial Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  Chi Squared Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  Chi Squared Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  F Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Noncentral
+                  F Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  noncentral
+                  T distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  noncentral
+                  T distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Normal
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Normal
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Poisson
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Poisson
+                  Distribution
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Students
+                  t Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Students
+                  t Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  Weibull
+                  Distribution CDF
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
+                
                                                  
+                  Weibull
+                  Distribution Quantile
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  NA
+                
                                                  
+              
                                                  
 
 

 
                                                  
 
-            
                                                  
-              Statistical Function
-            
                                                  
-                                                              		
 
-            
                                                  
-              Boost
-            
                                                  
-                                                              		
 
-            
                                                  
-              R
-            
                                                  
-                                                              		
 
-            
                                                  
-              DCDFLIB
-            
                                                  
-                                                              		
 
                                                  
 
 
                                                  
 
-            
                                                  
-              Beta Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.09
                                                  
 
                                                   
                                                  
 
                                                  (3.189e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.526e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.19
                                                  
 
                                                   
                                                  
 
                                                  (1.822e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Beta Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.185e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  30.51
-              [1]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  30.51[1]
                                                  
 
                                                   
                                                  
 
                                                  (3.616e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.52
                                                  
 
                                                   
                                                  
 
                                                  (2.989e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Binomial
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.41
                                                  
 
                                                   
                                                  
 
                                                  (9.175e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.59
                                                  
 
                                                   
                                                  
 
                                                  (7.476e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.081e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Binomial
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.57
                                                  
 
                                                   
                                                  
 
                                                  (6.925e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.407e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  7.43
                                                  
 
                                                   
                                                  
 
                                                  (3.274e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Cauchy
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.594e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.04
                                                  
 
                                                   
                                                  
 
                                                  (1.654e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Cauchy
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.21
                                                  
 
                                                   
                                                  
 
                                                  (1.752e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.448e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Chi
-              Squared Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.61
                                                  
 
                                                   
                                                  
 
                                                  (1.376e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.36
                                                  
 
                                                   
                                                  
 
                                                  (1.243e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.270e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Chi
-              Squared Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.252e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.34
                                                  
 
                                                   
                                                  
 
                                                  (5.700e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.47
                                                  
 
                                                   
                                                  
 
                                                  (1.477e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Exponential
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.342e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.25
                                                  
 
                                                   
                                                  
 
                                                  (1.677e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Exponential
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.827e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.07
                                                  
 
                                                   
                                                  
 
                                                  (9.470e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Fisher F Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.62
                                                  
 
                                                   
                                                  
 
                                                  (2.324e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.19
                                                  
 
                                                   
                                                  
 
                                                  (1.711e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.437e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Fisher F Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.53
                                                  
 
                                                   
                                                  
 
                                                  (1.577e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.033e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.63
                                                  
 
                                                   
                                                  
 
                                                  (2.719e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Gamma Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.18
                                                  
 
                                                   
                                                  
 
                                                  (1.582e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.63
                                                  
 
                                                   
                                                  
 
                                                  (1.309e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.980e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Gamma Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.19
                                                  
 
                                                   
                                                  
 
                                                  (4.770e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  6.94
                                                  
 
                                                   
                                                  
 
                                                  (1.513e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.179e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Hypergeometric
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  2.20
-              [2]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  2.20[2]
                                                  
 
                                                   
                                                  
 
                                                  (3.522e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.601e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Hypergeometric
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (8.279e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.57
                                                  
 
                                                   
                                                  
 
                                                  (2.125e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Logistic
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.398e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.75
                                                  
 
                                                   
                                                  
 
                                                  (2.588e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Logistic
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.893e-008s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.30
                                                  
 
                                                   
                                                  
 
                                                  (1.285e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Log-normal
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.831e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.39
                                                  
 
                                                   
                                                  
 
                                                  (2.539e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Log-normal
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.10
                                                  
 
                                                   
                                                  
 
                                                  (5.551e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.037e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Negative
-              Binomial Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.08
                                                  
 
                                                   
                                                  
 
                                                  (1.563e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.444e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.444e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Negative
-              Binomial Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.700e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  25.92
-              [3]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  25.92[3]
                                                  
 
                                                   
                                                  
 
                                                  (4.407e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.93
                                                  
 
                                                   
                                                  
 
                                                  (3.274e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              Chi Squared Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.06
                                                  
 
                                                   
                                                  
 
                                                  (2.841e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  25.01
                                                  
 
                                                   
                                                  
 
                                                  (1.405e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.617e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              Chi Squared Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  8.47
                                                  
 
                                                   
                                                  
 
                                                  (1.879e-003s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  144.91
-              [4]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  144.91[4]
                                                  
 
                                                   
                                                  
 
                                                  (3.214e-002s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.218e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              F Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  10.33
                                                  
 
                                                   
                                                  
 
                                                  (5.868e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.42
                                                  
 
                                                   
                                                  
 
                                                  (8.058e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (5.682e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Noncentral
-              F Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.64
                                                  
 
                                                   
                                                  
 
                                                  (7.869e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  6.63
                                                  
 
                                                   
                                                  
 
                                                  (9.256e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.396e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              noncentral
-              T distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.91
                                                  
 
                                                   
                                                  
 
                                                  (3.357e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (6.844e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              noncentral
-              T distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.57
                                                  
 
                                                   
                                                  
 
                                                  (9.265e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
-
                                                  1.00
-              [5]
-              
                                                  
+                
                                                  
+                  
                                                  
+
                                                  1.00[5]
                                                  
 
                                                   
                                                  
 
                                                  (5.916e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Normal
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.074e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.16
                                                  
 
                                                   
                                                  
 
                                                  (1.245e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  5.36
                                                  
 
                                                   
                                                  
 
                                                  (5.762e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Normal
-              Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.28
                                                  
 
                                                   
                                                  
 
                                                  (1.902e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.490e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  10.35
                                                  
 
                                                   
                                                  
 
                                                  (1.542e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Poisson
-              Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.43
                                                  
 
                                                   
                                                  
 
                                                  (1.198e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.25
                                                  
 
                                                   
                                                  
 
                                                  (1.110e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.937e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Poisson
-              Distribution
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.11
                                                  
 
                                                   
                                                  
 
                                                  (3.032e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.724e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  4.07
                                                  
 
                                                   
                                                  
 
                                                  (1.110e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Students
-              t Distribution CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  2.17
                                                  
 
                                                   
                                                  
 
                                                  (2.020e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.321e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.10
                                                  
 
                                                   
                                                  
 
                                                  (1.021e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Students
-              t Distribution Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.18
                                                  
 
                                                   
                                                  
 
                                                  (3.972e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.364e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  3.89
                                                  
 
                                                   
                                                  
 
                                                  (1.308e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Weibull Distribution
-              CDF
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.662e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.04
                                                  
 
                                                   
                                                  
 
                                                  (3.808e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              Weibull Distribution
-              Quantile
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.112e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.05
                                                  
 
                                                   
                                                  
 
                                                  (4.317e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              NA
-            
                                                  
-                                                              		
 
                                                  
                                                   
 
                                                  
-
                                                  [1] 
-                  There are a small number of our test cases where the R library
-                  fails to converge on a result: these tend to dominate the performance
-                  result.
-                
                                                  
-
                                                  [2] 
-                  This result is somewhat misleading: for small values of the parameters
-                  there is virtually no difference between the two libraries, but
-                  for large values the Boost implementation is much
-                  slower, albeit with much improved precision.
-                
                                                  
-
                                                  [3] 
-                  The R library appears to use a linear-search strategy, that can
-                  perform very badly in a small number of pathological cases, but
-                  may or may not be more efficient in "typical" cases
-                
                                                  
-
                                                  [4] 
-                  There are a small number of our test cases where the R library
-                  fails to converge on a result: these tend to dominate the performance
-                  result.
-                
                                                  
-
                                                  [5] 
-                  There are a small number of our test cases where the R library
-                  fails to converge on a result: these tend to dominate the performance
-                  result.
-                
                                                  
+
                                                  [1] 
+                    There are a small number of our test cases where the R library
+                    fails to converge on a result: these tend to dominate the performance
+                    result.
+                  
                                                  
+
                                                  [2] 
+                    This result is somewhat misleading: for small values of the parameters
+                    there is virtually no difference between the two libraries, but
+                    for large values the Boost implementation is much
+                    slower, albeit with much improved precision.
+                  
                                                  
+
                                                  [3] 
+                    The R library appears to use a linear-search strategy, that can
+                    perform very badly in a small number of pathological cases, but
+                    may or may not be more efficient in "typical" cases
+                  
                                                  
+
                                                  [4] 
+                    There are a small number of our test cases where the R library
+                    fails to converge on a result: these tend to dominate the performance
+                    result.
+                  
                                                  
+
                                                  [5] 
+                    There are a small number of our test cases where the R library
+                    fails to converge on a result: these tend to dominate the performance
+                    result.
+                  
                                                  
 
                                                  
 
                                                  
 
                                                  
@@ -3156,7 +3131,7 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html
index 126265bd3..c22829a74 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html
@@ -2,8 +2,8 @@
 
 
 Getting the Best Performance from this Library
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
-
                                                  
+
                                                  
 
                                                  
  Getting the Best Performance
       from this Library
@@ -33,7 +33,7 @@
         penalty for using the library in debug mode can be quite large.
       
                                                  
 
                                                  
-
                                                  Table 47. Performance Comparison of Release and Debug Settings
                                                  
+
                                                  Table 47. Performance Comparison of Release and Debug Settings
                                                  
 
                                                  @@ -42,235 +42,235 @@
 
+                
                                                  
+                  Function
+                
                                                  
+              
+                
                                                  
+                  Microsoft Visual C++ 8.0
+                
                                                  
+                
                                                  
+                  Debug Settings: /Od /ZI
+                
                                                  
+              
+                
                                                  
+                  Microsoft Visual C++ 8.0
+                
                                                  
+                
                                                  
+                  Release settings: /Ox /arch:SSE2
+                
                                                  
+              
+                
                                                  
+                  erf
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  erf_inv
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  ibeta
+                  and ibetac
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  ibeta_inv
+                  and ibetac_inv
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  ibeta_inva,
+                  ibetac_inva,
+                  ibeta_invb
+                  and ibetac_invb
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  gamma_p
+                  and gamma_q
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  gamma_p_inv
+                  and gamma_q_inv
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+                  gamma_p_inva
+                  and gamma_q_inva
+                
                                                  
+              
+                
                                                  
+              
+                
                                                  
+              
                                                  
 
 

 
                                                  
 
-            
                                                  
-              Function
-            
                                                  
-                                                              		
 
-            
                                                  
-              Microsoft Visual C++ 8.0
-            
                                                  
-            
                                                  
-              Debug Settings: /Od /ZI
-            
                                                  
-                                                              		
 
-            
                                                  
-              Microsoft Visual C++ 8.0
-            
                                                  
-            
                                                  
-              Release settings: /Ox /arch:SSE2
-            
                                                  
-                                                              		
 
                                                  
 
 
                                                  
 
-            
                                                  
-              erf
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  16.65
                                                  
 
                                                   
                                                  
 
                                                  (1.028e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.483e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              erf_inv
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  19.28
                                                  
 
                                                   
                                                  
 
                                                  (1.215e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (4.888e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              ibeta
-              and ibetac
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  8.32
                                                  
 
                                                   
                                                  
 
                                                  (1.540e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (1.852e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              ibeta_inv
-              and ibetac_inv
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  10.25
                                                  
 
                                                   
                                                  
 
                                                  (7.492e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (7.311e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              ibeta_inva,
-              ibetac_inva,
-              ibeta_invb
-              and ibetac_invb
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  8.57
                                                  
 
                                                   
                                                  
 
                                                  (2.441e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (2.847e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              gamma_p
-              and gamma_q
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  10.98
                                                  
 
                                                   
                                                  
 
                                                  (1.044e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.504e-007s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              gamma_p_inv
-              and gamma_q_inv
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  10.25
                                                  
 
                                                   
                                                  
 
                                                  (3.721e-005s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (3.631e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
 
                                                  
 
-            
                                                  
-              gamma_p_inva
-              and gamma_q_inva
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  11.26
                                                  
 
                                                   
                                                  
 
                                                  (1.124e-004s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
-            
                                                  
-              
                                                  
+                
                                                  
+                  
                                                  
 
                                                  1.00
                                                  
 
                                                   
                                                  
 
                                                  (9.982e-006s)
                                                  
 
                                                  
-            
                                                  
-                                                              		
 
                                                  
                                                   
 
                                                  
@@ -289,7 +289,7 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/interp.html b/doc/sf_and_dist/html/math_toolkit/perf/interp.html
index 26b519a6d..ec3e36b5f 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/interp.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/interp.html
@@ -2,8 +2,8 @@
 
 
 Interpreting these Results
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
-
                                                  
+
                                                  
 
                                                  
@@ -39,7 +39,7 @@
       
                                                  
 
                                                  
-
+
                                                  
 
                                                  [Caution][Caution]
 Caution
 
                                                  
 
                                                  
@@ -65,7 +65,7 @@
 
                                                  
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
index 6021d9ae6..5f511566e 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
@@ -2,8 +2,8 @@
 
 
 Performance Overview
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                  
 
                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                  
-
                                                  
+
                                                  
 
                                                  
@@ -54,17 +54,17 @@
         
                                                  
 
                                                  
         
                                                  
-
                                                    
-
                                                  1. 
-            Turn on your compilers optimisations: the difference between "release"
-            and "debug" builds can easily be a factor
-            of 20.
-          
                                                    2. 
-
                                                  2. 
-            Pick your compiler carefully: performance
-            differences of up to 8 fold have been found between some windows
-            compilers for example.
-          
                                                    3. 
+
                                                      
+
                                                    1. 
+              Turn on your compilers optimisations: the difference between "release"
+              and "debug" builds can easily be a factor
+              of 20.
+            
                                                      2. 
+
                                                    2. 
+              Pick your compiler carefully: performance
+              differences of up to 8 fold have been found between some windows
+              compilers for example.
+            
                                                      3. 
 
                                                    
 
                                                    
         
                                                    
@@ -88,7 +88,7 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
index c36b5bc19..e633d5104 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
@@ -2,8 +2,8 @@
 
 
 The Performance Test Application
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
-
                                                    
+
                                                    
 
                                                    
  The Performance Test
       Application
@@ -58,7 +58,7 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
index 521e41cca..5bb67d69c 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
@@ -2,8 +2,8 @@
 
 
 Performance Tuning Macros
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
-
                                                    
+
                                                    
 
                                                    
@@ -40,88 +40,89 @@
 
 
 
-              
                                                    
-                Macro
-              
                                                    
+                
                                                    
+                  Macro
+                
                                                    
               
 
-              
                                                    
-                Meaning
-              
                                                    
+                
                                                    
+                  Meaning
+                
                                                    
               
 
 
 
 
-              
                                                    
-                BOOST_MATH_POLY_METHOD
-              
                                                    
+                
                                                    
+                  BOOST_MATH_POLY_METHOD
+                
                                                    
               
 
-              
                                                    
-                Determines how polynomials and most rational functions are evaluated.
-                Define to one of the values 0, 1, 2 or 3: see below for the meaning
-                of these values.
-              
                                                    
+                
                                                    
+                  Determines how polynomials and most rational functions are evaluated.
+                  Define to one of the values 0, 1, 2 or 3: see below for the meaning
+                  of these values.
+                
                                                    
               
 
 
 
-              
                                                    
-                BOOST_MATH_RATIONAL_METHOD
-              
                                                    
+                
                                                    
+                  BOOST_MATH_RATIONAL_METHOD
+                
                                                    
               
 
-              
                                                    
-                Determines how symmetrical rational functions are evaluated: mostly
-                this only effects how the Lanczos approximation is evaluated, and
-                how the evaluate_rational
-                function behaves. Define to one of the values 0, 1, 2 or 3: see below
-                for the meaning of these values.
-              
                                                    
+                
                                                    
+                  Determines how symmetrical rational functions are evaluated: mostly
+                  this only effects how the Lanczos approximation is evaluated, and
+                  how the evaluate_rational
+                  function behaves. Define to one of the values 0, 1, 2 or 3: see
+                  below for the meaning of these values.
+                
                                                    
               
 
 
 
-              
                                                    
-                BOOST_MATH_MAX_POLY_ORDER
-              
                                                    
+                
                                                    
+                  BOOST_MATH_MAX_POLY_ORDER
+                
                                                    
               
 
-              
                                                    
-                The maximum order of polynomial or rational function that will be
-                evaluated by a method other than 0 (a simple "for" loop).
-              
                                                    
+                
                                                    
+                  The maximum order of polynomial or rational function that will
+                  be evaluated by a method other than 0 (a simple "for"
+                  loop).
+                
                                                    
               
 
 
 
-              
                                                    
-                BOOST_MATH_INT_TABLE_TYPE(RT, IT)
-              
                                                    
+                
                                                    
+                  BOOST_MATH_INT_TABLE_TYPE(RT, IT)
+                
                                                    
               
 
-              
                                                    
-                Many of the coefficients to the polynomials and rational functions
-                used by this library are integers. Normally these are stored as tables
-                as integers, but if mixed integer / floating point arithmetic is
-                much slower than regular floating point arithmetic then they can
-                be stored as tables of floating point values instead. If mixed arithmetic
-                is slow then add:
-              
                                                    
-              
                                                    
-                #define BOOST_MATH_INT_TABLE_TYPE(RT, IT) RT
-              
                                                    
-              
                                                    
-                to boost/math/tools/user.hpp, otherwise the default of:
-              
                                                    
-              
                                                    
-                #define BOOST_MATH_INT_TABLE_TYPE(RT, IT) IT
-              
                                                    
-              
                                                    
-                Set in boost/math/config.hpp is fine, and may well result in smaller
-                code.
-              
                                                    
+                
                                                    
+                  Many of the coefficients to the polynomials and rational functions
+                  used by this library are integers. Normally these are stored as
+                  tables as integers, but if mixed integer / floating point arithmetic
+                  is much slower than regular floating point arithmetic then they
+                  can be stored as tables of floating point values instead. If mixed
+                  arithmetic is slow then add:
+                
                                                    
+                
                                                    
+                  #define BOOST_MATH_INT_TABLE_TYPE(RT, IT) RT
+                
                                                    
+                
                                                    
+                  to boost/math/tools/user.hpp, otherwise the default of:
+                
                                                    
+                
                                                    
+                  #define BOOST_MATH_INT_TABLE_TYPE(RT, IT) IT
+                
                                                    
+                
                                                    
+                  Set in boost/math/config.hpp is fine, and may well result in smaller
+                  code.
+                
                                                    
               
 
 
@@ -138,85 +139,88 @@
 
 
 
-              
                                                    
-                Value
-              
                                                    
+                
                                                    
+                  Value
+                
                                                    
               
 
-              
                                                    
-                Effect
-              
                                                    
+                
                                                    
+                  Effect
+                
                                                    
               
 
 
 
 
-              
                                                    
-                0
-              
                                                    
+                
                                                    
+                  0
+                
                                                    
               
 
-              
                                                    
-                The polynomial or rational function is evaluated using Horner's method,
-                and a simple for-loop.
-              
                                                    
-              
                                                    
-                Note that if the order of the polynomial or rational function is
-                a runtime parameter, or the order is greater than the value of BOOST_MATH_MAX_POLY_ORDER, then
-                this method is always used, irrespective of the value of BOOST_MATH_POLY_METHOD or BOOST_MATH_RATIONAL_METHOD.
-              
                                                    
+                
                                                    
+                  The polynomial or rational function is evaluated using Horner's
+                  method, and a simple for-loop.
+                
                                                    
+                
                                                    
+                  Note that if the order of the polynomial or rational function is
+                  a runtime parameter, or the order is greater than the value of
+                  BOOST_MATH_MAX_POLY_ORDER,
+                  then this method is always used, irrespective of the value of
+                  BOOST_MATH_POLY_METHOD
+                  or BOOST_MATH_RATIONAL_METHOD.
+                
                                                    
               
 
 
 
-              
                                                    
-                1
-              
                                                    
+                
                                                    
+                  1
+                
                                                    
               
 
-              
                                                    
-                The polynomial or rational function is evaluated without the use
-                of a loop, and using Horner's method. This only occurs if the order
-                of the polynomial is known at compile time and is less than or equal
-                to BOOST_MATH_MAX_POLY_ORDER.
-              
                                                    
+                
                                                    
+                  The polynomial or rational function is evaluated without the use
+                  of a loop, and using Horner's method. This only occurs if the order
+                  of the polynomial is known at compile time and is less than or
+                  equal to BOOST_MATH_MAX_POLY_ORDER.
+                
                                                    
               
 
 
 
-              
                                                    
-                2
-              
                                                    
+                
                                                    
+                  2
+                
                                                    
               
 
-              
                                                    
-                The polynomial or rational function is evaluated without the use
-                of a loop, and using a second order Horner's method. In theory this
-                permits two operations to occur in parallel for polynomials, and
-                four in parallel for rational functions. This only occurs if the
-                order of the polynomial is known at compile time and is less than
-                or equal to BOOST_MATH_MAX_POLY_ORDER.
-              
                                                    
+                
                                                    
+                  The polynomial or rational function is evaluated without the use
+                  of a loop, and using a second order Horner's method. In theory
+                  this permits two operations to occur in parallel for polynomials,
+                  and four in parallel for rational functions. This only occurs if
+                  the order of the polynomial is known at compile time and is less
+                  than or equal to BOOST_MATH_MAX_POLY_ORDER.
+                
                                                    
               
 
 
 
-              
                                                    
-                3
-              
                                                    
+                
                                                    
+                  3
+                
                                                    
               
 
-              
                                                    
-                The polynomial or rational function is evaluated without the use
-                of a loop, and using a second order Horner's method. In theory this
-                permits two operations to occur in parallel for polynomials, and
-                four in parallel for rational functions. This differs from method
-                "2" in that the code is carefully ordered to make the parallelisation
-                more obvious to the compiler: rather than relying on the compiler's
-                optimiser to spot the parallelisation opportunities. This only occurs
-                if the order of the polynomial is known at compile time and is less
-                than or equal to BOOST_MATH_MAX_POLY_ORDER.
-              
                                                    
+                
                                                    
+                  The polynomial or rational function is evaluated without the use
+                  of a loop, and using a second order Horner's method. In theory
+                  this permits two operations to occur in parallel for polynomials,
+                  and four in parallel for rational functions. This differs from
+                  method "2" in that the code is carefully ordered to make
+                  the parallelisation more obvious to the compiler: rather than relying
+                  on the compiler's optimiser to spot the parallelisation opportunities.
+                  This only occurs if the order of the polynomial is known at compile
+                  time and is less than or equal to BOOST_MATH_MAX_POLY_ORDER.
+                
                                                    
               
 
 
@@ -234,7 +238,7 @@
         highly vectorisable processors in the future.
       
                                                    
 
                                                    
-
                                                    Table 49. A Comparison of Polynomial Evaluation Methods
                                                    
+
                                                    Table 49. A Comparison of Polynomial Evaluation Methods
                                                    
 
                                                    @@ -245,375 +249,375 @@
 
+                
                                                    
+                  Compiler/platform
+                
                                                    
+              
+                
                                                    
+                  Method 0
+                
                                                    
+              
+                
                                                    
+                  Method 1
+                
                                                    
+              
+                
                                                    
+                  Method 2
+                
                                                    
+              
+                
                                                    
+                  Method 3
+                
                                                    
+              
+                
                                                    
+                  Microsoft C++ 9.0, Polynomial evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  Microsoft C++ 9.0, Rational evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  Intel C++ 11.1 (Windows), Polynomial evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  Intel C++ 11.1 (Windows), Rational evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  GNU G++ 4.2 (Linux), Polynomial evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  GNU G++ 4.2 (Linux), Rational evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  Intel C++ 10.0 (Linux), Polynomial evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  Intel C++ 10.0 (Linux), Rational evaluation
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
                                                    
 
 

 
                                                    
 
-            
                                                    
-              Compiler/platform
-            
                                                    
-                                                                		
 
-            
                                                    
-              Method 0
-            
                                                    
-                                                                		
 
-            
                                                    
-              Method 1
-            
                                                    
-                                                                		
 
-            
                                                    
-              Method 2
-            
                                                    
-                                                                		
 
-            
                                                    
-              Method 3
-            
                                                    
-                                                                		
 
                                                    
 
 
                                                    
 
-            
                                                    
-              Microsoft C++ 9.0, Polynomial evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.26
                                                    
 
                                                     
                                                    
 
                                                    (7.421e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.22
                                                    
 
                                                     
                                                    
 
                                                    (7.226e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (5.901e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.04
                                                    
 
                                                     
                                                    
 
                                                    (6.115e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              Microsoft C++ 9.0, Rational evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (1.008e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (1.008e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.43
                                                    
 
                                                     
                                                    
 
                                                    (1.445e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.40
                                                    
 
                                                     
                                                    
 
                                                    (1.409e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              Intel C++ 11.1 (Windows), Polynomial evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.18
                                                    
 
                                                     
                                                    
 
                                                    (6.517e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.18
                                                    
 
                                                     
                                                    
 
                                                    (6.505e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (5.516e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (5.516e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              Intel C++ 11.1 (Windows), Rational evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (8.947e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.02
                                                    
 
                                                     
                                                    
 
                                                    (9.130e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.49
                                                    
 
                                                     
                                                    
 
                                                    (1.333e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.04
                                                    
 
                                                     
                                                    
 
                                                    (9.325e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              GNU G++ 4.2 (Linux), Polynomial evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.61
                                                    
 
                                                     
                                                    
 
                                                    (1.220e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.68
                                                    
 
                                                     
                                                    
 
                                                    (1.269e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.23
                                                    
 
                                                     
                                                    
 
                                                    (9.275e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (7.566e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              GNU G++ 4.2 (Linux), Rational evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.26
                                                    
 
                                                     
                                                    
 
                                                    (1.660e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.33
                                                    
 
                                                     
                                                    
 
                                                    (1.758e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (1.318e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.15
                                                    
 
                                                     
                                                    
 
                                                    (1.513e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              Intel C++ 10.0 (Linux), Polynomial evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.15
                                                    
 
                                                     
                                                    
 
                                                    (9.154e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.15
                                                    
 
                                                     
                                                    
 
                                                    (9.154e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (7.934e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (7.934e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              Intel C++ 10.0 (Linux), Rational evaluation
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (1.245e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (1.245e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.35
                                                    
 
                                                     
                                                    
 
                                                    (1.684e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.04
                                                    
 
                                                     
                                                    
 
                                                    (1.294e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
                                                     
 
                                                    
@@ -634,10 +638,10 @@
         tutorial.
       
                                                    
 
                                                    
-
                                                    Table 50. Performance Comparison with and Without Internal
-      Promotion to long double
                                                    
-
                                                    
+
                                                    Table 50. Performance Comparison with and Without Internal Promotion to long
+        double
                                                    
+
                                                    @@ -645,235 +649,235 @@
 
+                
                                                    
+                  Function
+                
                                                    
+              
+                
                                                    
+                  GCC 4.2 , Linux
+                
                                                    
+                
                                                    
+                  (with internal promotion of double to long double).
+                
                                                    
+              
+                
                                                    
+                  GCC 4.2, Linux
+                
                                                    
+                
                                                    
+                  (without promotion of double).
+                
                                                    
+              
+                
                                                    
+                  erf
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  erf_inv
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  ibeta
+                  and ibetac
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  ibeta_inv
+                  and ibetac_inv
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  ibeta_inva,
+                  ibetac_inva,
+                  ibeta_invb
+                  and ibetac_invb
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  gamma_p
+                  and gamma_q
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  gamma_p_inv
+                  and gamma_q_inv
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+                  gamma_p_inva
+                  and gamma_q_inva
+                
                                                    
+              
+                
                                                    
+              
+                
                                                    
+              
                                                    
 
 
 

 
                                                    
 
-            
                                                    
-              Function
-            
                                                    
-                                                                		
 
-            
                                                    
-              GCC 4.2 , Linux
-            
                                                    
-            
                                                    
-              (with internal promotion of double to long double).
-            
                                                    
-                                                                		
 
-            
                                                    
-              GCC 4.2, Linux
-            
                                                    
-            
                                                    
-              (without promotion of double).
-            
                                                    
-                                                                		
 
                                                    
 
 
                                                    
 
-            
                                                    
-              erf
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.48
                                                    
 
                                                     
                                                    
 
                                                    (1.387e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (9.377e-008s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              erf_inv
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.11
                                                    
 
                                                     
                                                    
 
                                                    (4.009e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (3.598e-007s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              ibeta
-              and ibetac
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.29
                                                    
 
                                                     
                                                    
 
                                                    (5.354e-006s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (4.137e-006s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              ibeta_inv
-              and ibetac_inv
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.44
                                                    
 
                                                     
                                                    
 
                                                    (2.220e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (1.538e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              ibeta_inva,
-              ibetac_inva,
-              ibeta_invb
-              and ibetac_invb
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.25
                                                    
 
                                                     
                                                    
 
                                                    (7.009e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (5.607e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              gamma_p
-              and gamma_q
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.26
                                                    
 
                                                     
                                                    
 
                                                    (3.116e-006s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (2.464e-006s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              gamma_p_inv
-              and gamma_q_inv
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.27
                                                    
 
                                                     
                                                    
 
                                                    (1.178e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (9.291e-006s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
 
                                                    
 
-            
                                                    
-              gamma_p_inva
-              and gamma_q_inva
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.20
                                                    
 
                                                     
                                                    
 
                                                    (2.765e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
-            
                                                    
-              
                                                    
+                
                                                    
+                  
                                                    
 
                                                    1.00
                                                    
 
                                                     
                                                    
 
                                                    (2.311e-005s)
                                                    
 
                                                    
-            
                                                    
-                                                                		
 
                                                    
                                                     
 
                                                    
@@ -892,7 +896,7 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy.html b/doc/sf_and_dist/html/math_toolkit/policy.html
index aae27f2f0..435f9584e 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy.html
@@ -2,8 +2,8 @@
 
 
 Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
-
                                                    
+
                                                    
 
                                                    
@@ -86,7 +86,7 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
index 669ba706b..41e0ff840 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
@@ -2,8 +2,8 @@
 
 
 Policy Overview
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                    
 
                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                    
-
                                                    
+
                                                    
 
                                                    
@@ -61,35 +61,35 @@
         
                                                    
 
                                                    
         
                                                    
-
                                                      
-
                                                    • 
-How
-            results from 'bad' arguments are handled, including those that
-            cannot be fully evaluated.
-          
                                                      • 
-
                                                    • 
-            How accuracy
-            is controlled by internal promotion to use more precise types.
-          
                                                      • 
-
                                                    • 
-            What working precision
-            should be used to calculate results.
-          
                                                      • 
-
                                                    • 
-            What to do when a mathematically
-            undefined function is used: Should this raise a run-time or compile-time
-            error?
-          
                                                      • 
-
                                                    • 
-            Whether discrete
-            functions, like the binomial, should return real or only integral
-            values, and how they are rounded.
-          
                                                      • 
-
                                                    • 
-            How many iterations a special function is permitted to perform in a series
-            evaluation or root finding algorithm before it gives up and raises an
-            evaluation_error.
-          
                                                      • 
+
                                                      
 
                                                      
         
                                                      
@@ -98,22 +98,22 @@
         
                                                      
 
                                                      
         
                                                      
-
                                                        
-
                                                      • 
-            Using macros
-            to change any default policy: the is the prefered method for installation
-            wide policies.
-          
                                                        • 
-
                                                      • 
-            At your chosen namespace
-            scope for distributions and/or functions: this is the prefered
-            method for project, namespace, or translation unit scope policies.
-          
                                                        • 
-
                                                      • 
-            In an ad-hoc manner by
-            passing a specific policy to a special function, or to a statistical
-            distribution.
-          
                                                        • 
+
                                                        
 
                                                        
       
                                                        
@@ -130,7 +130,7 @@
 
 
                                                        
 
                                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                        
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
index 7a205df75..3e6a0b7f3 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
@@ -2,8 +2,8 @@
 
 
 Policy Reference
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                        
 
                                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                        
-
                                                        
+
                                                        
 
                                                        
@@ -59,7 +59,7 @@
 
 
                                                        
 
                                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                        
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
index d3199573b..9901dcf0f 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
@@ -2,8 +2,8 @@
 
 
 Mathematically Undefined Function Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                        
 
                                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                        
-
                                                        
+
                                                        
 
                                                        
  Mathematically
         Undefined Function Policies
@@ -84,7 +84,7 @@
 
 
                                                        
 
                                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                        
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html
index c4276b5ef..a1b3811a9 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html
@@ -2,8 +2,8 @@
 
 
 Discrete Quantile Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                        
 
                                                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                        
-
                                                        
+
                                                        
 
                                                        
  Discrete
         Quantile Policies
@@ -55,7 +55,7 @@
           can take have the following meanings:
         
                                                        
 
                                                        
-
+
           real
         
                                                        
 
                                                        
@@ -93,21 +93,21 @@
           = 68.1584.
         
                                                        
 
                                                        
-
+
           integer_round_outwards
         
                                                        
 
                                                        
           This is the default policy: an integer value is returned so that:
         
                                                        
-
                                                          
-
                                                        • 
-            Lower quantiles (where the probability is less than 0.5) are rounded
-            down.
-          
                                                          • 
-
                                                        • 
-            Upper quantiles (where the probability is greater than 0.5) are rounded
-            up.
-          
                                                          • 
+
                                                            
+
                                                          • 
+              Lower quantiles (where the probability is less than 0.5) are rounded
+              down.
+            
                                                            • 
+
                                                          • 
+              Upper quantiles (where the probability is greater than 0.5) are rounded
+              up.
+            
                                                            • 
 
                                                          
 
                                                          
           This is normally the safest rounding policy, since it ensures that both
@@ -151,22 +151,22 @@
           in each tail.
         
                                                          
 
                                                          
-
+
           integer_round_inwards
         
                                                          
 
                                                          
           This is the opposite of integer_round_outwards: an
           integer value is returned so that:
         
                                                          
-
                                                            
-
                                                          • 
-            Lower quantiles (where the probability is less than 0.5) are rounded
-            up.
-          
                                                            • 
-
                                                          • 
-            Upper quantiles (where the probability is greater than 0.5) are rounded
-            down.
-          
                                                            • 
+
                                                              
+
                                                            • 
+              Lower quantiles (where the probability is less than 0.5) are rounded
+              up.
+            
                                                              • 
+
                                                            • 
+              Upper quantiles (where the probability is greater than 0.5) are rounded
+              down.
+            
                                                              • 
 
                                                            
 
                                                            
           For example:
@@ -214,7 +214,7 @@
           in each tail.
         
                                                            
 
                                                            
-
+
           integer_round_down
         
                                                            
 
                                                            
@@ -222,7 +222,7 @@
           or a lower quantile.
         
                                                            
 
                                                            
-
+
           integer_round_up
         
                                                            
 
                                                            
@@ -230,7 +230,7 @@
           a lower quantile.
         
                                                            
 
                                                            
-
+
           integer_round_nearest
         
                                                            
 
                                                            
@@ -285,7 +285,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
index 34b2928b9..f04745dd3 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
@@ -2,8 +2,8 @@
 
 
 Error Handling Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
 
         Error Handling Policies
@@ -30,16 +30,16 @@
 
                                                            
           There are two orthogonal aspects to error handling:
         
                                                            
-
                                                              
-
                                                            • 
-            What to do (if anything) with the error.
-          
                                                              • 
-
                                                            • 
-            What kind of error is being raised.
-          
                                                              • 
+
                                                                
+
                                                              • 
+              What to do (if anything) with the error.
+            
                                                                • 
+
                                                              • 
+              What kind of error is being raised.
+            
                                                                • 
 
                                                              
 
                                                              
-
+
           Available
           Actions When an Error is Raised
         
                                                              
@@ -62,7 +62,7 @@
           The various enumerated values have the following meanings:
         
                                                              
 
                                                              
-
+
           throw_on_error
         
                                                              
 
                                                              
@@ -76,105 +76,105 @@
 
 
 
-                
                                                              
-                  Error Type
-                
                                                              
+                  
                                                              
+                    Error Type
+                  
                                                              
                 
 
-                
                                                              
-                  Exception
-                
                                                              
+                  
                                                              
+                    Exception
+                  
                                                              
                 
 
 
 
 
-                
                                                              
-                  Domain Error
-                
                                                              
+                  
                                                              
+                    Domain Error
+                  
                                                              
                 
 
-                
                                                              
-                  std::domain_error
-                
                                                              
+                  
                                                              
+                    std::domain_error
+                  
                                                              
                 
 
 
 
-                
                                                              
-                  Pole Error
-                
                                                              
+                  
                                                              
+                    Pole Error
+                  
                                                              
                 
 
-                
                                                              
-                  std::domain_error
-                
                                                              
+                  
                                                              
+                    std::domain_error
+                  
                                                              
                 
 
 
 
-                
                                                              
-                  Overflow Error
-                
                                                              
+                  
                                                              
+                    Overflow Error
+                  
                                                              
                 
 
-                
                                                              
-                  std::overflow_error
-                
                                                              
+                  
                                                              
+                    std::overflow_error
+                  
                                                              
                 
 
 
 
-                
                                                              
-                  Underflow Error
-                
                                                              
+                  
                                                              
+                    Underflow Error
+                  
                                                              
                 
 
-                
                                                              
-                  std::underflow_error
-                
                                                              
+                  
                                                              
+                    std::underflow_error
+                  
                                                              
                 
 
 
 
-                
                                                              
-                  Denorm Error
-                
                                                              
+                  
                                                              
+                    Denorm Error
+                  
                                                              
                 
 
-                
                                                              
-                  std::underflow_error
-                
                                                              
+                  
                                                              
+                    std::underflow_error
+                  
                                                              
                 
 
 
 
-                
                                                              
-                  Evaluation Error
-                
                                                              
+                  
                                                              
+                    Evaluation Error
+                  
                                                              
                 
 
-                
                                                              
-                  boost::math::evaluation_error
-                
                                                              
+                  
                                                              
+                    boost::math::evaluation_error
+                  
                                                              
                 
 
 
 
-                
                                                              
-                  Indeterminate Result Error
-                
                                                              
+                  
                                                              
+                    Indeterminate Result Error
+                  
                                                              
                 
 
-                
                                                              
-                  std::domain_error
-                
                                                              
+                  
                                                              
+                    std::domain_error
+                  
                                                              
                 
 
 
 
                                                            
 
                                                            
-
+
           errno_on_error
         
                                                            
 
                                                            
@@ -189,105 +189,105 @@
 
 
 
-                
                                                            
-                  Error Type
-                
                                                            
+                  
                                                            
+                    Error Type
+                  
                                                            
                 
 
-                
                                                            
-                  errno value
-                
                                                            
+                  
                                                            
+                    errno value
+                  
                                                            
                 
 
 
 
 
-                
                                                            
-                  Domain Error
-                
                                                            
+                  
                                                            
+                    Domain Error
+                  
                                                            
                 
 
-                
                                                            
-                  EDOM
-                
                                                            
+                  
                                                            
+                    EDOM
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Pole Error
-                
                                                            
+                  
                                                            
+                    Pole Error
+                  
                                                            
                 
 
-                
                                                            
-                  EDOM
-                
                                                            
+                  
                                                            
+                    EDOM
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Overflow Error
-                
                                                            
+                  
                                                            
+                    Overflow Error
+                  
                                                            
                 
 
-                
                                                            
-                  ERANGE
-                
                                                            
+                  
                                                            
+                    ERANGE
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Underflow Error
-                
                                                            
+                  
                                                            
+                    Underflow Error
+                  
                                                            
                 
 
-                
                                                            
-                  ERANGE
-                
                                                            
+                  
                                                            
+                    ERANGE
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Denorm Error
-                
                                                            
+                  
                                                            
+                    Denorm Error
+                  
                                                            
                 
 
-                
                                                            
-                  ERANGE
-                
                                                            
+                  
                                                            
+                    ERANGE
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Evaluation Error
-                
                                                            
+                  
                                                            
+                    Evaluation Error
+                  
                                                            
                 
 
-                
                                                            
-                  EDOM
-                
                                                            
+                  
                                                            
+                    EDOM
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Indeterminate Result Error
-                
                                                            
+                  
                                                            
+                    Indeterminate Result Error
+                  
                                                            
                 
 
-                
                                                            
-                  EDOM
-                
                                                            
+                  
                                                            
+                    EDOM
+                  
                                                            
                 
 
 
 
                                                            
 
                                                            
-
+
           ignore_error
         
                                                            
 
                                                            
@@ -301,106 +301,106 @@
 
 
 
-                
                                                            
-                  Error Type
-                
                                                            
+                  
                                                            
+                    Error Type
+                  
                                                            
                 
 
-                
                                                            
-                  Returned Value
-                
                                                            
+                  
                                                            
+                    Returned Value
+                  
                                                            
                 
 
 
 
 
-                
                                                            
-                  Domain Error
-                
                                                            
+                  
                                                            
+                    Domain Error
+                  
                                                            
                 
 
-                
                                                            
-                  std::numeric_limits<T>::quiet_NaN()
-                
                                                            
+                  
                                                            
+                    std::numeric_limits<T>::quiet_NaN()
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Pole Error
-                
                                                            
+                  
                                                            
+                    Pole Error
+                  
                                                            
                 
 
-                
                                                            
-                  std::numeric_limits<T>::quiet_NaN()
-                
                                                            
+                  
                                                            
+                    std::numeric_limits<T>::quiet_NaN()
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Overflow Error
-                
                                                            
+                  
                                                            
+                    Overflow Error
+                  
                                                            
                 
 
-                
                                                            
-                  std::numeric_limits<T>::infinity()
-                
                                                            
+                  
                                                            
+                    std::numeric_limits<T>::infinity()
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Underflow Error
-                
                                                            
+                  
                                                            
+                    Underflow Error
+                  
                                                            
                 
 
-                
                                                            
-                  0
-                
                                                            
+                  
                                                            
+                    0
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Denorm Error
-                
                                                            
+                  
                                                            
+                    Denorm Error
+                  
                                                            
                 
 
-                
                                                            
-                  The denormalised value.
-                
                                                            
+                  
                                                            
+                    The denormalised value.
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Evaluation Error
-                
                                                            
+                  
                                                            
+                    Evaluation Error
+                  
                                                            
                 
 
-                
                                                            
-                  The best guess as to the result: which may be significantly in
-                  error.
-                
                                                            
+                  
                                                            
+                    The best guess as to the result: which may be significantly in
+                    error.
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Indeterminate Result Error
-                
                                                            
+                  
                                                            
+                    Indeterminate Result Error
+                  
                                                            
                 
 
-                
                                                            
-                  Depends on the function where the error occurred
-                
                                                            
+                  
                                                            
+                    Depends on the function where the error occurred
+                  
                                                            
                 
 
 
 
                                                            
 
                                                            
-
+
           user_error
         
                                                            
 
                                                            
@@ -449,7 +449,7 @@
           here.
         
                                                            
 
                                                            
-
+
           Kinds
           of Error Raised
         
                                                            
@@ -465,230 +465,231 @@
 
 
 
-                
                                                            
-                  Error Type
-                
                                                            
+                  
                                                            
+                    Error Type
+                  
                                                            
                 
 
-                
                                                            
-                  Policy Class
-                
                                                            
+                  
                                                            
+                    Policy Class
+                  
                                                            
                 
 
-                
                                                            
-                  Description
-                
                                                            
+                  
                                                            
+                    Description
+                  
                                                            
                 
 
 
 
 
-                
                                                            
-                  Domain Error
-                
                                                            
+                  
                                                            
+                    Domain Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::domain_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::domain_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when more or more arguments are outside the defined range
-                  of the function.
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::domain_error<throw_on_error>
-                
                                                            
-                
                                                            
-                  When the action is set to throw_on_error then
-                  throws std::domain_error
-                
                                                            
+                  
                                                            
+                    Raised when more or more arguments are outside the defined range
+                    of the function.
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::domain_error<throw_on_error>
+                  
                                                            
+                  
                                                            
+                    When the action is set to throw_on_error
+                    then throws std::domain_error
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Pole Error
-                
                                                            
+                  
                                                            
+                    Pole Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::pole_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::pole_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when more or more arguments would cause the function to
-                  be evaluated at a pole.
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::pole_error<throw_on_error>
-                
                                                            
-                
                                                            
-                  When the action is throw_on_error then throw
-                  a std::domain_error
-                
                                                            
+                  
                                                            
+                    Raised when more or more arguments would cause the function to
+                    be evaluated at a pole.
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::pole_error<throw_on_error>
+                  
                                                            
+                  
                                                            
+                    When the action is throw_on_error then throw
+                    a std::domain_error
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Overflow Error
-                
                                                            
+                  
                                                            
+                    Overflow Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::overflow_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::overflow_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when the result of the function is outside the representable
-                  range of the floating point type used.
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::overflow_error<throw_on_error>.
-                
                                                            
-                
                                                            
-                  When the action is throw_on_error then throws
-                  a std::overflow_error.
-                
                                                            
+                  
                                                            
+                    Raised when the result of the function is outside the representable
+                    range of the floating point type used.
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::overflow_error<throw_on_error>.
+                  
                                                            
+                  
                                                            
+                    When the action is throw_on_error then throws
+                    a std::overflow_error.
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Underflow Error
-                
                                                            
+                  
                                                            
+                    Underflow Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::underflow_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::underflow_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when the result of the function is too small to be represented
-                  in the floating point type used.
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::underflow_error<ignore_error>
-                
                                                            
-                
                                                            
-                  When the specified action is throw_on_error
-                  then throws a std::underflow_error
-                
                                                            
+                  
                                                            
+                    Raised when the result of the function is too small to be represented
+                    in the floating point type used.
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::underflow_error<ignore_error>
+                  
                                                            
+                  
                                                            
+                    When the specified action is throw_on_error
+                    then throws a std::underflow_error
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Denorm Error
-                
                                                            
+                  
                                                            
+                    Denorm Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::denorm_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::denorm_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when the result of the function is a denormalised value.
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::denorm_error<ignore_error>
-                
                                                            
-                
                                                            
-                  When the action is throw_on_error then throws
-                  a std::underflow_error
-                
                                                            
+                  
                                                            
+                    Raised when the result of the function is a denormalised value.
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::denorm_error<ignore_error>
+                  
                                                            
+                  
                                                            
+                    When the action is throw_on_error then throws
+                    a std::underflow_error
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Rounding Error
-                
                                                            
+                  
                                                            
+                    Rounding Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::rounding_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::rounding_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised When one of the rounding functions round,
-                  trunc
-                  or modf
-                  is called with an argument that has no integer representation,
-                  or is too large to be represented in the result type
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::rounding_error<throw_on_error>
-                
                                                            
-                
                                                            
-                  When the action is throw_on_error then throws
-                  boost::math::rounding_error
-                
                                                            
+                  
                                                            
+                    Raised When one of the rounding functions round,
+                    trunc
+                    or modf
+                    is called with an argument that has no integer representation,
+                    or is too large to be represented in the result type
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::rounding_error<throw_on_error>
+                  
                                                            
+                  
                                                            
+                    When the action is throw_on_error then throws
+                    boost::math::rounding_error
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Evaluation Error
-                
                                                            
+                  
                                                            
+                    Evaluation Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::evaluation_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::evaluation_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when the result of the function is well defined and finite,
-                  but we were unable to compute it. Typically this occurs when an
-                  iterative method fails to converge. Of course ideally this error
-                  should never be raised: feel free to report it as a bug if it is!
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::evaluation_error<throw_on_error>
-                
                                                            
-                
                                                            
-                  When the action is throw_on_error then throws
-                  boost::math::evaluation_error
-                
                                                            
+                  
                                                            
+                    Raised when the result of the function is well defined and finite,
+                    but we were unable to compute it. Typically this occurs when
+                    an iterative method fails to converge. Of course ideally this
+                    error should never be raised: feel free to report it as a bug
+                    if it is!
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::evaluation_error<throw_on_error>
+                  
                                                            
+                  
                                                            
+                    When the action is throw_on_error then throws
+                    boost::math::evaluation_error
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  Indeterminate Result Error
-                
                                                            
+                  
                                                            
+                    Indeterminate Result Error
+                  
                                                            
                 
 
-                
                                                            
-                  boost::math::policies::indeterminate_result_error<action>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::indeterminate_result_error<action>
+                  
                                                            
                 
 
-                
                                                            
-                  Raised when the result of a function is not defined for the values
-                  that were passed to it.
-                
                                                            
-                
                                                            
-                  Defaults to boost::math::policies::indeterminate_result_error<ignore_error>
-                
                                                            
-                
                                                            
-                  When the action is throw_on_error then throws
-                  std::domain_error
-                
                                                            
+                  
                                                            
+                    Raised when the result of a function is not defined for the values
+                    that were passed to it.
+                  
                                                            
+                  
                                                            
+                    Defaults to boost::math::policies::indeterminate_result_error<ignore_error>
+                  
                                                            
+                  
                                                            
+                    When the action is throw_on_error then throws
+                    std::domain_error
+                  
                                                            
                 
 
 
 
                                                            
 
                                                            
-
+
           Examples
         
                                                            
 
                                                            
@@ -773,7 +774,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
index d6b20d68f..10b80cedf 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
@@ -2,8 +2,8 @@
 
 
 Internal Promotion Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
  Internal
         Promotion Policies
@@ -41,50 +41,50 @@
 
 
 
-                
                                                            
-                  Policy
-                
                                                            
+                  
                                                            
+                    Policy
+                  
                                                            
                 
 
-                
                                                            
-                  Meaning
-                
                                                            
+                  
                                                            
+                    Meaning
+                  
                                                            
                 
 
 
 
 
-                
                                                            
-                  boost::math::policies::promote_float<B>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::promote_float<B>
+                  
                                                            
                 
 
-                
                                                            
-                  Indicates whether float
-                  arguments should be promoted to double
-                  precision internally: defaults to boost::math::policies::promote_float<true>
-                
                                                            
+                  
                                                            
+                    Indicates whether float
+                    arguments should be promoted to double
+                    precision internally: defaults to boost::math::policies::promote_float<true>
+                  
                                                            
                 
 
 
 
-                
                                                            
-                  boost::math::policies::promote_double<B>
-                
                                                            
+                  
                                                            
+                    boost::math::policies::promote_double<B>
+                  
                                                            
                 
 
-                
                                                            
-                  Indicates whether double
-                  arguments should be promoted to long
-                  double precision internally:
-                  defaults to boost::math::policies::promote_double<true>
-                
                                                            
+                  
                                                            
+                    Indicates whether double
+                    arguments should be promoted to long
+                    double precision internally:
+                    defaults to boost::math::policies::promote_double<true>
+                  
                                                            
                 
 
 
 
                                                            
 
                                                            
-
+
           Examples
         
                                                            
 
                                                            
@@ -161,7 +161,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
index 41b4f3f5d..009cc08b2 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
@@ -2,8 +2,8 @@
 
 
 Iteration Limits Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
  Iteration
         Limits Policies
@@ -61,7 +61,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
index 7d54586e1..2b0e692fc 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
@@ -2,8 +2,8 @@
 
 
 Setting Polices at Namespace Scope
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
  Setting
         Polices at Namespace Scope
@@ -161,7 +161,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
index d03cf06cf..100d572de 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
@@ -2,8 +2,8 @@
 
 
 Policy Class Reference
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
  Policy Class
         Reference
@@ -255,7 +255,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html
index 7d06e9f53..58a004a30 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html
@@ -2,8 +2,8 @@
 
 
 Using macros to Change the Policy Defaults
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
  Using
         macros to Change the Policy Defaults
@@ -36,7 +36,7 @@
         
                                                            
 
                                                            
-
+
                                                            
 
                                                            [Caution][Caution]
 Caution
 
                                                            
 
                                                            
@@ -47,7 +47,7 @@
 
                                                            
 
                                                            
-
+
                                                            
 
                                                            [Caution][Caution]
 Caution
 
                                                            
 
                                                            
@@ -61,7 +61,7 @@
           then you can do so by defining various macros in boost/math/tools/user.hpp.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_DOMAIN_ERROR_POLICY
         
                                                            
 
                                                            
@@ -71,7 +71,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_POLE_ERROR_POLICY
         
                                                            
 
                                                            
@@ -81,7 +81,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_OVERFLOW_ERROR_POLICY
         
                                                            
 
                                                            
@@ -91,7 +91,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_ROUNDING_ERROR_POLICY
         
                                                            
 
                                                            
@@ -101,7 +101,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_EVALUATION_ERROR_POLICY
         
                                                            
 
                                                            
@@ -111,7 +111,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_UNDERFLOW_ERROR_POLICY
         
                                                            
 
                                                            
@@ -121,7 +121,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_DENORM_ERROR_POLICY
         
                                                            
 
                                                            
@@ -131,7 +131,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY
         
                                                            
 
                                                            
@@ -142,7 +142,7 @@
           ignore_error or user_error.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_DIGITS10_POLICY
         
                                                            
 
                                                            
@@ -153,7 +153,7 @@
           recommended that you change this from the default.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_PROMOTE_FLOAT_POLICY
         
                                                            
 
                                                            
@@ -165,7 +165,7 @@
           off.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_PROMOTE_DOUBLE_POLICY
         
                                                            
 
                                                            
@@ -177,7 +177,7 @@
           off.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_DISCRETE_QUANTILE_POLICY
         
                                                            
 
                                                            
@@ -188,7 +188,7 @@
           Defaults to integer_round_outwards.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_ASSERT_UNDEFINED_POLICY
         
                                                            
 
                                                            
@@ -201,7 +201,7 @@
           whether or not a particular property is well defined.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_MAX_SERIES_ITERATION_POLICY
         
                                                            
 
                                                            
@@ -210,7 +210,7 @@
           Defaults to 1000000.
         
                                                            
 
                                                            
-
+
           BOOST_MATH_MAX_ROOT_ITERATION_POLICY
         
                                                            
 
                                                            
@@ -219,7 +219,7 @@
           Defaults to 200.
         
                                                            
 
                                                            
-
+
           Example
         
                                                            
 
                                                            
@@ -254,7 +254,7 @@
 
                                                            
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html
index d087b9044..1798f7b43 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html
@@ -2,8 +2,8 @@
 
 
 Precision Policies
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
  Precision
         Policies
@@ -132,7 +132,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
index 73654e94f..489648d66 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
@@ -2,8 +2,8 @@
 
 
 Policy Tutorial
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
@@ -59,7 +59,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
index 0b46fb5e9..2f181f215 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
@@ -2,8 +2,8 @@
 
 
 Setting Policies for Distributions on an Ad Hoc Basis
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
 
         Setting Policies for Distributions on an Ad Hoc Basis
@@ -103,7 +103,7 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
index 0f74ddda8..3279036e4 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
@@ -2,8 +2,8 @@
 
 
 Changing the Policy on an Ad Hoc Basis for the Special Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
 
         Changing the Policy on an Ad Hoc Basis for the Special Functions
@@ -162,7 +162,7 @@ errno = 33
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html
index ac388c960..851052179 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html
@@ -2,8 +2,8 @@
 
 
 Changing the Policy Defaults
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
 
         Changing the Policy Defaults
@@ -39,7 +39,7 @@
         
                                                            
 
                                                            
-
+
                                                            
 
                                                            [Tip][Tip]
 Tip
 
                                                            
 
                                                            
@@ -85,7 +85,7 @@
         
                                                            
 
                                                            
-
+
                                                            
 
                                                            [Important][Important]
 Important
 
                                                            
 
                                                            
@@ -102,26 +102,27 @@
 
                                                            
           That means there are only two safe ways to use these macros:
         
                                                            
-
                                                              
-
                                                            • 
-            Edit them in boost/math/tools/user.hpp,
-            so that the defaults are set on an installation-wide basis. Unfortunately
-            this may not be convenient if you are using a pre-installed Boost distribution
-            (on Linux for example).
-          
                                                              • 
-
                                                            • 
-            Set the defines in your project's Makefile or build environment, so that
-            they are set uniformly across all translation units.
-          
                                                              • 
+
                                                                
+
                                                              • 
+              Edit them in boost/math/tools/user.hpp,
+              so that the defaults are set on an installation-wide basis. Unfortunately
+              this may not be convenient if you are using a pre-installed Boost distribution
+              (on Linux for example).
+            
                                                                • 
+
                                                              • 
+              Set the defines in your project's Makefile or build environment, so
+              that they are set uniformly across all translation units.
+            
                                                                • 
 
                                                              
 
                                                              
           What you should not do is:
         
                                                              
-
                                                              • 
-            Set the defines in the source file using #define
-            as doing so almost certainly will break your program, unless you're absolutely
-            certain that the program is restricted to a single translation unit.
-          
                                                              
+
                                                              • 
+              Set the defines in the source file using #define
+              as doing so almost certainly will break your program, unless you're
+              absolutely certain that the program is restricted to a single translation
+              unit.
+            
                                                              
 
                                                              
           And, yes, you will find examples in our test programs where we break this
           rule: but only because we know there will always be a single translation
@@ -326,7 +327,7 @@ errno is set to: 33
 
                                                            
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html
index 5441c9661..04ef76f5d 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html
@@ -2,8 +2,8 @@
 
 
 Setting Policies at Namespace or Translation Unit Scope
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
                                                            
 
                                                            
 
                                                            
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                            
-
                                                            
+
                                                            
 
                                                            
 
         Setting Policies at Namespace or Translation Unit Scope
@@ -232,16 +232,17 @@ errno = 33
           
                                                            
 
                                                            
           
                                                            
-
                                                              
-
                                                            • 
-              Return infinity on overflow, rather than throwing an exception.
-            
                                                              • 
-
                                                            • 
-              Don't perform any promotion from double to long double internally.
-            
                                                              • 
-
                                                            • 
-              Return the closest integer result from the quantiles of discrete distributions.
-            
                                                              • 
+
                                                                
+
                                                              • 
+                Return infinity on overflow, rather than throwing an exception.
+              
                                                                • 
+
                                                              • 
+                Don't perform any promotion from double to long double internally.
+              
                                                                • 
+
                                                              • 
+                Return the closest integer result from the quantiles of discrete
+                distributions.
+              
                                                                • 
 
                                                              
 
                                                              
           
                                                              
@@ -377,7 +378,7 @@ Result of quantile(complement(binom, 0.05)) is: 8
         
                                                              
 
                                                              
-
+
                                                              
 
                                                              [Note][Note]
 Note
 
                                                              
 
                                                              
@@ -458,7 +459,7 @@ Result of quantile(complement(binom, 0.05)) is: 8
 
                                                              
 
                                                              
 
                                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                              
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html
index 74b1b50b3..0058e12f6 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html
@@ -2,8 +2,8 @@
 
 
 Policies Have Sensible Defaults
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                              
 
                                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                              
-
                                                              
+
                                                              
 
                                                              
 
         Policies Have Sensible Defaults
@@ -37,69 +37,70 @@
 
                                                              
 
                                                              Domain Error
                                                              
 
                                                              
-              Throws a std::domain_error exception.
-            
                                                              
+                Throws a std::domain_error exception.
+              
                                                              
 
                                                              Pole Error
                                                              
 
                                                              
-              Occurs when a function is evaluated at a pole: throws a std::domain_error exception.
-            
                                                              
+                Occurs when a function is evaluated at a pole: throws a std::domain_error exception.
+              
                                                              
 
                                                              Overflow Error
                                                              
 
                                                              
-              Throws a std::overflow_error exception.
-            
                                                              
+                Throws a std::overflow_error exception.
+              
                                                              
 
                                                              Underflow
                                                              
 
                                                              
-              Ignores the underflow, and returns zero.
-            
                                                              
+                Ignores the underflow, and returns zero.
+              
                                                              
 
                                                              Denormalised Result
                                                              
 
                                                              
-              Ignores the fact that the result is denormalised, and returns it.
-            
                                                              
+                Ignores the fact that the result is denormalised, and returns it.
+              
                                                              
 
                                                              Rounding Error
                                                              
 
                                                              
-              Throws a boost::math::rounding_error exception.
-            
                                                              
+                Throws a boost::math::rounding_error exception.
+              
                                                              
 
                                                              Internal Evaluation Error
                                                              
 
                                                              
-              Throws a boost::math::evaluation_error exception.
-            
                                                              
+                Throws a boost::math::evaluation_error exception.
+              
                                                              
 
                                                              Indeterminate Result Error
                                                              
 
                                                              
-              Returns a result that depends on the function where the error occurred.
-            
                                                              
+                Returns a result that depends on the function where the error occurred.
+              
                                                              
 
                                                              Promotion of float to double
                                                              
 
                                                              
-              Does occur by default - gives full float precision results.
-            
                                                              
+                Does occur by default - gives full float precision results.
+              
                                                              
 
                                                              Promotion of double to long double
                                                              
 
                                                              
-              Does occur by default if long double offers more precision than double.
-            
                                                              
+                Does occur by default if long double offers more precision than double.
+              
                                                              
 
                                                              Precision of Approximation Used
                                                              
 
                                                              
-              By default uses an approximation that will result in the lowest level
-              of error for the type of the result.
-            
                                                              
+                By default uses an approximation that will result in the lowest level
+                of error for the type of the result.
+              
                                                              
 
                                                              Behaviour of Discrete Quantiles
                                                              
 
                                                              
 
                                                              
-              The quantile function will by default return an integer result that
-              has been rounded outwards. That is to say lower
-              quantiles (where the probability is less than 0.5) are rounded downward,
-              and upper quantiles (where the probability is greater than 0.5) are
-              rounded upwards. This behaviour ensures that if an X% quantile is requested,
-              then at least the requested coverage will be present
-              in the central region, and no more than the requested
-              coverage will be present in the tails.
-            
                                                              
+                The quantile function will by default return an integer result that
+                has been rounded outwards. That is to say lower
+                quantiles (where the probability is less than 0.5) are rounded downward,
+                and upper quantiles (where the probability is greater than 0.5) are
+                rounded upwards. This behaviour ensures that if an X% quantile is
+                requested, then at least the requested coverage
+                will be present in the central region, and no more than
+                the requested coverage will be present in the tails.
+              
                                                              
 
                                                              
-              This behaviour can be changed so that the quantile functions are rounded
-              differently, or even return a real-valued result using Policies.
-              It is strongly recommended that you read the tutorial Understanding
-              Quantiles of Discrete Distributions before using the quantile
-              function on a discrete distribution. The reference
-              docs describe how to change the rounding policy for these distributions.
-            
                                                              
+                This behaviour can be changed so that the quantile functions are
+                rounded differently, or even return a real-valued result using Policies. It is
+                strongly recommended that you read the tutorial Understanding
+                Quantiles of Discrete Distributions before using the quantile
+                function on a discrete distribution. The reference
+                docs describe how to change the rounding policy for these
+                distributions.
+              
                                                              
 
                                                              
 
                                                              
 
                                                              
@@ -132,7 +133,7 @@
 
 
                                                              
 
                                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                              
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html
index ad9f8764d..bac49f33d 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html
@@ -2,8 +2,8 @@
 
 
 So How are Policies Used Anyway?
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                              
 
                                                              
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                              
-
                                                              
+
                                                              
 
                                                              
  So
         How are Policies Used Anyway?
@@ -30,25 +30,25 @@
 
                                                              
           The details follow later, but basically policies can be set by either:
         
                                                              
-
                                                                
-
                                                              • 
-            Defining some macros that change the default behaviour: this
-            is the recommended method for setting installation-wide policies.
-          
                                                                • 
-
                                                              • 
-            By instantiating a distribution object with an explicit policy: this
-            is mainly reserved for ad hoc policy changes.
-          
                                                                • 
-
                                                              • 
-            By passing a policy to a special function as an optional final argument:
-            this is mainly reserved for ad hoc policy changes.
-          
                                                                • 
-
                                                              • 
-            By using some helper macros to define a set of functions or distributions
-            in the current namespace that use a specific policy: this
-            is the recommended method for setting policies on a project- or translation-unit-wide
-            basis.
-          
                                                                • 
+
                                                                  
+
                                                                • 
+              Defining some macros that change the default behaviour: this
+              is the recommended method for setting installation-wide policies.
+            
                                                                  • 
+
                                                                • 
+              By instantiating a distribution object with an explicit policy: this
+              is mainly reserved for ad hoc policy changes.
+            
                                                                  • 
+
                                                                • 
+              By passing a policy to a special function as an optional final argument:
+              this is mainly reserved for ad hoc policy changes.
+            
                                                                  • 
+
                                                                • 
+              By using some helper macros to define a set of functions or distributions
+              in the current namespace that use a specific policy: this
+              is the recommended method for setting policies on a project- or translation-unit-wide
+              basis.
+            
                                                                  • 
 
                                                                
 
                                                                
           The following sections introduce these methods in more detail.
@@ -66,7 +66,7 @@
 
 
                                                                
 
                                                                
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html
index 2f9d0d01c..6cddc0b0f 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html
@@ -2,8 +2,8 @@
 
 
 Understanding Quantiles of Discrete Distributions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                                
 
                                                                
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                
-
                                                                
+
                                                                
 
                                                                
 
         Understanding Quantiles of Discrete Distributions
@@ -53,13 +53,13 @@
           As can be seen there is no random variable that corresponds to a probability
           of exactly 0.05, so we're left with two choices as shown in the figure:
         
                                                                
-
                                                                  
-
                                                                • 
-            We could round the result down to 18.
-          
                                                                  • 
-
                                                                • 
-            We could round the result up to 19.
-          
                                                                  • 
+
                                                                    
+
                                                                  • 
+              We could round the result down to 18.
+            
                                                                    • 
+
                                                                  • 
+              We could round the result up to 19.
+            
                                                                    • 
 
                                                                  
 
                                                                  
           In fact there's actually a third choice as well: we could "pretend"
@@ -77,16 +77,16 @@
 
                                                                  
           In coming to an answer we should realise that:
         
                                                                  
-
                                                                    
-
                                                                  • 
-            Calculating an integer result is often much faster than calculating a
-            real-valued result: in fact in our tests it was up to 20 times faster.
-          
                                                                    • 
-
                                                                  • 
-            Normally people calculate quantiles so that they can perform a test of
-            some kind: "If the random variable is less than N then
-            we can reject our null-hypothesis with 90% confidence."
-
                                                                    • 
+
                                                                      
+
                                                                    • 
+              Calculating an integer result is often much faster than calculating
+              a real-valued result: in fact in our tests it was up to 20 times faster.
+            
                                                                      • 
+
                                                                    • 
+              Normally people calculate quantiles so that they can perform a test
+              of some kind: "If the random variable is less than N
+              then we can reject our null-hypothesis with 90% confidence."
+            
                                                                      • 
 
                                                                    
 
                                                                    
           So there is a genuine benefit to calculating an integer result as well
@@ -177,7 +177,7 @@
           base your comparisons on CDF's instead.
         
                                                                    
 
                                                                    
-
+
           Other
           Rounding Policies are Available
         
                                                                    
@@ -191,50 +191,51 @@
 
                                                                    integer_round_outwards
                                                                    
 
                                                                    
 
                                                                    
-              This is the default policy as described above: lower quantiles are
-              rounded down (probability < 0.5), and upper quantiles (probability
-              > 0.5) are rounded up.
-            
                                                                    
+                This is the default policy as described above: lower quantiles are
+                rounded down (probability < 0.5), and upper quantiles (probability
+                > 0.5) are rounded up.
+              
                                                                    
 
                                                                    
-              This gives no more than the requested probability
-              in the tails, and at least the requested probability
-              in the central area.
-            
                                                                    
+                This gives no more than the requested probability
+                in the tails, and at least the requested probability
+                in the central area.
+              
                                                                    
 
                                                                    
 
                                                                    integer_round_inwards
                                                                    
 
                                                                    
 
                                                                    
-              This is the exact opposite of the default policy: lower quantiles are
-              rounded up (probability < 0.5), and upper quantiles (probability
-              > 0.5) are rounded down.
-            
                                                                    
+                This is the exact opposite of the default policy: lower quantiles
+                are rounded up (probability < 0.5), and upper quantiles (probability
+                > 0.5) are rounded down.
+              
                                                                    
 
                                                                    
-              This gives at least the requested probability
-              in the tails, and no more than the requested probability
-              in the central area.
-            
                                                                    
+                This gives at least the requested probability
+                in the tails, and no more than the requested
+                probability in the central area.
+              
                                                                    
 
                                                                    
 
                                                                    integer_round_down
                                                                    
 
                                                                    
-              This policy will always round the result down no matter whether it
-              is an upper or lower quantile
-            
                                                                    
+                This policy will always round the result down no matter whether it
+                is an upper or lower quantile
+              
                                                                    
 
                                                                    integer_round_up
                                                                    
 
                                                                    
-              This policy will always round the result up no matter whether it is
-              an upper or lower quantile
-            
                                                                    
+                This policy will always round the result up no matter whether it
+                is an upper or lower quantile
+              
                                                                    
 
                                                                    integer_round_nearest
                                                                    
 
                                                                    
-              This policy will always round the result to the nearest integer no
-              matter whether it is an upper or lower quantile
-            
                                                                    
+                This policy will always round the result to the nearest integer no
+                matter whether it is an upper or lower quantile
+              
                                                                    
 
                                                                    real
                                                                    
 
                                                                    
-              This policy will return a real valued result for the quantile of a
-              discrete distribution: this is generally much slower than finding an
-              integer result but does allow for more sophisticated rounding policies.
-            
                                                                    
+                This policy will return a real valued result for the quantile of
+                a discrete distribution: this is generally much slower than finding
+                an integer result but does allow for more sophisticated rounding
+                policies.
+              
                                                                    
 
 
                                                                  
 
                                                                  
@@ -428,7 +429,7 @@ Upper quantiles at p = 0.95.
 
 
                                                                  
 
                                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html
index c1d2d6976..5ad6474eb 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html
@@ -2,8 +2,8 @@
 
 
 Calling User Defined Error Handlers
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                                  
 
                                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                  
-
                                                                  
+
                                                                  
 
                                                                  
 
         Calling User Defined Error Handlers
@@ -207,25 +207,25 @@ Result of tgamma(-10) is: 1.#QNAN
 
                                                                  
 
                                                                  const char* function
                                                                  
 
                                                                  
-                The name of the function that raised the error, this string contains
-                one or more %1% format specifiers that should be replaced by the
-                name of type T.
-              
                                                                  
+                  The name of the function that raised the error, this string contains
+                  one or more %1% format specifiers that should be replaced by the
+                  name of type T.
+                
                                                                  
 
                                                                  const char* message
                                                                  
 
                                                                  
-                A message associated with the error, normally this contains a %1%
-                format specifier that should be replaced with the value of value:
-                however note that overflow and underflow messages do not contain
-                this %1% specifier (since the value of value
-                is immaterial in these cases).
-              
                                                                  
+                  A message associated with the error, normally this contains a %1%
+                  format specifier that should be replaced with the value of value:
+                  however note that overflow and underflow messages do not contain
+                  this %1% specifier (since the value of value
+                  is immaterial in these cases).
+                
                                                                  
 
                                                                  const T& value
                                                                  
 
                                                                  
-                The value that caused the error: either an argument to the function
-                if this is a domain or pole error, the tentative result if this is
-                a denorm or evaluation error, or zero or infinity for underflow or
-                overflow errors.
-              
                                                                  
+                  The value that caused the error: either an argument to the function
+                  if this is a domain or pole error, the tentative result if this
+                  is a denorm or evaluation error, or zero or infinity for underflow
+                  or overflow errors.
+                
                                                                  
 
                                                                  
 
                                                                  
 
                                                                  
@@ -623,7 +623,7 @@ Result of tgamma(-190.5) is: 0
 
 
                                                                  
 
                                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html
index 8556fc34d..b0031c1c6 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html
@@ -2,8 +2,8 @@
 
 
 So Just What is a Policy Anyway?
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                                  
 
                                                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                  
-
                                                                  
+
                                                                  
 
                                                                  
 
         So Just What is a Policy Anyway?
@@ -32,25 +32,25 @@
           special function, or a statistical distribution. With Policies you can
           control:
         
                                                                  
-
                                                                    
-
                                                                  • 
-            What action to take when an error occurs.
-          
                                                                    • 
-
                                                                  • 
-            What happens when you call a function that is mathematically undefined
-            (for example if you ask for the mean of a Cauchy distribution).
-          
                                                                    • 
-
                                                                  • 
-            What happens when you ask for a quantile of a discrete distribution.
-          
                                                                    • 
-
                                                                  • 
-            Whether the library is allowed to internally promote float
-            to double and double to long
-            double in order to improve precision.
-          
                                                                    • 
-
                                                                  • 
-            What precision to use when calculating the result.
-          
                                                                    • 
+
                                                                      
+
                                                                    • 
+              What action to take when an error occurs.
+            
                                                                      • 
+
                                                                    • 
+              What happens when you call a function that is mathematically undefined
+              (for example if you ask for the mean of a Cauchy distribution).
+            
                                                                      • 
+
                                                                    • 
+              What happens when you ask for a quantile of a discrete distribution.
+            
                                                                      • 
+
                                                                    • 
+              Whether the library is allowed to internally promote float to double
+              and double to long double
+              in order to improve precision.
+            
                                                                      • 
+
                                                                    • 
+              What precision to use when calculating the result.
+            
                                                                      • 
 
                                                                    
 
                                                                    
           Some of these policies could arguably be runtime variables, but then we
@@ -82,7 +82,7 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html
index 9301e2d79..78caf5ade 100644
--- a/doc/sf_and_dist/html/math_toolkit/special.html
+++ b/doc/sf_and_dist/html/math_toolkit/special.html
@@ -2,8 +2,8 @@
 
 
 Special Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
-
                                                                    
+
                                                                    
 
                                                                    
@@ -155,7 +155,7 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel.html
index 8c51fe364..eaa41f1fa 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel.html
@@ -2,8 +2,8 @@
 
 
 Bessel Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
-
                                                                    
+
                                                                    
 
                                                                    
@@ -57,7 +57,7 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
index c7cd53935..6e2eb06f7 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
@@ -2,8 +2,8 @@
 
 
 Bessel Functions of the First and Second Kinds
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
-
                                                                    
+
                                                                    
 
                                                                    
 
                                                                    
-
+
           Synopsis
         
                                                                    
 
                                                                    template <class T1, class T2>
@@ -44,7 +44,7 @@
 calculated-result-type cyl_neumann(T1 v, T2 x, const Policy&);
 
                                                                    
 
                                                                    
-
+
           Description
         
                                                                    
 
                                                                    
@@ -110,7 +110,7 @@
           
         
                                                                    
 
                                                                    
-
+
           Testing
         
                                                                    
 
                                                                    
@@ -119,7 +119,7 @@
           (with all the special case handling removed).
         
                                                                    
 
                                                                    
-
+
           Accuracy
         
                                                                    
 
                                                                    
@@ -135,7 +135,7 @@
           zero error. All values are relative errors in units of epsilon.
         
                                                                    
 
                                                                    
-
                                                                    Table 36. Errors Rates in cyl_bessel_j
                                                                    
+
                                                                    Table 36. Errors Rates in cyl_bessel_j
                                                                    
 
                                                                    @@ -146,165 +146,165 @@
 
+                  
                                                                    
+                    Significand Size
+                  
                                                                    
+                
+                  
                                                                    
+                    Platform and Compiler
+                  
                                                                    
+                
+                  
                                                                    
+                    J0 and J1
+                  
                                                                    
+                
+                  
                                                                    
+                    Jv
+                  
                                                                    
+                
+                  
                                                                    
+                    Jv (large values of x > 1000)
+                  
                                                                    
+                
+                  
                                                                    
+                    53
+                  
                                                                    
+                
+                  
                                                                    
+                    Win32 / Visual C++ 8.0
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=2.5 Mean=1.1
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=6.6
+                  
                                                                    
+                  
                                                                    
+                    Cephes Peak=2.5
+                    Mean=1.1
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=11 Mean=2.2
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=11
+                  
                                                                    
+                  
                                                                    
+                    Cephes Peak=17
+                    Mean=2.5
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=413 Mean=110
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=6x1011
+                  
                                                                    
+                  
                                                                    
+                    Cephes Peak=2x105
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    Red Hat Linux IA64 / G++ 3.4
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=7 Mean=3
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=117 Mean=10
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=2x104 Mean=6x103
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    SUSE Linux AMD64 / G++ 4.1
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=7 Mean=3
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=400 Mean=40
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=2x104 Mean=1x104
+                  
                                                                    
+                
+                  
                                                                    
+                    113
+                  
                                                                    
+                
+                  
                                                                    
+                    HP-UX / HP aCC 6
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=14 Mean=6
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=29 Mean=3
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=2700 Mean=450
+                  
                                                                    
+                
                                                                    
 
 

 
                                                                    
 
-              
                                                                    
-                Significand Size
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Platform and Compiler
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                J0 and J1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Jv
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Jv (large values of x > 1000)
-              
                                                                    
-                                                                                  		
 
                                                                    
 
 
                                                                    
 
-              
                                                                    
-                53
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Win32 / Visual C++ 8.0
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=2.5 Mean=1.1
-              
                                                                    
-              
                                                                    
-                GSL Peak=6.6
-              
                                                                    
-              
                                                                    
-                Cephes Peak=2.5
-                Mean=1.1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=11 Mean=2.2
-              
                                                                    
-              
                                                                    
-                GSL Peak=11
-              
                                                                    
-              
                                                                    
-                Cephes Peak=17
-                Mean=2.5
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=413 Mean=110
-              
                                                                    
-              
                                                                    
-                GSL Peak=6x1011
-              
                                                                    
-              
                                                                    
-                Cephes Peak=2x105
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Red Hat Linux IA64 / G++ 3.4
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=7 Mean=3
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=117 Mean=10
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=2x104 Mean=6x103
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                SUSE Linux AMD64 / G++ 4.1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=7 Mean=3
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=400 Mean=40
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=2x104 Mean=1x104
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                113
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                HP-UX / HP aCC 6
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=14 Mean=6
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=29 Mean=3
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=2700 Mean=450
-              
                                                                    
-                                                                                  		
 
                                                                    
                                                                     
 
                                                                    
 
                                                                    
 
                                                                    
-
                                                                    Table 37. Errors Rates in cyl_neumann
                                                                    
+
                                                                    Table 37. Errors Rates in cyl_neumann
                                                                    
 
                                                                    @@ -315,159 +315,159 @@
 
+                  
                                                                    
+                    Significand Size
+                  
                                                                    
+                
+                  
                                                                    
+                    Platform and Compiler
+                  
                                                                    
+                
+                  
                                                                    
+                    J0 and J1
+                  
                                                                    
+                
+                  
                                                                    
+                    Jn (integer orders)
+                  
                                                                    
+                
+                  
                                                                    
+                    Jv (fractional orders)
+                  
                                                                    
+                
+                  
                                                                    
+                    53
+                  
                                                                    
+                
+                  
                                                                    
+                    Win32 / Visual C++ 8.0
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=330 Mean=54
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=34 Mean=9
+                  
                                                                    
+                  
                                                                    
+                    Cephes Peak=330
+                    Mean=54
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=923 Mean=83
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=500 Mean=54
+                  
                                                                    
+                  
                                                                    
+                    Cephes Peak=923
+                    Mean=83
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=561 Mean=36
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=1.4x106 Mean=7x104
+                  
                                                                    
+                  
                                                                    
+                    Cephes Peak=+INF
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    Red Hat Linux IA64 / G++ 3.4
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=470 Mean=56
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=843 Mean=51
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=741 Mean=51
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    SUSE Linux AMD64 / G++ 4.1
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=1300 Mean=424
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=2x104 Mean=8x103
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=1x105 Mean=6x103
+                  
                                                                    
+                
+                  
                                                                    
+                    113
+                  
                                                                    
+                
+                  
                                                                    
+                    HP-UX / HP aCC 6
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=180 Mean=63
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=340 Mean=150
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=2x104 Mean=1200
+                  
                                                                    
+                
                                                                    
 
 

 
                                                                    
 
-              
                                                                    
-                Significand Size
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Platform and Compiler
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                J0 and J1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Jn (integer orders)
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Jv (fractional orders)
-              
                                                                    
-                                                                                  		
 
                                                                    
 
 
                                                                    
 
-              
                                                                    
-                53
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Win32 / Visual C++ 8.0
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=330 Mean=54
-              
                                                                    
-              
                                                                    
-                GSL Peak=34 Mean=9
-              
                                                                    
-              
                                                                    
-                Cephes Peak=330
-                Mean=54
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=923 Mean=83
-              
                                                                    
-              
                                                                    
-                GSL Peak=500 Mean=54
-              
                                                                    
-              
                                                                    
-                Cephes Peak=923
-                Mean=83
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=561 Mean=36
-              
                                                                    
-              
                                                                    
-                GSL Peak=1.4x106 Mean=7x104
-              
                                                                    
-              
                                                                    
-                Cephes Peak=+INF
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Red Hat Linux IA64 / G++ 3.4
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=470 Mean=56
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=843 Mean=51
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=741 Mean=51
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                SUSE Linux AMD64 / G++ 4.1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=1300 Mean=424
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=2x104 Mean=8x103
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=1x105 Mean=6x103
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                113
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                HP-UX / HP aCC 6
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=180 Mean=63
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=340 Mean=150
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=2x104 Mean=1200
-              
                                                                    
-                                                                                  		
 
                                                                    
                                                                     
 
                                                                    
@@ -494,7 +494,7 @@
           were found.
         
                                                                    
 
                                                                    
-
+
           Implementation
         
                                                                    
 
                                                                    
@@ -667,7 +667,7 @@ are also computed by recursions (involving gamma functions), but
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html
index 3ecf623bc..464a34a1c 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html
@@ -2,8 +2,8 @@
 
 
 Bessel Function Overview
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
-
                                                                    
+
                                                                    
 
                                                                    
 
                                                                    
-
+
           Ordinary
           Bessel Functions
         
                                                                    
@@ -103,7 +103,7 @@ and is known as either a Bessel
           
         
                                                                    
 
                                                                    
-
+
           Modified
           Bessel Functions
         
                                                                    
@@ -167,7 +167,7 @@ respectively:
           
         
                                                                    
 
                                                                    
-
+
           Spherical
           Bessel Functions
         
                                                                    
@@ -208,7 +208,7 @@ is also known as the
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
index d6e943e73..1dfb3be90 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
@@ -2,8 +2,8 @@
 
 
 Modified Bessel Functions of the First and Second Kinds
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                                                                    
 
                                                                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                    
-
                                                                    
+
                                                                    
 
                                                                    
 
                                                                    
-
+
           Synopsis
         
                                                                    
 
                                                                    template <class T1, class T2>
@@ -44,7 +44,7 @@
 calculated-result-type cyl_bessel_k(T1 v, T2 x, const Policy&);
 
                                                                    
 
                                                                    
-
+
           Description
         
                                                                    
 
                                                                    
@@ -109,7 +109,7 @@
           
         
                                                                    
 
                                                                    
-
+
           Testing
         
                                                                    
 
                                                                    
@@ -118,7 +118,7 @@
           (with all the special case handling removed).
         
                                                                    
 
                                                                    
-
+
           Accuracy
         
                                                                    
 
                                                                    
@@ -129,7 +129,7 @@
           zero error. All values are relative errors in units of epsilon.
         
                                                                    
 
                                                                    
-
                                                                    Table 38. Errors Rates in cyl_bessel_i
                                                                    
+
                                                                    Table 38. Errors Rates in cyl_bessel_i
                                                                    
 
                                                                    @@ -138,95 +138,95 @@
 
+                  
                                                                    
+                    Significand Size
+                  
                                                                    
+                
+                  
                                                                    
+                    Platform and Compiler
+                  
                                                                    
+                
+                  
                                                                    
+                    Iv
+                  
                                                                    
+                
+                  
                                                                    
+                    53
+                  
                                                                    
+                
+                  
                                                                    
+                    Win32 / Visual C++ 8.0
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=10 Mean=3.4 GSL Peak=6000
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    Red Hat Linux IA64 / G++ 3.4
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=11 Mean=3
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    SUSE Linux AMD64 / G++ 4.1
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=11 Mean=4
+                  
                                                                    
+                
+                  
                                                                    
+                    113
+                  
                                                                    
+                
+                  
                                                                    
+                    HP-UX / HP aCC 6
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=15 Mean=4
+                  
                                                                    
+                
                                                                    
 
 

 
                                                                    
 
-              
                                                                    
-                Significand Size
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Platform and Compiler
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Iv
-              
                                                                    
-                                                                                  		
 
                                                                    
 
 
                                                                    
 
-              
                                                                    
-                53
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Win32 / Visual C++ 8.0
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=10 Mean=3.4 GSL Peak=6000
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Red Hat Linux IA64 / G++ 3.4
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=11 Mean=3
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                SUSE Linux AMD64 / G++ 4.1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=11 Mean=4
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                113
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                HP-UX / HP aCC 6
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=15 Mean=4
-              
                                                                    
-                                                                                  		
 
                                                                    
                                                                     
 
                                                                    
 
                                                                    
 
                                                                    
-
                                                                    Table 39. Errors Rates in cyl_bessel_k
                                                                    
+
                                                                    Table 39. Errors Rates in cyl_bessel_k
                                                                    
 
                                                                    @@ -235,98 +235,98 @@
 
+                  
                                                                    
+                    Significand Size
+                  
                                                                    
+                
+                  
                                                                    
+                    Platform and Compiler
+                  
                                                                    
+                
+                  
                                                                    
+                    Kv
+                  
                                                                    
+                
+                  
                                                                    
+                    53
+                  
                                                                    
+                
+                  
                                                                    
+                    Win32 / Visual C++ 8.0
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=9 Mean=2
+                  
                                                                    
+                  
                                                                    
+                    GSL Peak=9
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    Red Hat Linux IA64 / G++ 3.4
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=10 Mean=2
+                  
                                                                    
+                
+                  
                                                                    
+                    64
+                  
                                                                    
+                
+                  
                                                                    
+                    SUSE Linux AMD64 / G++ 4.1
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=10 Mean=2
+                  
                                                                    
+                
+                  
                                                                    
+                    113
+                  
                                                                    
+                
+                  
                                                                    
+                    HP-UX / HP aCC 6
+                  
                                                                    
+                
+                  
                                                                    
+                    Peak=12 Mean=5
+                  
                                                                    
+                
                                                                    
 
 

 
                                                                    
 
-              
                                                                    
-                Significand Size
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Platform and Compiler
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Kv
-              
                                                                    
-                                                                                  		
 
                                                                    
 
 
                                                                    
 
-              
                                                                    
-                53
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Win32 / Visual C++ 8.0
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=9 Mean=2
-              
                                                                    
-              
                                                                    
-                GSL Peak=9
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Red Hat Linux IA64 / G++ 3.4
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=10 Mean=2
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                64
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                SUSE Linux AMD64 / G++ 4.1
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=10 Mean=2
-              
                                                                    
-                                                                                  		
 
                                                                    
 
                                                                    
 
-              
                                                                    
-                113
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                HP-UX / HP aCC 6
-              
                                                                    
-                                                                                  		
 
-              
                                                                    
-                Peak=12 Mean=5
-              
                                                                    
-                                                                                  		
 
                                                                    
                                                                     
 
                                                                    
 
                                                                    
 
                                                                    
-
+
           Implementation
         
                                                                    
 
                                                                    
@@ -344,16 +344,16 @@
           The 0 and 1 cases use minimax rational approximations on finite and infinite
           intervals. The coefficients are from:
         
                                                                    
-
                                                                      
-
                                                                    • 
-            J.M. Blair and C.A. Edwards, Stable rational minimax approximations
-            to the modified Bessel functions I_0(x) and I_1(x), Atomic
-            Energy of Canada Limited Report 4928, Chalk River, 1974.
-          
                                                                      • 
-
                                                                    • 
-            S. Moshier, Methods and Programs for Mathematical Functions,
-            Ellis Horwood Ltd, Chichester, 1989.
-          
                                                                      • 
+
                                                                        
+
                                                                      • 
+              J.M. Blair and C.A. Edwards, Stable rational minimax approximations
+              to the modified Bessel functions I_0(x) and I_1(x), Atomic
+              Energy of Canada Limited Report 4928, Chalk River, 1974.
+            
                                                                        • 
+
                                                                      • 
+              S. Moshier, Methods and Programs for Mathematical Functions,
+              Ellis Horwood Ltd, Chichester, 1989.
+            
                                                                        • 
 
                                                                      
 
                                                                      
           While the 0.5 case is a simple trigonometric function:
@@ -479,7 +479,7 @@ are also computed by recursions (involving gamma functions), but
 
 
                                                                      
 
                                                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
index 0ffa5bfff..01b150f94 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
@@ -2,8 +2,8 @@
 
 
 Spherical Bessel Functions of the First and Second Kinds
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                                                                      
 
                                                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                      
-
                                                                      
+
                                                                      
 
                                                                      
 
                                                                      
-
+
           Synopsis
         
                                                                      
 
                                                                      template <class T1, class T2>
@@ -44,7 +44,7 @@
 calculated-result-type sph_neumann(unsigned v, T2 x, const Policy&);
 
                                                                      
 
                                                                      
-
+
           Description
         
                                                                      
 
                                                                      
@@ -97,7 +97,7 @@ for small x:
           
         
                                                                      
 
                                                                      
-
+
           Testing
         
                                                                      
 
                                                                      
@@ -106,7 +106,7 @@ for small x:
           implementation (with all the special case handling removed).
         
                                                                      
 
                                                                      
-
+
           Accuracy
         
                                                                      
 
                                                                      
@@ -116,7 +116,7 @@ for small x:
           refer to these functions for accuracy data.
         
                                                                      
 
                                                                      
-
+
           Implementation
         
                                                                      
 
                                                                      
@@ -156,7 +156,7 @@ for small x:
 
 
                                                                      
 
                                                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint.html b/doc/sf_and_dist/html/math_toolkit/special/ellint.html
index 320e0000a..cc6d4bf62 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint.html
@@ -2,8 +2,8 @@
 
 
 Elliptic Integrals
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                                                      
 
                                                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                      
-
                                                                      
+
                                                                      
 
                                                                      
@@ -51,7 +51,7 @@
 
 
                                                                      
 
                                                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                      
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
index 967f0016f..e81a8c654 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
@@ -2,8 +2,8 @@
 
 
 Elliptic Integrals of the First Kind - Legendre Form
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                                                                      
 
                                                                      
-PrevUpHomeNext
+PrevUpHomeNext
 
                                                                      
-
                                                                      
+
                                                                      
 
                                                                      
 
                                                                      
-
+
           Synopsis
         
                                                                      
 
                                                                      
@@ -55,7 +55,7 @@
 }} // namespaces
 
                  
 
                  
-
+
           Description
         
                  
 
                  
@@ -123,7 +123,7 @@
 
                  
         
                  
 
                  
-
+
           Accuracy
         
                  
 
                  
@@ -134,10 +134,8 @@
           All values are relative errors in units of epsilon.
         
                  
 
                  
-
                  Table 41. Errors Rates in the Elliptic Integrals of the
-        First Kind
                  
-
                  
+
                  Table 41. Errors Rates in the Elliptic Integrals of the First Kind
                  
+
                  @@ -146,98 +144,98 @@
 
+                  
                  
+                    Significand Size
+                  
                  
+                
+                  
                  
+                    Platform and Compiler
+                  
                  
+                
+                  
                  
+                    F(φ, k)
+                  
                  
+                
+                  
                  
+                    K(k)
+                  
                  
+                
+                  
                  
+                    53
+                  
                  
+                
+                  
                  
+                    Win32 / Visual C++ 8.0
+                  
                  
+                
+                  
                  
+                    Peak=3 Mean=0.8
+                  
                  
+                
+                  
                  
+                    Peak=1.8 Mean=0.7
+                  
                  
+                
+                  
                  
+                    64
+                  
                  
+                
+                  
                  
+                    Red Hat Linux / G++ 3.4
+                  
                  
+                
+                  
                  
+                    Peak=2.6 Mean=1.7
+                  
                  
+                
+                  
                  
+                    Peak=2.2 Mean=1.8
+                  
                  
+                
+                  
                  
+                    113
+                  
                  
+                
+                  
                  
+                    HP-UX / HP aCC 6
+                  
                  
+                
+                  
                  
+                    Peak=4.6 Mean=1.5
+                  
                  
+                
+                  
                  
+                    Peak=3.7 Mean=1.5
+                  
                  
+                
                  
 
 
 

 
                  
 
-              
                  
-                Significand Size
-              
                  
-                                		
 
-              
                  
-                Platform and Compiler
-              
                  
-                                		
 
-              
                  
-                F(φ, k)
-              
                  
-                                		
 
-              
                  
-                K(k)
-              
                  
-                                		
 
                  
 
 
                  
 
-              
                  
-                53
-              
                  
-                                		
 
-              
                  
-                Win32 / Visual C++ 8.0
-              
                  
-                                		
 
-              
                  
-                Peak=3 Mean=0.8
-              
                  
-                                		
 
-              
                  
-                Peak=1.8 Mean=0.7
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                64
-              
                  
-                                		
 
-              
                  
-                Red Hat Linux / G++ 3.4
-              
                  
-                                		
 
-              
                  
-                Peak=2.6 Mean=1.7
-              
                  
-                                		
 
-              
                  
-                Peak=2.2 Mean=1.8
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                113
-              
                  
-                                		
 
-              
                  
-                HP-UX / HP aCC 6
-              
                  
-                                		
 
-              
                  
-                Peak=4.6 Mean=1.5
-              
                  
-                                		
 
-              
                  
-                Peak=3.7 Mean=1.5
-              
                  
-                                		
 
                  
                   
 
                  
 
                  
 
                  
-
+
           Testing
         
                  
 
                  
@@ -247,7 +245,7 @@
           this implementation.
         
                  
 
                  
-
+
           Implementation
         
                  
 
                  
@@ -276,7 +274,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
index 9c8d97d65..1aa7c0932 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
@@ -2,8 +2,8 @@
 
 
 Elliptic Integrals of the Second Kind - Legendre Form
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
 
                  
-
+
           Synopsis
         
                  
 
                  
@@ -55,7 +55,7 @@
 }} // namespaces
 
                  
 
                  
-
+
           Description
         
                  
 
                  
@@ -123,7 +123,7 @@
 
                  
         
                  
 
                  
-
+
           Accuracy
         
                  
 
                  
@@ -134,10 +134,8 @@
           All values are relative errors in units of epsilon.
         
                  
 
                  
-
                  Table 42. Errors Rates in the Elliptic Integrals of the
-        Second Kind
                  
-
                  
+
                  Table 42. Errors Rates in the Elliptic Integrals of the Second Kind
                  
+
                  @@ -146,98 +144,98 @@
 
+                  
                  
+                    Significand Size
+                  
                  
+                
+                  
                  
+                    Platform and Compiler
+                  
                  
+                
+                  
                  
+                    F(φ, k)
+                  
                  
+                
+                  
                  
+                    K(k)
+                  
                  
+                
+                  
                  
+                    53
+                  
                  
+                
+                  
                  
+                    Win32 / Visual C++ 8.0
+                  
                  
+                
+                  
                  
+                    Peak=4.6 Mean=1.2
+                  
                  
+                
+                  
                  
+                    Peak=3.5 Mean=1.0
+                  
                  
+                
+                  
                  
+                    64
+                  
                  
+                
+                  
                  
+                    Red Hat Linux / G++ 3.4
+                  
                  
+                
+                  
                  
+                    Peak=4.3 Mean=1.1
+                  
                  
+                
+                  
                  
+                    Peak=4.6 Mean=1.2
+                  
                  
+                
+                  
                  
+                    113
+                  
                  
+                
+                  
                  
+                    HP-UX / HP aCC 6
+                  
                  
+                
+                  
                  
+                    Peak=5.8 Mean=2.2
+                  
                  
+                
+                  
                  
+                    Peak=10.8 Mean=2.3
+                  
                  
+                
                  
 
 
 

 
                  
 
-              
                  
-                Significand Size
-              
                  
-                                		
 
-              
                  
-                Platform and Compiler
-              
                  
-                                		
 
-              
                  
-                F(φ, k)
-              
                  
-                                		
 
-              
                  
-                K(k)
-              
                  
-                                		
 
                  
 
 
                  
 
-              
                  
-                53
-              
                  
-                                		
 
-              
                  
-                Win32 / Visual C++ 8.0
-              
                  
-                                		
 
-              
                  
-                Peak=4.6 Mean=1.2
-              
                  
-                                		
 
-              
                  
-                Peak=3.5 Mean=1.0
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                64
-              
                  
-                                		
 
-              
                  
-                Red Hat Linux / G++ 3.4
-              
                  
-                                		
 
-              
                  
-                Peak=4.3 Mean=1.1
-              
                  
-                                		
 
-              
                  
-                Peak=4.6 Mean=1.2
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                113
-              
                  
-                                		
 
-              
                  
-                HP-UX / HP aCC 6
-              
                  
-                                		
 
-              
                  
-                Peak=5.8 Mean=2.2
-              
                  
-                                		
 
-              
                  
-                Peak=10.8 Mean=2.3
-              
                  
-                                		
 
                  
                   
 
                  
 
                  
 
                  
-
+
           Testing
         
                  
 
                  
@@ -247,7 +245,7 @@
           this implementation.
         
                  
 
                  
-
+
           Implementation
         
                  
 
                  
@@ -276,7 +274,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
index c45f64657..0f577cd85 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
@@ -2,8 +2,8 @@
 
 
 Elliptic Integrals of the Third Kind - Legendre Form
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
 
                  
-
+
           Synopsis
         
                  
 
                  
@@ -55,7 +55,7 @@
 }} // namespaces
 
                  
 
                  
-
+
           Description
         
                  
 
                  
@@ -129,7 +129,7 @@
 
                  
         
                  
 
                  
-
+
           Accuracy
         
                  
 
                  
@@ -140,10 +140,8 @@
           All values are relative errors in units of epsilon.
         
                  
 
                  
-
                  Table 43. Errors Rates in the Elliptic Integrals of the
-        Third Kind
                  
-
                  
+
                  Table 43. Errors Rates in the Elliptic Integrals of the Third Kind
                  
+
                  @@ -152,98 +150,98 @@
 
+                  
                  
+                    Significand Size
+                  
                  
+                
+                  
                  
+                    Platform and Compiler
+                  
                  
+                
+                  
                  
+                    Π(n, φ, k)
+                  
                  
+                
+                  
                  
+                    Π(n, k)
+                  
                  
+                
+                  
                  
+                    53
+                  
                  
+                
+                  
                  
+                    Win32 / Visual C++ 8.0
+                  
                  
+                
+                  
                  
+                    Peak=29 Mean=2.2
+                  
                  
+                
+                  
                  
+                    Peak=3 Mean=0.8
+                  
                  
+                
+                  
                  
+                    64
+                  
                  
+                
+                  
                  
+                    Red Hat Linux / G++ 3.4
+                  
                  
+                
+                  
                  
+                    Peak=14 Mean=1.3
+                  
                  
+                
+                  
                  
+                    Peak=2.3 Mean=0.8
+                  
                  
+                
+                  
                  
+                    113
+                  
                  
+                
+                  
                  
+                    HP-UX / HP aCC 6
+                  
                  
+                
+                  
                  
+                    Peak=10 Mean=1.4
+                  
                  
+                
+                  
                  
+                    Peak=4.2 Mean=1.1
+                  
                  
+                
                  
 
 
 

 
                  
 
-              
                  
-                Significand Size
-              
                  
-                                		
 
-              
                  
-                Platform and Compiler
-              
                  
-                                		
 
-              
                  
-                Π(n, φ, k)
-              
                  
-                                		
 
-              
                  
-                Π(n, k)
-              
                  
-                                		
 
                  
 
 
                  
 
-              
                  
-                53
-              
                  
-                                		
 
-              
                  
-                Win32 / Visual C++ 8.0
-              
                  
-                                		
 
-              
                  
-                Peak=29 Mean=2.2
-              
                  
-                                		
 
-              
                  
-                Peak=3 Mean=0.8
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                64
-              
                  
-                                		
 
-              
                  
-                Red Hat Linux / G++ 3.4
-              
                  
-                                		
 
-              
                  
-                Peak=14 Mean=1.3
-              
                  
-                                		
 
-              
                  
-                Peak=2.3 Mean=0.8
-              
                  
-                                		
 
                  
 
                  
 
-              
                  
-                113
-              
                  
-                                		
 
-              
                  
-                HP-UX / HP aCC 6
-              
                  
-                                		
 
-              
                  
-                Peak=10 Mean=1.4
-              
                  
-                                		
 
-              
                  
-                Peak=4.2 Mean=1.1
-              
                  
-                                		
 
                  
                   
 
                  
 
                  
 
                  
-
+
           Testing
         
                  
 
                  
@@ -253,7 +251,7 @@
           this implementation.
         
                  
 
                  
-
+
           Implementation
         
                  
 
                  
@@ -290,8 +288,7 @@
           Π(n, φ+mπ, k) = Π(n, φ, k) + 2mΠ(n, k) ; n <= 1
         
                  
 
                  
-          Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1
-          [1]
+          Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1]
         
                  
 
                  
           are used to move φ to the range [0, π/2].
@@ -311,12 +308,12 @@
         
                  
 
                  
 
                  
-
                  [1] 
-              I haven't been able to find a literature reference for this relation,
-              but it appears to be the convention used by Mathematica. Intuitively
-              the first 2 * m * Π(n, k) terms cancel out as the
-              derivative alternates between +∞ and -∞.
-            
                  
+
                  [1] 
+            I haven't been able to find a literature reference for this relation,
+            but it appears to be the convention used by Mathematica. Intuitively
+            the first 2 * m * Π(n, k) terms cancel out as the
+            derivative alternates between +∞ and -∞.
+
                @@ -331,7 +328,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html index b9c0e1b55..9442b2c1d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html @@ -2,8 +2,8 @@ Elliptic Integrals - Carlson Form - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -100,7 +100,7 @@ }} // namespaces

                - + Description

                @@ -236,7 +236,7 @@

                - + Testing

                @@ -245,17 +245,11 @@

                Spot tests compare selected values with test data given in:

                -
                -

                -

                -

                - B. C. Carlson, Numerical - computation of real or complex elliptic integrals. - Numerical Algorithms, Volume 10, Number 1 / March, 1995, pp 13-26. -

                -

                -

                -
                +

                + B. C. Carlson, Numerical + computation of real or complex elliptic integrals. + Numerical Algorithms, Volume 10, Number 1 / March, 1995, pp 13-26. +

                Random test data generated using NTL::RR at 1000-bit precision and our implementation checks for rounding-errors and/or regressions. @@ -265,7 +259,7 @@ to verify their correctness: see the above Carlson paper for details.

                - + Accuracy

                @@ -276,7 +270,7 @@ All values are relative errors in units of epsilon.

                -

                Table 40. Errors Rates in the Carlson Elliptic Integrals

                +

                Table 40. Errors Rates in the Carlson Elliptic Integrals

                @@ -288,138 +282,138 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + RF +

                + +

                + RD +

                + +

                + RJ +

                + +

                + RC +

                + +

                + 53 +

                + +

                + Win32 / Visual C++ 8.0 +

                + +

                + Peak=2.9 Mean=0.75 +

                + +

                + Peak=2.6 Mean=0.9 +

                + +

                + Peak=108 Mean=6.9 +

                + +

                + Peak=2.4 Mean=0.6 +

                + +

                + 64 +

                + +

                + Red Hat Linux / G++ 3.4 +

                + +

                + Peak=2.5 Mean=0.75 +

                + +

                + Peak=2.7 Mean=0.9 +

                + +

                + Peak=105 Mean=8 +

                + +

                + Peak=1.9 Mean=0.7 +

                + +

                + 113 +

                + +

                + HP-UX / HP aCC 6 +

                + +

                + Peak=5.3 Mean=1.6 +

                + +

                + Peak=2.9 Mean=0.99 +

                + +

                + Peak=180 Mean=12 +

                + +

                + Peak=1.8 Mean=0.7 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - RF -

                -                 		-

                - RD -

                -                 		-

                - RJ -

                -                 		-

                - RC -

                -
                -

                - 53 -

                -                 		-

                - Win32 / Visual C++ 8.0 -

                -                 		-

                - Peak=2.9 Mean=0.75 -

                -                 		-

                - Peak=2.6 Mean=0.9 -

                -                 		-

                - Peak=108 Mean=6.9 -

                -                 		-

                - Peak=2.4 Mean=0.6 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux / G++ 3.4 -

                -                 		-

                - Peak=2.5 Mean=0.75 -

                -                 		-

                - Peak=2.7 Mean=0.9 -

                -                 		-

                - Peak=105 Mean=8 -

                -                 		-

                - Peak=1.9 Mean=0.7 -

                -
                -

                - 113 -

                -                 		-

                - HP-UX / HP aCC 6 -

                -                 		-

                - Peak=5.3 Mean=1.6 -

                -                 		-

                - Peak=2.9 Mean=0.99 -

                -                 		-

                - Peak=180 Mean=12 -

                -                 		-

                - Peak=1.8 Mean=0.7 -

                -

                - + Implementation

                @@ -467,7 +461,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html index 0666598e9..2fd03ae66 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html @@ -2,8 +2,8 @@ Elliptic Integral Overview - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +

                Elliptic Integral Overview @@ -30,45 +30,33 @@

                The main reference for the elliptic integrals is:

                -
                -

                -

                -

                - M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical - Functions with Formulas, Graphs, and Mathematical Tables, National - Bureau of Standards Applied Mathematics Series, U.S. Government Printing - Office, Washington, D.C. -

                -

                -

                -
                +

                + M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical + Functions with Formulas, Graphs, and Mathematical Tables, National Bureau + of Standards Applied Mathematics Series, U.S. Government Printing Office, + Washington, D.C. +

                Mathworld also contain a lot of useful background information:

                -
                -

                -

                -

                - Weisstein, - Eric W. "Elliptic Integral." From MathWorld--A Wolfram Web - Resource. -

                -

                -

                -
                +

                + Weisstein, + Eric W. "Elliptic Integral." From MathWorld--A Wolfram Web + Resource. +

                As does Wikipedia Elliptic integral.

                - + Notation

                All variables are real numbers unless otherwise noted.

                - + Definition

                @@ -110,7 +98,7 @@

                - +
                [Note][Note] Note
                @@ -130,7 +118,7 @@
                - +
                [Caution][Caution] Caution
                @@ -244,7 +232,7 @@

                - +
                [Note][Note] Note
                @@ -257,7 +245,7 @@
                - + Duplication Theorem
                @@ -269,7 +257,7 @@

                - + Carlson's Formulas
                @@ -287,7 +275,7 @@

                - + Numerical Algorithms
                @@ -301,109 +289,106 @@ integrals with satisfactory precisions.

                - + References

                Special mention goes to:

                -
                -

                -

                -

                - A. M. Legendre, Traitd des Fonctions Elliptiques et des Integrales - Euleriennes, Vol. 1. Paris (1825). -

                -

                -

                -
                +

                + A. M. Legendre, Traitd des Fonctions Elliptiques et des Integrales + Euleriennes, Vol. 1. Paris (1825). +

                However the main references are:

                -
                  -
                1. - M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical - Functions with Formulas, Graphs, and Mathematical Tables, National Bureau - of Standards Applied Mathematics Series, U.S. Government Printing Office, - Washington, D.C. -
                  2. -
                2. - B.C. Carlson, Computing elliptic integrals by duplication, - Numerische Mathematik, vol 33, 1 (1979). -
                  3. -
                3. - B.C. Carlson, Elliptic Integrals of the First Kind, - SIAM Journal on Mathematical Analysis, vol 8, 231 (1977). -
                  4. -
                4. - B.C. Carlson, Short Proofs of Three Theorems on Elliptic Integrals, - SIAM Journal on Mathematical Analysis, vol 9, 524 (1978). -
                  5. -
                5. - B.C. Carlson and E.M. Notis, ALGORITHM 577: Algorithms for - Incomplete Elliptic Integrals, ACM Transactions on Mathematmal - Software, vol 7, 398 (1981). -
                  6. -
                6. - B. C. Carlson, On computing elliptic integrals and functions. - J. Math. and Phys., 44 (1965), pp. 36-51. -
                  7. -
                7. - B. C. Carlson, A table of elliptic integrals of the second - kind. Math. Comp., 49 (1987), pp. 595-606. (Supplement, ibid., - pp. S13-S17.) -
                  8. -
                8. - B. C. Carlson, A table of elliptic integrals of the third kind. - Math. Comp., 51 (1988), pp. 267-280. (Supplement, ibid., pp. S1-S5.) -
                  9. -
                9. - B. C. Carlson, A table of elliptic integrals: cubic cases. - Math. Comp., 53 (1989), pp. 327-333. -
                  10. -
                10. - B. C. Carlson, A table of elliptic integrals: one quadratic - factor. Math. Comp., 56 (1991), pp. 267-280. -
                  11. -
                11. - B. C. Carlson, A table of elliptic integrals: two quadratic - factors. Math. Comp., 59 (1992), pp. 165-180. -
                  12. -
                12. - B. C. Carlson, Numerical - computation of real or complex elliptic integrals. - Numerical Algorithms, Volume 10, Number 1 / March, 1995, p13-26. -
                  13. -
                13. - B. C. Carlson and John L. Gustafson, Asymptotic - Approximations for Symmetric Elliptic Integrals, SIAM - Journal on Mathematical Analysis, Volume 25, Issue 2 (March 1994), 288-303. -
                  14. +
                    +
                  1. + M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical + Functions with Formulas, Graphs, and Mathematical Tables, National + Bureau of Standards Applied Mathematics Series, U.S. Government Printing + Office, Washington, D.C. +
                    2. +
                  2. + B.C. Carlson, Computing elliptic integrals by duplication, + Numerische Mathematik, vol 33, 1 (1979). +
                    3. +
                  3. + B.C. Carlson, Elliptic Integrals of the First Kind, + SIAM Journal on Mathematical Analysis, vol 8, 231 (1977). +
                    4. +
                  4. + B.C. Carlson, Short Proofs of Three Theorems on Elliptic + Integrals, SIAM Journal on Mathematical Analysis, vol 9, + 524 (1978). +
                    5. +
                  5. + B.C. Carlson and E.M. Notis, ALGORITHM 577: Algorithms for + Incomplete Elliptic Integrals, ACM Transactions on Mathematmal + Software, vol 7, 398 (1981). +
                    6. +
                  6. + B. C. Carlson, On computing elliptic integrals and functions. + J. Math. and Phys., 44 (1965), pp. 36-51. +
                    7. +
                  7. + B. C. Carlson, A table of elliptic integrals of the second + kind. Math. Comp., 49 (1987), pp. 595-606. (Supplement, + ibid., pp. S13-S17.) +
                    8. +
                  8. + B. C. Carlson, A table of elliptic integrals of the third + kind. Math. Comp., 51 (1988), pp. 267-280. (Supplement, + ibid., pp. S1-S5.) +
                    9. +
                  9. + B. C. Carlson, A table of elliptic integrals: cubic cases. + Math. Comp., 53 (1989), pp. 327-333. +
                    10. +
                  10. + B. C. Carlson, A table of elliptic integrals: one quadratic + factor. Math. Comp., 56 (1991), pp. 267-280. +
                    11. +
                  11. + B. C. Carlson, A table of elliptic integrals: two quadratic + factors. Math. Comp., 59 (1992), pp. 165-180. +
                    12. +
                  12. + B. C. Carlson, Numerical + computation of real or complex elliptic integrals. + Numerical Algorithms, Volume 10, Number 1 / March, 1995, p13-26. +
                    13. +
                  13. + B. C. Carlson and John L. Gustafson, Asymptotic + Approximations for Symmetric Elliptic Integrals, + SIAM Journal on Mathematical Analysis, Volume 25, Issue 2 (March 1994), + 288-303. +

                  The following references, while not directly relevent to our implementation, may also be of interest:

                  -
                    -
                  1. - R. Burlisch, Numerical Compuation of Elliptic Integrals and - Elliptic Functions. Numerical Mathematik 7, 78-90. -
                    2. -
                  2. - R. Burlisch, An extension of the Bartky Transformation to Incomplete - Elliptic Integrals of the Third Kind. Numerical Mathematik - 13, 266-284. -
                    3. -
                  3. - R. Burlisch, Numerical Compuation of Elliptic Integrals and - Elliptic Functions. III. Numerical Mathematik 13, 305-315. -
                    4. -
                  4. - T. Fukushima and H. Ishizaki, Numerical - Computation of Incomplete Elliptic Integrals of a General Form. - Celestial Mechanics and Dynamical Astronomy, Volume 59, Number 3 / July, - 1994, 237-251. -
                    5. +
                      +
                    1. + R. Burlisch, Numerical Compuation of Elliptic Integrals and + Elliptic Functions. Numerical Mathematik 7, 78-90. +
                      2. +
                    2. + R. Burlisch, An extension of the Bartky Transformation to + Incomplete Elliptic Integrals of the Third Kind. Numerical + Mathematik 13, 266-284. +
                      3. +
                    3. + R. Burlisch, Numerical Compuation of Elliptic Integrals and + Elliptic Functions. III. Numerical Mathematik 13, 305-315. +
                      4. +
                    4. + T. Fukushima and H. Ishizaki, Numerical + Computation of Incomplete Elliptic Integrals of a General Form. + Celestial Mechanics and Dynamical Astronomy, Volume 59, Number 3 / + July, 1994, 237-251. +
                  @@ -418,7 +403,7 @@
                  -PrevUpHomeNext +PrevUpHomeNext
                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint.html b/doc/sf_and_dist/html/math_toolkit/special/expint.html index 12ed8aa1e..a94a454ce 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint.html @@ -2,8 +2,8 @@ Exponential Integrals - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -45,7 +45,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index d258bb618..1c9a62e78 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -2,8 +2,8 @@ Exponential Integral Ei - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -63,7 +63,7 @@

                - + Description 
                template <class T>
@@ -83,7 +83,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -95,7 +95,7 @@
           error.
         
                
 
                
-
                Table 46. Errors In the Function expint(z)
                
+
                Table 46. Errors In the Function expint(z)
                
 
                @@ -104,95 +104,95 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    Error
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=2.4 Mean=0.6
+                  
                
+                  
                
+                    GSL Peak=8.9 Mean=0.7
+                  
                
+                  
                
+                    SPECFUN (Cody) Peak=2.5 Mean=0.6
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    RedHat Linux IA_EM64, gcc-4.1
+                  
                
+                
+                  
                
+                    Peak=5.1 Mean=0.8
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-4.1
+                  
                
+                
+                  
                
+                    Peak=5.0 Mean=0.8
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=1.9 Mean=0.63
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                Error
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=2.4 Mean=0.6
-              
                
-              
                
-                GSL Peak=8.9 Mean=0.7
-              
                
-              
                
-                SPECFUN (Cody) Peak=2.5 Mean=0.6
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                RedHat Linux IA_EM64, gcc-4.1
-              
                
-                              		
 
-              
                
-                Peak=5.1 Mean=0.8
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-4.1
-              
                
-                              		
 
-              
                
-                Peak=5.0 Mean=0.8
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=1.9 Mean=0.63
-              
                
-                              		
 
                
                 
 
                
@@ -207,7 +207,7 @@
           slightly over the range [4,6].
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -222,7 +222,7 @@
           check.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -252,11 +252,9 @@
           a minimax rational approximation rescaled so that it is evaluated over
           [-1,1]. Note that while the rational approximation over [0,6] converges
           rapidly to the minimax solution it is rather ill-conditioned in practice.
-          Cody and Thacher
-          [2]
-          experienced the same issue and converted the polynomials into Chebeshev
-          form to ensure stable computation. By experiment we found that the polynomials
-          are just as stable in polynomial as Chebyshev form, provided
+          Cody and Thacher [2] experienced the same issue and converted the polynomials into
+          Chebeshev form to ensure stable computation. By experiment we found that
+          the polynomials are just as stable in polynomial as Chebyshev form, provided
           they are computed over the interval [-1,1].
         
                
 
                
@@ -284,12 +282,12 @@
         
                
 
                
 
                
-
                [2] 
-              W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations
-              for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649,
-              and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for
-              the exponential integral Ei(x), Math. Comp. 23 (1969), 289-303.
-            
                
+
                [2] 
+            W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations
+            for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649, and
+            W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the exponential
+            integral Ei(x), Math. Comp. 23 (1969), 289-303.
+          
                
 
                
 
                
 
@@ -304,7 +302,7 @@
 
                
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html
index 399083ff4..2ae7040d7 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html
@@ -2,8 +2,8 @@
 
 
 Exponential Integral En
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -63,7 +63,7 @@
 
                
         
                
 
                
-
+
           Description
         
                
 
                template <class T>
@@ -83,7 +83,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -94,7 +94,7 @@
           the one shown will have effectively zero error.
         
                
 
                
-
                Table 45. Errors In the Function expint(n, z)
                
+
                Table 45. Errors In the Function expint(n, z)
                
 
                @@ -104,128 +104,128 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    En
+                  
                
+                
+                  
                
+                    E1
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=7.1 Mean=1.8
+                  
                
+                  
                
+                    Cephes Peak=5.1
+                    Mean=1.3
+                  
                
+                
+                  
                
+                    Peak=0.99 Mean=0.5
+                  
                
+                  
                
+                    Cephes Peak=3.1
+                    Mean=1.1
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    RedHat Linux IA_EM64, gcc-4.1
+                  
                
+                
+                  
                
+                    Peak=9.9 Mean=2.1
+                  
                
+                
+                  
                
+                    Peak=0.97 Mean=0.4
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-4.1
+                  
                
+                
+                  
                
+                    Peak=9.9 Mean=2.1
+                  
                
+                
+                  
                
+                    Peak=0.97 Mean=0.4
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=23.3 Mean=3.7
+                  
                
+                
+                  
                
+                    Peak=1.6 Mean=0.5
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                En
-              
                
-                              		
 
-              
                
-                E1
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=7.1 Mean=1.8
-              
                
-              
                
-                Cephes Peak=5.1
-                Mean=1.3
-              
                
-                              		
 
-              
                
-                Peak=0.99 Mean=0.5
-              
                
-              
                
-                Cephes Peak=3.1
-                Mean=1.1
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                RedHat Linux IA_EM64, gcc-4.1
-              
                
-                              		
 
-              
                
-                Peak=9.9 Mean=2.1
-              
                
-                              		
 
-              
                
-                Peak=0.97 Mean=0.4
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-4.1
-              
                
-                              		
 
-              
                
-                Peak=9.9 Mean=2.1
-              
                
-                              		
 
-              
                
-                Peak=0.97 Mean=0.4
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=23.3 Mean=3.7
-              
                
-                              		
 
-              
                
-                Peak=1.6 Mean=0.5
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
+
           Testing
         
                
 
                
@@ -240,7 +240,7 @@
           check.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -297,7 +297,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/extern_c.html b/doc/sf_and_dist/html/math_toolkit/special/extern_c.html
deleted file mode 100644
index 473d8ba41..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/extern_c.html
+++ /dev/null
@@ -1,53 +0,0 @@
-
-
-
-TR1 and C99 external "C" Functions
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
                 C99 and TR1 C Functions
-        Overview
                
-
                 C99 C Functions
                
-
                 TR1 C Functions
-        Quick Reference
                
-
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
-
                
-
-
diff --git a/doc/sf_and_dist/html/math_toolkit/special/extern_c/c99.html b/doc/sf_and_dist/html/math_toolkit/special/extern_c/c99.html
deleted file mode 100644
index ede3938e9..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/extern_c/c99.html
+++ /dev/null
@@ -1,481 +0,0 @@
-
-
-
-C99 C Functions
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
-          Supported
-          C99 Functions
-        
                
-
                namespace boost{ namespace math{ namespace tr1{ extern "C"{
-
-typedef unspecified float_t;
-typedef unspecified double_t;
-
-double acosh(double x);
-float acoshf(float x);
-long double acoshl(long double x);
-
-double asinh(double x);
-float asinhf(float x);
-long double asinhl(long double x);
-
-double atanh(double x);
-float atanhf(float x);
-long double atanhl(long double x);
-
-double cbrt(double x);
-float cbrtf(float x);
-long double cbrtl(long double x);
-
-double copysign(double x, double y);
-float copysignf(float x, float y);
-long double copysignl(long double x, long double y);
-
-double erf(double x);
-float erff(float x);
-long double erfl(long double x);
-
-double erfc(double x);
-float erfcf(float x);
-long double erfcl(long double x);
-
-double expm1(double x);
-float expm1f(float x);
-long double expm1l(long double x);
-
-double fmax(double x, double y);
-float fmaxf(float x, float y);
-long double fmaxl(long double x, long double y);
-
-double fmin(double x, double y);
-float fminf(float x, float y);
-long double fminl(long double x, long double y);
-
-double hypot(double x, double y);
-float hypotf(float x, float y);
-long double hypotl(long double x, long double y);
-
-double lgamma(double x);
-float lgammaf(float x);
-long double lgammal(long double x);
-
-long long llround(double x);
-long long llroundf(float x);
-long long llroundl(long double x);
-
-double log1p(double x);
-float log1pf(float x);
-long double log1pl(long double x);
-
-long lround(double x);
-long lroundf(float x);
-long lroundl(long double x);
-
-double nextafter(double x, double y);
-float nextafterf(float x, float y);
-long double nextafterl(long double x, long double y);
-
-double nexttoward(double x, long double y);
-float nexttowardf(float x, long double y);
-long double nexttowardl(long double x, long double y);
-
-double round(double x);
-float roundf(float x);
-long double roundl(long double x);
-
-double tgamma(double x);
-float tgammaf(float x);
-long double tgammal(long double x);
-
-double trunc(double x);
-float truncf(float x);
-long double truncl(long double x);
-
-}}}} // namespaces
-
                
-
                
-          In addition sufficient additional overloads of the double
-          versions of the above functions are provided, so that calling the function
-          with any mixture of float,
-          double, long
-          double, or integer
-          arguments is supported, with the return type determined by the result
-          type calculation rules.
-        
                
-
                
-          For example:
-        
                
-
                acoshf(2.0f);  // float version, returns float.
-acosh(2.0f);   // also calls the float version and returns float.
-acosh(2.0);    // double version, returns double.
-acoshl(2.0L);  // long double version, returns a long double.
-acosh(2.0L);   // also calls the long double version.
-acosh(2);      // integer argument is treated as a double, returns double.
-
                
-
                
-
-          Quick
-          Reference
-        
                
-
                
-          More detailed descriptions of these functions are available in the C99
-          standard.
-        
                
-
                typedef unspecified float_t;
-typedef unspecified double_t;
-
                
-
                
-          In this implementation float_t
-          is the same as type float,
-          and double_t the same as
-          type double unless the preprocessor
-          symbol FLT_EVAL_METHOD is defined, in which case these are set as follows:
-        
                
-
                
-----
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                




                
-                
                
-                  FLT_EVAL_METHOD
-                
                
-                                		
-                
                
-                  float_t
-                
                
-                                		
-                
                
-                  double_t
-                
                
-                
                
-                
                
-                  0
-                
                
-                                		
-                
                
-                  float
-                
                
-                                		
-                
                
-                  double
-                
                
-                
                
-                
                
-                  1
-                
                
-                                		
-                
                
-                  double
-                
                
-                                		
-                
                
-                  double
-                
                
-                
                
-                
                
-                  2
-                
                
-                                		
-                
                
-                  long double
-                
                
-                                		
-                
                
-                  long double
-                
                
-                
                
-
                double acosh(double x);
-float acoshf(float x);
-long double acoshl(long double x);
-
                
-
                
-          Returns the inverse hyperbolic cosine of x.
-        
                
-
                
-          See also acosh
-          for the full template (header only) version of this function.
-        
                
-
                double asinh(double x);
-float asinhf(float x);
-long double asinhl(long double x);
-
                
-
                
-          Returns the inverse hyperbolic sine of x.
-        
                
-
                
-          See also asinh
-          for the full template (header only) version of this function.
-        
                
-
                double atanh(double x);
-float atanhf(float x);
-long double atanhl(long double x);
-
                
-
                
-          Returns the inverse hyperbolic tangent of x.
-        
                
-
                
-          See also atanh
-          for the full template (header only) version of this function.
-        
                
-
                double cbrt(double x);
-float cbrtf(float x);
-long double cbrtl(long double x);
-
                
-
                
-          Returns the cubed root of x.
-        
                
-
                
-          See also cbrt for
-          the full template (header only) version of this function.
-        
                
-
                double copysign(double x, double y);
-float copysignf(float x, float y);
-long double copysignl(long double x, long double y);
-
                
-
                
-          Returns a value with the magnitude of x and the sign
-          of y.
-        
                
-
                double erf(double x);
-float erff(float x);
-long double erfl(long double x);
-
                
-
                
-          Returns the error function of x:
-        
                
-
                
-          
-        
                
-
                
-          See also erf
-          for the full template (header only) version of this function.
-        
                
-
                double erfc(double x);
-float erfcf(float x);
-long double erfcl(long double x);
-
                
-
                
-          Returns the complementary error function of x 1-erf(x)
-          without the loss of precision implied by the subtraction.
-        
                
-
                
-          See also erfc
-          for the full template (header only) version of this function.
-        
                
-
                double expm1(double x);
-float expm1f(float x);
-long double expm1l(long double x);
-
                
-
                
-          Returns exp(x)-1
-          without the loss of precision implied by the subtraction.
-        
                
-
                
-          See also expm1
-          for the full template (header only) version of this function.
-        
                
-
                double fmax(double x, double y);
-float fmaxf(float x, float y);
-long double fmaxl(long double x, long double y);
-
                
-
                
-          Returns the larger (most positive) of x and y.
-        
                
-
                double fmin(double x, double y);
-float fminf(float x, float y);
-long double fminl(long double x, long double y);
-
                
-
                
-          Returns the smaller (most negative) of x and y.
-        
                
-
                double hypot(double x, double y);
-float hypotf(float x, float y);
-long double hypotl(long double x, long double y);
-
                
-
                
-          Returns sqrt(x*x
-          + y*y)
-          without the danger of numeric overflow implied by that formulation.
-        
                
-
                
-          See also hypot
-          for the full template (header only) version of this function.
-        
                
-
                double lgamma(double x);
-float lgammaf(float x);
-long double lgammal(long double x);
-
                
-
                
-          Returns the log of the gamma function of x.
-        
                
-
                
-          
-        
                
-
                
-          See also lgamma
-          for the full template (header only) version of this function.
-        
                
-
                long long llround(double x);
-long long llroundf(float x);
-long long llroundl(long double x);
-
                
-
                
-          Returns the value x rounded to the nearest integer
-          as a long long:
-          equivalent to floor(x + 0.5)
-        
                
-
                
-          See also round
-          for the full template (header only) version of this function.
-        
                
-
                double log1p(double x);
-float log1pf(float x);
-long double log1pl(long double x);
-
                
-
                
-          Returns the log(x+1) without the loss of precision implied
-          by that formulation.
-        
                
-
                
-          See also log1p
-          for the full template (header only) version of this function.
-        
                
-
                long lround(double x);
-long lroundf(float x);
-long lroundl(long double x);
-
                
-
                
-          Returns the value x rounded to the nearest integer
-          as a long: equivalent to
-          floor(x + 0.5)
-        
                
-
                
-          See also round
-          for the full template (header only) version of this function.
-        
                
-
                double nextafter(double x, double y);
-float nextafterf(float x, float y);
-long double nextafterl(long double x, long double y);
-
                
-
                
-          Returns the next representable floating point number after x
-          in the direction of y, or x if
-          x ==
-          y.
-        
                
-
                double nexttoward(double x, long double y);
-float nexttowardf(float x, long double y);
-long double nexttowardl(long double x, long double y);
-
                
-
                
-          As nextafter, but with
-          y always expressed as a long
-          double.
-        
                
-
                double round(double x);
-float roundf(float x);
-long double roundl(long double x);
-
                
-
                
-          Returns the value x rounded to the nearest integer:
-          equivalent to floor(x + 0.5)
-        
                
-
                
-          See also round
-          for the full template (header only) version of this function.
-        
                
-
                double tgamma(double x);
-float tgammaf(float x);
-long double tgammal(long double x);
-
                
-
                
-          Returns the gamma function of x:
-        
                
-
                
-          
-        
                
-
                
-          See also tgamma
-          for the full template (header only) version of this function.
-        
                
-
                double trunc(double x);
-float truncf(float x);
-long double truncl(long double x);
-
                
-
                
-          Returns x truncated to the nearest integer.
-        
                
-
                
-          See also trunc
-          for the full template (header only) version of this function.
-        
                
-
                
-          See also C99
-          ISO Standard
-        
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1.html b/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1.html
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+++ /dev/null
@@ -1,695 +0,0 @@
-
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-
-C99 and TR1 C Functions Overview
-
-
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                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
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-PrevUpHomeNext
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-          
                
-
                
-            Many of the special functions included in this library are also a part
-            of the either the C99
-            Standard ISO/IEC 9899:1999 or the Technical
-            Report on C++ Library Extensions. Therefore this library includes
-            a thin wrapper header boost/math/tr1.hpp
-            that provides compatibility with these two standards.
-          
                
-
                
-          
                
-
                
-            There are various pros and cons to using the library in this way:
-          
                
-
                
-          
                
-
                
-            Pros:
-          
                
-
                
-          
                
-
                  
-
                • 
-              The header to include is lightweight (i.e. fast to compile).
-            
                  • 
-
                • 
-              The functions have extern "C" linkage, and so are usable
-              from other languages (not just C and C++).
-            
                  • 
-
                • 
-              C99 and C++ TR1 Standard compatibility.
-            
                  • 
-
                
-
                
-          
                
-
                
-            Cons:
-          
                
-
                
-          
                
-
                  
-
                • 
-              You will need to compile and link to the external Boost.Math libraries.
-            
                  • 
-
                • 
-              Limited to support for the types, float,
-              double and long double.
-            
                  • 
-
                • 
-              Error handling is handled via setting ::errno and returning NaN's and
-              infinities: this may be less flexible than an C++ exception based approach.
-            
                  • 
-
                
-
                
-          
                
-
                
-
-
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-
-
                [Note]Note
                
-              The separate libraries are required only
-              if you choose to use boost/math/tr1.hpp rather than some other Boost.Math
-              header, the rest of Boost.Math remains header-only.
-            
                
-
                
-          
                
-
                
-            The separate libraries required in order to use tr1.hpp can be compiled
-            using bjam from within the libs/math/build directory, or from the Boost
-            root directory using the usual Boost-wide install procedure. Alternatively
-            the source files are located in libs/math/src and each have the same
-            name as the function they implement. The various libraries are named
-            as follows:
-          
                
-
                
-          
                
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-----
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-
                




                
-                  
                
-                    Name
-                  
                
-                                  		
-                  
                
-                    Type
-                  
                
-                                  		
-                  
                
-                    Functions
-                  
                
-                  
                
-                  
                
-                    boost_math_c99f-<suffix>
-                  
                
-                                  		
-                  
                
-                    float
-                  
                
-                                  		
-                  
                
-                    C99 Functions
-                  
                
-                  
                
-                  
                
-                    boost_math_c99-<suffix>
-                  
                
-                                  		
-                  
                
-                    double
-                  
                
-                                  		
-                  
                
-                    C99 Functions
-                  
                
-                  
                
-                  
                
-                    boost_math_c99l-<suffix>
-                  
                
-                                  		
-                  
                
-                    long double
-                  
                
-                                  		
-                  
                
-                    C99 Functions
-                  
                
-                  
                
-                  
                
-                    boost_math_tr1f-<suffix>
-                  
                
-                                  		
-                  
                
-                    float
-                  
                
-                                  		
-                  
                
-                    TR1 Functions
-                  
                
-                  
                
-                  
                
-                    boost_math_tr1-<suffix>
-                  
                
-                                  		
-                  
                
-                    double
-                  
                
-                                  		
-                  
                
-                    TR1 Functions
-                  
                
-                  
                
-                  
                
-                    boost_math_tr1l-<suffix>
-                  
                
-                                  		
-                  
                
-                    long double
-                  
                
-                                  		
-                  
                
-                    TR1 Functions
-                  
                
-                  
                
-
                
-          
                
-
                
-            Where <suffix> encodes the compiler and build options
-            used to build the libraries: for example "libboost_math_tr1-vc80-mt-gd.lib"
-            would be the statically linked TR1 library to use with Visual C++ 8.0,
-            in multithreading debug mode, with the DLL VC++ runtime, where as "boost_math_tr1-vc80-mt.lib"
-            would be import library for the TR1 DLL to be used with Visual C++ 8.0
-            with the release multithreaded DLL VC++ runtime. Refer to the getting
-            started guide for a full
-            explanation of the <suffix>
-            meanings.
-          
                
-
                
-          
                
-
                
-
-
-
-
-
-
                [Note]Note
                
-
                
-              Visual C++ users will typically have the correct library variant to
-              link against selected for them by boost/math/tr1.hpp based on your
-              compiler settings.
-            
                
-
                
-              Users will need to define BOOST_MATH_TR1_DYN_LINK when building their
-              code if they want to link against the DLL versions of these libraries
-              rather than the static versions.
-            
                
-
                
-              Users can disable auto-linking by defining BOOST_MATH_TR1_NO_LIB when
-              building: this is typically only used when linking against a customised
-              build of the libraries.
-            
                
-
                
-
                
-          
                
-
                
-
-
-
-
-
-
                [Note]Note
                
-              Linux and Unix users will generally only have one variant of these
-              libraries installed, and can generally just link against -lboost_math_tr1
-              etc.
-            
                
-
                
-          
-          
                
-
                
-
-            Usage
-            Recomendations
-          
                
-
                
-          
                
-
                
-            This library now presents the user with a choice:
-          
                
-
                
-          
                
-
                  
-
                • 
-              To include the header only versions of the functions and have an easier
-              time linking, but a longer compile time.
-            
                  • 
-
                • 
-              To include the TR1 headers and link against an external library.
-            
                  • 
-
                
-
                
-          
                
-
                
-            Which option you choose depends largely on how you prefer to work and
-            how your system is set up.
-          
                
-
                
-          
                
-
                
-            For example a casual user who just needs the acosh function, would probably
-            be better off including <boost/math/special_functions/acosh.hpp>
-            and using boost::math::acosh(x)
-            in their code.
-          
                
-
                
-          
                
-
                
-            However, for large scale software development where compile times are
-            significant, and where the Boost libraries are already built and installed
-            on the system, then including <boost/math/tr1.hpp>
-            and using boost::math::tr1::acosh(x)
-            will speed up compile times, reduce object files sizes (since there are
-            no templates being instantiated any more), and also speed up debugging
-            runtimes - since the externally compiled libraries can be compiler optimised,
-            rather than built using full settings - the difference in performance
-            between release and debug
-            builds can be as much as 20 times, so for complex applications
-            this can be a big win.
-          
                
-
                
-          
-          
                
-
                
-
-            Supported
-            C99 Functions
-          
                
-
                
-          
                
-
                
-            See also the quick
-            reference guide for these functions.
-          
                
-
                
-          
-
                
-
                namespace boost{ namespace math{ namespace tr1{ extern "C"{
-
-typedef unspecified float_t;
-typedef unspecified double_t;
-
-double acosh(double x);
-float acoshf(float x);
-long double acoshl(long double x);
-
-double asinh(double x);
-float asinhf(float x);
-long double asinhl(long double x);
-
-double atanh(double x);
-float atanhf(float x);
-long double atanhl(long double x);
-
-double cbrt(double x);
-float cbrtf(float x);
-long double cbrtl(long double x);
-
-double copysign(double x, double y);
-float copysignf(float x, float y);
-long double copysignl(long double x, long double y);
-
-double erf(double x);
-float erff(float x);
-long double erfl(long double x);
-
-double erfc(double x);
-float erfcf(float x);
-long double erfcl(long double x);
-
-double expm1(double x);
-float expm1f(float x);
-long double expm1l(long double x);
-
-double fmax(double x, double y);
-float fmaxf(float x, float y);
-long double fmaxl(long double x, long double y);
-
-double fmin(double x, double y);
-float fminf(float x, float y);
-long double fminl(long double x, long double y);
-
-double hypot(double x, double y);
-float hypotf(float x, float y);
-long double hypotl(long double x, long double y);
-
-double lgamma(double x);
-float lgammaf(float x);
-long double lgammal(long double x);
-
-long long llround(double x);
-long long llroundf(float x);
-long long llroundl(long double x);
-
-double log1p(double x);
-float log1pf(float x);
-long double log1pl(long double x);
-
-long lround(double x);
-long lroundf(float x);
-long lroundl(long double x);
-
-double nextafter(double x, double y);
-float nextafterf(float x, float y);
-long double nextafterl(long double x, long double y);
-
-double nexttoward(double x, long double y);
-float nexttowardf(float x, long double y);
-long double nexttowardl(long double x, long double y);
-
-double round(double x);
-float roundf(float x);
-long double roundl(long double x);
-
-double tgamma(double x);
-float tgammaf(float x);
-long double tgammal(long double x);
-
-double trunc(double x);
-float truncf(float x);
-long double truncl(long double x);
-
-}}}} // namespaces
-
                
-
                
-          
-          
                
-
                
-
-            Supported
-            TR1 Functions
-          
                
-
                
-          
                
-
                
-            See also the quick
-            reference guide for these functions.
-          
                
-
                
-          
-
                
-
                namespace boost{ namespace math{ namespace tr1{ extern "C"{
-   
-// [5.2.1.1] associated Laguerre polynomials:
-double assoc_laguerre(unsigned n, unsigned m, double x);
-float assoc_laguerref(unsigned n, unsigned m, float x);
-long double assoc_laguerrel(unsigned n, unsigned m, long double x);
-
-// [5.2.1.2] associated Legendre functions:
-double assoc_legendre(unsigned l, unsigned m, double x);
-float assoc_legendref(unsigned l, unsigned m, float x);
-long double assoc_legendrel(unsigned l, unsigned m, long double x);
-
-// [5.2.1.3] beta function:
-double beta(double x, double y);
-float betaf(float x, float y);
-long double betal(long double x, long double y);
-
-// [5.2.1.4] (complete) elliptic integral of the first kind:
-double comp_ellint_1(double k);
-float comp_ellint_1f(float k);
-long double comp_ellint_1l(long double k);
-
-// [5.2.1.5] (complete) elliptic integral of the second kind:
-double comp_ellint_2(double k);
-float comp_ellint_2f(float k);
-long double comp_ellint_2l(long double k);
-
-// [5.2.1.6] (complete) elliptic integral of the third kind:
-double comp_ellint_3(double k, double nu);
-float comp_ellint_3f(float k, float nu);
-long double comp_ellint_3l(long double k, long double nu);
-
-// [5.2.1.8] regular modified cylindrical Bessel functions:
-double cyl_bessel_i(double nu, double x);
-float cyl_bessel_if(float nu, float x);
-long double cyl_bessel_il(long double nu, long double x);
-
-// [5.2.1.9] cylindrical Bessel functions (of the first kind):
-double cyl_bessel_j(double nu, double x);
-float cyl_bessel_jf(float nu, float x);
-long double cyl_bessel_jl(long double nu, long double x);
-
-// [5.2.1.10] irregular modified cylindrical Bessel functions:
-double cyl_bessel_k(double nu, double x);
-float cyl_bessel_kf(float nu, float x);
-long double cyl_bessel_kl(long double nu, long double x);
-
-// [5.2.1.11] cylindrical Neumann functions;
-// cylindrical Bessel functions (of the second kind):
-double cyl_neumann(double nu, double x);
-float cyl_neumannf(float nu, float x);
-long double cyl_neumannl(long double nu, long double x);
-
-// [5.2.1.12] (incomplete) elliptic integral of the first kind:
-double ellint_1(double k, double phi);
-float ellint_1f(float k, float phi);
-long double ellint_1l(long double k, long double phi);
-
-// [5.2.1.13] (incomplete) elliptic integral of the second kind:
-double ellint_2(double k, double phi);
-float ellint_2f(float k, float phi);
-long double ellint_2l(long double k, long double phi);
-
-// [5.2.1.14] (incomplete) elliptic integral of the third kind:
-double ellint_3(double k, double nu, double phi);
-float ellint_3f(float k, float nu, float phi);
-long double ellint_3l(long double k, long double nu, long double phi);
-
-// [5.2.1.15] exponential integral:
-double expint(double x);
-float expintf(float x);
-long double expintl(long double x);
-
-// [5.2.1.16] Hermite polynomials:
-double hermite(unsigned n, double x);
-float hermitef(unsigned n, float x);
-long double hermitel(unsigned n, long double x);
-
-// [5.2.1.18] Laguerre polynomials:
-double laguerre(unsigned n, double x);
-float laguerref(unsigned n, float x);
-long double laguerrel(unsigned n, long double x);
-
-// [5.2.1.19] Legendre polynomials:
-double legendre(unsigned l, double x);
-float legendref(unsigned l, float x);
-long double legendrel(unsigned l, long double x);
-
-// [5.2.1.20] Riemann zeta function:
-double riemann_zeta(double);
-float riemann_zetaf(float);
-long double riemann_zetal(long double);
-
-// [5.2.1.21] spherical Bessel functions (of the first kind):
-double sph_bessel(unsigned n, double x);
-float sph_besself(unsigned n, float x);
-long double sph_bessell(unsigned n, long double x);
-
-// [5.2.1.22] spherical associated Legendre functions:
-double sph_legendre(unsigned l, unsigned m, double theta);
-float sph_legendref(unsigned l, unsigned m, float theta);
-long double sph_legendrel(unsigned l, unsigned m, long double theta);
-
-// [5.2.1.23] spherical Neumann functions;
-// spherical Bessel functions (of the second kind):
-double sph_neumann(unsigned n, double x);
-float sph_neumannf(unsigned n, float x);
-long double sph_neumannl(unsigned n, long double x);
-
-}}}} // namespaces
-
                
-
                
-          
                
-
                
-            In addition sufficient additional overloads of the double
-            versions of the above functions are provided, so that calling the function
-            with any mixture of float,
-            double, long
-            double, or integer
-            arguments is supported, with the return type determined by the result type
-            calculation rules.
-          
                
-
                
-          
-          
                
-
                
-
-            Currently
-            Unsupported C99 Functions
-          
                
-
                
-          
-
                
-
                double exp2(double x);
-float exp2f(float x);
-long double exp2l(long double x);
-
-double fdim(double x, double y);
-float fdimf(float x, float y);
-long double fdiml(long double x, long double y);
-
-double fma(double x, double y, double z);
-float fmaf(float x, float y, float z);
-long double fmal(long double x, long double y, long double z);
-
-int ilogb(double x);
-int ilogbf(float x);
-int ilogbl(long double x);
-
-long long llrint(double x);
-long long llrintf(float x);
-long long llrintl(long double x);
-
-double log2(double x);
-float log2f(float x);
-long double log2l(long double x);
-
-double logb(double x);
-float logbf(float x);
-long double logbl(long double x);
-
-long lrint(double x);
-long lrintf(float x);
-long lrintl(long double x);
-
-double nan(const char *str);
-float nanf(const char *str);
-long double nanl(const char *str);
-
-double nearbyint(double x);
-float nearbyintf(float x);
-long double nearbyintl(long double x);
-
-double remainder(double x, double y);
-float remainderf(float x, float y);
-long double remainderl(long double x, long double y);
-
-double remquo(double x, double y, int *pquo);
-float remquof(float x, float y, int *pquo);
-long double remquol(long double x, long double y, int *pquo);
-
-double rint(double x);
-float rintf(float x);
-long double rintl(long double x);
-
-double scalbln(double x, long ex);
-float scalblnf(float x, long ex);
-long double scalblnl(long double x, long ex);
-
-double scalbn(double x, int ex);
-float scalbnf(float x, int ex);
-long double scalbnl(long double x, int ex);
-
                
-
                
-          
-          
                
-
                
-
-            Currently
-            Unsupported TR1 Functions
-          
                
-
                
-          
-
                
-
                // [5.2.1.7] confluent hypergeometric functions:
-double conf_hyperg(double a, double c, double x);
-float conf_hypergf(float a, float c, float x);
-long double conf_hypergl(long double a, long double c, long double x);
-
-// [5.2.1.17] hypergeometric functions:
-double hyperg(double a, double b, double c, double x);
-float hypergf(float a, float b, float c, float x);
-long double hypergl(long double a, long double b, long double c,
-long double x);
-
                
-
                
-        
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
-
                
-
-
diff --git a/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1_ref.html b/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1_ref.html
deleted file mode 100644
index 4371ca9e9..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1_ref.html
+++ /dev/null
@@ -1,539 +0,0 @@
-
-
-
-TR1 C Functions Quick Reference
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
-          Supported
-          TR1 Functions
-        
                
-
                namespace boost{ namespace math{ namespace tr1{ extern "C"{
-   
-// [5.2.1.1] associated Laguerre polynomials:
-double assoc_laguerre(unsigned n, unsigned m, double x);
-float assoc_laguerref(unsigned n, unsigned m, float x);
-long double assoc_laguerrel(unsigned n, unsigned m, long double x);
-
-// [5.2.1.2] associated Legendre functions:
-double assoc_legendre(unsigned l, unsigned m, double x);
-float assoc_legendref(unsigned l, unsigned m, float x);
-long double assoc_legendrel(unsigned l, unsigned m, long double x);
-
-// [5.2.1.3] beta function:
-double beta(double x, double y);
-float betaf(float x, float y);
-long double betal(long double x, long double y);
-
-// [5.2.1.4] (complete) elliptic integral of the first kind:
-double comp_ellint_1(double k);
-float comp_ellint_1f(float k);
-long double comp_ellint_1l(long double k);
-
-// [5.2.1.5] (complete) elliptic integral of the second kind:
-double comp_ellint_2(double k);
-float comp_ellint_2f(float k);
-long double comp_ellint_2l(long double k);
-
-// [5.2.1.6] (complete) elliptic integral of the third kind:
-double comp_ellint_3(double k, double nu);
-float comp_ellint_3f(float k, float nu);
-long double comp_ellint_3l(long double k, long double nu);
-
-// [5.2.1.8] regular modified cylindrical Bessel functions:
-double cyl_bessel_i(double nu, double x);
-float cyl_bessel_if(float nu, float x);
-long double cyl_bessel_il(long double nu, long double x);
-
-// [5.2.1.9] cylindrical Bessel functions (of the first kind):
-double cyl_bessel_j(double nu, double x);
-float cyl_bessel_jf(float nu, float x);
-long double cyl_bessel_jl(long double nu, long double x);
-
-// [5.2.1.10] irregular modified cylindrical Bessel functions:
-double cyl_bessel_k(double nu, double x);
-float cyl_bessel_kf(float nu, float x);
-long double cyl_bessel_kl(long double nu, long double x);
-
-// [5.2.1.11] cylindrical Neumann functions;
-// cylindrical Bessel functions (of the second kind):
-double cyl_neumann(double nu, double x);
-float cyl_neumannf(float nu, float x);
-long double cyl_neumannl(long double nu, long double x);
-
-// [5.2.1.12] (incomplete) elliptic integral of the first kind:
-double ellint_1(double k, double phi);
-float ellint_1f(float k, float phi);
-long double ellint_1l(long double k, long double phi);
-
-// [5.2.1.13] (incomplete) elliptic integral of the second kind:
-double ellint_2(double k, double phi);
-float ellint_2f(float k, float phi);
-long double ellint_2l(long double k, long double phi);
-
-// [5.2.1.14] (incomplete) elliptic integral of the third kind:
-double ellint_3(double k, double nu, double phi);
-float ellint_3f(float k, float nu, float phi);
-long double ellint_3l(long double k, long double nu, long double phi);
-
-// [5.2.1.15] exponential integral:
-double expint(double x);
-float expintf(float x);
-long double expintl(long double x);
-
-// [5.2.1.16] Hermite polynomials:
-double hermite(unsigned n, double x);
-float hermitef(unsigned n, float x);
-long double hermitel(unsigned n, long double x);
-
-// [5.2.1.18] Laguerre polynomials:
-double laguerre(unsigned n, double x);
-float laguerref(unsigned n, float x);
-long double laguerrel(unsigned n, long double x);
-
-// [5.2.1.19] Legendre polynomials:
-double legendre(unsigned l, double x);
-float legendref(unsigned l, float x);
-long double legendrel(unsigned l, long double x);
-
-// [5.2.1.20] Riemann zeta function:
-double riemann_zeta(double);
-float riemann_zetaf(float);
-long double riemann_zetal(long double);
-
-// [5.2.1.21] spherical Bessel functions (of the first kind):
-double sph_bessel(unsigned n, double x);
-float sph_besself(unsigned n, float x);
-long double sph_bessell(unsigned n, long double x);
-
-// [5.2.1.22] spherical associated Legendre functions:
-double sph_legendre(unsigned l, unsigned m, double theta);
-float sph_legendref(unsigned l, unsigned m, float theta);
-long double sph_legendrel(unsigned l, unsigned m, long double theta);
-
-// [5.2.1.23] spherical Neumann functions;
-// spherical Bessel functions (of the second kind):
-double sph_neumann(unsigned n, double x);
-float sph_neumannf(unsigned n, float x);
-long double sph_neumannl(unsigned n, long double x);
-
-}}}} // namespaces
-
                
-
                
-          In addition sufficient additional overloads of the double
-          versions of the above functions are provided, so that calling the function
-          with any mixture of float,
-          double, long
-          double, or integer
-          arguments is supported, with the return type determined by the result
-          type calculation rules.
-        
                
-
                
-          For example:
-        
                
-
                expintf(2.0f);  // float version, returns float.
-expint(2.0f);   // also calls the float version and returns float.
-expint(2.0);    // double version, returns double.
-expintl(2.0L);  // long double version, returns a long double.
-expint(2.0L);   // also calls the long double version.
-expint(2);      // integer argument is treated as a double, returns double.
-
                
-
                
-
-          Quick
-          Reference
-        
                
-
                // [5.2.1.1] associated Laguerre polynomials:
-double assoc_laguerre(unsigned n, unsigned m, double x);
-float assoc_laguerref(unsigned n, unsigned m, float x);
-long double assoc_laguerrel(unsigned n, unsigned m, long double x);
-
                
-
                
-          The assoc_laguerre functions return:
-        
                
-
                
-          
-        
                
-
                
-          See also laguerre
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.2] associated Legendre functions:
-double assoc_legendre(unsigned l, unsigned m, double x);
-float assoc_legendref(unsigned l, unsigned m, float x);
-long double assoc_legendrel(unsigned l, unsigned m, long double x);
-
                
-
                
-          The assoc_legendre functions return:
-        
                
-
                
-          
-        
                
-
                
-          See also legendre_p
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.3] beta function:
-double beta(double x, double y);
-float betaf(float x, float y);
-long double betal(long double x, long double y);
-
                
-
                
-          Returns the beta function of x and y:
-        
                
-
                
-          
-        
                
-
                
-          See also beta
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.4] (complete) elliptic integral of the first kind:
-double comp_ellint_1(double k);
-float comp_ellint_1f(float k);
-long double comp_ellint_1l(long double k);
-
                
-
                
-          Returns the complete elliptic integral of the first kind of k:
-        
                
-
                
-          
-        
                
-
                
-          See also ellint_1
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.5] (complete) elliptic integral of the second kind:
-double comp_ellint_2(double k);
-float comp_ellint_2f(float k);
-long double comp_ellint_2l(long double k);
-
                
-
                
-          Returns the complete elliptic integral of the second kind of k:
-        
                
-
                
-          
-        
                
-
                
-          See also ellint_2
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.6] (complete) elliptic integral of the third kind:
-double comp_ellint_3(double k, double nu);
-float comp_ellint_3f(float k, float nu);
-long double comp_ellint_3l(long double k, long double nu);
-
                
-
                
-          Returns the complete elliptic integral of the third kind of k
-          and nu:
-        
                
-
                
-          
-        
                
-
                
-          See also ellint_3
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.8] regular modified cylindrical Bessel functions:
-double cyl_bessel_i(double nu, double x);
-float cyl_bessel_if(float nu, float x);
-long double cyl_bessel_il(long double nu, long double x);
-
                
-
                
-          Returns the modified bessel function of the first kind of nu
-          and x:
-        
                
-
                
-          
-        
                
-
                
-          See also cyl_bessel_i
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.9] cylindrical Bessel functions (of the first kind):
-double cyl_bessel_j(double nu, double x);
-float cyl_bessel_jf(float nu, float x);
-long double cyl_bessel_jl(long double nu, long double x);
-
                
-
                
-          Returns the bessel function of the first kind of nu
-          and x:
-        
                
-
                
-          
-        
                
-
                
-          See also cyl_bessel_j
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.10] irregular modified cylindrical Bessel functions:
-double cyl_bessel_k(double nu, double x);
-float cyl_bessel_kf(float nu, float x);
-long double cyl_bessel_kl(long double nu, long double x);
-
                
-
                
-          Returns the modified bessel function of the second kind of nu
-          and x:
-        
                
-
                
-          
-        
                
-
                
-          See also cyl_bessel_k
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.11] cylindrical Neumann functions;
-// cylindrical Bessel functions (of the second kind):
-double cyl_neumann(double nu, double x);
-float cyl_neumannf(float nu, float x);
-long double cyl_neumannl(long double nu, long double x);
-
                
-
                
-          Returns the bessel function of the second kind (Neumann function) of nu
-          and x:
-        
                
-
                
-          
-        
                
-
                
-          See also cyl_neumann
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.12] (incomplete) elliptic integral of the first kind:
-double ellint_1(double k, double phi);
-float ellint_1f(float k, float phi);
-long double ellint_1l(long double k, long double phi);
-
                
-
                
-          Returns the incomplete elliptic integral of the first kind of k
-          and phi:
-        
                
-
                
-          
-        
                
-
                
-          See also ellint_1
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.13] (incomplete) elliptic integral of the second kind:
-double ellint_2(double k, double phi);
-float ellint_2f(float k, float phi);
-long double ellint_2l(long double k, long double phi);
-
                
-
                
-          Returns the incomplete elliptic integral of the second kind of k
-          and phi:
-        
                
-
                
-          
-        
                
-
                
-          See also ellint_2
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.14] (incomplete) elliptic integral of the third kind:
-double ellint_3(double k, double nu, double phi);
-float ellint_3f(float k, float nu, float phi);
-long double ellint_3l(long double k, long double nu, long double phi);
-
                
-
                
-          Returns the incomplete elliptic integral of the third kind of k,
-          nu and phi:
-        
                
-
                
-          
-        
                
-
                
-          See also ellint_3
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.15] exponential integral:
-double expint(double x);
-float expintf(float x);
-long double expintl(long double x);
-
                
-
                
-          Returns the exponential integral Ei of x:
-        
                
-
                
-          
-        
                
-
                
-          See also expint
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.16] Hermite polynomials:
-double hermite(unsigned n, double x);
-float hermitef(unsigned n, float x);
-long double hermitel(unsigned n, long double x);
-
                
-
                
-          Returns the n'th Hermite polynomial of x:
-        
                
-
                
-          
-        
                
-
                
-          See also hermite
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.18] Laguerre polynomials:
-double laguerre(unsigned n, double x);
-float laguerref(unsigned n, float x);
-long double laguerrel(unsigned n, long double x);
-
                
-
                
-          Returns the n'th Laguerre polynomial of x:
-        
                
-
                
-          
-        
                
-
                
-          See also laguerre
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.19] Legendre polynomials:
-double legendre(unsigned l, double x);
-float legendref(unsigned l, float x);
-long double legendrel(unsigned l, long double x);
-
                
-
                
-          Returns the l'th Legendre polynomial of x:
-        
                
-
                
-          
-        
                
-
                
-          See also legendre_p
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.20] Riemann zeta function:
-double riemann_zeta(double);
-float riemann_zetaf(float);
-long double riemann_zetal(long double);
-
                
-
                
-          Returns the Riemann Zeta function of x:
-        
                
-
                
-          
-        
                
-
                
-          See also zeta for
-          the full template (header only) version of this function.
-        
                
-
                // [5.2.1.21] spherical Bessel functions (of the first kind):
-double sph_bessel(unsigned n, double x);
-float sph_besself(unsigned n, float x);
-long double sph_bessell(unsigned n, long double x);
-
                
-
                
-          Returns the spherical Bessel function of the first kind of x
-          jn(x):
-        
                
-
                
-          
-        
                
-
                
-          See also sph_bessel
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.22] spherical associated Legendre functions:
-double sph_legendre(unsigned l, unsigned m, double theta);
-float sph_legendref(unsigned l, unsigned m, float theta);
-long double sph_legendrel(unsigned l, unsigned m, long double theta);
-
                
-
                
-          Returns the spherical associated Legendre function of l,
-          m and theta:
-        
                
-
                
-          
-        
                
-
                
-          See also spherical_harmonic
-          for the full template (header only) version of this function.
-        
                
-
                // [5.2.1.23] spherical Neumann functions;
-// spherical Bessel functions (of the second kind):
-double sph_neumann(unsigned n, double x);
-float sph_neumannf(unsigned n, float x);
-long double sph_neumannl(unsigned n, long double x);
-
                
-
                
-          Returns the spherical Neumann function of x yn(x):
-        
                
-
                
-          
-        
                
-
                
-          See also sph_bessel
-          for the full template (header only) version of this function.
-        
                
-
                
-
-          Currently
-          Unsupported TR1 Functions
-        
                
-
                // [5.2.1.7] confluent hypergeometric functions:
-double conf_hyperg(double a, double c, double x);
-float conf_hypergf(float a, float c, float x);
-long double conf_hypergl(long double a, long double c, long double x);
-
-// [5.2.1.17] hypergeometric functions:
-double hyperg(double a, double b, double c, double x);
-float hypergf(float a, float b, float c, float x);
-long double hypergl(long double a, long double b, long double c,
-long double x);
-
                
-
                
-
-
-
-
-
-
                [Note]Note
                
-            These two functions are not implemented as they are not believed to be
-            numerically stable.
-          
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
-
                
-
-
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials.html b/doc/sf_and_dist/html/math_toolkit/special/factorials.html
index b73c25153..173e570bf 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials.html
@@ -2,8 +2,8 @@
 
 
 Factorials and Binomial Coefficients
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
  Factorials and Binomial
       Coefficients
@@ -51,7 +51,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
index 1d7d32cfc..3ba95d0ba 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
@@ -2,8 +2,8 @@
 
 
 Binomial Coefficients
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
  Binomial
         Coefficients
@@ -65,7 +65,7 @@
           if the result is too large to represent in type T.
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -74,14 +74,14 @@
           function for larger arguments.
         
                
 
                
-
+
           Testing
         
                
 
                
           The spot tests for the binomial coefficients use data generated by functions.wolfram.com.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -118,7 +118,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
index 4eda36276..abfed9d7e 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
@@ -2,8 +2,8 @@
 
 
 Double Factorial
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
         Double Factorial
@@ -64,7 +64,7 @@
           of i! is possible.
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -72,14 +72,14 @@
           so error rates should be no more than a couple of epsilon higher.
         
                
 
                
-
+
           Testing
         
                
 
                
           The spot tests for the double factorial use data generated by functions.wolfram.com.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -111,7 +111,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
index 88d36f1cf..0fa2c8dfe 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
@@ -2,8 +2,8 @@
 
 
 Factorial
-
-
+
+
 
 
 
@@ -20,14 +20,14 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -54,7 +54,7 @@
 }} // namespaces
 
                
 
                
-
+
           Description
         
                
 
                template <class T>
@@ -112,7 +112,7 @@
           the size of further tables that depend on the factorials.
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -121,7 +121,7 @@
           will be the same as for tgamma.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -130,7 +130,7 @@
           function handle those cases already.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -151,7 +151,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
index dc668aadf..d5e5d2162 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
@@ -2,8 +2,8 @@
 
 
 Falling Factorial
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
         Falling Factorial
@@ -76,7 +76,7 @@
           the type of the result is T.
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -84,14 +84,14 @@
           function.
         
                
 
                
-
+
           Testing
         
                
 
                
           The spot tests for the falling factorials use data generated by functions.wolfram.com.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -113,7 +113,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
index bcdbf132d..f032542ff 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
@@ -2,8 +2,8 @@
 
 
 Rising Factorial
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
         Rising Factorial
@@ -80,7 +80,7 @@
           the type of the result is T.
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -88,14 +88,14 @@
           function.
         
                
 
                
-
+
           Testing
         
                
 
                
           The spot tests for the rising factorials use data generated by functions.wolfram.com.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -117,7 +117,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/fpclass.html b/doc/sf_and_dist/html/math_toolkit/special/fpclass.html
deleted file mode 100644
index 54e012d58..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/fpclass.html
+++ /dev/null
@@ -1,235 +0,0 @@
-
-
-
-Floating-Point Classification: Infinities and NaN's
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
-        Synopsis
-      
                
-
                #define FP_ZERO        /* implementation specific value */
-#define FP_NORMAL      /* implementation specific value */
-#define FP_INFINITE    /* implementation specific value */
-#define FP_NAN         /* implementation specific value */
-#define FP_SUBNORMAL   /* implementation specific value */
-
-template <class T>
-int fpclassify(T t);
-
-template <class T>
-bool isfinite(T z); // Neither infinity nor NaN.
-
-template <class T>
-bool isinf(T t); // Infinity (+ or -).
-
-template <class T>
-bool isnan(T t); // NaN.
-
-template <class T>
-bool isnormal(T t); // isfinite and not denormalised.
-
-#include <boost\math\special_functions\fpclassify.hpp>
-
                
-
                
-        to use these functions.
-      
                
-
                
-
-        Description
-      
                
-
                
-        These functions provide the same functionality as the macros with the same
-        name in C99, indeed if the C99 macros are available, then these functions
-        are implemented in terms of them, otherwise they rely on std::numeric_limits<>
-        to function.
-      
                
-
                
-        Note that the definition of these functions does not suppress the
-        definition of these names as macros by math.h on those platforms
-        that already provide these as macros. That mean that the following have differing
-        meanings:
-      
                
-
                using namespace boost::math;
-
-// This might call a global macro if defined,
-// but might not work if the type of z is unsupported 
-// by the std lib macro:
-isnan(z);
-//
-// This calls the Boost version
-// (found via the "using namespace boost::math" declaration)
-// it works for any type that has numeric_limits support for type z:
-(isnan)(z); 
-//
-// As above but with namespace qualification.
-(boost::math::isnan)(z); 
-//
-// This will cause a compiler error if isnan is a native macro:
-boost::math::isnan(z);
-// So always use instead:
-(boost::math::isnan)(z);
-//
-// You can also add a using statment,
-// globally to a .cpp file, or to a local function in a .hpp file.
-using boost::math::isnan;
-// so you can write the shorter and less cluttered
-(isnan)(z)
-// But, as above, if isnan is a native macro, this causes a compiler error,
-// because the macro always 'gets' the name first, unless enclosed in () brackets.
-
                
-
                
-        Detailed descriptions for each of these functions follows:
-      
                
-
                template <class T>
-int fpclassify(T t);
-
                
-
                
-        Returns an integer value that classifies the value t:
-      
                
-
                
----
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                



                
-              
                
-                fpclassify value
-              
                
-                              		
-              
                
-                class of t.
-              
                
-              
                
-              
                
-                FP_ZERO
-              
                
-                              		
-              
                
-                If t is zero.
-              
                
-              
                
-              
                
-                FP_NORMAL
-              
                
-                              		
-              
                
-                If t is a non-zero, non-denormalised finite
-                value.
-              
                
-              
                
-              
                
-                FP_INFINITE
-              
                
-                              		
-              
                
-                If t is plus or minus infinity.
-              
                
-              
                
-              
                
-                FP_NAN
-              
                
-                              		
-              
                
-                If t is a NaN.
-              
                
-              
                
-              
                
-                FP_SUBNORMAL
-              
                
-                              		
-              
                
-                If t is a denormalised number.
-              
                
-              
                
-
                template <class T>
-bool isfinite(T z);
-
                
-
                
-        Returns true only if z is not an infinity or a NaN.
-      
                
-
                template <class T>
-bool isinf(T t);
-
                
-
                
-        Returns true only if z is plus or minus infinity.
-      
                
-
                template <class T>
-bool isnan(T t);
-
                
-
                
-        Returns true only if z is a NaN.
-      
                
-
                template <class T>
-bool isnormal(T t);
-
                
-
                
-        Returns true only if z is a normal number (not zero,
-        infinite, NaN, or denormalised).
-      
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
-
                
-
-
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
index 5c1b6c1ae..26e7c5a77 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
@@ -2,8 +2,8 @@
 
 
 Inverse Hyperbolic Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
@@ -46,7 +46,7 @@
 
 
                
 
                
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
index 5aeb6571d..ffdadde4f 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
@@ -2,8 +2,8 @@
 
 
 acosh
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
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-
                
+
                
 
                
@@ -67,14 +67,14 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
           Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -90,7 +90,7 @@
           to at least 50 decimal digits.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -132,7 +132,7 @@
 
 
                
 
                
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
index c01477f4a..be431886a 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
@@ -2,8 +2,8 @@
 
 
 asinh
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
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-
                
+
                
 
                
@@ -62,14 +62,14 @@
 
                
         
                
 
                
-
+
           Accuracy
         
                
 
                
           Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -85,7 +85,7 @@
           to at least 50 decimal digits.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -127,7 +127,7 @@
 
 
                
 
                
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
index 4d2384765..276163722 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
@@ -2,8 +2,8 @@
 
 
 atanh
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
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-
                
+
                
 
                
@@ -76,14 +76,14 @@ denoting
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
           Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -99,7 +99,7 @@ denoting
           to at least 50 decimal digits.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -137,7 +137,7 @@ denoting
 
 
                
 
                
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
index e32fe1995..8fc49f4d8 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
@@ -2,8 +2,8 @@
 
 
 Inverse Hyperbolic Functions Overview
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
  Inverse
         Hyperbolic Functions Overview
@@ -36,43 +36,18 @@
           the exponential function is well defined for real numbers, complex number,
           quaternions, octonions, and matrices of complex numbers, among others.
         
                
-
                
-
                
-            
                
-
                
-              Graph of exp on R
-            
                
-
                
-          
                
-
                
-
                
-
                
-            
                
-
                
-              exp_on_r
-            
                
-
                
-          
                
-
                
-
                
-
                
-            
                
-
                
-              Real and Imaginary parts of exp on
-              C
-            
                
-
                
-          
                
-
                
-
                
-
                
-            
                
-
                
-              im_exp_on_c
-            
                
-
                
-          
                
-
                
+
                
+            Graph of exp on R
+          
                
+
                
+            exp_on_r
+          
                
+
                
+            Real and Imaginary parts of exp on C
+          
                
+
                
+            im_exp_on_c
+          
                
 
                
           The hyperbolic functions are defined as power series which can be computed
           (for reals, complex, quaternions and octonions) as:
@@ -86,44 +61,20 @@
 
                
           Hyperbolic tangent: 
         
                
-
                
-
                
-            
                
-
                
-              Trigonometric functions on R (cos:
-              purple; sin: red; tan: blue)
-            
                
-
                
-          
                
-
                
-
                
-
                
-            
                
-
                
-              trigonometric
-            
                
-
                
-          
                
-
                
-
                
-
                
-            
                
-
                
-              Hyperbolic functions on r (cosh: purple;
-              sinh: red; tanh: blue)
-            
                
-
                
-          
                
-
                
-
                
-
                
-            
                
-
                
-              hyperbolic
-            
                
-
                
-          
                
-
                
+
                
+            Trigonometric functions on R (cos: purple;
+            sin: red; tan: blue)
+          
                
+
                
+            trigonometric
+          
                
+
                
+            Hyperbolic functions on r (cosh: purple;
+            sinh: red; tanh: blue)
+          
                
+
                
+            hyperbolic
+          
                
 
                
           The hyperbolic sine is one to one on the set of real numbers, with range
           the full set of reals, while the hyperbolic tangent is also one to one
@@ -158,7 +109,7 @@
 
 
                
 
                
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/next_float.html b/doc/sf_and_dist/html/math_toolkit/special/next_float.html
deleted file mode 100644
index 119750a8d..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/next_float.html
+++ /dev/null
@@ -1,82 +0,0 @@
-
-
-
-Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values
-
-
-
-
-
-
-
-
-
-
-
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-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
                 Finding
-        the Next Representable Value in a Specific Direction (nextafter)
                
-
                 Finding
-        the Next Greater Representable Value (float_next)
                
-
                 Finding
-        the Next Smaller Representable Value (float_prior)
                
-
                 Calculating
-        the Representation Distance Between Two Floating Point Values (ULP) float_distance
                
-
                 Advancing
-        a Floating Point Value by a Specific Representation Distance (ULP) float_advance
                
-
                
-
                
-        Unit of
-        Least Precision or Unit in the Last Place is the gap between two
-        different, but as close as possible, floating-point numbers.
-      
                
-
                
-        Most decimal values, for example 0.1, cannot be exactly represented as floating-point
-        values, but will be stored as the closest representable floating-point.
-      
                
-
                
-        Functions are provided for finding adjacent greater and lesser floating-point
-        values, and estimating the number of gaps between any two floating-point
-        values.
-      
                
-
                
-        The floating-point type FPT must have has a fixed number of bits in the representation.
-        The number of bits may set at runtime, but must be the same for all numbers.
-        For example, NTL::quad_float
-        type (fixed 128-bit representation) or NTL::RR
-        type (arbitrary but fixed decimal digits, default 150) but not
-        a type that extends the representation to provide an exact representation
-        for any number, for example XRC
-        eXact Real in C.
-      
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_advance.html b/doc/sf_and_dist/html/math_toolkit/special/next_float/float_advance.html
deleted file mode 100644
index 22eb58c5e..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_advance.html
+++ /dev/null
@@ -1,77 +0,0 @@
-
-
-
-Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-          Function float_advance advances a floating point number by a specified
-          number of ULP.
-        
                
-
                
-
-          Synopsis
-        
                
-
                
-          
-
                
-
                #include <boost/math/special_functions/next.hpp>
-
                
-
                
-        
                
-
                namespace boost{ namespace math{
-
-template <class FPT>
-FPT float_advance(FPT val, int distance);
-
-}} // namespaces
-
                
-
                
-
-          Description
-          - float_advance
-        
                
-
                
-          Returns a floating point number r such that float_distance(val, r) ==
-          distance.
-        
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_distance.html b/doc/sf_and_dist/html/math_toolkit/special/next_float/float_distance.html
deleted file mode 100644
index 6a593522c..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_distance.html
+++ /dev/null
@@ -1,111 +0,0 @@
-
-
-
-Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-          Function float_distance finds the number of gaps/bits/ULP between any two
-          floating-point values. If the significands of floating-point numbers are
-          viewed as integers, then their difference is the number of ULP/gaps/bits
-          different.
-        
                
-
                
-
-          Synopsis
-        
                
-
                
-          
-
                
-
                #include <boost/math/special_functions/next.hpp>
-
                
-
                
-        
                
-
                namespace boost{ namespace math{
-
-template <class FPT>
-FPT float_distance(FPT a, FPT b);
-
-}} // namespaces
-
                
-
                
-
-          Description
-          - float_distance
-        
                
-
                
-          Returns the distance between a and b:
-          the result is always a signed integer value (stored in floating-point type
-          FPT) representing the number of distinct representations between a
-          and b.
-        
                
-
                
-          Note that
-        
                
-
                  
-
                • 
-float_distance(a, a)
-            always returns 0.
-          
                  • 
-
                • 
-float_distance(float_next(a), a)
-            always returns 1.
-          
                  • 
-
                • 
-float_distance(float_prior(a), a)
-            always returns -1.
-          
                  • 
-
                
-
                
-          The function float_distance
-          is equivalent to calculating the number of ULP (Units in the Last Place)
-          between a and b except that it
-          returns a signed value indicating whether a
-          > b
-          or not.
-        
                
-
                
-          If the distance is too great then it may not be able to be represented
-          as an exact integer by type FPT, but in practice this is unlikely to be
-          a issue.
-        
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
-
                
-
-
diff --git a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_next.html b/doc/sf_and_dist/html/math_toolkit/special/next_float/float_next.html
deleted file mode 100644
index c4f20e2bf..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_next.html
+++ /dev/null
@@ -1,79 +0,0 @@
-
-
-
-Finding the Next Greater Representable Value (float_next)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
-          Synopsis
-        
                
-
                
-          
-
                
-
                #include <boost/math/special_functions/next.hpp>
-
                
-
                
-        
                
-
                namespace boost{ namespace math{
-
-template <class FPT>
-FPT float_next(FPT val);
-
-}} // namespaces
-
                
-
                
-
-          Description
-          - float_next
-        
                
-
                
-          Returns the next representable value which is greater than x.
-          If x is non-finite then returns the result of a domain_error. If there is no such value greater
-          than x then returns an overflow_error.
-        
                
-
                
-          Has the same effect as
-        
                
-
                nextafter(val, std::numeric_limits<FPT>::max());
-
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
-
                
-
-
diff --git a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_prior.html b/doc/sf_and_dist/html/math_toolkit/special/next_float/float_prior.html
deleted file mode 100644
index 101c5a481..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/next_float/float_prior.html
+++ /dev/null
@@ -1,79 +0,0 @@
-
-
-
-Finding the Next Smaller Representable Value (float_prior)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
-          Synopsis
-        
                
-
                
-          
-
                
-
                #include <boost/math/special_functions/next.hpp>
-
                
-
                
-        
                
-
                namespace boost{ namespace math{
-
-template <class FPT>
-FPT float_prior(FPT val);
-
-}} // namespaces
-
                
-
                
-
-          Description
-          - float_prior
-        
                
-
                
-          Returns the next representable value which is less than x.
-          If x is non-finite then returns the result of a domain_error. If there is no such value less
-          than x then returns an overflow_error.
-        
                
-
                
-          Has the same effect as
-        
                
-
                nextafter(val, -std::numeric_limits<FPT>::max());  // Note most negative value -max.
-
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
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-
                
-PrevUpHomeNext
-
                
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/next_float/nextafter.html b/doc/sf_and_dist/html/math_toolkit/special/next_float/nextafter.html
deleted file mode 100644
index 445b6b4e2..000000000
--- a/doc/sf_and_dist/html/math_toolkit/special/next_float/nextafter.html
+++ /dev/null
@@ -1,113 +0,0 @@
-
-
-
-Finding the Next Representable Value in a Specific Direction (nextafter)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                
-
                
-
                
-PrevUpHomeNext
-
                
-
                
-
                
-
                
-
-          Synopsis
-        
                
-
                
-          
-
                
-
                #include <boost/math/special_functions/next.hpp>
-
                
-
                
-        
                
-
                namespace boost{ namespace math{
- 
-template <class FPT>
-FPT nextafter(FPT val, FPT direction);
- 
-}} // namespaces
-
                
-
                
-
-          Description
-          - nextafter
-        
                
-
                
-          This is an implementation of the nextafter
-          function included in the C99 standard. (It is also effectively an implementation
-          of the C99 'nexttoward' legacy function which differs only having a long
-          double direction, and can generally serve in its place if required).
-        
                
-
                
-
-
-
-
-
-
                [Note]Note
                
-            The C99 functions must use suffixes f and l to distinguish float and
-            long double versions. C++ uses the template mechanism instead.
-          
                
-
                
-          Returns the next representable value after x in the
-          direction of y. If x
-          == y
-          then returns x. If x is non-finite
-          then returns the result of a domain_error.
-          If there is no such value in the direction of y then
-          returns an overflow_error.
-        
                
-
                
-
-          Examples
-          - nextafter
-        
                
-
                
-          The two representations using a 32-bit float either side of unity are:
-          
-
                
-
                The nearest (exact) representation of 1.F is      1.00000000
-nextafter(1.F, 999) is                            1.00000012
-nextafter(1/f, -999) is                           0.99999994
-
-The nearest (not exact) representation of 0.1F is 0.100000001
-nextafter(0.1F, 10) is                            0.100000009
-nextafter(0.1F, 10) is                            0.099999994
-
                
-
                
-        
                
-
                
-
-
-
-
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
-      Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
-      and Thijs van den Berg
                
-        Distributed under the Boost Software License, Version 1.0. (See accompanying
-        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-      
                
-
                
-
                
-
                
-PrevUpHomeNext
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers.html b/doc/sf_and_dist/html/math_toolkit/special/powers.html
index 45b2e7f20..036ce8d3b 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers.html
@@ -2,8 +2,8 @@
 
 
 Logs, Powers, Roots and Exponentials
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
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-
                
+
                
 
                
  Logs, Powers, Roots and
       Exponentials
@@ -50,7 +50,7 @@
 
 
                
 
                
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diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
index ce6f8bc65..a662d031f 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
@@ -2,8 +2,8 @@
 
 
 cbrt
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
@@ -71,7 +71,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -79,7 +79,7 @@
           should have approximately 2 epsilon accuracy.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -99,7 +99,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html
index ab7bed013..be57dff51 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html
@@ -2,8 +2,8 @@
 
 
 Compile Time Power of a Runtime Base
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
  Compile Time Power
         of a Runtime Base
@@ -32,7 +32,7 @@
           computes the compile-time integral power of a run-time base.
         
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -49,7 +49,7 @@
 }}
 
                
 
                
-
+
           Rationale
           and Usage
         
                
@@ -91,28 +91,28 @@
           Only 3 different products were actually computed.
         
                
 
                
-
+
           Return Type
         
                
 
                
           The return type of these functions is computed using the result
           type calculation rules. For example:
         
                
-
                  
-
                • 
-            If T is a float, the return
-            type is a float.
-          
                  • 
-
                • 
-            If T is a long double,
-            the return type is a long double.
-          
                  • 
-
                • 
-            Otherwise, the return type is a double.
-          
                  • 
+
                    
+
                  • 
+              If T is a float, the return
+              type is a float.
+            
                    • 
+
                  • 
+              If T is a long double,
+              the return type is a long double.
+            
                    • 
+
                  • 
+              Otherwise, the return type is a double.
+            
                    • 
 
                  
 
                  
-
+
           Policies
         
                  
 
                  
@@ -126,24 +126,24 @@
 
                  
         
                  
 
                  
-
+
           Error
           Handling
         
                  
 
                  
           Two cases of errors can occur when using pow:
         
                  
-
                    
-
                  • 
-            In case of null base and negative exponent, an overflow_error
-            occurs since this operation is a division by 0 (it equals to 1/0).
-          
                    • 
-
                  • 
-            In case of null base and null exponent, an indeterminate_result_error
-            occurs since the result of this operation is indeterminate. Those errors
-            follow the general
-            policies of error handling in Boost.Math.
-          
                    • 
+
                    
 
                    
           The default overflow error policy is throw_on_error.
@@ -151,43 +151,44 @@
           exception. As shown in the link given above, other error handling policies
           can be used:
         
                    
-
                      
-
                    • 
-errno_on_error: Sets
-            ::errno
-            to ERANGE and returns
-            std::numeric_limits<T>::infinity().
-          
                      • 
-
                    • 
-ignore_error: Returns
-            std::numeric_limits<T>::infinity().
-          
                      • 
-
                    • 
-user_error: Returns the
-            result of boost::math::policies::user_overflow_error: this function
-            must be defined by the user.
-          
                      • 
+
                        
+
                      • 
+              errno_on_error: Sets
+              ::errno
+              to ERANGE and returns
+              std::numeric_limits<T>::infinity().
+            
                        • 
+
                      • 
+              ignore_error: Returns
+              std::numeric_limits<T>::infinity().
+            
                        • 
+
                      • 
+              user_error: Returns
+              the result of boost::math::policies::user_overflow_error:
+              this function must be defined by the user.
+            
                        • 
 
                      
 
                      
           The default indeterminate result error policy is ignore_error,
           which for this function returns 1 since it's the most commonly chosen result
           for a power of 0. Here again, other error handling policies can be used:
         
                      
-
                        
-
                      • 
-throw_on_error: Throws
-            std::domain_error
-
                        • 
-
                      • 
-errno_on_error: Sets
-            ::errno
-            to EDOM and returns 1.
-          
                        • 
-
                      • 
-user_error: Returns the
-            result of boost::math::policies::user_indeterminate_result_error: this
-            function must be defined by the user.
-          
                        • 
+
                          
+
                        • 
+              throw_on_error: Throws
+              std::domain_error
+            
                          • 
+
                        • 
+              errno_on_error: Sets
+              ::errno
+              to EDOM and returns
+              1.
+            
                          • 
+
                        • 
+              user_error: Returns
+              the result of boost::math::policies::user_indeterminate_result_error:
+              this function must be defined by the user.
+            
                          • 
 
                        
 
                        
           Here is an example of error handling customization where we want to specify
@@ -231,7 +232,7 @@
 double result = pow<-5>(base);
                - + Acknowledgements

                @@ -242,7 +243,7 @@ improving the implementation.

                - + References

                @@ -262,7 +263,7 @@ improving the implementation.

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html index 8373bc45c..67317187e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html @@ -2,8 +2,8 @@ expm1 - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -80,7 +80,7 @@

                - + Accuracy

                @@ -88,7 +88,7 @@ should have approximately 1 epsilon accuracy.

                - + Testing

                @@ -108,7 +108,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html index 131b643f3..ae9f1e2aa 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html @@ -2,8 +2,8 @@ hypot - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -58,7 +58,7 @@ in such a representable.

                - + Implementation

                @@ -88,7 +88,7 @@ in such a

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html index e17ef8a75..7e07556f0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html @@ -2,8 +2,8 @@ log1p - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -93,7 +93,7 @@

                - + Accuracy

                @@ -101,7 +101,7 @@ should have approximately 1 epsilon accuracy.

                - + Testing

                @@ -121,7 +121,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html index bebba83a5..0051989d3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html @@ -2,8 +2,8 @@ powm1 - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -74,14 +74,14 @@

                - + Accuracy

                Should have approximately 2-3 epsilon accuracy.

                - + Testing

                @@ -101,7 +101,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html index 97e2b66ce..483ddb66e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html @@ -2,8 +2,8 @@ sqrt1pm1 - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -76,7 +76,7 @@

                - + Accuracy

                @@ -84,7 +84,7 @@ should have approximately 3 epsilon accuracy.

                - + Testing

                @@ -104,7 +104,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/rounding.html b/doc/sf_and_dist/html/math_toolkit/special/rounding.html deleted file mode 100644 index 9419da32b..000000000 --- a/doc/sf_and_dist/html/math_toolkit/special/rounding.html +++ /dev/null @@ -1,52 +0,0 @@ - - - -Rounding Truncation and Integer Conversion - - - - - - - - - - - - - - - -
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                -
                -
                -PrevUpHomeNext -
                -
                -
                -
                -
                Rounding Functions
                -
                Truncation Functions
                -
                Integer and Fractional - Part Splitting (modf)
                -
                -
                - - - -
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani - and Thijs van den Berg

                - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

                -
                -
                -
                -PrevUpHomeNext -
                - - diff --git a/doc/sf_and_dist/html/math_toolkit/special/rounding/modf.html b/doc/sf_and_dist/html/math_toolkit/special/rounding/modf.html deleted file mode 100644 index d93493a03..000000000 --- a/doc/sf_and_dist/html/math_toolkit/special/rounding/modf.html +++ /dev/null @@ -1,86 +0,0 @@ - - - -Integer and Fractional Part Splitting (modf) - - - - - - - - - - - - - - - -
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                -
                -
                -PrevUpHomeNext -
                -
                -
                -

                - -

                -
                #include <boost/math/special_functions/modf.hpp>
                -

                -

                -
                template <class T>
-T modf(const T& v, T* ipart);
-
-template <class T, class Policy>
-T modf(const T& v, T* ipart, const Policy&);
-
-template <class T>
-T modf(const T& v, int* ipart);
-
-template <class T, class Policy>
-T modf(const T& v, int* ipart, const Policy&);
-
-template <class T>
-T modf(const T& v, long* ipart);
-
-template <class T, class Policy>
-T modf(const T& v, long* ipart, const Policy&);
-
-template <class T>
-T modf(const T& v, long long* ipart);
-
-template <class T, class Policy>
-T modf(const T& v, long long* ipart, const Policy&);
-
                -

                - The modf functions store - the integer part of v in *ipart and return the fractional part - of v. -

                -

                - If the argument v is either non-finite or else outside - the range of the result type, then returns the result of rounding_error: - by default this throws an instance of boost::math::rounding_error. -

                -
                - - - -
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani - and Thijs van den Berg

                - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

                -
                -
                -
                -PrevUpHomeNext -
                - - diff --git a/doc/sf_and_dist/html/math_toolkit/special/rounding/round.html b/doc/sf_and_dist/html/math_toolkit/special/rounding/round.html deleted file mode 100644 index d0f201cc7..000000000 --- a/doc/sf_and_dist/html/math_toolkit/special/rounding/round.html +++ /dev/null @@ -1,87 +0,0 @@ - - - -Rounding Functions - - - - - - - - - - - - - - - -
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                -
                -
                -PrevUpHomeNext -
                -
                -
                -

                - -

                -
                #include <boost/math/special_functions/round.hpp>
                -

                -

                -
                template <class T>
-T round(const T& v);
-
-template <class T, class Policy>
-T round(const T& v, const Policy&);
-
-template <class T>
-int iround(const T& v);
-
-template <class T, class Policy>
-int iround(const T& v, const Policy&);
-
-template <class T>
-long lround(const T& v);
-
-template <class T, class Policy>
-long lround(const T& v, const Policy&);
-
-template <class T>
-long long llround(const T& v);
-
-template <class T, class Policy>
-long long llround(const T& v, const Policy&);
-
                -

                - These functions return the closest integer to the argument v. -

                -

                - Halfway cases are rounded away from zero, regardless of the current rounding - direction. -

                -

                - If the argument v is either non-finite or else outside - the range of the result type, then returns the result of rounding_error: - by default this throws an instance of boost::math::rounding_error. -

                -
                - - - -
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani - and Thijs van den Berg

                - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

                -
                -
                -
                -PrevUpHomeNext -
                - - diff --git a/doc/sf_and_dist/html/math_toolkit/special/rounding/trunc.html b/doc/sf_and_dist/html/math_toolkit/special/rounding/trunc.html deleted file mode 100644 index b740d9f4c..000000000 --- a/doc/sf_and_dist/html/math_toolkit/special/rounding/trunc.html +++ /dev/null @@ -1,89 +0,0 @@ - - - -Truncation Functions - - - - - - - - - - - - - - - -
                Boost C++ LibrariesHomeLibrariesPeopleFAQMore
                -
                -
                -PrevUpHomeNext -
                -
                -
                -

                - -

                -
                #include <boost/math/special_functions/trunc.hpp>
                -

                -

                -
                template <class T>
-T trunc(const T& v);
-
-template <class T, class Policy>
-T trunc(const T& v, const Policy&);
-
-template <class T>
-int itrunc(const T& v);
-
-template <class T, class Policy>
-int itrunc(const T& v, const Policy&);
-
-template <class T>
-long ltrunc(const T& v);
-
-template <class T, class Policy>
-long ltrunc(const T& v, const Policy&);
-
-template <class T>
-long long lltrunc(const T& v);
-
-template <class T, class Policy>
-long long lltrunc(const T& v, const Policy&);
-
                -

                - The trunc functions round their argument to the integer value, nearest - to but no larger in magnitude than the argument. -

                -

                - For example itrunc(3.7) would - return 3 and ltrunc(-4.6) would - return -4. -

                -

                - If the argument v is either non-finite or else outside - the range of the result type, then returns the result of rounding_error: - by default this throws an instance of boost::math::rounding_error. -

                -
                - - - -
                Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani - and Thijs van den Berg

                - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

                -
                -
                -
                -PrevUpHomeNext -
                - - diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html index 55ffdcdab..a961debca 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html @@ -2,8 +2,8 @@ Beta Functions - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -48,7 +48,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html index 4bc2b007c..02ea8c784 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html @@ -2,8 +2,8 @@ Derivative of the Incomplete Beta Function - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -49,7 +49,7 @@ }} // namespaces

                - + Description

                @@ -76,14 +76,14 @@

                - + Accuracy

                Almost identical to the incomplete beta function ibeta.

                - + Implementation

                @@ -104,7 +104,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html index 17f8a3e4f..c3d014317 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html @@ -2,8 +2,8 @@ Beta - - + + @@ -20,14 +20,14 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -48,7 +48,7 @@ }} // namespaces

                - + Description

                @@ -86,7 +86,7 @@ type calculation rules when T1 and T2 are different types.

                - + Accuracy

                @@ -98,7 +98,7 @@ zero error.

                -

                Table 22. Peak Errors In the Beta Function

                +

                Table 22. Peak Errors In the Beta Function

                @@ -108,132 +108,132 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + Errors in range +

                +

                + 0.4 < a,b < 100 +

                + +

                + Errors in range +

                +

                + 1e-6 < a,b < 36 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=99 Mean=22 +

                +

                + (GSL Peak=1178 Mean=238) +

                +

                + (Cephes=1612) +

                + +

                + Peak=10.7 Mean=2.6 +

                +

                + (GSL Peak=12 Mean=2.0) +

                +

                + (Cephes=174) +

                + +

                + 64 +

                + +

                + Red Hat Linux IA32, g++ 3.4.4 +

                + +

                + Peak=112.1 Mean=26.9 +

                + +

                + Peak=15.8 Mean=3.6 +

                + +

                + 64 +

                + +

                + Red Hat Linux IA64, g++ 3.4.4 +

                + +

                + Peak=61.4 Mean=19.5 +

                + +

                + Peak=12.2 Mean=3.6 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=42.03 Mean=13.94 +

                + +

                + Peak=9.8 Mean=3.1 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - Errors in range -

                -

                - 0.4 < a,b < 100 -

                -                 		-

                - Errors in range -

                -

                - 1e-6 < a,b < 36 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=99 Mean=22 -

                -

                - (GSL Peak=1178 Mean=238) -

                -

                - (Cephes=1612) -

                -                 		-

                - Peak=10.7 Mean=2.6 -

                -

                - (GSL Peak=12 Mean=2.0) -

                -

                - (Cephes=174) -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA32, g++ 3.4.4 -

                -                 		-

                - Peak=112.1 Mean=26.9 -

                -                 		-

                - Peak=15.8 Mean=3.6 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA64, g++ 3.4.4 -

                -                 		-

                - Peak=61.4 Mean=19.5 -

                -                 		-

                - Peak=12.2 Mean=3.6 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=42.03 Mean=13.94 -

                -                 		-

                - Peak=9.8 Mean=3.1 -

                -
                @@ -244,7 +244,7 @@ very small.

                - + Testing

                @@ -253,7 +253,7 @@ at 1000-bit precision.

                - + Implementation

                @@ -329,7 +329,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html index 512484d85..2d47db16e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html @@ -2,8 +2,8 @@ Incomplete Beta Functions - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -67,7 +67,7 @@ }} // namespaces

                - + Description

                @@ -163,7 +163,7 @@

                - + Accuracy

                @@ -182,7 +182,7 @@ with the wider exponent range of the long double types.

                -

                Table 23. Errors In the Function ibeta(a,b,x)

                +

                Table 23. Errors In the Function ibeta(a,b,x)

                @@ -193,183 +193,183 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0 < a,b < 10 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 0 < a,b < 100 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 1x10-5 < a,b < 1x105 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=42.3 Mean=2.9 +

                +

                + (GSL Peak=682 Mean=32.5) +

                +

                + (Cephes Peak=42.7 + Mean=7.0) +

                + +

                + Peak=108 Mean=16.6 +

                +

                + (GSL Peak=690 Mean=151) +

                +

                + (Cephes Peak=1545 + Mean=218) +

                + +

                + Peak=4x103 Mean=203 +

                +

                + (GSL Peak~3x105 Mean~2x104) +

                +

                + (Cephes Peak~5x105 Mean~2x104) +

                + +

                + 64 +

                + +

                + Redhat Linux IA32, gcc-3.4.4 +

                + +

                + Peak=21.9 Mean=3.1 +

                + +

                + Peak=270.7 Mean=26.8 +

                + +

                + Peak~5x104 Mean=3x103 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4.4 +

                + +

                + Peak=15.4 Mean=3.0 +

                + +

                + Peak=112.9 Mean=14.3 +

                + +

                + Peak~5x104 Mean=3x103 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=20.9 Mean=2.6 +

                + +

                + Peak=88.1 Mean=14.3 +

                + +

                + Peak~2x104 Mean=1x103 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0 < a,b < 10 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 0 < a,b < 100 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 1x10-5 < a,b < 1x105 -

                -

                - and -

                -

                - 0 < x < 1 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=42.3 Mean=2.9 -

                -

                - (GSL Peak=682 Mean=32.5) -

                -

                - (Cephes Peak=42.7 - Mean=7.0) -

                -                 		-

                - Peak=108 Mean=16.6 -

                -

                - (GSL Peak=690 Mean=151) -

                -

                - (Cephes Peak=1545 - Mean=218) -

                -                 		-

                - Peak=4x103 Mean=203 -

                -

                - (GSL Peak~3x105 Mean~2x104) -

                -

                - (Cephes Peak~5x105 Mean~2x104) -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA32, gcc-3.4.4 -

                -                 		-

                - Peak=21.9 Mean=3.1 -

                -                 		-

                - Peak=270.7 Mean=26.8 -

                -                 		-

                - Peak~5x104 Mean=3x103 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4.4 -

                -                 		-

                - Peak=15.4 Mean=3.0 -

                -                 		-

                - Peak=112.9 Mean=14.3 -

                -                 		-

                - Peak~5x104 Mean=3x103 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=20.9 Mean=2.6 -

                -                 		-

                - Peak=88.1 Mean=14.3 -

                -                 		-

                - Peak~2x104 Mean=1x103 -

                -

                -

                Table 24. Errors In the Function ibetac(a,b,x)

                +

                Table 24. Errors In the Function ibetac(a,b,x)

                @@ -380,163 +380,163 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0 < a,b < 10 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 0 < a,b < 100 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 1x10-5 < a,b < 1x105 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=13.9 Mean=2.0 +

                + +

                + Peak=56.2 Mean=14 +

                + +

                + Peak=3x103 Mean=159 +

                + +

                + 64 +

                + +

                + Redhat Linux IA32, gcc-3.4.4 +

                + +

                + Peak=21.1 Mean=3.6 +

                + +

                + Peak=221.7 Mean=25.8 +

                + +

                + Peak~9x104 Mean=3x103 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4.4 +

                + +

                + Peak=10.6 Mean=2.2 +

                + +

                + Peak=73.9 Mean=11.9 +

                + +

                + Peak~9x104 Mean=3x103 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=9.9 Mean=2.6 +

                + +

                + Peak=117.7 Mean=15.1 +

                + +

                + Peak~3x104 Mean=1x103 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0 < a,b < 10 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 0 < a,b < 100 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 1x10-5 < a,b < 1x105 -

                -

                - and -

                -

                - 0 < x < 1 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=13.9 Mean=2.0 -

                -                 		-

                - Peak=56.2 Mean=14 -

                -                 		-

                - Peak=3x103 Mean=159 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA32, gcc-3.4.4 -

                -                 		-

                - Peak=21.1 Mean=3.6 -

                -                 		-

                - Peak=221.7 Mean=25.8 -

                -                 		-

                - Peak~9x104 Mean=3x103 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4.4 -

                -                 		-

                - Peak=10.6 Mean=2.2 -

                -                 		-

                - Peak=73.9 Mean=11.9 -

                -                 		-

                - Peak~9x104 Mean=3x103 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=9.9 Mean=2.6 -

                -                 		-

                - Peak=117.7 Mean=15.1 -

                -                 		-

                - Peak~3x104 Mean=1x103 -

                -

                -

                Table 25. Errors In the Function beta(a, b, x)

                +

                Table 25. Errors In the Function beta(a, b, x)

                @@ -547,163 +547,163 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0 < a,b < 10 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 0 < a,b < 100 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 1x10-5 < a,b < 1x105 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=39 Mean=2.9 +

                + +

                + Peak=91 Mean=12.7 +

                + +

                + Peak=635 Mean=25 +

                + +

                + 64 +

                + +

                + Redhat Linux IA32, gcc-3.4.4 +

                + +

                + Peak=26 Mean=3.6 +

                + +

                + Peak=180.7 Mean=30.1 +

                + +

                + Peak~7x104 Mean=3x103 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4.4 +

                + +

                + Peak=13 Mean=2.4 +

                + +

                + Peak=67.1 Mean=13.4 +

                + +

                + Peak~7x104 Mean=3x103 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=27.3 Mean=3.6 +

                + +

                + Peak=49.8 Mean=9.1 +

                + +

                + Peak~6x104 Mean=3x103 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0 < a,b < 10 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 0 < a,b < 100 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 1x10-5 < a,b < 1x105 -

                -

                - and -

                -

                - 0 < x < 1 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=39 Mean=2.9 -

                -                 		-

                - Peak=91 Mean=12.7 -

                -                 		-

                - Peak=635 Mean=25 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA32, gcc-3.4.4 -

                -                 		-

                - Peak=26 Mean=3.6 -

                -                 		-

                - Peak=180.7 Mean=30.1 -

                -                 		-

                - Peak~7x104 Mean=3x103 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4.4 -

                -                 		-

                - Peak=13 Mean=2.4 -

                -                 		-

                - Peak=67.1 Mean=13.4 -

                -                 		-

                - Peak~7x104 Mean=3x103 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=27.3 Mean=3.6 -

                -                 		-

                - Peak=49.8 Mean=9.1 -

                -                 		-

                - Peak~6x104 Mean=3x103 -

                -

                -

                Table 26. Errors In the Function betac(a,b,x)

                +

                Table 26. Errors In the Function betac(a,b,x)

                @@ -714,163 +714,163 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0 < a,b < 10 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 0 < a,b < 100 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 1x10-5 < a,b < 1x105 +

                +

                + and +

                +

                + 0 < x < 1 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=12.0 Mean=2.4 +

                + +

                + Peak=91 Mean=15 +

                + +

                + Peak=4x103 Mean=113 +

                + +

                + 64 +

                + +

                + Redhat Linux IA32, gcc-3.4.4 +

                + +

                + Peak=19.8 Mean=3.8 +

                + +

                + Peak=295.1 Mean=33.9 +

                + +

                + Peak~1x105 Mean=5x103 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4.4 +

                + +

                + Peak=11.2 Mean=2.4 +

                + +

                + Peak=63.5 Mean=13.6 +

                + +

                + Peak~1x105 Mean=5x103 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=15.6 Mean=3.5 +

                + +

                + Peak=39.8 Mean=8.9 +

                + +

                + Peak~9x104 Mean=5x103 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0 < a,b < 10 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 0 < a,b < 100 -

                -

                - and -

                -

                - 0 < x < 1 -

                -                 		-

                - 1x10-5 < a,b < 1x105 -

                -

                - and -

                -

                - 0 < x < 1 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=12.0 Mean=2.4 -

                -                 		-

                - Peak=91 Mean=15 -

                -                 		-

                - Peak=4x103 Mean=113 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA32, gcc-3.4.4 -

                -                 		-

                - Peak=19.8 Mean=3.8 -

                -                 		-

                - Peak=295.1 Mean=33.9 -

                -                 		-

                - Peak~1x105 Mean=5x103 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4.4 -

                -                 		-

                - Peak=11.2 Mean=2.4 -

                -                 		-

                - Peak=63.5 Mean=13.6 -

                -                 		-

                - Peak~1x105 Mean=5x103 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=15.6 Mean=3.5 -

                -                 		-

                - Peak=39.8 Mean=8.9 -

                -                 		-

                - Peak~9x104 Mean=5x103 -

                -

                - + Testing

                @@ -888,7 +888,7 @@ have test data that is fully independent of the code.

                - + Implementation

                @@ -938,6 +938,7 @@

                +

                Where Q(a,x) is an incomplete @@ -981,7 +982,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html index 32946d4e8..ed78dcc8a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html @@ -2,8 +2,8 @@ The Incomplete Beta Function Inverses - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +

                The Incomplete Beta Function Inverses @@ -87,7 +87,7 @@ }} // namespaces

                - + Description

                @@ -108,7 +108,7 @@

                - +
                [Tip][Tip] Tip
                @@ -323,7 +323,7 @@

                - + Accuracy

                @@ -335,31 +335,31 @@ or 1.

                - + Testing

                There are two sets of tests:

                -
                  -
                • - Basic sanity checks attempt to "round-trip" from a, - b and x to p or - q and back again. These tests have quite generous - tolerances: in general both the incomplete beta and its inverses change - so rapidly, that round tripping to more than a couple of significant - digits isn't possible. This is especially true when p - or q is very near one: in this case there isn't - enough "information content" in the input to the inverse function - to get back where you started. -
                  • -
                • - Accuracy checks using high precision test values. These measure the accuracy - of the result, given exact input values. -
                  • +
                    +
                  • + Basic sanity checks attempt to "round-trip" from a, + b and x to p or + q and back again. These tests have quite generous + tolerances: in general both the incomplete beta and its inverses change + so rapidly, that round tripping to more than a couple of significant + digits isn't possible. This is especially true when p + or q is very near one: in this case there isn't + enough "information content" in the input to the inverse + function to get back where you started. +
                    • +
                  • + Accuracy checks using high precision test values. These measure the + accuracy of the result, given exact input values. +
                  - + Implementation of ibeta_inv and ibetac_inv
                  @@ -527,7 +527,7 @@ rapidly converges on the true value.

                  - + Implementation of inverses on the a and b parameters
                  @@ -564,7 +564,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html index 7cc25e676..277ce3b66 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html @@ -2,8 +2,8 @@ Error Functions - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -45,7 +45,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html index cd6171857..c9072bcdd 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html @@ -2,8 +2,8 @@ Error Functions - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -69,7 +69,7 @@

                - + Description 
                template <class T>
@@ -106,7 +106,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -119,7 +119,7 @@
           the one shown will have effectively zero error.
         
                
 
                
-
                Table 27. Errors In the Function erf(z)
                
+
                Table 27. Errors In the Function erf(z)
                
 
                @@ -130,202 +130,202 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    z < 0.5
+                  
                
+                
+                  
                
+                    0.5 < z < 8
+                  
                
+                
+                  
                
+                    z > 8
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    GSL Peak=2.0 Mean=0.3
+                  
                
+                  
                
+                    Cephes Peak=1.1
+                    Mean=0.7
+                  
                
+                
+                  
                
+                    Peak=0.9 Mean=0.09
+                  
                
+                  
                
+                    GSL Peak=2.3 Mean=0.3
+                  
                
+                  
                
+                    Cephes Peak=1.3
+                    Mean=0.2
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    GSL Peak=0 Mean=0
+                  
                
+                  
                
+                    Cephes Peak=0
+                    Mean=0
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    RedHat Linux IA32, gcc-3.3
+                  
                
+                
+                  
                
+                    Peak=0.7 Mean=0.07
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0.9 Mean=0.2
+                  
                
+                
+                  
                
+                    Peak=0.9 Mean=0.2
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0.9 Mean=0.07
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-3.4.4
+                  
                
+                
+                  
                
+                    Peak=0.7 Mean=0.07
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    Peak=0.9 Mean=0.1
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0.5 Mean=0.03
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=0.8 Mean=0.1
+                  
                
+                  
                
+                    HP-UX
+                    C Library Lib Peak=0.9 Mean=0.2
+                  
                
+                
+                  
                
+                    Peak=0.9 Mean=0.1
+                  
                
+                  
                
+                    HP-UX
+                    C Library Lib Peak=0.5 Mean=0.02
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    HP-UX
+                    C Library Lib Peak=0 Mean=0
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                z < 0.5
-              
                
-                              		
 
-              
                
-                0.5 < z < 8
-              
                
-                              		
 
-              
                
-                z > 8
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                GSL Peak=2.0 Mean=0.3
-              
                
-              
                
-                Cephes Peak=1.1
-                Mean=0.7
-              
                
-                              		
 
-              
                
-                Peak=0.9 Mean=0.09
-              
                
-              
                
-                GSL Peak=2.3 Mean=0.3
-              
                
-              
                
-                Cephes Peak=1.3
-                Mean=0.2
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                GSL Peak=0 Mean=0
-              
                
-              
                
-                Cephes Peak=0
-                Mean=0
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                RedHat Linux IA32, gcc-3.3
-              
                
-                              		
 
-              
                
-                Peak=0.7 Mean=0.07
-              
                
-              
                
-                GNU C Lib
-                Peak=0.9 Mean=0.2
-              
                
-                              		
 
-              
                
-                Peak=0.9 Mean=0.2
-              
                
-              
                
-                GNU C Lib
-                Peak=0.9 Mean=0.07
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-3.4.4
-              
                
-                              		
 
-              
                
-                Peak=0.7 Mean=0.07
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
-              
                
-                Peak=0.9 Mean=0.1
-              
                
-              
                
-                GNU C Lib
-                Peak=0.5 Mean=0.03
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=0.8 Mean=0.1
-              
                
-              
                
-                HP-UX C
-                Library Lib Peak=0.9 Mean=0.2
-              
                
-                              		
 
-              
                
-                Peak=0.9 Mean=0.1
-              
                
-              
                
-                HP-UX C
-                Library Lib Peak=0.5 Mean=0.02
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                HP-UX C
-                Library Lib Peak=0 Mean=0
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
                Table 28. Errors In the Function erfc(z)
                
+
                Table 28. Errors In the Function erfc(z)
                
 
                @@ -336,202 +336,202 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    z < 0.5
+                  
                
+                
+                  
                
+                    0.5 < z < 8
+                  
                
+                
+                  
                
+                    z > 8
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=0.7 Mean=0.06
+                  
                
+                  
                
+                    GSL Peak=1.0 Mean=0.4
+                  
                
+                  
                
+                    Cephes Peak=0.7
+                    Mean=0.06
+                  
                
+                
+                  
                
+                    Peak=0.99 Mean=0.3
+                  
                
+                  
                
+                    GSL Peak=2.6 Mean=0.6
+                  
                
+                  
                
+                    Cephes Peak=3.6
+                    Mean=0.7
+                  
                
+                
+                  
                
+                    Peak=1.0 Mean=0.2
+                  
                
+                  
                
+                    GSL Peak=3.9 Mean=0.4
+                  
                
+                  
                
+                    Cephes Peak=2.7
+                    Mean=0.4
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    RedHat Linux IA32, gcc-3.3
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    Peak=1.4 Mean=0.3
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=1.3 Mean=0.3
+                  
                
+                
+                  
                
+                    Peak=1.6 Mean=0.4
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=1.3 Mean=0.4
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-3.4.4
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    Peak=1.4 Mean=0.3
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    Peak=1.5 Mean=0.4
+                  
                
+                  
                
+                    GNU C Lib
+                    Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=0 Mean=0
+                  
                
+                  
                
+                    HP-UX
+                    C Library Peak=0 Mean=0
+                  
                
+                
+                  
                
+                    Peak=1.5 Mean=0.3
+                  
                
+                  
                
+                    HP-UX
+                    C Library Peak=0.9 Mean=0.08
+                  
                
+                
+                  
                
+                    Peak=1.6 Mean=0.4
+                  
                
+                  
                
+                    HP-UX
+                    C Library Peak=0.9 Mean=0.1
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                z < 0.5
-              
                
-                              		
 
-              
                
-                0.5 < z < 8
-              
                
-                              		
 
-              
                
-                z > 8
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=0.7 Mean=0.06
-              
                
-              
                
-                GSL Peak=1.0 Mean=0.4
-              
                
-              
                
-                Cephes Peak=0.7
-                Mean=0.06
-              
                
-                              		
 
-              
                
-                Peak=0.99 Mean=0.3
-              
                
-              
                
-                GSL Peak=2.6 Mean=0.6
-              
                
-              
                
-                Cephes Peak=3.6
-                Mean=0.7
-              
                
-                              		
 
-              
                
-                Peak=1.0 Mean=0.2
-              
                
-              
                
-                GSL Peak=3.9 Mean=0.4
-              
                
-              
                
-                Cephes Peak=2.7
-                Mean=0.4
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                RedHat Linux IA32, gcc-3.3
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
-              
                
-                Peak=1.4 Mean=0.3
-              
                
-              
                
-                GNU C Lib
-                Peak=1.3 Mean=0.3
-              
                
-                              		
 
-              
                
-                Peak=1.6 Mean=0.4
-              
                
-              
                
-                GNU C Lib
-                Peak=1.3 Mean=0.4
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-3.4.4
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
-              
                
-                Peak=1.4 Mean=0.3
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
-              
                
-                Peak=1.5 Mean=0.4
-              
                
-              
                
-                GNU C Lib
-                Peak=0 Mean=0
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=0 Mean=0
-              
                
-              
                
-                HP-UX C
-                Library Peak=0 Mean=0
-              
                
-                              		
 
-              
                
-                Peak=1.5 Mean=0.3
-              
                
-              
                
-                HP-UX C
-                Library Peak=0.9 Mean=0.08
-              
                
-                              		
 
-              
                
-                Peak=1.6 Mean=0.4
-              
                
-              
                
-                HP-UX C
-                Library Peak=0.9 Mean=0.1
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
+
           Testing
         
                
 
                
@@ -546,7 +546,7 @@
           check.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -633,7 +633,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
index 5dd76ece5..450d830d7 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
@@ -2,8 +2,8 @@
 
 
 Error Function Inverses
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -69,7 +69,7 @@
 
                
         
                
 
                
-
+
           Description
         
                
 
                template <class T>
@@ -103,7 +103,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -113,29 +113,30 @@
           error functions.
         
                
 
                
-
+
           Testing
         
                
 
                
           There are two sets of tests:
         
                
-
                  
-
                • 
-            Basic sanity checks attempt to "round-trip" from x
-            to p and back again. These tests have quite generous
-            tolerances: in general both the error functions and their inverses change
-            so rapidly in some places that round tripping to more than a couple of
-            significant digits isn't possible. This is especially true when p
-            is very near one: in this case there isn't enough "information content"
-            in the input to the inverse function to get back where you started.
-          
                  • 
-
                • 
-            Accuracy checks using high-precision test values. These measure the accuracy
-            of the result, given exact input values.
-          
                  • 
+
                    
+
                  • 
+              Basic sanity checks attempt to "round-trip" from x
+              to p and back again. These tests have quite generous
+              tolerances: in general both the error functions and their inverses
+              change so rapidly in some places that round tripping to more than a
+              couple of significant digits isn't possible. This is especially true
+              when p is very near one: in this case there isn't
+              enough "information content" in the input to the inverse
+              function to get back where you started.
+            
                    • 
+
                  • 
+              Accuracy checks using high-precision test values. These measure the
+              accuracy of the result, given exact input values.
+            
                    • 
 
                  
 
                  
-
+
           Implementation
         
                  
 
                  
@@ -205,7 +206,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
index 16a742770..f93a7ec36 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
@@ -2,8 +2,8 @@
 
 
 Gamma Functions
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
@@ -52,7 +52,7 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
index 41c2baa2f..e65a5b862 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
@@ -2,8 +2,8 @@
 
 
 Digamma
-
-
+
+
 
 
 
@@ -20,14 +20,14 @@
 
 
                  
 
                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
 
                  
-
+
           Synopsis
         
                  
 
                  
@@ -48,7 +48,7 @@
 }} // namespaces
 
                
 
                
-
+
           Description
         
                
 
                
@@ -82,7 +82,7 @@
           T otherwise.
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -102,163 +102,163 @@
 
 
 
-                
                
-                  Significand Size
-                
                
+                  
                
+                    Significand Size
+                  
                
                 
 
-                
                
-                  Platform and Compiler
-                
                
+                  
                
+                    Platform and Compiler
+                  
                
                 
 
-                
                
-                  Random Positive Values
-                
                
+                  
                
+                    Random Positive Values
+                  
                
                 
 
-                
                
-                  Values Near The Positive Root
-                
                
+                  
                
+                    Values Near The Positive Root
+                  
                
                 
 
-                
                
-                  Values Near Zero
-                
                
+                  
                
+                    Values Near Zero
+                  
                
                 
 
-                
                
-                  Negative Values
-                
                
+                  
                
+                    Negative Values
+                  
                
                 
 
 
 
 
-                
                
-                  53
-                
                
+                  
                
+                    53
+                  
                
                 
 
-                
                
-                  Win32 Visual C++ 8
-                
                
+                  
                
+                    Win32 Visual C++ 8
+                  
                
                 
 
-                
                
-                  Peak=0.98 Mean=0.36
-                
                
+                  
                
+                    Peak=0.98 Mean=0.36
+                  
                
                 
 
-                
                
-                  Peak=0.99 Mean=0.5
-                
                
+                  
                
+                    Peak=0.99 Mean=0.5
+                  
                
                 
 
-                
                
-                  Peak=0.95 Mean=0.5
-                
                
+                  
                
+                    Peak=0.95 Mean=0.5
+                  
                
                 
 
-                
                
-                  Peak=214 Mean=16
-                
                
+                  
                
+                    Peak=214 Mean=16
+                  
                
                 
 
 
 
-                
                
-                  64
-                
                
+                  
                
+                    64
+                  
                
                 
 
-                
                
-                  Linux IA32 / GCC
-                
                
+                  
                
+                    Linux IA32 / GCC
+                  
                
                 
 
-                
                
-                  Peak=1.4 Mean=0.4
-                
                
+                  
                
+                    Peak=1.4 Mean=0.4
+                  
                
                 
 
-                
                
-                  Peak=1.3 Mean=0.45
-                
                
+                  
                
+                    Peak=1.3 Mean=0.45
+                  
                
                 
 
-                
                
-                  Peak=0.98 Mean=0.35
-                
                
+                  
                
+                    Peak=0.98 Mean=0.35
+                  
                
                 
 
-                
                
-                  Peak=180 Mean=13
-                
                
+                  
                
+                    Peak=180 Mean=13
+                  
                
                 
 
 
 
-                
                
-                  64
-                
                
+                  
                
+                    64
+                  
                
                 
 
-                
                
-                  Linux IA64 / GCC
-                
                
+                  
                
+                    Linux IA64 / GCC
+                  
                
                 
 
-                
                
-                  Peak=0.92 Mean=0.4
-                
                
+                  
                
+                    Peak=0.92 Mean=0.4
+                  
                
                 
 
-                
                
-                  Peak=1.3 Mean=0.45
-                
                
+                  
                
+                    Peak=1.3 Mean=0.45
+                  
                
                 
 
-                
                
-                  Peak=0.98 Mean=0.4
-                
                
+                  
                
+                    Peak=0.98 Mean=0.4
+                  
                
                 
 
-                
                
-                  Peak=180 Mean=13
-                
                
+                  
                
+                    Peak=180 Mean=13
+                  
                
                 
 
 
 
-                
                
-                  113
-                
                
+                  
                
+                    113
+                  
                
                 
 
-                
                
-                  HPUX IA64, aCC A.06.06
-                
                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
                 
 
-                
                
-                  Peak=0.9 Mean=0.4
-                
                
+                  
                
+                    Peak=0.9 Mean=0.4
+                  
                
                 
 
-                
                
-                  Peak=1.1 Mean=0.5
-                
                
+                  
                
+                    Peak=1.1 Mean=0.5
+                  
                
                 
 
-                
                
-                  Peak=0.99 Mean=0.4
-                
                
+                  
                
+                    Peak=0.99 Mean=0.4
+                  
                
                 
 
-                
                
-                  Peak=64 Mean=6
-                
                
+                  
                
+                    Peak=64 Mean=6
+                  
                
                 
 
 
@@ -270,7 +270,7 @@
           absolute error will remain very low.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -280,7 +280,7 @@
           see below).
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -389,7 +389,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
index 348cc3a3b..689a87584 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
@@ -2,8 +2,8 @@
 
 
 Derivative of the Incomplete Gamma Function
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -49,7 +49,7 @@
 }} // namespaces
                - + Description

                @@ -80,7 +80,7 @@ otherwise the return type is simply T1.

                - + Accuracy

                @@ -88,7 +88,7 @@ refer to the documentation for that function for more information.

                - + Implementation

                @@ -109,7 +109,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html index e51a88b5d..267ce4bc4 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html @@ -2,8 +2,8 @@ Ratios of Gamma Functions - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +

                Ratios of Gamma Functions @@ -51,7 +51,7 @@ }} // namespaces

                - + Description 
                template <class T1, class T2> 
@@ -117,7 +117,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -127,7 +127,7 @@
           effectively zero error.
         
                
 
                
-
                Table 16. Errors In the Function tgamma_delta_ratio(a, delta)
                
+
                Table 16. Errors In the Function tgamma_delta_ratio(a, delta)
                
 
                @@ -136,104 +136,102 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    20 < a < 80
+                  
                
+                  
                
+                    and
+                  
                
+                  
                
+                    delta < 1
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=16.9 Mean=1.7
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA32, gcc-3.4.4
+                  
                
+                
+                  
                
+                    Peak=24 Mean=2.7
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-3.4.4
+                  
                
+                
+                  
                
+                    Peak=12.8 Mean=1.8
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=21.4 Mean=2.3
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                20 < a < 80
-              
                
-              
                
-                and
-              
                
-              
                
-                delta < 1
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=16.9 Mean=1.7
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA32, gcc-3.4.4
-              
                
-                              		
 
-              
                
-                Peak=24 Mean=2.7
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-3.4.4
-              
                
-                              		
 
-              
                
-                Peak=12.8 Mean=1.8
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=21.4 Mean=2.3
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
                Table 17. Errors In the Function tgamma_ratio(a,
-        b)
                
-
                
+
                Table 17. Errors In the Function tgamma_ratio(a, b)
                
+
                @@ -241,95 +239,95 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    6 < a,b < 50
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=34 Mean=9
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA32, gcc-3.4.4
+                  
                
+                
+                  
                
+                    Peak=91 Mean=23
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-3.4.4
+                  
                
+                
+                  
                
+                    Peak=35.6 Mean=9.3
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=43.9 Mean=13.2
+                  
                
+                
                
 
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                6 < a,b < 50
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=34 Mean=9
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA32, gcc-3.4.4
-              
                
-                              		
 
-              
                
-                Peak=91 Mean=23
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-3.4.4
-              
                
-                              		
 
-              
                
-                Peak=35.6 Mean=9.3
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=43.9 Mean=13.2
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
+
           Testing
         
                
 
                
@@ -338,7 +336,7 @@
           a deliberately naive calculation of Γ(x)/Γ(y).
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -365,7 +363,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
index 846716a40..3effd02a3 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
@@ -2,8 +2,8 @@
 
 
 Incomplete Gamma Functions
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -67,7 +67,7 @@
 }} // namespaces
                - + Description

                @@ -160,7 +160,7 @@

                - + Accuracy

                @@ -185,7 +185,7 @@ All values are in units of epsilon.

                -

                Table 18. Errors In the Function gamma_p(a,z)

                +

                Table 18. Errors In the Function gamma_p(a,z)

                @@ -196,183 +196,183 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0.5 < a < 100 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 1x10-12 < a < 5x10-2 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 1e-6 < a < 1.7x106 +

                +

                + and +

                +

                + 1 < z < 100*a +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=36 Mean=9.1 +

                +

                + (GSL Peak=342 Mean=46) +

                +

                + (Cephes Peak=491 + Mean=102) +

                + +

                + Peak=4.5 Mean=1.4 +

                +

                + (GSL Peak=4.8 Mean=0.76) +

                +

                + (Cephes Peak=21 + Mean=5.6) +

                + +

                + Peak=244 Mean=21 +

                +

                + (GSL Peak=1022 Mean=1054) +

                +

                + (Cephes Peak~8x106 Mean~7x104) +

                + +

                + 64 +

                + +

                + RedHat Linux IA32, gcc-3.3 +

                + +

                + Peak=241 Mean=36 +

                + +

                + Peak=4.7 Mean=1.5 +

                + +

                + Peak~30,220 Mean=1929 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4 +

                + +

                + Peak=41 Mean=10 +

                + +

                + Peak=4.7 Mean=1.4 +

                + +

                + Peak~30,790 Mean=1864 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=40.2 Mean=10.2 +

                + +

                + Peak=5 Mean=1.6 +

                + +

                + Peak=5,476 Mean=440 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0.5 < a < 100 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -                 		-

                - 1x10-12 < a < 5x10-2 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -                 		-

                - 1e-6 < a < 1.7x106 -

                -

                - and -

                -

                - 1 < z < 100*a -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=36 Mean=9.1 -

                -

                - (GSL Peak=342 Mean=46) -

                -

                - (Cephes Peak=491 - Mean=102) -

                -                 		-

                - Peak=4.5 Mean=1.4 -

                -

                - (GSL Peak=4.8 Mean=0.76) -

                -

                - (Cephes Peak=21 - Mean=5.6) -

                -                 		-

                - Peak=244 Mean=21 -

                -

                - (GSL Peak=1022 Mean=1054) -

                -

                - (Cephes Peak~8x106 Mean~7x104) -

                -
                -

                - 64 -

                -                 		-

                - RedHat Linux IA32, gcc-3.3 -

                -                 		-

                - Peak=241 Mean=36 -

                -                 		-

                - Peak=4.7 Mean=1.5 -

                -                 		-

                - Peak~30,220 Mean=1929 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4 -

                -                 		-

                - Peak=41 Mean=10 -

                -                 		-

                - Peak=4.7 Mean=1.4 -

                -                 		-

                - Peak~30,790 Mean=1864 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=40.2 Mean=10.2 -

                -                 		-

                - Peak=5 Mean=1.6 -

                -                 		-

                - Peak=5,476 Mean=440 -

                -

                -

                Table 19. Errors In the Function gamma_q(a,z)

                +

                Table 19. Errors In the Function gamma_q(a,z)

                @@ -383,182 +383,182 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0.5 < a < 100 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 1x10-12 < a < 5x10-2 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 1x10-6 < a < 1.7x106 +

                +

                + and +

                +

                + 1 < z < 100*a +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=28.3 Mean=7.2 +

                +

                + (GSL Peak=201 Mean=13) +

                +

                + (Cephes Peak=556 + Mean=97) +

                + +

                + Peak=4.8 Mean=1.6 +

                +

                + (GSL Peak~1.3x1010 Mean=1x10+9) +

                +

                + (Cephes Peak~3x1011 Mean=4x1010) +

                + +

                + Peak=469 Mean=33 +

                +

                + (GSL Peak=27,050 Mean=2159) +

                +

                + (Cephes Peak~8x106 Mean~7x105) +

                + +

                + 64 +

                + +

                + RedHat Linux IA32, gcc-3.3 +

                + +

                + Peak=280 Mean=33 +

                + +

                + Peak=4.1 Mean=1.6 +

                + +

                + Peak=11,490 Mean=732 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4 +

                + +

                + Peak=32 Mean=9.4 +

                + +

                + Peak=4.7 Mean=1.5 +

                + +

                + Peak=6815 Mean=414 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=37 Mean=10 +

                + +

                + Peak=11.2 Mean=2.0 +

                + +

                + Peak=4,999 Mean=298 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0.5 < a < 100 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -                 		-

                - 1x10-12 < a < 5x10-2 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -                 		-

                - 1x10-6 < a < 1.7x106 -

                -

                - and -

                -

                - 1 < z < 100*a -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=28.3 Mean=7.2 -

                -

                - (GSL Peak=201 Mean=13) -

                -

                - (Cephes Peak=556 - Mean=97) -

                -                 		-

                - Peak=4.8 Mean=1.6 -

                -

                - (GSL Peak~1.3x1010 Mean=1x10+9) -

                -

                - (Cephes Peak~3x1011 Mean=4x1010) -

                -                 		-

                - Peak=469 Mean=33 -

                -

                - (GSL Peak=27,050 Mean=2159) -

                -

                - (Cephes Peak~8x106 Mean~7x105) -

                -
                -

                - 64 -

                -                 		-

                - RedHat Linux IA32, gcc-3.3 -

                -                 		-

                - Peak=280 Mean=33 -

                -                 		-

                - Peak=4.1 Mean=1.6 -

                -                 		-

                - Peak=11,490 Mean=732 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4 -

                -                 		-

                - Peak=32 Mean=9.4 -

                -                 		-

                - Peak=4.7 Mean=1.5 -

                -                 		-

                - Peak=6815 Mean=414 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=37 Mean=10 -

                -                 		-

                - Peak=11.2 Mean=2.0 -

                -                 		-

                - Peak=4,999 Mean=298 -

                -

                -

                Table 20. Errors In the Function tgamma_lower(a,z)

                +

                Table 20. Errors In the Function tgamma_lower(a,z)

                @@ -568,132 +568,132 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0.5 < a < 100 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 1x10-12 < a < 5x10-2 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=5.5 Mean=1.4 +

                + +

                + Peak=3.6 Mean=0.78 +

                + +

                + 64 +

                + +

                + RedHat Linux IA32, gcc-3.3 +

                + +

                + Peak=402 Mean=79 +

                + +

                + Peak=3.4 Mean=0.8 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4 +

                + +

                + Peak=6.8 Mean=1.4 +

                + +

                + Peak=3.4 Mean=0.78 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=6.1 Mean=1.8 +

                + +

                + Peak=3.7 Mean=0.89 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0.5 < a < 100 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -                 		-

                - 1x10-12 < a < 5x10-2 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=5.5 Mean=1.4 -

                -                 		-

                - Peak=3.6 Mean=0.78 -

                -
                -

                - 64 -

                -                 		-

                - RedHat Linux IA32, gcc-3.3 -

                -                 		-

                - Peak=402 Mean=79 -

                -                 		-

                - Peak=3.4 Mean=0.8 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4 -

                -                 		-

                - Peak=6.8 Mean=1.4 -

                -                 		-

                - Peak=3.4 Mean=0.78 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=6.1 Mean=1.8 -

                -                 		-

                - Peak=3.7 Mean=0.89 -

                -

                -

                Table 21. Errors In the Function tgamma(a,z)

                +

                Table 21. Errors In the Function tgamma(a,z)

                @@ -703,132 +703,132 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + 0.5 < a < 100 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 1x10-12 < a < 5x10-2 +

                +

                + and +

                +

                + 0.01*a < z < 100*a +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=5.9 Mean=1.5 +

                + +

                + Peak=1.8 Mean=0.6 +

                + +

                + 64 +

                + +

                + RedHat Linux IA32, gcc-3.3 +

                + +

                + Peak=596 Mean=116 +

                + +

                + Peak=3.2 Mean=0.84 +

                + +

                + 64 +

                + +

                + Redhat Linux IA64, gcc-3.4.4 +

                + +

                + Peak=40.2 Mean=2.5 +

                + +

                + Peak=3.2 Mean=0.8 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=364 Mean=17.6 +

                + +

                + Peak=12.7 Mean=1.8 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - 0.5 < a < 100 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -                 		-

                - 1x10-12 < a < 5x10-2 -

                -

                - and -

                -

                - 0.01*a < z < 100*a -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=5.9 Mean=1.5 -

                -                 		-

                - Peak=1.8 Mean=0.6 -

                -
                -

                - 64 -

                -                 		-

                - RedHat Linux IA32, gcc-3.3 -

                -                 		-

                - Peak=596 Mean=116 -

                -                 		-

                - Peak=3.2 Mean=0.84 -

                -
                -

                - 64 -

                -                 		-

                - Redhat Linux IA64, gcc-3.4.4 -

                -                 		-

                - Peak=40.2 Mean=2.5 -

                -                 		-

                - Peak=3.2 Mean=0.8 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=364 Mean=17.6 -

                -                 		-

                - Peak=12.7 Mean=1.8 -

                -

                - + Testing

                @@ -844,7 +844,7 @@ fraction (see below) is unstable for small a and z.

                - + Implementation

                @@ -1013,28 +1013,29 @@ by Temme (see references below).

                - + References
                -
                  -
                • - N. M. Temme, A Set of Algorithms for the Incomplete Gamma Functions, - Probability in the Engineering and Informational Sciences, 8, 1994. -
                  • -
                • - N. M. Temme, The Asymptotic Expansion of the Incomplete Gamma Functions, - Siam J. Math Anal. Vol 10 No 4, July 1979, p757. -
                  • -
                • - A. R. Didonato and A. H. Morris, Computation of the Incomplete Gamma - Function Ratios and their Inverse. ACM TOMS, Vol 12, No 4, Dec 1986, - p377. -
                  • -
                • - W. Gautschi, The Incomplete Gamma Functions Since Tricomi, In Tricomi's - Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, - n. 147, Accademia Nazionale dei Lincei, Roma, 1998, pp. 203--237. http://citeseer.ist.psu.edu/gautschi98incomplete.html -
                  • +
                    +
                  • + N. M. Temme, A Set of Algorithms for the Incomplete Gamma Functions, + Probability in the Engineering and Informational Sciences, 8, 1994. +
                    • +
                  • + N. M. Temme, The Asymptotic Expansion of the Incomplete Gamma Functions, + Siam J. Math Anal. Vol 10 No 4, July 1979, p757. +
                    • +
                  • + A. R. Didonato and A. H. Morris, Computation of the Incomplete Gamma + Function Ratios and their Inverse. ACM TOMS, Vol 12, No 4, Dec 1986, + p377. +
                    • +
                  • + W. Gautschi, The Incomplete Gamma Functions Since Tricomi, In Tricomi's + Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, + n. 147, Accademia Nazionale dei Lincei, Roma, 1998, pp. 203--237. + http://citeseer.ist.psu.edu/gautschi98incomplete.html +
                @@ -1049,7 +1050,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html index 014e07107..23950b9e2 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html @@ -2,8 +2,8 @@ Incomplete Gamma Function Inverses - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -67,7 +67,7 @@ }} // namespaces

                - + Description

                @@ -94,7 +94,7 @@

                - +
                [Tip][Tip] Tip
                @@ -173,7 +173,7 @@ 0.

                - + Accuracy

                @@ -187,30 +187,31 @@ functions.

                - + Testing

                There are two sets of tests:

                -
                  -
                • - Basic sanity checks attempt to "round-trip" from a - and x to p or q - and back again. These tests have quite generous tolerances: in general - both the incomplete gamma, and its inverses, change so rapidly that round - tripping to more than a couple of significant digits isn't possible. - This is especially true when p or q - is very near one: in this case there isn't enough "information content" - in the input to the inverse function to get back where you started. -
                  • -
                • - Accuracy checks using high precision test values. These measure the accuracy - of the result, given exact input values. -
                  • +
                    +
                  • + Basic sanity checks attempt to "round-trip" from a + and x to p or q + and back again. These tests have quite generous tolerances: in general + both the incomplete gamma, and its inverses, change so rapidly that + round tripping to more than a couple of significant digits isn't possible. + This is especially true when p or q + is very near one: in this case there isn't enough "information + content" in the input to the inverse function to get back where + you started. +
                    • +
                  • + Accuracy checks using high precision test values. These measure the + accuracy of the result, given exact input values. +
                  - + Implementation

                  @@ -259,7 +260,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html index cc7131fdc..a7a6d5b84 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html @@ -2,8 +2,8 @@ Log Gamma - - + + @@ -20,14 +20,14 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -54,7 +54,7 @@ }} // namespaces

                - + Description

                @@ -98,7 +98,7 @@ T otherwise.

                - + Accuracy

                @@ -127,229 +127,229 @@ -

                - Significand Size -

                +

                + Significand Size +

                -

                - Platform and Compiler -

                +

                + Platform and Compiler +

                -

                - Factorials and Half factorials -

                +

                + Factorials and Half factorials +

                -

                - Values Near Zero -

                +

                + Values Near Zero +

                -

                - Values Near 1 or 2 -

                +

                + Values Near 1 or 2 +

                -

                - Values Near a Negative Pole -

                +

                + Values Near a Negative Pole +

                -

                - 53 -

                +

                + 53 +

                -

                - Win32 Visual C++ 8 -

                +

                + Win32 Visual C++ 8 +

                -

                - Peak=0.88 Mean=0.14 -

                -

                - (GSL=33) (Cephes=1.5) -

                +

                + Peak=0.88 Mean=0.14 +

                +

                + (GSL=33) (Cephes=1.5) +

                -

                - Peak=0.96 Mean=0.46 -

                -

                - (GSL=5.2) (Cephes=1.1) -

                +

                + Peak=0.96 Mean=0.46 +

                +

                + (GSL=5.2) (Cephes=1.1) +

                -

                - Peak=0.86 Mean=0.46 -

                -

                - (GSL=1168) (Cephes~500000) -

                +

                + Peak=0.86 Mean=0.46 +

                +

                + (GSL=1168) (Cephes~500000) +

                -

                - Peak=4.2 Mean=1.3 -

                -

                - (GSL=25) (Cephes=1.6) -

                +

                + Peak=4.2 Mean=1.3 +

                +

                + (GSL=25) (Cephes=1.6) +

                -

                - 64 -

                +

                + 64 +

                -

                - Linux IA32 / GCC -

                +

                + Linux IA32 / GCC +

                -

                - Peak=1.9 Mean=0.43 -

                -

                - (GNU C Lib - Peak=1.7 Mean=0.49) -

                +

                + Peak=1.9 Mean=0.43 +

                +

                + (GNU C Lib + Peak=1.7 Mean=0.49) +

                -

                - Peak=1.4 Mean=0.57 -

                -

                - (GNU C Lib - Peak= 0.96 Mean=0.54) -

                +

                + Peak=1.4 Mean=0.57 +

                +

                + (GNU C Lib + Peak= 0.96 Mean=0.54) +

                -

                - Peak=0.86 Mean=0.35 -

                -

                - (GNU C Lib - Peak=0.74 Mean=0.26) -

                +

                + Peak=0.86 Mean=0.35 +

                +

                + (GNU C Lib + Peak=0.74 Mean=0.26) +

                -

                - Peak=6.0 Mean=1.8 -

                -

                - (GNU C Lib - Peak=3.0 Mean=0.86) -

                +

                + Peak=6.0 Mean=1.8 +

                +

                + (GNU C Lib + Peak=3.0 Mean=0.86) +

                -

                - 64 -

                +

                + 64 +

                -

                - Linux IA64 / GCC -

                +

                + Linux IA64 / GCC +

                -

                - Peak=0.99 Mean=0.12 -

                -

                - (GNU C Lib - Peak 0) -

                +

                + Peak=0.99 Mean=0.12 +

                +

                + (GNU C Lib + Peak 0) +

                -

                - Pek=1.2 Mean=0.6 -

                -

                - (GNU C Lib - Peak 0) -

                +

                + Pek=1.2 Mean=0.6 +

                +

                + (GNU C Lib + Peak 0) +

                -

                - Peak=0.86 Mean=0.16 -

                -

                - (GNU C Lib - Peak 0) -

                +

                + Peak=0.86 Mean=0.16 +

                +

                + (GNU C Lib + Peak 0) +

                -

                - Peak=2.3 Mean=0.69 -

                -

                - (GNU C Lib - Peak 0) -

                +

                + Peak=2.3 Mean=0.69 +

                +

                + (GNU C Lib + Peak 0) +

                -

                - 113 -

                +

                + 113 +

                -

                - HPUX IA64, aCC A.06.06 -

                +

                + HPUX IA64, aCC A.06.06 +

                -

                - Peak=0.96 Mean=0.13 -

                -

                - (HP-UX - C Library Peak 0) -

                +

                + Peak=0.96 Mean=0.13 +

                +

                + (HP-UX + C Library Peak 0) +

                -

                - Peak=0.99 Mean=0.53 -

                -

                - (HP-UX - C Library Peak 0) -

                +

                + Peak=0.99 Mean=0.53 +

                +

                + (HP-UX + C Library Peak 0) +

                -

                - Peak=0.9 Mean=0.4 -

                -

                - (HP-UX - C Library Peak 0) -

                +

                + Peak=0.9 Mean=0.4 +

                +

                + (HP-UX + C Library Peak 0) +

                -

                - Peak=3.0 Mean=0.9 -

                -

                - (HP-UX - C Library Peak 0) -

                +

                + Peak=3.0 Mean=0.9 +

                +

                + (HP-UX + C Library Peak 0) +

                - + Testing

                @@ -360,7 +360,7 @@ Random tests in key problem areas are also used.

                - + Implementation

                @@ -482,7 +482,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html index 6cc2035e1..8cca0df30 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html @@ -2,8 +2,8 @@ Gamma - - + + @@ -20,14 +20,14 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -54,7 +54,7 @@ }} // namespaces

                - + Description 
                template <class T>
@@ -129,7 +129,7 @@
 
                
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -152,239 +152,239 @@
 
 
 
-                
                
-                  Significand Size
-                
                
+                  
                
+                    Significand Size
+                  
                
                 
 
-                
                
-                  Platform and Compiler
-                
                
+                  
                
+                    Platform and Compiler
+                  
                
                 
 
-                
                
-                  Factorials and Half factorials
-                
                
+                  
                
+                    Factorials and Half factorials
+                  
                
                 
 
-                
                
-                  Values Near Zero
-                
                
+                  
                
+                    Values Near Zero
+                  
                
                 
 
-                
                
-                  Values Near 1 or 2
-                
                
+                  
                
+                    Values Near 1 or 2
+                  
                
                 
 
-                
                
-                  Values Near a Negative Pole
-                
                
+                  
                
+                    Values Near a Negative Pole
+                  
                
                 
 
 
 
 
-                
                
-                  53
-                
                
+                  
                
+                    53
+                  
                
                 
 
-                
                
-                  Win32 Visual C++ 8
-                
                
+                  
                
+                    Win32 Visual C++ 8
+                  
                
                 
 
-                
                
-                  Peak=1.9 Mean=0.7
-                
                
-                
                
-                  (GSL=3.9)
-                
                
-                
                
-                  (Cephes=3.0)
-                
                
+                  
                
+                    Peak=1.9 Mean=0.7
+                  
                
+                  
                
+                    (GSL=3.9)
+                  
                
+                  
                
+                    (Cephes=3.0)
+                  
                
                 
 
-                
                
-                  Peak=2.0 Mean=1.1
-                
                
-                
                
-                  (GSL=4.5)
-                
                
-                
                
-                  (Cephes=1)
-                
                
+                  
                
+                    Peak=2.0 Mean=1.1
+                  
                
+                  
                
+                    (GSL=4.5)
+                  
                
+                  
                
+                    (Cephes=1)
+                  
                
                 
 
-                
                
-                  Peak=2.0 Mean=1.1
-                
                
-                
                
-                  (GSL=7.9)
-                
                
-                
                
-                  (Cephes=1.0)
-                
                
+                  
                
+                    Peak=2.0 Mean=1.1
+                  
                
+                  
                
+                    (GSL=7.9)
+                  
                
+                  
                
+                    (Cephes=1.0)
+                  
                
                 
 
-                
                
-                  Peak=2.6 Mean=1.3
-                
                
-                
                
-                  (GSL=2.5)
-                
                
-                
                
-                  (Cephes=2.7)
-                
                
+                  
                
+                    Peak=2.6 Mean=1.3
+                  
                
+                  
                
+                    (GSL=2.5)
+                  
                
+                  
                
+                    (Cephes=2.7)
+                  
                
                 
 
 
 
-                
                
-                  64
-                
                
+                  
                
+                    64
+                  
                
                 
 
-                
                
-                  Linux IA32 / GCC
-                
                
+                  
                
+                    Linux IA32 / GCC
+                  
                
                 
 
-                
                
-                  Peak=300 Mean=49.5
-                
                
-                
                
-                  (GNU C Lib
-                  Peak=395 Mean=89)
-                
                
+                  
                
+                    Peak=300 Mean=49.5
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak=395 Mean=89)
+                  
                
                 
 
-                
                
-                  Peak=3.0 Mean=1.4
-                
                
-                
                
-                  (GNU C Lib
-                  Peak=11 Mean=3.3)
-                
                
+                  
                
+                    Peak=3.0 Mean=1.4
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak=11 Mean=3.3)
+                  
                
                 
 
-                
                
-                  Peak=5.0 Mean=1.8
-                
                
-                
                
-                  (GNU C Lib
-                  Peak=0.92 Mean=0.2)
-                
                
+                  
                
+                    Peak=5.0 Mean=1.8
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak=0.92 Mean=0.2)
+                  
                
                 
 
-                
                
-                  Peak=157 Mean=65
-                
                
-                
                
-                  (GNU C Lib
-                  Peak=205 Mean=108)
-                
                
+                  
                
+                    Peak=157 Mean=65
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak=205 Mean=108)
+                  
                
                 
 
 
 
-                
                
-                  64
-                
                
+                  
                
+                    64
+                  
                
                 
 
-                
                
-                  Linux IA64 / GCC
-                
                
+                  
                
+                    Linux IA64 / GCC
+                  
                
                 
 
-                
                
-                  GNU C Lib
-                  Peak 2.8 Mean=0.9
-                
                
-                
                
-                  (GNU C Lib
-                  Peak 0.7)
-                
                
+                  
                
+                    GNU C Lib
+                    Peak 2.8 Mean=0.9
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak 0.7)
+                  
                
                 
 
-                
                
-                  Peak=4.8 Mean=1.5
-                
                
-                
                
-                  (GNU C Lib
-                  Peak 0)
-                
                
+                  
                
+                    Peak=4.8 Mean=1.5
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak 0)
+                  
                
                 
 
-                
                
-                  Peak=4.8 Mean=1.5
-                
                
-                
                
-                  (GNU C Lib
-                  Peak 0)
-                
                
+                  
                
+                    Peak=4.8 Mean=1.5
+                  
                
+                  
                
+                    (GNU C Lib
+                    Peak 0)
+                  
                
                 
 
-                
                
-                  Peak=5.0 Mean=1.7 (GNU
-                  C Lib Peak 0)
-                
                
+                  
                
+                    Peak=5.0 Mean=1.7 (GNU
+                    C Lib Peak 0)
+                  
                
                 
 
 
 
-                
                
-                  113
-                
                
+                  
                
+                    113
+                  
                
                 
 
-                
                
-                  HPUX IA64, aCC A.06.06
-                
                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
                 
 
-                
                
-                  Peak=2.5 Mean=1.1
-                
                
-                
                
-                  (HP-UX
-                  C Library Peak 0)
-                
                
+                  
                
+                    Peak=2.5 Mean=1.1
+                  
                
+                  
                
+                    (HP-UX
+                    C Library Peak 0)
+                  
                
                 
 
-                
                
-                  Peak=3.5 Mean=1.7
-                
                
-                
                
-                  (HP-UX
-                  C Library Peak 0)
-                
                
+                  
                
+                    Peak=3.5 Mean=1.7
+                  
                
+                  
                
+                    (HP-UX
+                    C Library Peak 0)
+                  
                
                 
 
-                
                
-                  Peak=3.5 Mean=1.6
-                
                
-                
                
-                  (HP-UX
-                  C Library Peak 0)
-                
                
+                  
                
+                    Peak=3.5 Mean=1.6
+                  
                
+                  
                
+                    (HP-UX
+                    C Library Peak 0)
+                  
                
                 
 
-                
                
-                  Peak=5.2 Mean=1.92
-                
                
-                
                
-                  (HP-UX
-                  C Library Peak 0)
-                
                
+                  
                
+                    Peak=5.2 Mean=1.92
+                  
                
+                  
                
+                    (HP-UX
+                    C Library Peak 0)
+
                - + Testing

                @@ -399,7 +399,7 @@ a lanczos approximation accurate to around 100 decimal digits.

                - + Implementation

                @@ -474,7 +474,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html index d03545078..c44ed8098 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html @@ -2,8 +2,8 @@ Polynomials - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -47,7 +47,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html index 10993be43..d19e0e26b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html @@ -2,8 +2,8 @@ Hermite Polynomials - - + + @@ -20,14 +20,14 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -51,7 +51,7 @@ }} // namespaces

                - + Description

                @@ -119,24 +119,24 @@

                n

                - The degree n of the last polynomial calculated. -

                + The degree n of the last polynomial calculated. +

                x

                - The abscissa value -

                + The abscissa value +

                Hn

                - The value of the polynomial evaluated at degree n. -

                + The value of the polynomial evaluated at degree n. +

                Hnm1

                - The value of the polynomial evaluated at degree n-1. -

                + The value of the polynomial evaluated at degree n-1. +

                - + Accuracy

                @@ -146,7 +146,7 @@ zero error.

                -

                Table 34. Peak Errors In the Hermite Polynomial

                +

                Table 34. Peak Errors In the Hermite Polynomial

                @@ -155,92 +155,92 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + Errors in range +

                +

                + 0 < l < 20 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=4.5 Mean=1.5 +

                + +

                + 64 +

                + +

                + Red Hat Linux IA32, g++ 4.1 +

                + +

                + Peak=6 Mean=2 +

                + +

                + 64 +

                + +

                + Red Hat Linux IA64, g++ 3.4.4 +

                + +

                + Peak=6 Mean=2 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=6 Mean=4 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - Errors in range -

                -

                - 0 < l < 20 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=4.5 Mean=1.5 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA32, g++ 4.1 -

                -                 		-

                - Peak=6 Mean=2 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA64, g++ 3.4.4 -

                -                 		-

                - Peak=6 Mean=2 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=6 Mean=4 -

                -
                @@ -253,7 +253,7 @@ is very close to a root.

                - + Testing

                @@ -263,7 +263,7 @@ precision.

                - + Implementation

                @@ -284,7 +284,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html index 800fe51dd..1e0b06ec6 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html @@ -2,8 +2,8 @@ Laguerre (and Associated) Polynomials - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -62,7 +62,7 @@ }} // namespaces

                - + Description

                @@ -143,20 +143,20 @@

                n

                - The degree n of the last polynomial calculated. -

                + The degree n of the last polynomial calculated. +

                x

                - The abscissa value -

                + The abscissa value +

                Ln

                - The value of the polynomial evaluated at degree n. -

                + The value of the polynomial evaluated at degree n. +

                Lnm1

                - The value of the polynomial evaluated at degree n-1. -

                + The value of the polynomial evaluated at degree n-1. + 

                template <class T1, class T2, class T3>
@@ -189,28 +189,28 @@
 
                
 
                n
                
 
                
-              The degree of the last polynomial calculated.
-            
                
+                The degree of the last polynomial calculated.
+              
                
 
                m
                
 
                
-              The order of the Associated Polynomial.
-            
                
+                The order of the Associated Polynomial.
+              
                
 
                x
                
 
                
-              The abscissa value.
-            
                
+                The abscissa value.
+              
                
 
                Ln
                
 
                
-              The value of the polynomial evaluated at degree n.
-            
                
+                The value of the polynomial evaluated at degree n.
+              
                
 
                Lnm1
                
 
                
-              The value of the polynomial evaluated at degree n-1.
-            
                
+                The value of the polynomial evaluated at degree n-1.
+
                - + Accuracy

                @@ -220,7 +220,7 @@ zero error.

                -

                Table 32. Peak Errors In the Laguerre Polynomial

                +

                Table 32. Peak Errors In the Laguerre Polynomial

                @@ -229,101 +229,99 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + Errors in range +

                +

                + 0 < l < 20 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=3000 Mean=185 +

                + +

                + 64 +

                + +

                + SUSE Linux IA32, g++ 4.1 +

                + +

                + Peak=1x104 Mean=828 +

                + +

                + 64 +

                + +

                + Red Hat Linux IA64, g++ 3.4.4 +

                + +

                + Peak=1x104 Mean=828 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=680 Mean=40 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - Errors in range -

                -

                - 0 < l < 20 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=3000 Mean=185 -

                -
                -

                - 64 -

                -                 		-

                - SUSE Linux IA32, g++ 4.1 -

                -                 		-

                - Peak=1x104 Mean=828 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA64, g++ 3.4.4 -

                -                 		-

                - Peak=1x104 Mean=828 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=680 Mean=40 -

                -

                -

                Table 33. Peak Errors In the Associated Laguerre - Polynomial

                -
                +

                Table 33. Peak Errors In the Associated Laguerre Polynomial

                +
                @@ -331,92 +329,92 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + Errors in range +

                +

                + 0 < l < 20 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=433 Mean=11 +

                + +

                + 64 +

                + +

                + SUSE Linux IA32, g++ 4.1 +

                + +

                + Peak=61.4 Mean=19.5 +

                + +

                + 64 +

                + +

                + Red Hat Linux IA64, g++ 3.4.4 +

                + +

                + Peak=61.4 Mean=19.5 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=540 Mean=13.94 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - Errors in range -

                -

                - 0 < l < 20 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=433 Mean=11 -

                -
                -

                - 64 -

                -                 		-

                - SUSE Linux IA32, g++ 4.1 -

                -                 		-

                - Peak=61.4 Mean=19.5 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA64, g++ 3.4.4 -

                -                 		-

                - Peak=61.4 Mean=19.5 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=540 Mean=13.94 -

                -
                @@ -429,7 +427,7 @@ is very close to a root.

                - + Testing

                @@ -439,7 +437,7 @@ precision.

                - + Implementation

                @@ -460,7 +458,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html index 8718a4b60..2094ebae3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html @@ -2,8 +2,8 @@ Legendre (and Associated) Polynomials - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -84,7 +84,7 @@

                - + Description 
                template <class T>
@@ -139,7 +139,7 @@
         
                
 
                
-
+
                
 
                [Caution][Caution]
 Caution
 
                
 
                
@@ -225,20 +225,20 @@
 
                
 
                l
                
 
                
-              The degree of the last polynomial calculated.
-            
                
+                The degree of the last polynomial calculated.
+              
                
 
                x
                
 
                
-              The abscissa value
-            
                
+                The abscissa value
+              
                
 
                Pl
                
 
                
-              The value of the polynomial evaluated at degree l.
-            
                
+                The value of the polynomial evaluated at degree l.
+              
                
 
                Plm1
                
 
                
-              The value of the polynomial evaluated at degree l-1.
-            
                
+                The value of the polynomial evaluated at degree l-1.
+              
                
 
                
 
 
                template <class T1, class T2, class T3>
@@ -271,28 +271,28 @@
 
                
 
                l
                
 
                
-              The degree of the last polynomial calculated.
-            
                
+                The degree of the last polynomial calculated.
+              
                
 
                m
                
 
                
-              The order of the Associated Polynomial.
-            
                
+                The order of the Associated Polynomial.
+              
                
 
                x
                
 
                
-              The abscissa value
-            
                
+                The abscissa value
+              
                
 
                Pl
                
 
                
-              The value of the polynomial evaluated at degree l.
-            
                
+                The value of the polynomial evaluated at degree l.
+              
                
 
                Plm1
                
 
                
-              The value of the polynomial evaluated at degree l-1.
-            
                
+                The value of the polynomial evaluated at degree l-1.
+              
                
 
                
 
 
                
-
+
           Accuracy
         
                
 
                
@@ -302,7 +302,7 @@
           zero error.
         
                
 
                
-
                Table 29. Peak Errors In the Legendre P Function
                
+
                Table 29. Peak Errors In the Legendre P Function
                
 
                @@ -312,129 +312,127 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    Errors in range
+                  
                
+                  
                
+                    0 < l < 20
+                  
                
+                
+                  
                
+                    Errors in range
+                  
                
+                  
                
+                    20 < l < 120
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=211 Mean=20
+                  
                
+                
+                  
                
+                    Peak=300 Mean=33
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    SUSE Linux IA32, g++ 4.1
+                  
                
+                
+                  
                
+                    Peak=70 Mean=10
+                  
                
+                
+                  
                
+                    Peak=700 Mean=60
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Red Hat Linux IA64, g++ 3.4.4
+                  
                
+                
+                  
                
+                    Peak=70 Mean=10
+                  
                
+                
+                  
                
+                    Peak=700 Mean=60
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=35 Mean=6
+                  
                
+                
+                  
                
+                    Peak=292 Mean=41
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                Errors in range
-              
                
-              
                
-                0 < l < 20
-              
                
-                              		
 
-              
                
-                Errors in range
-              
                
-              
                
-                20 < l < 120
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=211 Mean=20
-              
                
-                              		
 
-              
                
-                Peak=300 Mean=33
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                SUSE Linux IA32, g++ 4.1
-              
                
-                              		
 
-              
                
-                Peak=70 Mean=10
-              
                
-                              		
 
-              
                
-                Peak=700 Mean=60
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Red Hat Linux IA64, g++ 3.4.4
-              
                
-                              		
 
-              
                
-                Peak=70 Mean=10
-              
                
-                              		
 
-              
                
-                Peak=700 Mean=60
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=35 Mean=6
-              
                
-                              		
 
-              
                
-                Peak=292 Mean=41
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
                Table 30. Peak Errors In the Associated Legendre
-        P Function
                
-
                
+
                Table 30. Peak Errors In the Associated Legendre P Function
                
+
                @@ -442,98 +440,98 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    Errors in range
+                  
                
+                  
                
+                    0 < l < 20
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=1200 Mean=7
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    SUSE Linux IA32, g++ 4.1
+                  
                
+                
+                  
                
+                    Peak=80 Mean=5
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Red Hat Linux IA64, g++ 3.4.4
+                  
                
+                
+                  
                
+                    Peak=80 Mean=5
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=42 Mean=4
+                  
                
+                
                
 
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                Errors in range
-              
                
-              
                
-                0 < l < 20
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=1200 Mean=7
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                SUSE Linux IA32, g++ 4.1
-              
                
-                              		
 
-              
                
-                Peak=80 Mean=5
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Red Hat Linux IA64, g++ 3.4.4
-              
                
-                              		
 
-              
                
-                Peak=80 Mean=5
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=42 Mean=4
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
                Table 31. Peak Errors In the Legendre Q Function
                
+
                Table 31. Peak Errors In the Legendre Q Function
                
 
                @@ -543,120 +541,120 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    Errors in range
+                  
                
+                  
                
+                    0 < l < 20
+                  
                
+                
+                  
                
+                    Errors in range
+                  
                
+                  
                
+                    20 < l < 120
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=50 Mean=7
+                  
                
+                
+                  
                
+                    Peak=4600 Mean=370
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    SUSE Linux IA32, g++ 4.1
+                  
                
+                
+                  
                
+                    Peak=51 Mean=8
+                  
                
+                
+                  
                
+                    Peak=6000 Mean=480
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Red Hat Linux IA64, g++ 3.4.4
+                  
                
+                
+                  
                
+                    Peak=51 Mean=8
+                  
                
+                
+                  
                
+                    Peak=6000 Mean=480
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=90 Mean=10
+                  
                
+                
+                  
                
+                    Peak=1700 Mean=140
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                Errors in range
-              
                
-              
                
-                0 < l < 20
-              
                
-                              		
 
-              
                
-                Errors in range
-              
                
-              
                
-                20 < l < 120
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=50 Mean=7
-              
                
-                              		
 
-              
                
-                Peak=4600 Mean=370
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                SUSE Linux IA32, g++ 4.1
-              
                
-                              		
 
-              
                
-                Peak=51 Mean=8
-              
                
-                              		
 
-              
                
-                Peak=6000 Mean=480
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Red Hat Linux IA64, g++ 3.4.4
-              
                
-                              		
 
-              
                
-                Peak=51 Mean=8
-              
                
-                              		
 
-              
                
-                Peak=6000 Mean=480
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=90 Mean=10
-              
                
-                              		
 
-              
                
-                Peak=1700 Mean=140
-              
                
-                              		
 
                
                 
 
                
@@ -675,7 +673,7 @@
           given here.
         
                
 
                
-
+
           Testing
         
                
 
                
@@ -685,7 +683,7 @@
           precision.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -706,7 +704,7 @@
 
                
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
index 6acd0fcc7..fb168def3 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
@@ -2,8 +2,8 @@
 
 
 Spherical Harmonics
-
-
+
+
 
 
 
@@ -20,14 +20,14 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
 
                
-
+
           Synopsis
         
                
 
                
@@ -60,7 +60,7 @@
 }} // namespaces
                - + Description

                @@ -96,7 +96,7 @@

                - +
                [Caution][Caution] Caution
                @@ -155,7 +155,7 @@

                - + Accuracy

                @@ -170,7 +170,7 @@ All values are in units of epsilon.

                -

                Table 35. Peak Errors In the Sperical Harmonic Functions

                +

                Table 35. Peak Errors In the Sperical Harmonic Functions

                @@ -179,92 +179,92 @@ +

                + Significand Size +

                + +

                + Platform and Compiler +

                + +

                + Errors in range +

                +

                + 0 < l < 20 +

                + +

                + 53 +

                + +

                + Win32, Visual C++ 8 +

                + +

                + Peak=2x104 Mean=700 +

                + +

                + 64 +

                + +

                + SUSE Linux IA32, g++ 4.1 +

                + +

                + Peak=2900 Mean=100 +

                + +

                + 64 +

                + +

                + Red Hat Linux IA64, g++ 3.4.4 +

                + +

                + Peak=2900 Mean=100 +

                + +

                + 113 +

                + +

                + HPUX IA64, aCC A.06.06 +

                + +

                + Peak=6700 Mean=230 +

                +
                -

                - Significand Size -

                -                 		-

                - Platform and Compiler -

                -                 		-

                - Errors in range -

                -

                - 0 < l < 20 -

                -
                -

                - 53 -

                -                 		-

                - Win32, Visual C++ 8 -

                -                 		-

                - Peak=2x104 Mean=700 -

                -
                -

                - 64 -

                -                 		-

                - SUSE Linux IA32, g++ 4.1 -

                -                 		-

                - Peak=2900 Mean=100 -

                -
                -

                - 64 -

                -                 		-

                - Red Hat Linux IA64, g++ 3.4.4 -

                -                 		-

                - Peak=2900 Mean=100 -

                -
                -

                - 113 -

                -                 		-

                - HPUX IA64, aCC A.06.06 -

                -                 		-

                - Peak=6700 Mean=230 -

                -
                @@ -276,7 +276,7 @@ arbitrarily large when the function is very close to a root.

                - + Testing

                @@ -286,7 +286,7 @@ precision.

                - + Implementation

                @@ -311,7 +311,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc.html b/doc/sf_and_dist/html/math_toolkit/special/sinc.html index 208fc2221..a766086bc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc.html @@ -2,8 +2,8 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +

                Sinus Cardinal and Hyperbolic Sinus Cardinal Functions @@ -46,7 +46,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html index d0f70d332..c807c044d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html @@ -2,8 +2,8 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +

                Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview @@ -56,25 +56,13 @@ implementation of quaternions and octonions.

                -
                -

                -

                -

                - Sinus Cardinal of index pi (purple) - and Hyperbolic Sinus Cardinal of index pi (red) on R -

                -

                -

                -
                -
                -

                -

                -

                - sinc_pi_and_sinhc_pi_on_r -

                -

                -

                -
                +

                + Sinus Cardinal of index pi (purple) and + Hyperbolic Sinus Cardinal of index pi (red) on R +

                +

                + sinc_pi_and_sinhc_pi_on_r +

                @@ -88,7 +76,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html index 2ece1cd9f..0728ea740 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html @@ -2,8 +2,8 @@ sinc_pi - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -81,7 +81,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html index da7452eef..9071aca70 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html @@ -2,8 +2,8 @@ sinhc_pi - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -85,7 +85,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas.html b/doc/sf_and_dist/html/math_toolkit/special/zetas.html index e8626cbc2..cd5cab3d5 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas.html @@ -2,8 +2,8 @@ Zeta Functions - - + + @@ -20,9 +20,9 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                @@ -40,7 +40,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index d7947ce4e..cb3a6c75c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -2,8 +2,8 @@ Riemann Zeta Function - - + + @@ -20,14 +20,14 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -62,7 +62,7 @@

                - + Description 
                template <class T>
@@ -85,7 +85,7 @@
           
         
                
 
                
-
+
           Accuracy
         
                
 
                
@@ -97,7 +97,7 @@
           shown will have effectively zero error.
         
                
 
                
-
                Table 44. Errors In the Function zeta(z)
                
+
                Table 44. Errors In the Function zeta(z)
                
 
                @@ -107,134 +107,134 @@
 
+                  
                
+                    Significand Size
+                  
                
+                
+                  
                
+                    Platform and Compiler
+                  
                
+                
+                  
                
+                    z > 0
+                  
                
+                
+                  
                
+                    z < 0
+                  
                
+                
+                  
                
+                    53
+                  
                
+                
+                  
                
+                    Win32, Visual C++ 8
+                  
                
+                
+                  
                
+                    Peak=0.99 Mean=0.1
+                  
                
+                  
                
+                    GSL Peak=8.7 Mean=1.0
+                  
                
+                  
                
+                    Cephes Peak=2.1
+                    Mean=1.1
+                  
                
+                
+                  
                
+                    Peak=7.1 Mean=3.0
+                  
                
+                  
                
+                    GSL Peak=137 Mean=14
+                  
                
+                  
                
+                    Cephes Peak=5084
+                    Mean=470
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    RedHat Linux IA_EM64, gcc-4.1
+                  
                
+                
+                  
                
+                    Peak=0.99 Mean=0.5
+                  
                
+                
+                  
                
+                    Peak=570 Mean=60
+                  
                
+                
+                  
                
+                    64
+                  
                
+                
+                  
                
+                    Redhat Linux IA64, gcc-4.1
+                  
                
+                
+                  
                
+                    Peak=0.99 Mean=0.5
+                  
                
+                
+                  
                
+                    Peak=559 Mean=56
+                  
                
+                
+                  
                
+                    113
+                  
                
+                
+                  
                
+                    HPUX IA64, aCC A.06.06
+                  
                
+                
+                  
                
+                    Peak=1.0 Mean=0.4
+                  
                
+                
+                  
                
+                    Peak=1018 Mean=79
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Significand Size
-              
                
-                              		
 
-              
                
-                Platform and Compiler
-              
                
-                              		
 
-              
                
-                z > 0
-              
                
-                              		
 
-              
                
-                z < 0
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                53
-              
                
-                              		
 
-              
                
-                Win32, Visual C++ 8
-              
                
-                              		
 
-              
                
-                Peak=0.99 Mean=0.1
-              
                
-              
                
-                GSL Peak=8.7 Mean=1.0
-              
                
-              
                
-                Cephes Peak=2.1
-                Mean=1.1
-              
                
-                              		
 
-              
                
-                Peak=7.1 Mean=3.0
-              
                
-              
                
-                GSL Peak=137 Mean=14
-              
                
-              
                
-                Cephes Peak=5084
-                Mean=470
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                RedHat Linux IA_EM64, gcc-4.1
-              
                
-                              		
 
-              
                
-                Peak=0.99 Mean=0.5
-              
                
-                              		
 
-              
                
-                Peak=570 Mean=60
-              
                
-                              		
 
                
 
                
 
-              
                
-                64
-              
                
-                              		
 
-              
                
-                Redhat Linux IA64, gcc-4.1
-              
                
-                              		
 
-              
                
-                Peak=0.99 Mean=0.5
-              
                
-                              		
 
-              
                
-                Peak=559 Mean=56
-              
                
-                              		
 
                
 
                
 
-              
                
-                113
-              
                
-                              		
 
-              
                
-                HPUX IA64, aCC A.06.06
-              
                
-                              		
 
-              
                
-                Peak=1.0 Mean=0.4
-              
                
-                              		
 
-              
                
-                Peak=1018 Mean=79
-              
                
-                              		
 
                
                 
 
                
 
                
 
                
-
+
           Testing
         
                
 
                
@@ -249,7 +249,7 @@
           check.
         
                
 
                
-
+
           Implementation
         
                
 
                
@@ -327,7 +327,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/status.html b/doc/sf_and_dist/html/math_toolkit/status.html
index d3612ce83..8a8d1e608 100644
--- a/doc/sf_and_dist/html/math_toolkit/status.html
+++ b/doc/sf_and_dist/html/math_toolkit/status.html
@@ -2,8 +2,8 @@
 
 
 Library Status
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
@@ -45,7 +45,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/status/compilers.html b/doc/sf_and_dist/html/math_toolkit/status/compilers.html
index 0e9f48d93..83c518c38 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/compilers.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/compilers.html
@@ -2,8 +2,8 @@
 
 
 Compilers
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
@@ -37,7 +37,7 @@
 
                
         
                
 
                
-
                Table 55. Supported/Tested Compilers
                
+
                Table 55. Supported/Tested Compilers
                
 
                @@ -47,500 +47,509 @@
 
+                  
                
+                    Platform
+                  
                
+                
+                  
                
+                    Compiler
+                  
                
+                
+                  
                
+                    Has long double support
+                  
                
+                
+                  
                
+                    Notes
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    MSVC 7.1 and later
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free at level 4 with this
+                    compiler.
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    Intel 8.1 and later
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free at level 4 with this
+                    compiler. However, The tests cases tend to generate a lot of
+                    warnings relating to numeric underflow of the test data: these
+                    are harmless.
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    GNU Mingw32 C++
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    GNU Cygwin C++
+                  
                
+                
+                  
                
+                    No
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                
+                  
                
+                    Long double support has been disabled because there are no native
+                    long double C std library functions available.
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    Borland C++ 5.8.2 (Developer studio 2006)
+                  
                
+                
+                  
                
+                    No
+                  
                
+                
+                  
                
+                    We have only partial compatability with this compiler:
+                  
                
+                  
                
+                    Long double support has been disabled because the native long
+                    double C standard library functions really only forward to the
+                    double versions. This can result in unpredictable behaviour when
+                    using the long double overloads: for example sqrtl
+                    applied to a finite value, can result in an infinite result.
+                  
                
+                  
                
+                    Some functions still fail to compile, there are no known workarounds
+                    at present.
+                  
                
+                
+                  
                
+                    Linux
+                  
                
+                
+                  
                
+                    GNU C++ 3.4 and later
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                
+                
+                  
                
+                    Linux
+                  
                
+                
+                  
                
+                    Intel C++ 10.0 and later
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler. However, The tests cases tend to generate a lot of
+                    warnings relating to numeric underflow of the test data: these
+                    are harmless.
+                  
                
+                
+                  
                
+                    Linux
+                  
                
+                
+                  
                
+                    Intel C++ 8.1 and 9.1
+                  
                
+                
+                  
                
+                    No
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    Long double support has been disabled with these compiler releases
+                    because calling the standard library long double math functions
+                    can result in a segfault. The issue is Linux distribution and
+                    glibc version specific and is Intel bug report #409291. Fully
+                    up to date releases of Intel 9.1 (post version l_cc_c_9.1.046)
+                    shouldn't have this problem. If you need long double support
+                    with this compiler, then comment out the define of BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+                    at line 55 of boost/math/tools/config.hpp.
+                  
                
+                  
                
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler. However, The tests cases tend to generate a lot of
+                    warnings relating to numeric underflow of the test data: these
+                    are harmless.
+                  
                
+                
+                  
                
+                    Linux
+                  
                
+                
+                  
                
+                    QLogic PathScale 3.0
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    Some tests involving conceptual checks fail to build, otherwise
+                    there appear to be no issues.
+                  
                
+                
+                  
                
+                    Linux
+                  
                
+                
+                  
                
+                    Sun Studio 12
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    Some tests involving function overload resolution fail to build,
+                    these issues should be rairly encountered in practice.
+                  
                
+                
+                  
                
+                    Solaris
+                  
                
+                
+                  
                
+                    Sun Studio 12
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    Some tests involving function overload resolution fail to build,
+                    these issues should be rairly encountered in practice.
+                  
                
+                
+                  
                
+                    Solaris
+                  
                
+                
+                  
                
+                    GNU C++ 4.x
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    We aim to keep our headers warning free with -Wall with this
+                    compiler.
+                  
                
+                
+                  
                
+                    HP Tru64
+                  
                
+                
+                  
                
+                    Compaq C++ 7.1
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                
+                  
                
+                    HP-UX Itanium
+                  
                
+                
+                  
                
+                    HP aCC 6.x
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    Unfortunately this compiler emits quite a few warnings from libraries
+                    upon which we depend (TR1, Array etc).
+                  
                
+                
+                  
                
+                    HP-UX PA-RISC
+                  
                
+                
+                  
                
+                    GNU C++ 3.4
+                  
                
+                
+                  
                
+                    No
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                
+                  
                
+                    Apple Mac OS X, Intel
+                  
                
+                
+                  
                
+                    Darwin/GNU C++ 4.x
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                
+                  
                
+                    Apple Mac OS X, PowerPC
+                  
                
+                
+                  
                
+                    Darwin/GNU C++ 4.x
+                  
                
+                
+                  
                
+                    No
+                  
                
+                
+                  
                
+                    All tests OK.
+                  
                
+                  
                
+                    Long double support has been disabled on this platform due to
+                    the rather strange nature of Darwin's 106-bit long double implementation.
+                    It should be possible to make this work if someone is prepared
+                    to offer assistance.
+                  
                
+                
+                  
                
+                    IMB AIX
+                  
                
+                
+                  
                
+                    IBM xlc 5.3
+                  
                
+                
+                  
                
+                    Yes
+                  
                
+                
+                  
                
+                    All tests pass except for our fpclassify tests which fail due
+                    to a bug in std::numeric_limits,
+                    the bug effects the test code, not fpclassify itself. The IBM
+                    compiler group are aware of the problem.
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Platform
-              
                
-                              		
 
-              
                
-                Compiler
-              
                
-                              		
 
-              
                
-                Has long double support
-              
                
-                              		
 
-              
                
-                Notes
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                MSVC 7.1 and later
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free at level 4 with this compiler.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                Intel 8.1 and later
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free at level 4 with this compiler.
-                However, The tests cases tend to generate a lot of warnings relating
-                to numeric underflow of the test data: these are harmless.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                GNU Mingw32 C++
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                GNU Cygwin C++
-              
                
-                              		
 
-              
                
-                No
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                
-              
                
-                Long double support has been disabled because there are no native
-                long double C std library functions available.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                Borland C++ 5.8.2 (Developer studio 2006)
-              
                
-                              		
 
-              
                
-                No
-              
                
-                              		
 
-              
                
-                We have only partial compatability with this compiler:
-              
                
-              
                
-                Long double support has been disabled because the native long double
-                C standard library functions really only forward to the double versions.
-                This can result in unpredictable behaviour when using the long double
-                overloads: for example sqrtl
-                applied to a finite value, can result in an infinite result.
-              
                
-              
                
-                Some functions still fail to compile, there are no known workarounds
-                at present.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Linux
-              
                
-                              		
 
-              
                
-                GNU C++ 3.4 and later
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Linux
-              
                
-                              		
 
-              
                
-                Intel C++ 10.0 and later
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free with -Wall with this compiler.
-                However, The tests cases tend to generate a lot of warnings relating
-                to numeric underflow of the test data: these are harmless.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Linux
-              
                
-                              		
 
-              
                
-                Intel C++ 8.1 and 9.1
-              
                
-                              		
 
-              
                
-                No
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                Long double support has been disabled with these compiler releases
-                because calling the standard library long double math functions can
-                result in a segfault. The issue is Linux distribution and glibc version
-                specific and is Intel bug report #409291. Fully up to date releases
-                of Intel 9.1 (post version l_cc_c_9.1.046) shouldn't have this problem.
-                If you need long double support with this compiler, then comment
-                out the define of BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS at line
-                55 of boost/math/tools/config.hpp.
-              
                
-              
                
-                We aim to keep our headers warning free with -Wall with this compiler.
-                However, The tests cases tend to generate a lot of warnings relating
-                to numeric underflow of the test data: these are harmless.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Linux
-              
                
-                              		
 
-              
                
-                QLogic PathScale 3.0
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                Some tests involving conceptual checks fail to build, otherwise there
-                appear to be no issues.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Linux
-              
                
-                              		
 
-              
                
-                Sun Studio 12
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                Some tests involving function overload resolution fail to build,
-                these issues should be rairly encountered in practice.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Solaris
-              
                
-                              		
 
-              
                
-                Sun Studio 12
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                Some tests involving function overload resolution fail to build,
-                these issues should be rairly encountered in practice.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Solaris
-              
                
-                              		
 
-              
                
-                GNU C++ 4.x
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                We aim to keep our headers warning free with -Wall with this compiler.
-              
                
-                              		
 
                
 
                
 
-              
                
-                HP Tru64
-              
                
-                              		
 
-              
                
-                Compaq C++ 7.1
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-                              		
 
                
 
                
 
-              
                
-                HP-UX Itanium
-              
                
-                              		
 
-              
                
-                HP aCC 6.x
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                Unfortunately this compiler emits quite a few warnings from libraries
-                upon which we depend (TR1, Array etc).
-              
                
-                              		
 
                
 
                
 
-              
                
-                HP-UX PA-RISC
-              
                
-                              		
 
-              
                
-                GNU C++ 3.4
-              
                
-                              		
 
-              
                
-                No
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Apple Mac OS X, Intel
-              
                
-                              		
 
-              
                
-                Darwin/GNU C++ 4.x
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-                              		
 
                
 
                
 
-              
                
-                Apple Mac OS X, PowerPC
-              
                
-                              		
 
-              
                
-                Darwin/GNU C++ 4.x
-              
                
-                              		
 
-              
                
-                No
-              
                
-                              		
 
-              
                
-                All tests OK.
-              
                
-              
                
-                Long double support has been disabled on this platform due to the
-                rather strange nature of Darwin's 106-bit long double implementation.
-                It should be possible to make this work if someone is prepared to
-                offer assistance.
-              
                
-                              		
 
                
 
                
 
-              
                
-                IMB AIX
-              
                
-                              		
 
-              
                
-                IBM xlc 5.3
-              
                
-                              		
 
-              
                
-                Yes
-              
                
-                              		
 
-              
                
-                All tests pass except for our fpclassify tests which fail due to
-                a bug in std::numeric_limits, the bug effects
-                the test code, not fpclassify itself. The IBM compiler group are
-                aware of the problem.
-              
                
-                              		
 
                
                 
 
                
 
                
-

                 
                
+

                
+        
                
 
                
-
                Table 56. Unsupported Compilers
                
+
                Table 56. Unsupported Compilers
                
 
                @@ -548,40 +557,40 @@
 
+                  
                
+                    Platform
+                  
                
+                
+                  
                
+                    Compiler
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    Borland C++ 5.9.2 (Borland Developer Studio 2007)
+                  
                
+                
+                  
                
+                    Windows
+                  
                
+                
+                  
                
+                    MSVC 6 and 7
+                  
                
+                
                
 
 

 
                
 
-              
                
-                Platform
-              
                
-                              		
 
-              
                
-                Compiler
-              
                
-                              		
 
                
 
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                Borland C++ 5.9.2 (Borland Developer Studio 2007)
-              
                
-                              		
 
                
 
                
 
-              
                
-                Windows
-              
                
-                              		
 
-              
                
-                MSVC 6 and 7
-              
                
-                              		
 
                
                 
 
                
@@ -624,7 +633,7 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/status/credits.html b/doc/sf_and_dist/html/math_toolkit/status/credits.html
index 80c2bb2e6..cf9c57680 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/credits.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/credits.html
@@ -2,8 +2,8 @@
 
 
 Credits and Acknowledgements
-
-
+
+
 
 
 
@@ -19,9 +19,9 @@
 
 
                
 
                
-PrevUpHome
+PrevUpHome
 
                
-
                
+
                
 
                
@@ -104,7 +104,7 @@
 
 
                
 
                
-PrevUpHome
+PrevUpHome
 
                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html
index 9d2f204fa..b4e352915 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/history1.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html
@@ -2,8 +2,8 @@
 
 
 History and What's New
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                
 
                
-PrevUpHomeNext
+PrevUpHomeNext
 
                
-
                
+
                
 
                
@@ -30,284 +30,286 @@
         
         
                
 
                
-
+
           Boost-1.41.0
         
                
 
                
         
                
-
                • 
-            Significantly improved performance for the incomplete gamma function
-            and it's inverse.
-          
                
+
                • 
+              Significantly improved performance for the incomplete gamma function
+              and it's inverse.
+            
                
 
                
         
         
                
 
                
-
+
           Boost-1.40.0
         
                
 
                
         
                
-
                  
-
                • 
-            Added support for MPFR as a bignum type.
-          
                  • 
-
                • 
-            Added some full specializations of the policy classes to reduce compile
-            times.
-          
                  • 
-
                • 
-            Added logistic and hypergeometric distributions, from Gautam Sewani's
-            Google Summer of Code project.
-          
                  • 
-
                • 
-            Added Laplace distribution submitted by Thijs van den Berg.
-          
                  • 
-
                • 
-            Updated performance test code to include new distributions, and improved
-            the performance of the non-central distributions.
-          
                  • 
-
                • 
-            Added SSE2 optimised Lanczos
-            approximation code, from Gautam Sewani's Google Summer of Code
-            project.
-          
                  • 
-
                • 
-            Fixed bug in cyl_bessel_i that used an incorrect approximation for ν =
-            0.5, also effects the non-central Chi Square Distribution when ν = 3, see
-            bug report #2877.
-          
                  • 
-
                • 
-            Fixed minor bugs #2873.
-          
                  • 
+
                    
+
                  • 
+              Added support for MPFR as a bignum type.
+            
                    • 
+
                  • 
+              Added some full specializations of the policy classes to reduce compile
+              times.
+            
                    • 
+
                  • 
+              Added logistic and hypergeometric distributions, from Gautam Sewani's
+              Google Summer of Code project.
+            
                    • 
+
                  • 
+              Added Laplace distribution submitted by Thijs van den Berg.
+            
                    • 
+
                  • 
+              Updated performance test code to include new distributions, and improved
+              the performance of the non-central distributions.
+            
                    • 
+
                  • 
+              Added SSE2 optimised Lanczos
+              approximation code, from Gautam Sewani's Google Summer of Code
+              project.
+            
                    • 
+
                  • 
+              Fixed bug in cyl_bessel_i that used an incorrect approximation for
+              ν = 0.5, also effects the non-central Chi Square Distribution when ν =
+              3, see bug report #2877.
+            
                    • 
+
                  • 
+              Fixed minor bugs #2873.
+            
                    • 
 
                  
 
                  
         
         
                  
 
                  
-
+
           Boost-1.38.0
         
                  
 
                  
         
                  
-
                    
-
                  • 
-            Added Johan Råde's optimised floating point classification routines.
-          
                    • 
-
                  • 
-            Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
-          
                    • 
+
                      
+
                    • 
+              Added Johan Råde's optimised floating point classification routines.
+            
                      • 
+
                    • 
+              Fixed code so that it compiles in GCC's -pedantic mode (bug report
+              #1451).
+            
                      • 
 
                    
 
                    
         
         
                    
 
                    
-
+
           Boost-1.37.0
         
                    
 
                    
         
                    
-
                    • 
-            Improved accuracy and testing of the inverse hypergeometric functions.
-          
                    
+
                    • 
+              Improved accuracy and testing of the inverse hypergeometric functions.
+            
                    
 
                    
         
         
                    
 
                    
-
+
           Boost-1.36.0
         
                    
 
                    
         
                    
-
                      
-
                    • 
-            Added Noncentral Chi Squared Distribution.
-          
                      • 
-
                    • 
-            Added Noncentral Beta Distribution.
-          
                      • 
-
                    • 
-            Added Noncentral F Distribution.
-          
                      • 
-
                    • 
-            Added Noncentral T Distribution.
-          
                      • 
-
                    • 
-            Added Exponential Integral Functions.
-          
                      • 
-
                    • 
-            Added Zeta Function.
-          
                      • 
-
                    • 
-            Added Rounding and Truncation functions.
-          
                      • 
-
                    • 
-            Added Compile time powers of runtime bases.
-          
                      • 
-
                    • 
-            Added SSE2 optimizations for Lanczos evaluation.
-          
                      • 
+
                        
+
                      • 
+              Added Noncentral Chi Squared Distribution.
+            
                        • 
+
                      • 
+              Added Noncentral Beta Distribution.
+            
                        • 
+
                      • 
+              Added Noncentral F Distribution.
+            
                        • 
+
                      • 
+              Added Noncentral T Distribution.
+            
                        • 
+
                      • 
+              Added Exponential Integral Functions.
+            
                        • 
+
                      • 
+              Added Zeta Function.
+            
                        • 
+
                      • 
+              Added Rounding and Truncation functions.
+            
                        • 
+
                      • 
+              Added Compile time powers of runtime bases.
+            
                        • 
+
                      • 
+              Added SSE2 optimizations for Lanczos evaluation.
+            
                        • 
 
                      
 
                      
         
         
                      
 
                      
-
+
           Boost-1.35.0:
           Post Review First Official Release
         
                      
 
                      
         
                      
-
                        
-
                      • 
-            Added Policy based framework that allows fine grained control over function
-            behaviour.
-          
                        • 
-
                      • 
-Breaking change: Changed default behaviour
-            for domain, pole and overflow errors to throw an exception (based on
-            review feedback), this behaviour can be customised using Policy's.
-          
                        • 
-
                      • 
-Breaking change: Changed exception thrown
-            when an internal evaluation error occurs to boost::math::evaluation_error.
-          
                        • 
-
                      • 
-Breaking change: Changed discrete quantiles
-            to return an integer result: this is anything up to 20 times faster than
-            finding the true root, this behaviour can be customised using Policy's.
-          
                        • 
-
                      • 
-            Polynomial/rational function evaluation is now customisable and hopefully
-            faster than before.
-          
                        • 
-
                      • 
-            Added performance test program.
-          
                        • 
+
                          
+
                        • 
+              Added Policy based framework that allows fine grained control over
+              function behaviour.
+            
                          • 
+
                        • 
+              Breaking change: Changed default behaviour
+              for domain, pole and overflow errors to throw an exception (based on
+              review feedback), this behaviour can be customised using Policy's.
+            
                          • 
+
                        • 
+              Breaking change: Changed exception
+              thrown when an internal evaluation error occurs to boost::math::evaluation_error.
+            
                          • 
+
                        • 
+              Breaking change: Changed discrete
+              quantiles to return an integer result: this is anything up to 20 times
+              faster than finding the true root, this behaviour can be customised
+              using Policy's.
+            
                          • 
+
                        • 
+              Polynomial/rational function evaluation is now customisable and hopefully
+              faster than before.
+            
                          • 
+
                        • 
+              Added performance test program.
+            
                          • 
 
                        
 
                        
         
         
                        
 
                        
-
+
           Milestone
           4: Second Review Candidate (1st March 2007)
         
                        
 
                        
         
                        
-
                          
-
                        • 
-            Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
-            them into line with the rest of the code.
-          
                          • 
-
                        • 
-            Added C# "Distribution Explorer" demo application.
-          
                          • 
+
                            
+
                          • 
+              Moved Xiaogang Zhang's Bessel Functions code into the library, and
+              brought them into line with the rest of the code.
+            
                            • 
+
                          • 
+              Added C# "Distribution Explorer" demo application.
+            
                            • 
 
                          
 
                          
         
         
                          
 
                          
-
+
           Milestone
           3: First Review Candidate (31st Dec 2006)
         
                          
 
                          
         
                          
-
                            
-
                          • 
-            Implemented the main probability distribution and density functions.
-          
                            • 
-
                          • 
-            Implemented digamma.
-          
                            • 
-
                          • 
-            Added more factorial functions.
-          
                            • 
-
                          • 
-            Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
-            harmonic functions from TR1.
-          
                            • 
-
                          • 
-            Moved Xiaogang Zhang's elliptic integral code into the library, and brought
-            them into line with the rest of the code.
-          
                            • 
-
                          • 
-            Moved Hubert Holin's existing Boost.Math special functions into this
-            library and brought them into line with the rest of the code.
-          
                            • 
+
                              
+
                            • 
+              Implemented the main probability distribution and density functions.
+            
                              • 
+
                            • 
+              Implemented digamma.
+            
                              • 
+
                            • 
+              Added more factorial functions.
+            
                              • 
+
                            • 
+              Implemented the Hermite, Legendre and Laguerre polynomials plus the
+              spherical harmonic functions from TR1.
+            
                              • 
+
                            • 
+              Moved Xiaogang Zhang's elliptic integral code into the library, and
+              brought them into line with the rest of the code.
+            
                              • 
+
                            • 
+              Moved Hubert Holin's existing Boost.Math special functions into this
+              library and brought them into line with the rest of the code.
+            
                              • 
 
                            
 
                            
         
         
                            
 
                            
-
+
           Milestone
           2: Released September 10th 2006
         
                            
 
                            
         
                            
-
                              
-
                            • 
-            Implement preview release of the statistical distributions.
-          
                              • 
-
                            • 
-            Added statistical distributions tutorial.
-          
                              • 
-
                            • 
-            Implemented root finding algorithms.
-          
                              • 
-
                            • 
-            Implemented the inverses of the incomplete gamma and beta functions.
-          
                              • 
-
                            • 
-            Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
-          
                              • 
-
                            • 
-            Integrated the statistical results generated from the test data with
-            Boost.Test: uses a database of expected results, indexed by test, floating
-            point type, platform, and compiler.
-          
                              • 
-
                            • 
-            Improved lgamma near 1 and 2 (rational approximations).
-          
                              • 
-
                            • 
-            Improved erf/erfc inverses (rational approximations).
-          
                              • 
-
                            • 
-            Implemented Rational function generation (the Remez method).
-          
                              • 
+
                                
+
                              • 
+              Implement preview release of the statistical distributions.
+            
                                • 
+
                              • 
+              Added statistical distributions tutorial.
+            
                                • 
+
                              • 
+              Implemented root finding algorithms.
+            
                                • 
+
                              • 
+              Implemented the inverses of the incomplete gamma and beta functions.
+            
                                • 
+
                              • 
+              Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
+            
                                • 
+
                              • 
+              Integrated the statistical results generated from the test data with
+              Boost.Test: uses a database of expected results, indexed by test, floating
+              point type, platform, and compiler.
+            
                                • 
+
                              • 
+              Improved lgamma near 1 and 2 (rational approximations).
+            
                                • 
+
                              • 
+              Improved erf/erfc inverses (rational approximations).
+            
                                • 
+
                              • 
+              Implemented Rational function generation (the Remez method).
+            
                                • 
 
                              
 
                              
         
         
                              
 
                              
-
+
           Milestone
           1: Released March 31st 2006
         
                              
 
                              
         
                              
-
                                
-
                              • 
-            Implement gamma/beta/erf functions along with their incomplete counterparts.
-          
                                • 
-
                              • 
-            Generate high quality test data, against which future improvements can
-            be judged.
-          
                                • 
-
                              • 
-            Provide tools for the evaluation of infinite series, continued fractions,
-            and rational functions.
-          
                                • 
-
                              • 
-            Provide tools for testing against tabulated test data, and collecting
-            statistics on error rates.
-          
                                • 
-
                              • 
-            Provide sufficient docs for people to be able to find their way around
-            the library.
-          
                                • 
+
                                  
+
                                • 
+              Implement gamma/beta/erf functions along with their incomplete counterparts.
+            
                                  • 
+
                                • 
+              Generate high quality test data, against which future improvements
+              can be judged.
+            
                                  • 
+
                                • 
+              Provide tools for the evaluation of infinite series, continued fractions,
+              and rational functions.
+            
                                  • 
+
                                • 
+              Provide tools for testing against tabulated test data, and collecting
+              statistics on error rates.
+            
                                  • 
+
                                • 
+              Provide sufficient docs for people to be able to find their way around
+              the library.
+            
                                  • 
 
                                
 
                                
         
                                
@@ -334,7 +336,7 @@
 
 
                                
 
                                
-PrevUpHomeNext
+PrevUpHomeNext
 
                                
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/status/issues.html b/doc/sf_and_dist/html/math_toolkit/status/issues.html
index a9fd8a261..e2dcdb29d 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/issues.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/issues.html
@@ -2,8 +2,8 @@
 
 
 Known Issues, and Todo List
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                
 
                                
-PrevUpHomeNext
+PrevUpHomeNext
 
                                
-
                                
+
                                
 
                                
@@ -43,110 +43,113 @@
         with it.
       
                                
 
                                
-
+
         tgamma
       
                                
-
                                
+
                                
 
                                
-
+
         Incomplete Beta
       
                                
-
                                • 
-          Investigate Didonato and Morris' asymptotic expansion for large a and b
-          (medium priority).
-        
                                
+
                                • 
+            Investigate Didonato and Morris' asymptotic expansion for large a and
+            b (medium priority).
+          
                                
 
                                
-
+
         Inverse Gamma
       
                                
-
                                • 
-          Investigate whether we can skip iteration altogether if the first approximation
-          is good enough (Medium Priority).
-        
                                
+
                                • 
+            Investigate whether we can skip iteration altogether if the first approximation
+            is good enough (Medium Priority).
+          
                                
 
                                
-
+
         Polynomials
       
                                
-
                                • 
-          The Legendre and Laguerre Polynomials have surprisingly different error
-          rates on different platforms, considering they are evaluated with only
-          basic arithmetic operations. Maybe this is telling us something, or maybe
-          not (Low Priority).
-        
                                
+
                                • 
+            The Legendre and Laguerre Polynomials have surprisingly different error
+            rates on different platforms, considering they are evaluated with only
+            basic arithmetic operations. Maybe this is telling us something, or maybe
+            not (Low Priority).
+          
                                
 
                                
-
+
         Elliptic Integrals
       
                                
-
                                  
-
                                • 
-          Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google
-          Summer of Code student project, and are based on Carlson's original papers.
-          However, Carlson has revised his algorithms since then (refer to the references
-          in the elliptic integral docs for a list), to improve performance and accuracy,
-          we may be able to take advantage of these improvements too (Low Priority).
-        
                                  • 
-
                                • 
-
                                  Carlson's algorithms (mainly RJ) are somewhat prone to internal overflow/underflow
-          when the arguments are very large or small. The homogeneity relations:
                                  
-
                                  RF(ka,
-          kb, kc) = k-1/2 RF(a, b, c)
                                  
-
                                  and
                                  
-
                                  RJ(ka, kb, kc, kr) = k-3/2 RJ(a, b, c, r)
                                  
-
                                  could
-          be used to sidestep trouble here: provided the problem domains can be accurately
-          identified. (Medium Priority).
                                  
-
                                  • 
-
                                • 
-          Carlson's RC can be reduced to elementary funtions (asin and log), would
-          it be more efficient evaluated this way, rather than by Carlson's algorithms?
-          (Low Priority).
-        
                                  • 
-
                                • 
-          Should we add an implementation of Carlson's RG? It's not required for
-          the Legendre form integrals, but some people may find it useful (Low Priority).
-        
                                  • 
-
                                • 
-          There are a several other integrals: D(φ, k), Z(β, k), Λ0(β, k) and Bulirsch's
-          el functions that could be implemented using Carlson's
-          integrals (Low Priority).
-        
                                  • 
-
                                • 
-          The integrals K(k) and E(k) could be implemented using rational approximations
-          (both for efficiency and accuracy), assuming we can find them. (Medium
-          Priority).
-        
                                  • 
-
                                • 
-          There is a sub-domain of ellint_3
-          that is unimplemented (see the docs for details), currently it's not clear
-          how to solve this issue, or if it's ever likely to be an real problem in
-          practice - especially as most other implementations don't support this
-          domain either (Medium Priority).
-        
                                  • 
+
                                    
+
                                  • 
+            Carlson's algorithms are essentially unchanged from Xiaogang Zhang's
+            Google Summer of Code student project, and are based on Carlson's original
+            papers. However, Carlson has revised his algorithms since then (refer
+            to the references in the elliptic integral docs for a list), to improve
+            performance and accuracy, we may be able to take advantage of these improvements
+            too (Low Priority).
+          
                                    • 
+
                                  • 
+            
                                    Carlson's algorithms (mainly RJ) are somewhat prone to internal overflow/underflow
+            when the arguments are very large or small. The homogeneity relations:
                                    
+ 
                                    RF(ka,
+            kb, kc) = k-1/2 RF(a, b, c)
                                    
+ 
                                    and
                                    
+ 
                                    RJ(ka, kb, kc, kr) = k-3/2 RJ(a, b, c, r)
                                    
+ 
                                    could
+            be used to sidestep trouble here: provided the problem domains can be
+            accurately identified. (Medium Priority).
                                    
+
+          
                                    • 
+
                                  • 
+            Carlson's RC can be reduced to elementary funtions (asin and log), would
+            it be more efficient evaluated this way, rather than by Carlson's algorithms?
+            (Low Priority).
+          
                                    • 
+
                                  • 
+            Should we add an implementation of Carlson's RG? It's not required for
+            the Legendre form integrals, but some people may find it useful (Low
+            Priority).
+          
                                    • 
+
                                  • 
+            There are a several other integrals: D(φ, k), Z(β, k), Λ0(β, k) and Bulirsch's
+            el functions that could be implemented using Carlson's
+            integrals (Low Priority).
+          
                                    • 
+
                                  • 
+            The integrals K(k) and E(k) could be implemented using rational approximations
+            (both for efficiency and accuracy), assuming we can find them. (Medium
+            Priority).
+          
                                    • 
+
                                  • 
+            There is a sub-domain of ellint_3
+            that is unimplemented (see the docs for details), currently it's not
+            clear how to solve this issue, or if it's ever likely to be an real problem
+            in practice - especially as most other implementations don't support
+            this domain either (Medium Priority).
+          
                                    • 
 
                                  
 
                                  
-
+
         Inverse
         Hyperbolic Functions
       
                                  
-
                                  • 
-          These functions are inherited from previous Boost versions, before log1p became widely
-          available. Would they be better expressed in terms of this function? This
-          is probably only an issue for very high precision types (Low Priority).
-        
                                  
+
                                  • 
+            These functions are inherited from previous Boost versions, before log1p became widely
+            available. Would they be better expressed in terms of this function?
+            This is probably only an issue for very high precision types (Low Priority).
+          
                                  
 
                                  
-
+
         Statistical
         distributions
       
                                  
-
                                  • 
-          Student's t Perhaps switch to normal distribution as a better approximation
-          for very large degrees of freedom?
-        
                                  
+
                                  • 
+            Student's t Perhaps switch to normal distribution as a better approximation
+            for very large degrees of freedom?
+          
                                  
 
                                  
-
+
         Feature Requests
       
                                  
 
                                  
@@ -165,1091 +168,1091 @@
 
 
 
-              
                                  
-                Distribution
-              
                                  
+                
                                  
+                  Distribution
+                
                                  
               
 
-              
                                  
-                R
-              
                                  
+                
                                  
+                  R
+                
                                  
               
 
-              
                                  
-                Mathematica 6
-              
                                  
+                
                                  
+                  Mathematica 6
+                
                                  
               
 
-              
                                  
-                NIST
-              
                                  
+                
                                  
+                  NIST
+                
                                  
               
 
-              
                                  
-                Regress+
-              
                                  
+                
                                  
+                  Regress+
+                
                                  
               
 
-              
                                  
-                Matlab
-              
                                  
+                
                                  
+                  Matlab
+                
                                  
               
 
 
 
 
-              
                                  
-                Inverse Gausian / Inverse Normal
-              
                                  
+                
                                  
+                  Inverse Gausian / Inverse Normal
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
 
 
-              
                                  
-                Geometric
-              
                                  
+                
                                  
+                  Geometric
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
 
 
-              
                                  
-                Multinomial
-              
                                  
+                
                                  
+                  Multinomial
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
 
 
-              
                                  
-                Tukey Lambda
-              
                                  
+                
                                  
+                  Tukey Lambda
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Half Normal / Folded Normal
-              
                                  
+                
                                  
+                  Half Normal / Folded Normal
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Chi
-              
                                  
+                
                                  
+                  Chi
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Gumbel
-              
                                  
+                
                                  
+                  Gumbel
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Discrete Uniform
-              
                                  
+                
                                  
+                  Discrete Uniform
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
 
 
-              
                                  
-                Log Series
-              
                                  
+                
                                  
+                  Log Series
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Nakagami (generalised Chi)
-              
                                  
+                
                                  
+                  Nakagami (generalised Chi)
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
 
 
-              
                                  
-                Log Logistic
-              
                                  
+                
                                  
+                  Log Logistic
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
 
 
-              
                                  
-                Tukey (Studentized range)
-              
                                  
+                
                                  
+                  Tukey (Studentized range)
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Wilcoxon rank sum
-              
                                  
+                
                                  
+                  Wilcoxon rank sum
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Wincoxon signed rank
-              
                                  
+                
                                  
+                  Wincoxon signed rank
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Non-central Beta
-              
                                  
+                
                                  
+                  Non-central Beta
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Laplace
-              
                                  
+                
                                  
+                  Laplace
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Maxwell
-              
                                  
+                
                                  
+                  Maxwell
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Beta-Binomial
-              
                                  
+                
                                  
+                  Beta-Binomial
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Beta-negative Binomial
-              
                                  
+                
                                  
+                  Beta-negative Binomial
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Zipf
-              
                                  
+                
                                  
+                  Zipf
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Birnbaum-Saunders / Fatigue Life
-              
                                  
+                
                                  
+                  Birnbaum-Saunders / Fatigue Life
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Double Exponential
-              
                                  
+                
                                  
+                  Double Exponential
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Power Normal
-              
                                  
+                
                                  
+                  Power Normal
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Power Lognormal
-              
                                  
+                
                                  
+                  Power Lognormal
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Cosine
-              
                                  
+                
                                  
+                  Cosine
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Double Gamma
-              
                                  
+                
                                  
+                  Double Gamma
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Double Weibul
-              
                                  
+                
                                  
+                  Double Weibul
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Hyperbolic Secant
-              
                                  
+                
                                  
+                  Hyperbolic Secant
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Laplace
-              
                                  
+                
                                  
+                  Laplace
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Semicircular
-              
                                  
+                
                                  
+                  Semicircular
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Bradford
-              
                                  
+                
                                  
+                  Bradford
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Birr / Fisk
-              
                                  
+                
                                  
+                  Birr / Fisk
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
 
-              
                                  
-                Reciprocal
-              
                                  
+                
                                  
+                  Reciprocal
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
-              
                                  
-                X
-              
                                  
+                
                                  
+                  X
+                
                                  
               
 
-              
                                  
-                -
-              
                                  
+                
                                  
+                  -
+                
                                  
               
 
 
@@ -1257,20 +1260,20 @@
 
                                  
         Also asked for more than once:
       
                                  
-
                                    
-
                                  • 
-          Add support for interpolated distributions, possibly combine with numeric
-          integration and differentiation.
-        
                                    • 
-
                                  • 
-          Add support for bivariate and multivariate distributions: most especially
-          the normal.
-        
                                    • 
-
                                  • 
-          Add support for the log of the cdf and pdf: this is mainly a performance
-          optimisation since we can avoid some special function calls for some distributions
-          by returning the log of the result.
-        
                                    • 
+
                                      
+
                                    • 
+            Add support for interpolated distributions, possibly combine with numeric
+            integration and differentiation.
+          
                                      • 
+
                                    • 
+            Add support for bivariate and multivariate distributions: most especially
+            the normal.
+          
                                      • 
+
                                    • 
+            Add support for the log of the cdf and pdf: this is mainly a performance
+            optimisation since we can avoid some special function calls for some
+            distributions by returning the log of the result.
+          
                                      • 
 
                                    
 
                                  
 
@@ -1285,7 +1288,7 @@
 
                                  
 
                                  
 
                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit.html b/doc/sf_and_dist/html/math_toolkit/toolkit.html
index df5e005c1..7bd85bbbf 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit.html
@@ -2,8 +2,8 @@
 
 
 Internal Details and Tools (Experimental)
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                  
 
                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                  
-
                                  
+
                                  
 
                                  
@@ -69,7 +69,7 @@
 
 
                                  
 
                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
index c82a9811c..bce21a9e1 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
@@ -2,8 +2,8 @@
 
 
 Reused Utilities
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                                  
 
                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                  
-
                                  
+
                                  
 
                                  
@@ -55,7 +55,7 @@
 
 
                                  
 
                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                  
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
index 6a4c822d3..683d6dedc 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
@@ -2,8 +2,8 @@
 
 
 Continued Fraction Evaluation
-
-
+
+
 
 
 
@@ -20,15 +20,15 @@
 
 
                                  
 
                                  
-PrevUpHomeNext
+PrevUpHomeNext
 
                                  
-
                                  
+
                                  
 
                                  
 
                                  
-
+
           Synopsis
         
                                  
 
                                  
@@ -78,7 +78,7 @@
 }}} // namespaces
                - + Description

                @@ -116,48 +116,48 @@ -

                - Expression -

                +

                + Expression +

                -

                - Description -

                +

                + Description +

                -

                - Gen::result_type -

                +

                + Gen::result_type +

                -

                - The type that is the result of invoking operator(). This can be - either an arithmetic type, or a std::pair<> of arithmetic - types. -

                +

                + The type that is the result of invoking operator(). This can + be either an arithmetic type, or a std::pair<> of arithmetic + types. +

                -

                - g() -

                +

                + g() +

                -

                - Returns an object of type Gen::result_type. -

                -

                - Each time this operator is called then the next pair of a - and b values is returned. Or, if result_type - is an arithmetic type, then the next b value - is returned and all the a values are assumed - to 1. -

                +

                + Returns an object of type Gen::result_type. +

                +

                + Each time this operator is called then the next pair of a + and b values is returned. Or, if result_type + is an arithmetic type, then the next b value + is returned and all the a values are assumed + to 1. +

                @@ -178,7 +178,7 @@ a continued fraction for convergence.

                - + Implementation

                @@ -188,7 +188,7 @@ Lentz, W.J. 1976, Applied Optics, vol. 15, pp. 668-671.

                - + Examples

                @@ -281,7 +281,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html index b0c12a958..1f4691291 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html @@ -2,8 +2,8 @@ Numeric Constants - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -59,7 +59,7 @@ }}} // namespaces

                - + Description

                @@ -92,275 +92,275 @@ -

                - Constant -

                +

                + Constant +

                -

                - Meaning -

                +

                + Meaning +

                -

                - Value -

                +

                + Value +

                -

                - pi -

                +

                + pi +

                -

                - π -

                +

                + π +

                -

                - 3.1415926535897932384... -

                +

                + 3.1415926535897932384... +

                -

                - root_pi -

                +

                + root_pi +

                -

                - √π -

                +

                + √π +

                -

                - 1.772453850905516027... -

                +

                + 1.772453850905516027... +

                -

                - root_half_pi -

                +

                + root_half_pi +

                -

                - √(π/2) -

                +

                + √(π/2) +

                -

                - 1.253314137315500251... -

                +

                + 1.253314137315500251... +

                -

                - root_two_pi -

                +

                + root_two_pi +

                -

                - √(2*π) -

                +

                + √(2*π) +

                -

                - 2.506628274631000502... -

                +

                + 2.506628274631000502... +

                -

                - root_ln_four -

                +

                + root_ln_four +

                -

                - √(ln(4)) -

                +

                + √(ln(4)) +

                -

                - 1.17741002251547469... -

                +

                + 1.17741002251547469... +

                -

                - e -

                +

                + e +

                -

                - e -

                +

                + e +

                -

                - 2.71828182845904523536... -

                +

                + 2.71828182845904523536... +

                -

                - half -

                +

                + half +

                -

                - 0.5 -

                +

                + 0.5 +

                -

                - 0.5 -

                +

                + 0.5 +

                -

                - euler -

                +

                + euler +

                -

                - Euler's constant -

                +

                + Euler's constant +

                -

                - 0.577215664901532860606 -

                +

                + 0.577215664901532860606 +

                -

                - root_two -

                +

                + root_two +

                -

                - √2 -

                +

                + √2 +

                -

                - 1.4142135623730950488... -

                +

                + 1.4142135623730950488... +

                -

                - ln_two -

                +

                + ln_two +

                -

                - ln(2) -

                +

                + ln(2) +

                -

                - 0.6931471805599453094... -

                +

                + 0.6931471805599453094... +

                -

                - ln_ln_two -

                +

                + ln_ln_two +

                -

                - ln(ln(2)) -

                +

                + ln(ln(2)) +

                -

                - -0.3665129205816643... -

                +

                + -0.3665129205816643... +

                -

                - third -

                +

                + third +

                -

                - 1/3 -

                +

                + 1/3 +

                -

                - 0.333333333333333333... -

                +

                + 0.333333333333333333... +

                -

                - twothirds -

                +

                + twothirds +

                -

                - 2/3 -

                +

                + 2/3 +

                -

                - 0.666666666666666666... -

                +

                + 0.666666666666666666... +

                -

                - pi_minus_three -

                +

                + pi_minus_three +

                -

                - π-3 -

                +

                + π-3 +

                -

                - 0.14159265358979323846... -

                +

                + 0.14159265358979323846... +

                -

                - four_minus_pi -

                +

                + four_minus_pi +

                -

                - 4-π -

                +

                + 4-π +

                -

                - 0.85840734641020676153735... -

                +

                + 0.85840734641020676153735... +

                @@ -378,7 +378,7 @@
                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html index 367f5f22b..f712386e5 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html @@ -2,8 +2,8 @@ Locating Function Minima - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + synopsis

                @@ -45,7 +45,7 @@ std::pair<T, T> brent_find_minima(F f, T min, T max, int bits, boost::uintmax_t& max_iter);

                - + Description

                @@ -57,30 +57,31 @@

                f

                - The function to minimise. The function should be smooth over the range - [min,max], with no maxima occurring in that interval. -

                + The function to minimise. The function should be smooth over the + range [min,max], with no maxima occurring in that interval. +

                min

                - The lower endpoint of the range in which to search for the minima. -

                + The lower endpoint of the range in which to search for the minima. +

                max

                - The upper endpoint of the range in which to search for the minima. -

                + The upper endpoint of the range in which to search for the minima. +

                bits

                - The number of bits precision to which the minima should be found. Note - that in principle, the minima can not be located to greater accuracy - than the square root of machine epsilon, therefore if bits - is set to a value greater than one half of the bits in type T, then - the value will be ignored. -

                + The number of bits precision to which the minima should be found. + Note that in principle, the minima can not be located to greater + accuracy than the square root of machine epsilon, therefore if bits + is set to a value greater than one half of the bits in type T, then + the value will be ignored. +

                max_iter

                - The maximum number of iterations to use in the algorithm, if not provided - the algorithm will just keep on going until the minima is found. -

                + The maximum number of iterations to use in the algorithm, if not + provided the algorithm will just keep on going until the minima is + found. +

                @@ -88,7 +89,7 @@ the abscissa at the minima and the value of f(x) at the minima.

                - + Implementation

                @@ -121,7 +122,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html index 1afcdc65c..912511a2c 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html @@ -2,8 +2,8 @@ Polynomial and Rational Function Evaluation - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + synopsis

                @@ -79,7 +79,7 @@ V evaluate_rational(const T* num, const U* denom, V z, unsigned count);

                - + Description

                @@ -193,7 +193,7 @@ evaluation with compile-time array sizes may offer slightly better performance.

                - + Implementation

                @@ -232,7 +232,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html index 3d452c9b6..c4b22e3ee 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html @@ -2,8 +2,8 @@ Root Finding With Derivatives - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -61,7 +61,7 @@ }}} // namespaces

                - + Description

                @@ -78,105 +78,105 @@

                Parameters of the root finding functions

                -
                F - f
                +
                F f

                - Type F must be a callable function object that accepts one parameter - and returns a tuple: -

                + Type F must be a callable function object that accepts one parameter + and returns a tuple: +

                - For the second order iterative methods (Newton Raphson) the tuple should - have two elements containing the evaluation of the function and it's - first derivative. -

                + For the second order iterative methods (Newton Raphson) the tuple + should have two elements containing the evaluation of the function + and it's first derivative. +

                - For the third order methods (Halley and Schroeder) the tuple should - have three elements containing the evaluation of the function and its - first and second derivatives. -

                + For the third order methods (Halley and Schroeder) the tuple should + have three elements containing the evaluation of the function and + its first and second derivatives. +

                T guess

                - The initial starting value. -

                + The initial starting value. +

                T min

                - The minimum possible value for the result, this is used as an initial - lower bracket. -

                + The minimum possible value for the result, this is used as an initial + lower bracket. +

                T max

                - The maximum possible value for the result, this is used as an initial - upper bracket. -

                + The maximum possible value for the result, this is used as an initial + upper bracket. +

                int digits

                - The desired number of binary digits. -

                + The desired number of binary digits. +

                uintmax_t max_iter

                - An optional maximum number of iterations to perform. -

                + An optional maximum number of iterations to perform. +

                When using these functions you should note that:

                -
                  -
                • - They may be very sensitive to the initial guess, typically they converge - very rapidly if the initial guess has two or three decimal digits correct. - However convergence can be no better than bisection, or in some rare - cases even worse than bisection if the initial guess is a long way from - the correct value and the derivatives are close to zero. -
                  • -
                • - These functions include special cases to handle zero first (and second - where appropriate) derivatives, and fall back to bisection in this case. - However, it is helpful if F is defined to return an arbitrarily small - value of the correct sign rather than zero. -
                  • -
                • - If the derivative at the current best guess for the result is infinite - (or very close to being infinite) then these functions may terminate - prematurely. A large first derivative leads to a very small next step, - triggering the termination condition. Derivative based iteration may - not be appropriate in such cases. -
                  • -
                • - These functions fall back to bisection if the next computed step would - take the next value out of bounds. The bounds are updated after each - step to ensure this leads to convergence. However, a good initial guess - backed up by asymptotically-tight bounds will improve performance no - end rather than relying on bisection. -
                  • -
                • - The value of digits is crucial to good performance - of these functions, if it is set too high then at best you will get one - extra (unnecessary) iteration, and at worst the last few steps will proceed - by bisection. Remember that the returned value can never be more accurate - than f(x) can be evaluated, and that if f(x) suffers from cancellation - errors as it tends to zero then the computed steps will be effectively - random. The value of digits should be set so that - iteration terminates before this point: remember that for second and - third order methods the number of correct digits in the result is increasing - quite substantially with each iteration, digits - should be set by experiment so that the final iteration just takes the - next value into the zone where f(x) becomes inaccurate. -
                  • -
                • - Finally: you may well be able to do better than these functions by hand-coding - the heuristics used so that they are tailored to a specific function. - You may also be able to compute the ratio of derivatives used by these - methods more efficiently than computing the derivatives themselves. As - ever, algebraic simplification can be a big win. -
                  • +
                    +
                  • + They may be very sensitive to the initial guess, typically they converge + very rapidly if the initial guess has two or three decimal digits correct. + However convergence can be no better than bisection, or in some rare + cases even worse than bisection if the initial guess is a long way + from the correct value and the derivatives are close to zero. +
                    • +
                  • + These functions include special cases to handle zero first (and second + where appropriate) derivatives, and fall back to bisection in this + case. However, it is helpful if F is defined to return an arbitrarily + small value of the correct sign rather than zero. +
                    • +
                  • + If the derivative at the current best guess for the result is infinite + (or very close to being infinite) then these functions may terminate + prematurely. A large first derivative leads to a very small next step, + triggering the termination condition. Derivative based iteration may + not be appropriate in such cases. +
                    • +
                  • + These functions fall back to bisection if the next computed step would + take the next value out of bounds. The bounds are updated after each + step to ensure this leads to convergence. However, a good initial guess + backed up by asymptotically-tight bounds will improve performance no + end rather than relying on bisection. +
                    • +
                  • + The value of digits is crucial to good performance + of these functions, if it is set too high then at best you will get + one extra (unnecessary) iteration, and at worst the last few steps + will proceed by bisection. Remember that the returned value can never + be more accurate than f(x) can be evaluated, and that if f(x) suffers + from cancellation errors as it tends to zero then the computed steps + will be effectively random. The value of digits + should be set so that iteration terminates before this point: remember + that for second and third order methods the number of correct digits + in the result is increasing quite substantially with each iteration, + digits should be set by experiment so that the + final iteration just takes the next value into the zone where f(x) + becomes inaccurate. +
                    • +
                  • + Finally: you may well be able to do better than these functions by + hand-coding the heuristics used so that they are tailored to a specific + function. You may also be able to compute the ratio of derivatives + used by these methods more efficiently than computing the derivatives + themselves. As ever, algebraic simplification can be a big win. +

                  - + Newton Raphson Method
                  @@ -196,7 +196,7 @@

                  - + Halley's Method
                  @@ -220,7 +220,7 @@

                  - + Schroeder's Method
                  @@ -244,7 +244,7 @@ iteration.

                  - + Example

                  @@ -379,7 +379,7 @@

                  -PrevUpHomeNext +PrevUpHomeNext
                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html index aa291c69e..775169aab 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html @@ -2,8 +2,8 @@ Root Finding Without Derivatives - - + + @@ -20,15 +20,15 @@
                  -PrevUpHomeNext +PrevUpHomeNext
                  -
                  +
                  - + Synopsis

                  @@ -141,7 +141,7 @@ }}} // namespaces

                  - + Description

                  @@ -209,31 +209,32 @@

                  f

                  - A unary functor which is the function whose root is to be found. -

                  + A unary functor which is the function whose root is to be found. +

                  min

                  - The left bracket of the interval known to contain the root. -

                  + The left bracket of the interval known to contain the root. +

                  max

                  - The right bracket of the interval known to contain the root. It is - a precondition that min < max and f(min)*f(max) - <= 0, the function signals evaluation error if these - preconditions are violated. The action taken is controlled by the evaluation - error policy. A best guess may be returned, perhaps significantly wrong. -

                  + The right bracket of the interval known to contain the root. It is + a precondition that min < max and f(min)*f(max) + <= 0, the function signals evaluation error if these + preconditions are violated. The action taken is controlled by the + evaluation error policy. A best guess may be returned, perhaps significantly + wrong. +

                  tol

                  - A binary functor that specifies the termination condition: the function - will return the current brackets enclosing the root when tol(min,max) - becomes true. -

                  + A binary functor that specifies the termination condition: the function + will return the current brackets enclosing the root when tol(min,max) + becomes true. +

                  max_iter

                  - The maximum number of invocations of f(x) to make - while searching for the root. -

                  + The maximum number of invocations of f(x) to + make while searching for the root. +

                  @@ -307,40 +308,41 @@

                  f

                  - A unary functor that is the function whose root is to be solved. f(x) - must be uniformly increasing or decreasing on x. -

                  + A unary functor that is the function whose root is to be solved. + f(x) must be uniformly increasing or decreasing on x. +

                  guess

                  - An initial approximation to the root -

                  + An initial approximation to the root +

                  factor

                  - A scaling factor that is used to bracket the root: the value guess - is multiplied (or divided as appropriate) by factor - until two values are found that bracket the root. A value such as 2 - is a typical choice for factor. -

                  + A scaling factor that is used to bracket the root: the value guess + is multiplied (or divided as appropriate) by factor + until two values are found that bracket the root. A value such as + 2 is a typical choice for factor. +

                  rising

                  - Set to true if f(x) is rising - on x and false if f(x) - is falling on x. This value is used along with - the result of f(guess) to determine if guess - is above or below the root. -

                  + Set to true if f(x) is + rising on x and false if + f(x) is falling on x. This + value is used along with the result of f(guess) + to determine if guess is above or below the + root. +

                  tol

                  - A binary functor that determines the termination condition for the - search for the root. tol is passed the current - brackets at each step, when it returns true then the current brackets - are returned as the result. -

                  + A binary functor that determines the termination condition for the + search for the root. tol is passed the current + brackets at each step, when it returns true then the current brackets + are returned as the result. +

                  max_iter

                  - The maximum number of function invocations to perform in the search - for the root. -

                  + The maximum number of function invocations to perform in the search + for the root. +

                  @@ -434,42 +436,42 @@

                  f

                  - A unary functor that is the function whose root is to be solved. f(x) - need not be uniformly increasing or decreasing on x - and may have multiple roots. -

                  + A unary functor that is the function whose root is to be solved. + f(x) need not be uniformly increasing or decreasing on x + and may have multiple roots. +

                  a

                  - The lower bound for the initial bracket of the root. -

                  + The lower bound for the initial bracket of the root. +

                  b

                  - The upper bound for the initial bracket of the root. It is a precondition - that a < b and that a - and b bracket the root to find so that f(a)*f(b) - < 0. -

                  + The upper bound for the initial bracket of the root. It is a precondition + that a < b and that a + and b bracket the root to find so that f(a)*f(b) + < 0. +

                  fa

                  - Optional: the value of f(a). -

                  + Optional: the value of f(a). +

                  fb

                  - Optional: the value of f(b). -

                  + Optional: the value of f(b). +

                  tol

                  - A binary functor that determines the termination condition for the - search for the root. tol is passed the current - brackets at each step, when it returns true then the current brackets - are returned as the result. -

                  + A binary functor that determines the termination condition for the + search for the root. tol is passed the current + brackets at each step, when it returns true then the current brackets + are returned as the result. +

                  max_iter

                  - The maximum number of function invocations to perform in the search - for the root. On exit max_iter is set to actual - number of function invocations used. -

                  + The maximum number of function invocations to perform in the search + for the root. On exit max_iter is set to actual + number of function invocations used. +

                @@ -559,7 +561,7 @@ as soon as both ends of the interval round to the same nearest integer.

                - + Implementation

                @@ -587,7 +589,7 @@

                -PrevUpHomeNext +PrevUpHomeNext
                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html index f7a14c725..e839040b6 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html @@ -2,8 +2,8 @@ Series Evaluation - - + + @@ -20,15 +20,15 @@
                -PrevUpHomeNext +PrevUpHomeNext
                -
                +
                - + Synopsis

                @@ -70,7 +70,7 @@ }}} // namespaces

                - + Description

                @@ -100,22 +100,22 @@ value of the sum to which the terms of the series should be added. This is useful in two situations:

                -
                  -
                • - Where the first value of the series has a different formula to successive - terms. In this case the first value in the series can be passed as the - last argument and the logic of the function object can then be simplified - to return subsequent terms. -
                  • -
                • - Where the series is being added (or subtracted) from some other value: - termination of the series will likely occur much more rapidly if that - other value is passed as the last argument. For example, there are several - functions that can be expressed as 1 - S(z) where - S(z) is an infinite series. In this case, pass -1 as the last argument - and then negate the result of the summation to get the result of 1 - - S(z). -
                  • +
                    +
                  • + Where the first value of the series has a different formula to successive + terms. In this case the first value in the series can be passed as + the last argument and the logic of the function object can then be + simplified to return subsequent terms. +
                    • +
                  • + Where the series is being added (or subtracted) from some other value: + termination of the series will likely occur much more rapidly if that + other value is passed as the last argument. For example, there are + several functions that can be expressed as 1 - S(z) + where S(z) is an infinite series. In this case, pass -1 as the last + argument and then negate the result of the summation to get the result + of 1 - S(z). +

                  The two kahan_sum_series variants of these algorithms @@ -127,7 +127,7 @@ summation in this way.

                  - + Example

                  @@ -196,7 +196,7 @@

                  -PrevUpHomeNext +PrevUpHomeNext
                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html index 73edbb5fc..eca80a60e 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html @@ -2,8 +2,8 @@ Testing and Development - - + + @@ -20,9 +20,9 @@
                  -PrevUpHomeNext +PrevUpHomeNext
                  -
                  +
                  @@ -48,7 +48,7 @@
                  -PrevUpHomeNext +PrevUpHomeNext
                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html index 353292fbf..877ab893e 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html @@ -2,8 +2,8 @@ Relative Error and Testing - - + + @@ -20,15 +20,15 @@
                  -PrevUpHomeNext +PrevUpHomeNext
                  -
                  +
                  - + Synopsis

                  @@ -45,7 +45,7 @@ test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);

                  - + Description 
                  template <class T>
@@ -61,14 +61,14 @@
 
                  
           In addition the value returned is zero if:
         
                  
-
                    
-
                  • 
-            Both a and v are infinite.
-          
                    • 
-
                  • 
-            Both a and v are denormalised
-            numbers or zero.
-          
                    • 
+
                      
+
                    • 
+              Both a and v are infinite.
+            
                      • 
+
                    • 
+              Both a and v are denormalised
+              numbers or zero.
+            
                      • 
 
                    
 
                    
           Otherwise if only one of a and v
@@ -89,51 +89,43 @@
 
                    
 
                    
 
                    
-
                    unsigned
-          worst()const;
                    
+
                    unsigned worst()const;
                    
 
                    
-              Returns the row at which the worst error occurred.
-            
                    
-
                    T
-          min()const;
                    
+                Returns the row at which the worst error occurred.
+              
                    
+
                    T min()const;
                    
 
                    
-              Returns the smallest relative error found.
-            
                    
-
                    T
-          max()const;
                    
+                Returns the smallest relative error found.
+              
                    
+
                    T max()const;
                    
 
                    
-              Returns the largest relative error found.
-            
                    
-
                    T
-          mean()const;
                    
+                Returns the largest relative error found.
+              
                    
+
                    T mean()const;
                    
 
                    
-              Returns the mean error found.
-            
                    
-
                    boost::uintmax_t
-          count()const;
                    
+                Returns the mean error found.
+              
                    
+
                    boost::uintmax_t count()const;
                    
 
                    
-              Returns the number of test cases.
-            
                    
-
                    T
-          variance()const;
                    
+                Returns the number of test cases.
+              
                    
+
                    T variance()const;
                    
 
                    
-              Returns the variance of the errors found.
-            
                    
-
                    T
-          variance1()const;
                    
+                Returns the variance of the errors found.
+              
                    
+
                    T variance1()const;
                    
 
                    
-              Returns the unbiased variance of the errors found.
-            
                    
-
                    T
-          rms()const
                    
+                Returns the unbiased variance of the errors found.
+              
                    
+
                    T rms()const
                    
 
                    
-              Returns the Root Mean Square, or quadratic mean of the errors.
-            
                    
-
                    test_result& operator+=(const test_result&
-          t)
                    
+                Returns the Root Mean Square, or quadratic mean of the errors.
+              
                    
+
                    test_result&
+            operator+=(const test_result& t)
                    
 
                    
-              Combines two test_result's into a single result.
-            
                    
+                Combines two test_result's into a single result.
+              
                    
 
                    
 
                    
 
                    
@@ -165,7 +157,7 @@
           is mainly a debugging/development aid (and a good place for a breakpoint).
         
                    
 
                    
-
+
           Example
         
                    
 
                    
@@ -230,7 +222,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
index 4537db970..f8722ad42 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
@@ -2,8 +2,8 @@
 
 
 Minimax Approximations and the Remez Algorithm
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
  Minimax Approximations
         and the Remez Algorithm
@@ -55,12 +55,13 @@
 
                    
 
                    main.cpp
                    
 
                    
-              Contains the command line parser, and all the calls to the Remez code.
-            
                    
+                Contains the command line parser, and all the calls to the Remez
+                code.
+              
                    
 
                    f.cpp
                    
 
                    
-              Contains the function to approximate.
-            
                    
+                Contains the function to approximate.
+              
                    
 
                    
 
                    
 
                    
@@ -110,158 +111,160 @@
 
                    
 
                    variant N
                    
 
                    
-              Sets the current function variant to N. This allows multiple functions
-              that are to be approximated to be compiled into the same executable.
-              Defaults to 0.
-            
                    
+                Sets the current function variant to N. This allows multiple functions
+                that are to be approximated to be compiled into the same executable.
+                Defaults to 0.
+              
                    
 
                    range a b
                    
 
                    
-              Sets the domain for the approximation to the range [a,b], defaults
-              to [0,1].
-            
                    
+                Sets the domain for the approximation to the range [a,b], defaults
+                to [0,1].
+              
                    
 
                    relative
                    
 
                    
-              Sets the Remez code to optimise for relative error. This is the default
-              at program startup. Note that relative error can only be used if f(x)
-              has no roots over the range being optimised.
-            
                    
+                Sets the Remez code to optimise for relative error. This is the default
+                at program startup. Note that relative error can only be used if
+                f(x) has no roots over the range being optimised.
+              
                    
 
                    absolute
                    
 
                    
-              Sets the Remez code to optimise for absolute error.
-            
                    
+                Sets the Remez code to optimise for absolute error.
+              
                    
 
                    pin [true|false]
                    
 
                    
-              "Pins" the code so that the rational approximation passes
-              through the origin. Obviously only set this to true
-              if R(0) must be zero. This is typically used when trying to preserve
-              a root at [0,0] while also optimising for relative error.
-            
                    
+                "Pins" the code so that the rational approximation passes
+                through the origin. Obviously only set this to true
+                if R(0) must be zero. This is typically used when trying to preserve
+                a root at [0,0] while also optimising for relative error.
+              
                    
 
                    order N D
                    
 
                    
-              Sets the order of the approximation to N in the
-              numerator and D in the denominator. If D
-              is zero then the result will be a polynomial approximation. There will
-              be N+D+2 coefficients in total, the first coefficient of the numerator
-              is zero if pin was set to true, and the first
-              coefficient of the denominator is always one.
-            
                    
+                Sets the order of the approximation to N in
+                the numerator and D in the denominator. If
+                D is zero then the result will be a polynomial
+                approximation. There will be N+D+2 coefficients in total, the first
+                coefficient of the numerator is zero if pin
+                was set to true, and the first coefficient of the denominator is
+                always one.
+              
                    
 
                    working-precision N
                    
 
                    
-              Sets the working precision of NTL::RR to N binary
-              digits. Defaults to 250.
-            
                    
+                Sets the working precision of NTL::RR to N binary
+                digits. Defaults to 250.
+              
                    
 
                    target-precision N
                    
 
                    
-              Sets the precision of printed output to N binary
-              digits: set to the same number of digits as the type that will be used
-              to evaluate the approximation. Defaults to 53 (for double precision).
-            
                    
+                Sets the precision of printed output to N binary
+                digits: set to the same number of digits as the type that will be
+                used to evaluate the approximation. Defaults to 53 (for double precision).
+              
                    
 
                    skew val
                    
 
                    
-              "Skews" the initial interpolated control points towards one
-              end or the other of the range. Positive values skew the initial control
-              points towards the left hand side of the range, and negative values
-              towards the right hand side. If an approximation won't converge (a
-              common situation) try adjusting the skew parameter until the first
-              step yields the smallest possible error. val should
-              be in the range [-100,+100], the default is zero.
-            
                    
+                "Skews" the initial interpolated control points towards
+                one end or the other of the range. Positive values skew the initial
+                control points towards the left hand side of the range, and negative
+                values towards the right hand side. If an approximation won't converge
+                (a common situation) try adjusting the skew parameter until the first
+                step yields the smallest possible error. val
+                should be in the range [-100,+100], the default is zero.
+              
                    
 
                    brake val
                    
 
                    
-              Sets a brake on each step so that the change in the control points
-              is braked by val%. Defaults to 50, try a higher
-              value if an approximation won't converge, or a lower value to get speedier
-              convergence.
-            
                    
+                Sets a brake on each step so that the change in the control points
+                is braked by val%. Defaults to 50, try a higher
+                value if an approximation won't converge, or a lower value to get
+                speedier convergence.
+              
                    
 
                    x-offset val
                    
 
                    
-              Sets the x-offset to val: the approximation will
-              be generated for f(S * (x + X)) + Y
-              where X is the x-offset, S
-              is the x-scale and Y is the y-offset. Defaults
-              to zero. To avoid rounding errors, take care to specify a value that
-              can be exactly represented as a floating point number.
-            
                    
+                Sets the x-offset to val: the approximation
+                will be generated for f(S * (x + X)) + Y
+                where X is the x-offset, S
+                is the x-scale and Y is the y-offset. Defaults
+                to zero. To avoid rounding errors, take care to specify a value that
+                can be exactly represented as a floating point number.
+              
                    
 
                    x-scale val
                    
 
                    
-              Sets the x-scale to val: the approximation will
-              be generated for f(S * (x + X)) + Y
-              where S is the x-scale, X
-              is the x-offset and Y is the y-offset. Defaults
-              to one. To avoid rounding errors, take care to specify a value that
-              can be exactly represented as a floating point number.
-            
                    
+                Sets the x-scale to val: the approximation will
+                be generated for f(S * (x + X)) + Y
+                where S is the x-scale, X
+                is the x-offset and Y is the y-offset. Defaults
+                to one. To avoid rounding errors, take care to specify a value that
+                can be exactly represented as a floating point number.
+              
                    
 
                    y-offset val
                    
 
                    
-              Sets the y-offset to val: the approximation will
-              be generated for f(S * (x + X)) + Y
-              where X is the x-offset, S
-              is the x-scale and Y is the y-offset. Defaults
-              to zero. To avoid rounding errors, take care to specify a value that
-              can be exactly represented as a floating point number.
-            
                    
+                Sets the y-offset to val: the approximation
+                will be generated for f(S * (x + X)) + Y
+                where X is the x-offset, S
+                is the x-scale and Y is the y-offset. Defaults
+                to zero. To avoid rounding errors, take care to specify a value that
+                can be exactly represented as a floating point number.
+              
                    
 
                    y-offset auto
                    
 
                    
-              Sets the y-offset to the average value of f(x) evaluated at the two
-              endpoints of the range plus the midpoint of the range. The calculated
-              value is deliberately truncated to float precision
-              (and should be stored as a float in your code).
-              The approximation will be generated for f(x + X) + Y where X is
-              the x-offset and Y is the y-offset. Defaults to
-              zero.
-            
                    
+                Sets the y-offset to the average value of f(x) evaluated at the two
+                endpoints of the range plus the midpoint of the range. The calculated
+                value is deliberately truncated to float precision
+                (and should be stored as a float in your code).
+                The approximation will be generated for f(x + X) + Y where X
+                is the x-offset and Y is the y-offset. Defaults
+                to zero.
+              
                    
 
                    graph N
                    
 
                    
-              Prints N evaluations of f(x) at evenly spaced points over the range
-              being optimised. If unspecified then N defaults
-              to 3. Use to check that f(x) is indeed smooth over the range of interest.
-            
                    
+                Prints N evaluations of f(x) at evenly spaced points over the range
+                being optimised. If unspecified then N defaults
+                to 3. Use to check that f(x) is indeed smooth over the range of interest.
+              
                    
 
                    step N
                    
 
                    
-              Performs N steps, or one step if N
-              is unspecified. After each step prints: the peek error at the extrema
-              of the error function of the approximation, the theoretical error term
-              solved for on the last step, and the maximum relative change in the
-              location of the Chebyshev control points. The approximation is converged
-              on the minimax solution when the two error terms are (approximately)
-              equal, and the change in the control points has decreased to a suitably
-              small value.
-            
                    
+                Performs N steps, or one step if N
+                is unspecified. After each step prints: the peek error at the extrema
+                of the error function of the approximation, the theoretical error
+                term solved for on the last step, and the maximum relative change
+                in the location of the Chebyshev control points. The approximation
+                is converged on the minimax solution when the two error terms are
+                (approximately) equal, and the change in the control points has decreased
+                to a suitably small value.
+              
                    
 
                    test [float|double|long]
                    
 
                    
-              Tests the current approximation at float, double, or long double precision.
-              Useful to check for rounding errors in evaluating the approximation
-              at fixed precision. Tests are conducted at the extrema of the error
-              function of the approximation, and at the zeros of the error function.
-            
                    
+                Tests the current approximation at float, double, or long double
+                precision. Useful to check for rounding errors in evaluating the
+                approximation at fixed precision. Tests are conducted at the extrema
+                of the error function of the approximation, and at the zeros of the
+                error function.
+              
                    
 
                    test [float|double|long] N
                    
 
                    
-              Tests the current approximation at float, double, or long double precision.
-              Useful to check for rounding errors in evaluating the approximation
-              at fixed precision. Tests are conducted at N evenly spaced points over
-              the range of the approximation. If none of [float|double|long] are
-              specified then tests using NTL::RR, this can be used to obtain the
-              error function of the approximation.
-            
                    
+                Tests the current approximation at float, double, or long double
+                precision. Useful to check for rounding errors in evaluating the
+                approximation at fixed precision. Tests are conducted at N evenly
+                spaced points over the range of the approximation. If none of [float|double|long]
+                are specified then tests using NTL::RR, this can be used to obtain
+                the error function of the approximation.
+              
                    
 
                    rescale a b
                    
 
                    
-              Takes the current Chebeshev control points, and rescales them over
-              a new interval [a,b]. Sometimes this can be used to obtain starting
-              control points for an approximation that can not otherwise be converged.
-            
                    
+                Takes the current Chebeshev control points, and rescales them over
+                a new interval [a,b]. Sometimes this can be used to obtain starting
+                control points for an approximation that can not otherwise be converged.
+              
                    
 
                    rotate
                    
 
                    
-              Moves one term from the numerator to the denominator, but keeps the
-              Chebyshev control points the same. Sometimes this can be used to obtain
-              starting control points for an approximation that can not otherwise
-              be converged.
-            
                    
+                Moves one term from the numerator to the denominator, but keeps the
+                Chebyshev control points the same. Sometimes this can be used to
+                obtain starting control points for an approximation that can not
+                otherwise be converged.
+              
                    
 
                    info
                    
 
                    
-              Prints out the current approximation: the location of the zeros of
-              the error function, the location of the Chebyshev control points, the
-              x and y offsets, and of course the coefficients of the polynomials.
-            
                    
+                Prints out the current approximation: the location of the zeros of
+                the error function, the location of the Chebyshev control points,
+                the x and y offsets, and of course the coefficients of the polynomials.
+              
                    
 
                    
 
                    
 
                    
@@ -277,7 +280,7 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html
index 041038bee..c6cf94033 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html
@@ -2,8 +2,8 @@
 
 
 Polynomials
-
-
+
+
 
 
 
@@ -20,14 +20,14 @@
 
 
                    
 
                    
-PrevUpHomeNext
+PrevUpHomeNext
 
                    
-
                    
+
                    
 
                    
 
                    
-
+
           Synopsis
         
                    
 
                    
@@ -103,7 +103,7 @@
 }}} // namespaces
                  - + Description

                  @@ -132,7 +132,7 @@

                  -PrevUpHomeNext +PrevUpHomeNext
                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html index d480ddd00..3ee48ec52 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html @@ -2,8 +2,8 @@ Graphing, Profiling, and Generating Test Data for Special Functions - - + + @@ -20,9 +20,9 @@
                  -PrevUpHomeNext +PrevUpHomeNext
                  -
                  +

                  Graphing, Profiling, and Generating Test Data for Special Functions @@ -32,21 +32,21 @@ associated helper functions are designed so that in just a few lines of code you should be able to:

                  -
                    -
                  • - Profile a continued fraction, or infinite series for convergence and - accuracy. -
                    • -
                  • - Generate csv data from a special function that can be imported into your - favorite graphing program (or spreadsheet) for further analysis. -
                    • -
                  • - Generate high precision test data. -
                    • +
                      +
                    • + Profile a continued fraction, or infinite series for convergence and + accuracy. +
                      • +
                    • + Generate csv data from a special function that can be imported into + your favorite graphing program (or spreadsheet) for further analysis. +
                      • +
                    • + Generate high precision test data. +
                    - + Synopsis 
                    namespace boost{ namespace math{ namespace tools{
@@ -147,7 +147,7 @@
 }}} // namespaces
                    - + Description

                    @@ -156,28 +156,28 @@

                    The functionality of test_data is split into the following parts:

                    -
                      -
                    • - A functor that implements the function for which data is being generated: - this is the bit you have to write. -
                      • -
                    • - One of more parameters that are to be passed to the functor, these are - described in fairly abstract terms: give me N points distributed like - this etc. -
                      • -
                    • - The class test_data, that takes the functor and descriptions of the parameters - and computes how ever many output points have been requested, these are - stored in a sorted container. -
                      • -
                    • - Routines to iterate over the test_data container and output the data - in either csv format, or as C++ source code (as a table using Boost.Array). -
                      • +
                        +
                      • + A functor that implements the function for which data is being generated: + this is the bit you have to write. +
                        • +
                      • + One of more parameters that are to be passed to the functor, these + are described in fairly abstract terms: give me N points distributed + like this etc. +
                        • +
                      • + The class test_data, that takes the functor and descriptions of the + parameters and computes how ever many output points have been requested, + these are stored in a sorted container. +
                        • +
                      • + Routines to iterate over the test_data container and output the data + in either csv format, or as C++ source code (as a table using Boost.Array). +
                      - + Example 1: Output Data for Graph Plotting
                      @@ -211,7 +211,7 @@

                      - + Example 2: Creating Test Data
                      @@ -307,7 +307,7 @@
                      - +
                      [Caution][Caution] Caution

                      @@ -353,18 +353,18 @@

                      The first #define serves two purposes:

                      -
                        -
                      • - It reduces the file sizes considerably: all those static_cast's - add up to a lot of bytes otherwise (they are needed to suppress compiler - warnings when T is narrower - than a long double). -
                        • -
                      • - It provides a useful customisation point: for example if we were testing - a user-defined type that has more precision than a long - double we could change it to: -
                        • +
                          +
                        • + It reduces the file sizes considerably: all those static_cast's + add up to a lot of bytes otherwise (they are needed to suppress compiler + warnings when T is + narrower than a long double). +
                          • +
                        • + It provides a useful customisation point: for example if we were testing + a user-defined type that has more precision than a long + double we could change it to: +

                        #define SC_(x) lexical_cast<T>(BOOST_STRINGIZE(x)) @@ -375,7 +375,7 @@ used by default as it's rather hard on the compiler when the table is large.

                        - + Example 3: Profiling a Continued Fraction for Convergence and Accuracy
                        @@ -481,7 +481,7 @@ of a and z.

                        - + reference

                        @@ -544,7 +544,7 @@

                      -PrevUpHomeNext +PrevUpHomeNext
                      diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html index 55f3cce94..ad629930e 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html @@ -2,8 +2,8 @@ Overview - - + + @@ -20,9 +20,9 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      -
                      +
                      @@ -53,7 +53,7 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt.html b/doc/sf_and_dist/html/math_toolkit/using_udt.html index 283d6f30e..4b6808274 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt.html @@ -2,8 +2,8 @@ Use with User-Defined Floating-Point Types - - + + @@ -20,9 +20,9 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      -
                      +

                      Use with User-Defined Floating-Point Types @@ -52,7 +52,7 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html index 2c82620d8..e5613040b 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html @@ -2,8 +2,8 @@ Conceptual Archetypes and Testing - - + + @@ -20,9 +20,9 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      -
                      +

                      Conceptual Archetypes and Testing @@ -173,7 +173,7 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html index f4441a6c7..62c3bc245 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html @@ -2,8 +2,8 @@ Conceptual Requirements for Real Number Types - - + + @@ -20,9 +20,9 @@
                      -PrevUpHomeNext +PrevUpHomeNext
                      -
                      +

                      Conceptual Requirements for Real Number Types @@ -42,7 +42,7 @@ behaves just like a built in floating point type.

                      - + Basic Arithmetic Requirements
                      @@ -64,912 +64,912 @@ -

                      - Expression -

                      +

                      + Expression +

                      -

                      - Result Type -

                      +

                      + Result Type +

                      -

                      - Notes -

                      +

                      + Notes +

                      -

                      - RealType(cr) -

                      +

                      + RealType(cr) +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - RealType is copy constructible. -

                      +

                      + RealType is copy constructible. +

                      -

                      - RealType(ca) -

                      +

                      + RealType(ca) +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - RealType is copy constructible from the arithmetic types. -

                      +

                      + RealType is copy constructible from the arithmetic types. +

                      -

                      - r = - cr -

                      +

                      + r = + cr +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Assignment operator. -

                      +

                      + Assignment operator. +

                      -

                      - r = - ca -

                      +

                      + r = + ca +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Assignment operator from the arithmetic types. -

                      +

                      + Assignment operator from the arithmetic types. +

                      -

                      - r += - cr -

                      +

                      + r += + cr +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Adds cr to r. -

                      +

                      + Adds cr to r. +

                      -

                      - r += - ca -

                      +

                      + r += + ca +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Adds ar to r. -

                      +

                      + Adds ar to r. +

                      -

                      - r -= - cr -

                      +

                      + r -= + cr +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Subtracts cr from r. -

                      +

                      + Subtracts cr from r. +

                      -

                      - r -= - ca -

                      +

                      + r -= + ca +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Subtracts ca from r. -

                      +

                      + Subtracts ca from r. +

                      -

                      - r *= - cr -

                      +

                      + r *= + cr +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Multiplies r by cr. -

                      +

                      + Multiplies r by cr. +

                      -

                      - r *= - ca -

                      +

                      + r *= + ca +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Multiplies r by ca. -

                      +

                      + Multiplies r by ca. +

                      -

                      - r /= - cr -

                      +

                      + r /= + cr +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Divides r by cr. -

                      +

                      + Divides r by cr. +

                      -

                      - r /= - ca -

                      +

                      + r /= + ca +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Divides r by ca. -

                      +

                      + Divides r by ca. +

                      -

                      - -r -

                      +

                      + -r +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Unary Negation. -

                      +

                      + Unary Negation. +

                      -

                      - +r -

                      +

                      + +r +

                      -

                      - RealType& -

                      +

                      + RealType& +

                      -

                      - Identity Operation. -

                      +

                      + Identity Operation. +

                      -

                      - cr + - cr2 -

                      +

                      + cr + + cr2 +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Addition -

                      +

                      + Binary Addition +

                      -

                      - cr + - ca -

                      +

                      + cr + + ca +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Addition -

                      +

                      + Binary Addition +

                      -

                      - ca + - cr -

                      +

                      + ca + + cr +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Addition -

                      +

                      + Binary Addition +

                      -

                      - cr - - cr2 -

                      +

                      + cr - + cr2 +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Subtraction -

                      +

                      + Binary Subtraction +

                      -

                      - cr - - ca -

                      +

                      + cr - + ca +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Subtraction -

                      +

                      + Binary Subtraction +

                      -

                      - ca - - cr -

                      +

                      + ca - + cr +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Subtraction -

                      +

                      + Binary Subtraction +

                      -

                      - cr * - cr2 -

                      +

                      + cr * + cr2 +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Multiplication -

                      +

                      + Binary Multiplication +

                      -

                      - cr * - ca -

                      +

                      + cr * + ca +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Multiplication -

                      +

                      + Binary Multiplication +

                      -

                      - ca * - cr -

                      +

                      + ca * + cr +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Multiplication -

                      +

                      + Binary Multiplication +

                      -

                      - cr / - cr2 -

                      +

                      + cr / + cr2 +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Subtraction -

                      +

                      + Binary Subtraction +

                      -

                      - cr / - ca -

                      +

                      + cr / + ca +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Subtraction -

                      +

                      + Binary Subtraction +

                      -

                      - ca / - cr -

                      +

                      + ca / + cr +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - Binary Subtraction -

                      +

                      + Binary Subtraction +

                      -

                      - cr == - cr2 -

                      +

                      + cr == + cr2 +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Equality Comparison -

                      +

                      + Equality Comparison +

                      -

                      - cr == - ca -

                      +

                      + cr == + ca +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Equality Comparison -

                      +

                      + Equality Comparison +

                      -

                      - ca == - cr -

                      +

                      + ca == + cr +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Equality Comparison -

                      +

                      + Equality Comparison +

                      -

                      - cr != - cr2 -

                      +

                      + cr != + cr2 +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Inequality Comparison -

                      +

                      + Inequality Comparison +

                      -

                      - cr != - ca -

                      +

                      + cr != + ca +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Inequality Comparison -

                      +

                      + Inequality Comparison +

                      -

                      - ca != - cr -

                      +

                      + ca != + cr +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Inequality Comparison -

                      +

                      + Inequality Comparison +

                      -

                      - cr <= - cr2 -

                      +

                      + cr <= + cr2 +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Less than equal to. -

                      +

                      + Less than equal to. +

                      -

                      - cr <= - ca -

                      +

                      + cr <= + ca +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Less than equal to. -

                      +

                      + Less than equal to. +

                      -

                      - ca <= - cr -

                      +

                      + ca <= + cr +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Less than equal to. -

                      +

                      + Less than equal to. +

                      -

                      - cr >= - cr2 -

                      +

                      + cr >= + cr2 +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Greater than equal to. -

                      +

                      + Greater than equal to. +

                      -

                      - cr >= - ca -

                      +

                      + cr >= + ca +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Greater than equal to. -

                      +

                      + Greater than equal to. +

                      -

                      - ca >= - cr -

                      +

                      + ca >= + cr +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Greater than equal to. -

                      +

                      + Greater than equal to. +

                      -

                      - cr < - cr2 -

                      +

                      + cr < + cr2 +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Less than comparison. -

                      +

                      + Less than comparison. +

                      -

                      - cr < - ca -

                      +

                      + cr < + ca +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Less than comparison. -

                      +

                      + Less than comparison. +

                      -

                      - ca < - cr -

                      +

                      + ca < + cr +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Less than comparison. -

                      +

                      + Less than comparison. +

                      -

                      - cr > - cr2 -

                      +

                      + cr > + cr2 +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Greater than comparison. -

                      +

                      + Greater than comparison. +

                      -

                      - cr > - ca -

                      +

                      + cr > + ca +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Greater than comparison. -

                      +

                      + Greater than comparison. +

                      -

                      - ca > - cr -

                      +

                      + ca > + cr +

                      -

                      - bool -

                      +

                      + bool +

                      -

                      - Greater than comparison. -

                      +

                      + Greater than comparison. +

                      -

                      - boost::math::tools::digits<RealType>() -

                      +

                      + boost::math::tools::digits<RealType>() +

                      -

                      - int -

                      +

                      + int +

                      -

                      - The number of digits in the significand of RealType. -

                      +

                      + The number of digits in the significand of RealType. +

                      -

                      - boost::math::tools::max_value<RealType>() -

                      +

                      + boost::math::tools::max_value<RealType>() +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - The largest representable number by type RealType. -

                      +

                      + The largest representable number by type RealType. +

                      -

                      - boost::math::tools::min_value<RealType>() -

                      +

                      + boost::math::tools::min_value<RealType>() +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - The smallest representable number by type RealType. -

                      +

                      + The smallest representable number by type RealType. +

                      -

                      - boost::math::tools::log_max_value<RealType>() -

                      +

                      + boost::math::tools::log_max_value<RealType>() +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - The natural logarithm of the largest representable number by type - RealType. -

                      +

                      + The natural logarithm of the largest representable number by type + RealType. +

                      -

                      - boost::math::tools::log_min_value<RealType>() -

                      +

                      + boost::math::tools::log_min_value<RealType>() +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - The natural logarithm of the smallest representable number by type - RealType. -

                      +

                      + The natural logarithm of the smallest representable number by type + RealType. +

                      -

                      - boost::math::tools::epsilon<RealType>() -

                      +

                      + boost::math::tools::epsilon<RealType>() +

                      -

                      - RealType -

                      +

                      + RealType +

                      -

                      - The machine epsilon of RealType. -

                      +

                      + The machine epsilon of RealType. +

                      @@ -977,34 +977,35 @@

                      Note that:

                      -
                        -
                      1. - The functions log_max_value - and log_min_value can be - synthesised from the others, and so no explicit specialisation is required. -
                        2. -
                      2. - The function epsilon can - be synthesised from the others, so no explicit specialisation is required - provided the precision of RealType does not vary at runtime (see the header - boost/math/bindings/rr.hpp - for an example where the precision does vary at runtime). -
                        3. -
                      3. - The functions digits, - max_value and min_value, all get synthesised automatically - from std::numeric_limits. However, if numeric_limits is not specialised for - type RealType, then you will get a compiler error when code tries to use - these functions, unless you explicitly specialise - them. For example if the precision of RealType varies at runtime, then - numeric_limits support - may not be appropriate, see boost/math/bindings/rr.hpp - for examples. -
                        4. +
                          +
                        1. + The functions log_max_value + and log_min_value can + be synthesised from the others, and so no explicit specialisation is + required. +
                          2. +
                        2. + The function epsilon + can be synthesised from the others, so no explicit specialisation is + required provided the precision of RealType does not vary at runtime + (see the header boost/math/bindings/rr.hpp + for an example where the precision does vary at runtime). +
                          3. +
                        3. + The functions digits, + max_value and min_value, all get synthesised automatically + from std::numeric_limits. However, if numeric_limits is not specialised for + type RealType, then you will get a compiler error when code tries to + use these functions, unless you explicitly specialise + them. For example if the precision of RealType varies at runtime, then + numeric_limits support + may not be appropriate, see boost/math/bindings/rr.hpp + for examples. +
                        - +
                        [Warning][Warning] Warning
                        @@ -1034,7 +1035,7 @@
                        - + Standard Library Support Requirements
                        @@ -1059,258 +1060,258 @@ -

                        - Expression -

                        +

                        + Expression +

                        -

                        - Result Type -

                        +

                        + Result Type +

                        -

                        - fabs(cr1) -

                        +

                        + fabs(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - abs(cr1) -

                        +

                        + abs(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - ceil(cr1) -

                        +

                        + ceil(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - floor(cr1) -

                        +

                        + floor(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - exp(cr1) -

                        +

                        + exp(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - pow(cr1, - cr2) -

                        +

                        + pow(cr1, + cr2) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - sqrt(cr1) -

                        +

                        + sqrt(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - log(cr1) -

                        +

                        + log(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - frexp(cr1, - &i) -

                        +

                        + frexp(cr1, + &i) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - ldexp(cr1, - i) -

                        +

                        + ldexp(cr1, + i) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - cos(cr1) -

                        +

                        + cos(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - sin(cr1) -

                        +

                        + sin(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - asin(cr1) -

                        +

                        + asin(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - tan(cr1) -

                        +

                        + tan(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - atan(cr1) -

                        +

                        + atan(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - fmod(cr1) -

                        +

                        + fmod(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - round(cr1) -

                        +

                        + round(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - iround(cr1) -

                        +

                        + iround(cr1) +

                        -

                        - int -

                        +

                        + int +

                        -

                        - trunc(cr1) -

                        +

                        + trunc(cr1) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - itrunc(cr1) -

                        +

                        + itrunc(cr1) +

                        -

                        - int -

                        +

                        + int +

                        @@ -1359,7 +1360,7 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html index 4dc8b2a87..1b6b7137b 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html @@ -2,8 +2,8 @@ Conceptual Requirements for Distribution Types - - + + @@ -20,9 +20,9 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        -
                        +

                        Conceptual Requirements for Distribution Types @@ -50,330 +50,331 @@ -

                        - Expression -

                        +

                        + Expression +

                        -

                        - Result Type -

                        +

                        + Result Type +

                        -

                        - Notes -

                        +

                        + Notes +

                        -

                        - DistributionType::value_type -

                        +

                        + DistributionType::value_type +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - The real-number type RealType upon which the - distribution operates. -

                        +

                        + The real-number type RealType upon which the + distribution operates. +

                        -

                        - DistributionType::policy_type -

                        +

                        + DistributionType::policy_type +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - The Policy to use when - evaluating functions that depend on this distribution. -

                        +

                        + The Policy to use when + evaluating functions that depend on this distribution. +

                        -

                        - d = cd -

                        +

                        + d = cd +

                        -

                        - Distribution& -

                        +

                        + Distribution& +

                        -

                        - Distribution types are assignable. -

                        +

                        + Distribution types are assignable. +

                        -

                        - Distribution(cd) -

                        +

                        + Distribution(cd) +

                        -

                        - Distribution -

                        +

                        + Distribution +

                        -

                        - Distribution types are copy constructible. -

                        +

                        + Distribution types are copy constructible. +

                        -

                        - pdf(cd, cr) -

                        +

                        + pdf(cd, cr) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the PDF of the distribution. -

                        +

                        + Returns the PDF of the distribution. +

                        -

                        - cdf(cd, cr) -

                        +

                        + cdf(cd, cr) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the CDF of the distribution. -

                        +

                        + Returns the CDF of the distribution. +

                        -

                        - cdf(complement(cd, cr)) -

                        +

                        + cdf(complement(cd, cr)) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the complement of the CDF of the distribution, the same as: - 1-cdf(cd, cr) -

                        +

                        + Returns the complement of the CDF of the distribution, the same + as: 1-cdf(cd, + cr) +

                        -

                        - quantile(cd, cr) -

                        +

                        + quantile(cd, cr) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the quantile of the distribution. -

                        +

                        + Returns the quantile of the distribution. +

                        -

                        - quantile(complement(cd, cr)) -

                        +

                        + quantile(complement(cd, cr)) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the quantile of the distribution, starting from the complement - of the probability, the same as: quantile(cd, 1-cr) -

                        +

                        + Returns the quantile of the distribution, starting from the complement + of the probability, the same as: quantile(cd, 1-cr) +

                        -

                        - chf(cd, cr) -

                        +

                        + chf(cd, cr) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the cumulative hazard function of the distribution. -

                        +

                        + Returns the cumulative hazard function of the distribution. +

                        -

                        - hazard(cd, cr) -

                        +

                        + hazard(cd, cr) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the hazard function of the distribution. -

                        +

                        + Returns the hazard function of the distribution. +

                        -

                        - kurtosis(cd) -

                        +

                        + kurtosis(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the kurtosis of the distribution. -

                        +

                        + Returns the kurtosis of the distribution. +

                        -

                        - kurtosis_excess(cd) -

                        +

                        + kurtosis_excess(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the kurtosis excess of the distribution. -

                        +

                        + Returns the kurtosis excess of the distribution. +

                        -

                        - mean(cd) -

                        +

                        + mean(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the mean of the distribution. -

                        +

                        + Returns the mean of the distribution. +

                        -

                        - mode(cd) -

                        +

                        + mode(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the mode of the distribution. -

                        +

                        + Returns the mode of the distribution. +

                        -

                        - skewness(cd) -

                        +

                        + skewness(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the skewness of the distribution. -

                        +

                        + Returns the skewness of the distribution. +

                        -

                        - standard_deviation(cd) -

                        +

                        + standard_deviation(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the standard deviation of the distribution. -

                        +

                        + Returns the standard deviation of the distribution. +

                        -

                        - variance(cd) -

                        +

                        + variance(cd) +

                        -

                        - RealType -

                        +

                        + RealType +

                        -

                        - Returns the variance of the distribution. -

                        +

                        + Returns the variance of the distribution. +

                        @@ -391,7 +392,7 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html index 5e414f056..5c8c4c094 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html @@ -2,8 +2,8 @@ Using With MPFR / GMP - a High-Precision Floating-Point Library - - + + @@ -20,9 +20,9 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        -
                        +

                        Using With MPFR / GMP - a High-Precision Floating-Point Library @@ -84,7 +84,7 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html index 3247e034d..d7925e1cc 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html @@ -2,8 +2,8 @@ Using With NTL - a High-Precision Floating-Point Library - - + + @@ -20,9 +20,9 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        -
                        +

                        Using With NTL - a High-Precision Floating-Point Library @@ -64,7 +64,7 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        diff --git a/doc/sf_and_dist/html/math_toolkit/utils.html b/doc/sf_and_dist/html/math_toolkit/utils.html index 13bfade42..190afb71e 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils.html +++ b/doc/sf_and_dist/html/math_toolkit/utils.html @@ -2,8 +2,8 @@ Floating Point Utilities - - + + @@ -20,9 +20,9 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        -
                        +
                        @@ -69,7 +69,7 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html index c6d71f0ed..963948c70 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html @@ -2,8 +2,8 @@ Floating-Point Classification: Infinities and NaN's - - + + @@ -20,15 +20,15 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        -
                        +
                        - + Synopsis 
                        #define FP_ZERO        /* implementation specific value */
@@ -58,7 +58,7 @@
         to use these functions.
       
                        
 
                        
-
+
         Description
       
                        
 
                        
@@ -117,76 +117,76 @@
 
 
 
-              
                        
-                fpclassify value
-              
                        
+                
                        
+                  fpclassify value
+                
                        
               
 
-              
                        
-                class of t.
-              
                        
+                
                        
+                  class of t.
+                
                        
               
 
 
 
 
-              
                        
-                FP_ZERO
-              
                        
+                
                        
+                  FP_ZERO
+                
                        
               
 
-              
                        
-                If t is zero.
-              
                        
+                
                        
+                  If t is zero.
+                
                        
               
 
 
 
-              
                        
-                FP_NORMAL
-              
                        
+                
                        
+                  FP_NORMAL
+                
                        
               
 
-              
                        
-                If t is a non-zero, non-denormalised finite
-                value.
-              
                        
+                
                        
+                  If t is a non-zero, non-denormalised finite
+                  value.
+                
                        
               
 
 
 
-              
                        
-                FP_INFINITE
-              
                        
+                
                        
+                  FP_INFINITE
+                
                        
               
 
-              
                        
-                If t is plus or minus infinity.
-              
                        
+                
                        
+                  If t is plus or minus infinity.
+                
                        
               
 
 
 
-              
                        
-                FP_NAN
-              
                        
+                
                        
+                  FP_NAN
+                
                        
               
 
-              
                        
-                If t is a NaN.
-              
                        
+                
                        
+                  If t is a NaN.
+                
                        
               
 
 
 
-              
                        
-                FP_SUBNORMAL
-              
                        
+                
                        
+                  FP_SUBNORMAL
+                
                        
               
 
-              
                        
-                If t is a denormalised number.
-              
                        
+                
                        
+                  If t is a denormalised number.
+                
                        
               
 
 
@@ -229,7 +229,7 @@
 
 
                        
 
                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                        
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float.html
index fa26b96a5..3590c5050 100644
--- a/doc/sf_and_dist/html/math_toolkit/utils/next_float.html
+++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float.html
@@ -2,8 +2,8 @@
 
 
 Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                        
 
                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                        
-
                        
+
                        
 
                        
  Floating-Point Representation
       Distance (ULP), and Finding Adjacent Floating-Point Values
@@ -76,7 +76,7 @@
 
 
                        
 
                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                        
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html
index 8938a1528..8de887f39 100644
--- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html
+++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html
@@ -2,8 +2,8 @@
 
 
 Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance
-
-
+
+
 
 
 
@@ -20,9 +20,9 @@
 
 
                        
 
                        
-PrevUpHomeNext
+PrevUpHomeNext
 
                        
-
                        
+
                        
 
                        
  Advancing
         a Floating Point Value by a Specific Representation Distance (ULP) float_advance
@@ -32,7 +32,7 @@
           number of ULP.
         
                        
 
                        
-
+
           Synopsis
         
                        
 
                        
@@ -50,7 +50,7 @@
 }} // namespaces
                        - + Description - float_advance
                        @@ -71,7 +71,7 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html index df95941b6..b921556af 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html @@ -2,8 +2,8 @@ Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance - - + + @@ -20,9 +20,9 @@
                        -PrevUpHomeNext +PrevUpHomeNext
                        -
                        +

                        Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance @@ -34,7 +34,7 @@ different.

                        - + Synopsis

                        @@ -52,7 +52,7 @@ }} // namespaces

                        - + Description - float_distance
                        @@ -65,19 +65,19 @@

                        Note that

                        -
                          -
                        • -float_distance(a, a) - always returns 0. -
                          • -
                        • -float_distance(float_next(a), a) - always returns 1. -
                          • -
                        • -float_distance(float_prior(a), a) - always returns -1. -
                          • +
                            +
                          • + float_distance(a, a) + always returns 0. +
                            • +
                          • + float_distance(float_next(a), a) + always returns 1. +
                            • +
                          • + float_distance(float_prior(a), a) + always returns -1. +

                          The function float_distance @@ -105,7 +105,7 @@

                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html index 98a3f7eb4..8478acede 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html @@ -2,8 +2,8 @@ Finding the Next Greater Representable Value (float_next) - - + + @@ -20,15 +20,15 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +
                          - + Synopsis

                          @@ -46,7 +46,7 @@ }} // namespaces

                          - + Description - float_next
                          @@ -73,7 +73,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html index 3a220ba77..f9a3b2446 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html @@ -2,8 +2,8 @@ Finding the Next Smaller Representable Value (float_prior) - - + + @@ -20,15 +20,15 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +
                          - + Synopsis

                          @@ -46,7 +46,7 @@ }} // namespaces

                          - + Description - float_prior
                          @@ -73,7 +73,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html index 680bf1bbe..59cbf93ba 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html @@ -2,8 +2,8 @@ Finding the Next Representable Value in a Specific Direction (nextafter) - - + + @@ -20,15 +20,15 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +
                          - + Synopsis

                          @@ -46,7 +46,7 @@ }} // namespaces

                          - + Description - nextafter
                          @@ -58,7 +58,7 @@

                          - +
                          [Note][Note] Note

                          @@ -76,7 +76,7 @@ returns an overflow_error.

                          - + Examples - nextafter
                          @@ -107,7 +107,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding.html index ab7150416..f957d1cce 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding.html @@ -2,8 +2,8 @@ Rounding Truncation and Integer Conversion - - + + @@ -20,9 +20,9 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +

                          Rounding Truncation and Integer Conversion @@ -46,7 +46,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html index b11a5f550..a6db616ba 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html @@ -2,8 +2,8 @@ Integer and Fractional Part Splitting (modf) - - + + @@ -20,9 +20,9 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +

                          Integer and Fractional Part Splitting (modf) @@ -81,7 +81,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html index 9fe6e0a88..d9738476b 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html @@ -2,8 +2,8 @@ Rounding Functions - - + + @@ -20,9 +20,9 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +
                          @@ -81,7 +81,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html index 6e55937d3..05bd8eb0e 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html @@ -2,8 +2,8 @@ Truncation Functions - - + + @@ -20,9 +20,9 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +
                          @@ -83,7 +83,7 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          diff --git a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html index 4193e2ff7..b7c19226c 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html @@ -2,8 +2,8 @@ Sign Manipulation Functions - - + + @@ -20,15 +20,15 @@
                          -PrevUpHomeNext +PrevUpHomeNext
                          -
                          +
                          - + Synopsis

                          @@ -52,7 +52,7 @@ }} // namespaces

                          - + Description 
                          template<class T> 
@@ -92,7 +92,7 @@
 
 
                          
 
                          
-PrevUpHomeNext
+PrevUpHomeNext