Merge changes from Boost.Math to release.

New constants code, new Hankel and owens_t special functions, new skew normal distribution.
Updated docs.

[SVN r78472]

build/Jamfile.v2

@@ -16,7 +16,7 @@ project
       #<toolset>gcc:<cxxflags>-fvisibility=hidden
       <toolset>intel-linux:<cxxflags>-fvisibility=hidden
       <toolset>sun:<cxxflags>-xldscope=hidden
-      [ check-target-builds ../config//has_gcc_visibility : <toolset>gcc:<cxxflags>-fvisibility=hidden : ]
+      [ check-target-builds ../config//has_gcc_visibility "gcc visibility" : <toolset>gcc:<cxxflags>-fvisibility=hidden : ]
     ;
 
 cpp-pch pch : ../src/tr1/pch.hpp : <include>../src/tr1 <link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1 ; 
@@ -96,7 +96,7 @@ lib boost_math_tr1l : ../src/tr1/$(TR1_SOURCES)l.cpp pch
          <link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
          <dependency>../config//has_long_double_support
          <include>../src/tr1
-         [ check-target-builds ../config//has_long_double_support : : <build>no ]
+         [ check-target-builds ../config//has_long_double_support "long double support" : : <build>no ]
    ;
 
 lib boost_math_c99 : ../src/tr1/$(C99_SOURCES).cpp pch
@@ -116,7 +116,7 @@ lib boost_math_c99l : ../src/tr1/$(C99_SOURCES)l.cpp pch
          <link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
          <dependency>../config//has_long_double_support
          <include>../src/tr1
-         [ check-target-builds ../config//has_long_double_support : : <build>no ]
+         [ check-target-builds ../config//has_long_double_support "long double support" : : <build>no ]
    ;
 
 boost-install boost_math_c99 boost_math_c99f boost_math_c99l boost_math_tr1 boost_math_tr1f boost_math_tr1l ;

doc/sf_and_dist/constants.qbk

@@ -1,75 +1,710 @@
-[section:constants Numeric Constants]
+[section:constants Mathematical Constants]
 
-[h4 Synopsis]
+[section:intro Introduction]
 
-``
-#include <boost/math/constants/constants.hpp>
-``
+Boost.Math provides a collection of mathematical constants.
 
-   namespace boost{ namespace math{ namespace constants{
-   
-   template <class T> T pi();
-   template <class T> T root_pi();
-   template <class T> T root_half_pi();
-   template <class T> T root_two_pi();
-   template <class T> T root_ln_four();
-   template <class T> T e();
-   template <class T> T half();
-   template <class T> T euler();
-   template <class T> T root_two();
-   template <class T> T ln_two();
-   template <class T> T ln_ln_two();
-   template <class T> T third();
-   template <class T> T twothirds();
-   template <class T> T pi_minus_three();
-   template <class T> T four_minus_pi();
-   
-   }}} // namespaces
+[h4 Why use Boost.Math mathematical constants?]
 
-[h4 Description]
+* Readable. For the very many jobs just using built-in like `double`, you can just write expressions like
+``double area = pi * r * r;``
+(If that's all you want, jump direct to [link math_toolkit.constants.tutorial.non_templ use in non-template code]!)
+* Effortless - avoiding a search of reference sources.
+* Usable with both builtin floating point types, and user-defined, possibly extended precision, types such as
+NTL, MPFR/GMP, mp_float: in the latter case the constants are computed to the necessary precision and then cached.
+* Accurate - ensuring that the values are as accurate as possible for the 
+chosen floating-point type 
+  * No loss of accuracy from repeated rounding of intermediate computations.
+  * Result is computed with higher precision and only rounded once.
+  * Less risk of inaccurate result from functions pow, trig and log at [@http://en.wikipedia.org/wiki/Corner_case corner cases].
+  * Less risk of [@http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html cancellation error]. 
+* Faster - can avoid (re-)calculation at runtime. This can be significant if:
+  * Functions pow, trig or log are used.
+  * Inside an inner loop.
+  * Using a high-precision UDT.
+  * Compiler optimizations possible with built-in types, especially `double`, are not available.
+* Portable - as possible between different systems using different floating-point precisions:
+see [link math_toolkit.constants.tutorial.templ use in template code].
+* Tested - by comparison with other published sources, or separately computed at long double precision.
 
-The header `boost/math/constants/constants.hpp` contains some numeric constants
-that we have found useful in the development of this library.  New constants are 
-added on an ad-hoc basis based on need.
+[endsect] [/section:intro Introduction]
 
-Usage is like this:
-	
-   template <class T>
-   T circumference(T r)
+[section:tutorial Tutorial]
+
+[section:non_templ Use in non-template code]
+
+When using the math constants at your chosen fixed precision in non-template code,
+you can simply add a `using` declaration, for example, `using boost::math::double_constants`,
+to make the constants of the correct precision for your code
+visible in the current scope, and then use each constant ['as a simple variable]:
+
+   #include <boost/math/constants.hpp>
+
+   double area(double r)
    {
-      return 2 * boost::math::constants::pi<T>() * r;
+      using boost::math::double_constants;
+      return pi * r * r;
    }
 
-All the constants are accurate to at least the 34 decimal digits required for 128-bit
-long doubles, and most are accurate to 100 digits or more when used with 
-a suitable arbitrary precision type.
+Had our function been written as taking a `float` rather than a `double`,
+we could have written instead:
 
-The following table summarises the constants we have at present:
+   #include <boost/math/constants.hpp>
+
+   float area(float r)
+   {
+      using boost::math::float_constants;
+      return pi * r * r;
+   }
+
+Likewise, constants that are suitable for use at `long double` precision
+are available in the namespace `boost::math::long_double_constants`.
+
+You can see the full list of available constants at [link math_toolkit.constants.constants].
+
+[endsect]
+ 
+[section:templ Use in template code]
+
+When using the constants inside a function template, we need to ensure that
+we use a constant of the correct precision for our template parameters.
+We can do this by calling the function-template versions, `pi<FPType>()`, of the constants
+like this:
+
+   #include <boost/math/constants.hpp>
+
+   template <class Real>
+   Real area(Real r)
+   {
+      using namespace boost::math::constants;
+      return pi<Real>() * r * r;
+   }
+
+Although this syntax is a little less "cute" than the non-template version,
+the code is no less efficient
+(at least for the built-in types `float`, `double` and `long double`) :
+the function template versions of the constants are simple inline functions that
+return a constant of the correct precision for the type used. In addition, these
+functions are declared `constexp` for those compilers that support this, allowing
+the result to be used in constant-expressions provided the template argument is a literal type.
+
+[tip Keep in mind the difference between the variable version,
+just `pi`, and the template-function version:
+the template-function requires both a <[~floating-point-type]>
+and function call `()` brackets, for example: `pi<double>()`.
+You cannot write `double p = pi<>()`, nor `double p = pi()`.]
+
+[note You can always use [*both] variable and template-function versions
+[*provided calls are fully qualified], for example:
+``
+double my_pi1 = boost::math::constants::pi<double>();
+double my_pi2 = boost::math::double_constants::pi;
+``
+]
+
+[warning It may be tempting to simply define
+``
+using namespace boost::math::double_constants;
+using namespace boost::math::constants;
+``
+but if you do define two namespaces, this will, of course, create ambiguity!
+``
+double my_pi = pi(); // error C2872: 'pi' : ambiguous symbol
+double my_pi2 = pi; // Context does not allow for disambiguation of overloaded function
+``
+Although the  mistake above is fairly obvious,
+it is also not too difficult to do this accidentally, or worse, create it in someone elses code.
+
+Therefore is it prudent to avoid this risk by [*localising the scope of such definitions], as shown above.]
+
+[tip Be very careful with the type provided as parameter.
+For example, providing an [*integer] instead of a floating-point type can be disastrous (a C++ feature).
+
+``cout << "Area = " << area(2) << endl; // Area = 12!!!``
+
+You should get a compiler warning
+[pre
+warning : 'return' : conversion from 'double' to 'int', possible loss of data
+] [/pre]
+Failure to heed this warning can lead to very wrong answers!
+
+You can also avoid this by being explicit about the type of `Area`.
+``cout << "Area = " << area<double>(2) << endl; // Area = 12.566371``
+]
+
+[endsect] [/section:templ Use in template code]
+
+[section:user_def Use With User Defined Types]
+
+The syntax for using the function-call constants with user-defined types is the same
+as it is in the template class, which is to say we use:
+
+   #include <boost/math/constants.hpp>
+
+   boost::math::constants::pi<UserDefinedType>();
+
+However, since the precision of the user-defined type may be much greater than that
+of the built-in floating pointer types, how the value returned is created is as follows:
+
+* If the precision of the type is known at compile time:
+   * If the precision is less than or equal to that of a `float` and the type is constructable from a `float`
+     then our code returns a `float` literal.  If the user-defined type is a literal type
+     then the function call that returns the constant will be a `constexp`.
+   * If the precision is less than or equal to that of a `double` and the type is constructable from a `double`
+     then our code returns a `double` literal.  If the user-defined type is a literal type
+     then the function call that returns the constant will be a `constexp`.
+   * If the precision is less than or equal to that of a `long double` and the type is constructable from a `long double`
+     then our code returns a `long double` literal.  If the user-defined type is a literal type
+     then the function call that returns the constant will be a `constexp`.
+   * If the precision is less than 100 decimal digits, then the constant will be constructed 
+      (just the once, then cached in a thread-safe manner) from a string representation of the constant.
+   * Otherwise the value is computed (just once, then cached in a thread-safe manner).
+* If the precision is unknown at compile time then:
+   * If the runtime precision (obtained from a call to `boost::math::tools::digits<T>()`) is
+     less than 100 decimal digits, then the constant is constructed "on the fly" from the string
+     representation of the constant.
+   * Otherwise the value is constructed "on the fly" by calculating then value of the constant
+     using the current default precision of the type.  Note that this can make use of the constants
+     rather expensive.
+
+In addition, it is possible to pass a `Policy` type as a second template argument, and use this to control
+the precision:
+
+   #include <boost/math/constants/constants.hpp>
+
+   typedef boost::math::policies::policy<boost::math::policies::digits2<80> > my_policy_type;
+   boost::math::constants::pi<MyType, my_policy_type>();
+
+[note Boost.Math doesn't know how to control the internal precision of `MyType`, the policy
+just controls how the selection process above is carried out, and the calculation precision
+if the result is computed.]
+
+It is also possible to control which method is used to construct the constant by specialising
+the traits class `construction_traits`:
+
+   namespace boost{ namespace math{ namespace constant{
+
+   template <class T, class Policy>
+   struct construction_traits
+   {
+      typedef mpl::int_<N> type;
+   };
+
+   }}} // namespaces
+
+Where ['N] takes one of the following values:
 
 [table
-[[Constant][Meaning][Value]]
-[[pi][[pi]][3.1415926535897932384...]]
-[[root_pi][[radic][pi]][1.772453850905516027...]]
-[[root_half_pi][[radic]([pi]/2)][1.253314137315500251...]]
-[[root_two_pi][[radic](2*[pi])][2.506628274631000502...]]
-[[root_ln_four][[radic](ln(4))][1.17741002251547469...]]
-[[e][['e]][2.71828182845904523536...]]
-[[half][0.5][0.5]]
-[[euler][Euler's constant][0.577215664901532860606]]
-[[root_two][[radic]2][1.4142135623730950488...]]
-[[ln_two][ln(2)][0.6931471805599453094...]]
-[[ln_ln_two][ln(ln(2))][-0.3665129205816643...]]
-[[third][1/3][0.333333333333333333...]]
-[[twothirds][2/3][0.666666666666666666...]]
-[[pi_minus_three][[pi]-3][0.14159265358979323846...]]
-[[four_minus_pi][4-[pi]][0.85840734641020676153735...]]
+[[['N]][Meaning]]
+[[0][The precision is unavailable at compile time;
+either construct from a decimal digit string or calculate on the fly depending upon the runtime precision.]]
+[[1][Return a float precision constant.]]
+[[2][Return a double precision constant.]]
+[[3][Return a long double precision constant.]]
+[[4][Construct the result from the string representation, and cache the result.]]
+[[Any other value ['N]][Sets the compile time precision to ['N] bits.]]
 ]
 
-[endsect][/section Numeric Constants]
+[h5 Custom Specializing a constant]
 
-[/ 
-  Copyright 2008 John Maddock and Paul A. Bristow.
-  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).
+In addition, for user-defined types that need special handling, it's possible to \[partially-\] specialize
+the internal structure used by each constant.  For example, suppose we're using the C++ wrapper around MPFR
+`mpfr_class`: this has its own representation of Pi which we may well wish to use in place of the above
+mechanism.  We can achieve this by specialising the class template `boost::math::constants::detail::constant_pi`:
+
+   namespace boost{ namespace math{ namespace constants{ namespace detail{
+
+   template<>
+   struct constant_pi<mpfr_class>
+   {
+      template<int N>
+      inline T get(const mpl::int_<N>&)
+      {
+         // The template param N is one of the values in the table above,
+         // we can either handle all cases in one as is the case here,
+         // or overload "get" for the different options.
+         mpfr_class result;
+         mpfr_const_pi(result.get_mpfr_t(), GMP_RNDN);
+         return result;
+      }
+   };
+
+   }}}} // namespaces
+
+[h5 Diagnosing what meta-programmed code is doing]
+
+Finally, since it can be tricky to diagnose what meta-programmed code is doing, there is a
+diagnostic routine that prints information about how this library will handle a specific type,
+it can be used like this:
+
+   #include <boost/math/constants/info.hpp>
+
+   int main()
+   {
+      boost::math::constants::print_info_on_type<MyType>();
+   }
+
+If you wish, you can also pass an optional std::ostream argument to the `print_info_on_type` function.
+Typical output for a user-defined type looks like this:
+
+[pre
+Information on the Implementation and Handling of
+Mathematical Constants for Type class boost::math::concepts::real_concept
+
+Checking for std::numeric_limits<class boost::math::concepts::real_concept> specialisation: no
+boost::math::policies::precision<class boost::math::concepts::real_concept, Policy>
+reports that there is no compile type precision available.
+boost::math::tools::digits<class boost::math::concepts::real_concept>()
+reports that the current runtime precision is
+53 binary digits.
+No compile time precision is available, the construction method
+will be decided at runtime and results will not be cached
+- this may lead to poor runtime performance.
+Current runtime precision indicates that
+the constant will be constructed from a string on each call.
 ]
+
+[endsect] [/section:user_def Use With User Defined Types]
+
+[endsect] [/section:tutorial Tutorial]
+
+[section:constants The Mathematical Constants]
+
+This section lists the mathematical constants, their use(s) (and sometimes rationale for their inclusion).
+[table Mathematical Constants
+[[name] [formula] [Value (6 decimals)] [Uses and Rationale]]
+[[[*Rational fractions]] [] [] [] ]
+[[half] [1/2] [0.5] [] ]
+[[third] [1/3] [0.333333] [] ]
+[[two_thirds] [2/3] [0.66667] [] ]
+[[three_quarters] [3/4] [0.75] [] ]
+
+[[[*two and related]] [] [] [] ]
+[[root_two] [[radic]2] [1.41421] [] ]
+[[root_three] [[radic]3] [1.73205] [] ]
+[[half_root_two] [[radic]2 /2] [0.707106] [] ]
+[[ln_two] [ln(2)] [0.693147] [] ]
+[[ln_ten] [ln(10)] [2.30258] [] ]
+[[ln_ln_two] [ln(ln(2))] [-0.366512] [Gumbel distribution median] ]
+[[root_ln_four] [[radic]ln(4)] [1.177410] [] ]
+[[one_div_root_two] [1/[radic]2] [0.707106] [] ]
+
+[[[*[pi] and related]] [] [] [] ]
+[[pi] [pi] [3.14159] [Ubiquitous. Archimedes constant [@http://en.wikipedia.org/wiki/Pi [pi]]]]
+[[half_pi] [[pi]/2] [1.570796] [] ]
+[[third_pi] [[pi]/3] [1.04719] [] ]
+[[sixth_pi] [[pi]/6] [0.523598] [] ]
+[[two_pi] [2[pi]] [6.28318] [Many uses, most simply, circumference of a circle]]
+[[two_thirds_pi] [2/3 [pi]] [2.09439] [[@http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere volume of a hemi-sphere] = 4/3 [pi] r[cubed]]]
+[[three_quarters_pi] [3/4 [pi]] [2.35619] [[@http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere volume of a hemi-sphere] = 4/3 [pi] r[cubed]]]
+[[four_thirds_pi] [4/3 [pi]] [4.18879] [[@http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere volume of a sphere] = 4/3 [pi] r[cubed]]]
+[[one_div_two_pi] [1/(2[pi])] [1.59155] [Widely used]]
+[[root_pi] [[radic][pi]][1.77245] [Widely used]]
+[[root_half_pi] [[radic] [pi]/2] [1.25331] [Widely used]]
+[[root_two_pi][[radic] [pi]*2] [2.50662] [Widely used]]
+[[one_div_root_pi] [1/[radic][pi]] [0.564189] [] ]
+[[one_div_root_two_pi] [1/[radic](2[pi])] [0.398942] [] ]
+[[root_one_div_pi] [[radic](1/[pi]] [0.564189] [] ]
+[[pi_minus_three] [[pi]-3] [1.41593] [] ]
+[[four_minus_pi] [4 -[pi]] [0.858407] [] ]
+[[pow23_four_minus_pi] [4[super 2/3] - [pi]] [0.795316] [] ]
+[[pi_pow_e] [[pi][super e]] [22.4591] [] ]
+
+[[pi_sqr] [[pi][super 2]] [9.86960] [] ]
+[[pi_sqr_div_six] [[pi][super 2]/6] [1.64493] [] ]
+[[pi_cubed] [[pi][super 3]] [31.00627] [] ]
+[[cbrt_pi] [[radic][super 3] [pi]] [1.46459] [] ]
+[[one_div_cbrt_pi] [1/[radic][super 3] [pi]] [0.682784] [] ]
+
+[[[*Euler's e and related]] [] [] [] ]
+[[e] [e] [2.71828] [[@http://en.wikipedia.org/wiki/E_(mathematical_constant) Euler's constant e]] ]
+[[exp_minus_half] [e [super -1/2]] [0.606530] [] ]
+[[e_pow_pi] [e [super [pi]]] [23.14069] [] ] 
+[[root_e] [[radic] e] [1.64872] [] ]
+[[log10_e] [log10(e)] [0.434294] [] ]
+[[one_div_log10_e] [1/log10(e)] [2.30258] [] ]
+
+[[[*Trigonometric]] [] [] [] ]
+[[degree] [radians = [pi] / 180] [0.017453] [] ]
+[[radian] [degrees = 180 / [pi]] [57.2957] [] ]
+[[sin_one] [sin(1)] [0.841470] [] ]
+[[cos_one] [cos(1)] [0.54030] [] ]
+[[sinh_one] [sinh(1)] [1.17520] [] ]
+[[cosh_one] [cosh(1)] [1.54308] [] ]
+
+[[[*Phi]] [ Phidias golden ratio] [[@http://en.wikipedia.org/wiki/Golden_ratio Phidias golden ratio]] [] ]
+[[phi] [(1 + [radic]5) /2] [1.61803] [finance] ]
+[[ln_phi] [ln([phi])] [0.48121] [] ]
+[[one_div_ln_phi] [1/ln([phi])] [2.07808] [] ]
+
+[[[*Euler's Gamma]] [] [] [] ]
+[[euler] [euler] [0.577215] [[@http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant Euler-Mascheroni gamma constant]] ]
+[[one_div_euler] [1/euler] [1.73245] [] ]
+[[euler_sqr] [euler[super 2]] [0.333177] [] ]
+
+[[[*Misc]] [] [] [] ]
+[[zeta_two] [[zeta](2)] [1.64493] [[@http://en.wikipedia.org/wiki/Riemann_zeta_function Riemann zeta function]] ]
+[[zeta_three] [[zeta](3)] [1.20205] [[@http://en.wikipedia.org/wiki/Riemann_zeta_function Riemann zeta function]] ]
+[[catalan] [['K]] [0.915965] [[@http://mathworld.wolfram.com/CatalansConstant.html Catalan (or Glaisher) combinatorial constant] ]]
+[[glaisher] [['A]] [1.28242] [[@https://oeis.org/A074962/constant Decimal expansion of Glaisher-Kinkelin constant] ]]
+[[khinchin] [['k]] [2.685452] [[@https://oeis.org/A002210/constant Decimal expansion of Khinchin constant] ]]
+
+[[extreme_value_skewness] [12[radic]6 [zeta](3)/ [pi][super 3]] [1.139547] [Extreme value distribution] ]
+[[rayleigh_skewness] [2[radic][pi]([pi]-3)/(4 - [pi])[super 3/2]] [0.631110] [Rayleigh distribution skewness] ]
+[[rayleigh_kurtosis_excess] [-(6[pi][super 2]-24[pi]+16)/(4-[pi])[super 2]] [0.245089] [[@http://en.wikipedia.org/wiki/Rayleigh_distribution Rayleigh distribution kurtosis excess]] ]
+[[rayleigh_kurtosis] [3+(6[pi][super 2]-24[pi]+16)/(4-[pi])[super 2]] [3.245089] [Rayleigh distribution kurtosis] ]
+
+] [/table]
+
+
+[note Integer values are *not included* in this list of math constants, however interesting,
+because they can be so easily and exactly constructed, even for UDT, for example: `static_cast<cpp_float>(42)`.]
+
+[tip If you know the approximate value of the constant, you can search for the value to find Boost.Math chosen name in this table.]
+
+[endsect]  [/section:constants The constants]
+
+[section:new_const Defining New Constants]
+
+The library provides some helper code to assist in defining new constants;
+the process for defining a constant called `my_constant` goes like this:
+
+1. [*Define a function that calculates the value of the constant].
+This should be a template function, and be placed in `boost/math/constants/calculate_constants.hpp`
+if the constant is to be added to this library,
+or else defined at the top of your source file if not.
+
+The function should look like this:
+
+  namespace boost{ namespace math{ namespace constants{ namespace detail{
+
+  template <class Real>
+  template <int N>
+  Real constant_my_constant<Real>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
+  {
+    int required_precision = N ? N : tools::digits<Real>();
+    Real result = /* value computed to required_precision bits */ ;
+    return result;
+  }
+
+  }}}} // namespaces
+  
+Then define a placeholder for the constant itself:
+
+   namespace boost{ namespace math{ namespace constants{
+
+   BOOST_DEFINE_MATH_CONSTANT(my_constant, 0.0, "0");
+
+   }}}
+
+
+For example, to calculate [pi]/2, add to `boost/math/constants/calculate_constants.hpp`
+
+  template <class T>
+  template<int N> 
+  inline T constant_half_pi<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
+  {
+     BOOST_MATH_STD_USING
+     return pi<T, policies::policy<policies::digits2<N> > >() / static_cast<T>(2);
+  }
+
+Then to `boost/math/constants/constants.hpp` add:
+
+   BOOST_DEFINE_MATH_CONSTANT(half_pi, 0.0, "0");  // Actual values are temporary, we'll replace them later.
+
+[note Previously defined constants like pi and e can be used, but by *not simply calling* `pi<T>()`;
+specifying the precision via the policy 
+`pi<T, policies::policy<policies::digits2<N> > >()`
+is essential to ensure full accuracy.]
+
+[warning Newly defined constants can only be used once they are included in
+`boost/math/constants/constants.hpp`. So if you add 
+`template <class T, class N> T constant_my_constant{...}`,
+then you cannot define `constant_my_constant`
+until you add the temporary `BOOST_DEFINE_MATH_CONSTANT(my_constant, 0.0, "0")`.
+Failing to do this will result in surprising compile errors:
+``
+  error C2143: syntax error : missing ';' before '<'
+  error C2433: 'constant_root_two_div_pi' : 'inline' not permitted on data declarations
+  error C2888: 'T constant_root_two_div_pi' : symbol cannot be defined within namespace 'detail'
+  error C2988: unrecognizable template declaration/definition
+``
+]
+
+2. [*You will need an arbitrary precision type to use to calculate the value]. This library
+currently supports either `cpp_float`, `NTL::RR` or `mpfr_class` used via the bindings in `boost/math/bindings`.
+The default is to use `NTL::RR` unless you define an alternate macro, for example,
+`USE_MPFR` or `USE_CPP_FLOAT` at the start of your program.
+
+3. It is necessary to link to the Boost.Regex library,
+and probably to your chosen arbitrary precision type library.
+
+4. The complete program to generate the constant `half_pi` using function `calculate_half_pi` is then:
+
+   #define USE_CPP_FLOAT // If required.
+   #include <boost/math/constants/generate.hpp>
+
+   int main()
+   {
+      BOOST_CONSTANTS_GENERATE(half_pi);
+   }
+
+The output from the program is a snippet of C++ code
+(actually a macro call) that can be cut and pasted
+into `boost/math/constants/constants.hpp` or else into your own code, for example:
+
+[pre
+  BOOST_DEFINE_MATH_CONSTANT(half_pi, 1.570796326794896619231321691639751442e+00, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404326e+00");
+]
+
+This macro BOOST_DEFINE_MATH_CONSTANT  inserts a C++ struct code snippet that
+declares the `float`, `double` and `long double` versions of the constant,
+plus a decimal digit string representation correct to 100 decimal
+digits, and all the meta-programming machinery needed to select between them.
+
+The result of an expanded macro for Pi is shown below.
+
+[import ./pp_pi.hpp]
+
+[preprocessed_pi]
+
+
+[endsect] [/section:new_const Defining New Constants]
+
+[section:FAQ FAQs]
+
+[h4 Why are ['these] Constants Chosen?]
+It is, of course, impossible to please everyone with a list like this.
+
+Some of the criteria we have used are:
+
+* Used in Boost.Math.
+* Commonly used.
+* Expensive to compute.
+* Requested by users.
+* [@http://en.wikipedia.org/wiki/Mathematical_constant Used in science and mathematics.]
+* No integer values (because so cheap to construct).[br] 
+(You can easily define your own if found convenient, for example: `FPT one =static_cast<FPT>(42);`).
+
+[h4 How are constants named?]
+* Not macros, so no upper case.
+* All lower case (following C++ standard names).
+* No CamelCase.
+* Underscore as _ delimiter between words.
+* Numbers spelt as words rather than decimal digits (except following pow).
+* Abbreviation conventions: 
+  * root for square root.
+  * cbrt for cube root.
+  * pow for pow function using decimal digits like pow23 for n[super 2/3].
+  * div for divided by or operator /.
+  * minus for operator -, plus for operator +.
+  * sqr for squared.
+  * cubed for cubed n[super 3].
+  * words for greek, like [pi], [zeta] and [Gamma].
+  * words like half, third, three_quarters, sixth for fractions.  (Digit(s) can get muddled).
+  * log10 for log[sub 10]
+  * ln for log[sub e]
+
+[h4 How are the constants derived?]
+
+The constants have all been calculated using high-precision software working
+with up to 300-bit precision giving about 100 decimal digits.
+(The precision can be arbitrarily chosen and is limited only by compute time).
+
+[h4 How Accurate are the constants?]
+The minimum accuracy chosen (100 decimal digits) exceeds the
+accuracy of reasonably-foreseeable floating-point hardware (256-bit)
+and should meet most high-precision computations.
+
+[h4 How are the constants tested?]
+
+# Comparison using Boost.Test BOOST_CHECK_CLOSE_FRACTION using long double literals,
+with at least 35 decimal digits, enough to be accurate for all long double implementations.
+The tolerance is usually twice `long double epsilon`.
+
+# Comparison with calculation at long double precision. 
+This often requires a slightly higher tolerance than two epsilon
+because of computational noise from round-off etc,
+especially when trig and other functions are called.
+
+# Comparison with independent published values,
+for example, using [@http://oeis.org/ The On-Line Encyclopedia of Integer Sequences (OEIS)]
+again using at least 35 decimal digits strings.
+
+# Comparison with independely calculated values using arbitrary precision tools like
+[@http://www.wolfram.com/mathematica/ Mathematica], again using at least 35 decimal digits literal strings.
+
+[warning We have not yet been able to [*check] that
+[*all] constants are accurate at the full arbitrary precision,
+at present 100 decimal digits.
+But certain key values like `e` and `pi` appear to be accurate
+and internal consistencies suggest that others are this accurate too.
+]
+
+[h4 Why is Portability important?]
+
+Code written using math constants is easily portable even when using different
+floating-point types with differing precision.
+
+It is a mistake to expect that results of computations will be [*identical], but
+you can achieve the [*best accuracy possible for the floating-point type in use].
+
+This has no extra cost to the user, but reduces irritating,
+and often confusing and very hard-to-trace effects,
+caused by the intrinsically limited precision of floating-point calculations.
+
+A harmless symptom of this limit is a spurious least-significant digit;
+at worst, slightly inaccurate constants sometimes cause iterating algorithms
+to diverge wildly because internal comparisons just fail.
+
+[h4 What is the Internal Format of the constants, and why?]
+
+See [link math_toolkit.constants.tutorial tutorial] above for normal use,
+but this FAQ explains the internal details used for the constants. 
+
+Constants are stored as 100 decimal digit values.
+However, some compilers do not accept decimal digits strings as long as this.
+So the constant is split into two parts, with the first containing at least 
+128-bit long double precision (35 decimal digits),
+and for consistency should be in scientific format with a signed exponent.
+
+The second part is the value of the constant expressed as a string literal,
+accurate to at least 100 decimal digits (in practice that means at least 102 digits).
+Again for consistency use scientific format with a signed exponent.
+
+For types with precision greater than a long double,
+then if T is constructible `T `is constructible from a `const char*`
+then it's directly constructed from the string,
+otherwise we fall back on lexical_cast to convert to type `T`.
+(Using a string is necessary because you can't use a numeric constant
+since even a `long double` might not have enough digits).
+
+So, for example, a constant like pi is internally defined as
+
+  BOOST_DEFINE_MATH_CONSTANT(pi, 3.141592653589793238462643383279502884e+00, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00");
+
+In this case the significand is 109 decimal digits, ensuring 100 decimal digits are exact, and exponent is zero.
+
+See [link math_toolkit.constants.new_const defining new constants] to calculate new constants.
+
+A macro definition like this can be pasted into user code where convenient,
+or into `boost/math/constants.hpp` if it is to be added to the Boost.Math library.
+
+[h4 What Floating-point Types could I use?]
+
+Apart from the built-in floating-point types `float`, `double`, `long double`,
+there are several arbitrary precision floating-point classes available,
+but most are not licensed for commercial use.
+
+[h5  Boost.Multiprecision by Christopher Kormanyos]
+
+This work is based on an earlier work called e-float:
+Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations,
+in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. 
+[@http://doi.acm.org/10.1145/1916461.1916469]
+[@https://svn.boost.org/svn/boost/sandbox/e_float/ e_float]
+but is now re-factored and available under the Boost license in the Boost-sandbox at
+[@https://svn.boost.org/svn/boost/sandbox/multiprecision/ multiprecision]
+where it is being refined and prepared for review.
+
+[h5 Boost.cpp_float by John Maddock using Expression Templates]
+
+[@https://svn.boost.org/svn/boost/sandbox/big_number/ Big Number]
+which is a reworking of [@https://svn.boost.org/svn/boost/sandbox/e_float/ e_float]
+by Christopher Kormanyos to use expression templates for faster execution.
+
+[h5 NTL class quad_float]
+
+[@http://shoup.net/ntl/ NTL] by Victor Shoup has fixed and arbitrary high precision fixed and floating-point types.
+However none of these are licenced for commercial use.
+
+  #include <NTL/quad_float.h> // quad precision 106-bit, about 32 decimal digits.
+  using NTL::to_quad_float; // Less precise than arbitrary precision NTL::RR.
+
+NTL class `quad_float`, which gives a form of quadruple precision,
+106-bit significand (but without an extended exponent range.)
+With an IEC559/IEEE 754 compatible processor,
+for example Intel X86 family, with 64-bit double, and 53-bit significand,
+using the significands of [*two] 64-bit doubles,
+if `std::numeric_limits<double>::digits10` is 16,
+then we get about twice the precision,
+so `std::numeric_limits<quad_float>::digits10()` should be 32.
+(the default `std::numeric_limits<RR>::digits10()` should be about 40).
+(which seems to agree with experiments).
+We output constants (including some noisy bits,
+an approximation to `std::numeric_limits<RR>::max_digits10()`)
+by adding 2 extra decimal digits, so using `quad_float::SetOutputPrecision(32 + 2);`
+
+Apple Mac/Darwin uses a similar ['doubledouble] 106-bit for its built-in `long double` type.
+
+[note The precision of all `doubledouble` floating-point types is rather odd and values given are only approximate.]
+
+[h5 NTL class RR]
+
+Arbitrary precision floating point with NTL class RR,
+default is 150 bit (about 50 decimal digits)
+used here with 300 bit to output 100 decimal digits,
+enough for many practical non-'number-theoretic' C++ applications.
+
+NTL is [*not licenced for commercial use].
+
+This class is used in Boost.Math and an option when using big_number projects to calculate new math constants.
+
+[h5 GMP and MPFR]
+
+[@gmplib.org GMP] and [@http://www.mpfr.org/ MPFR] have also been used to compute constants,
+but are licensed under the [@http://www.gnu.org/copyleft/lesser.html Lesser GPL license]
+and are [*not licensed for commercial use].
+
+[h4 What happened to a previous collection of constants proposed for Boost?]
+
+A review concluded that the way in which the constants were presented did not meet many peoples needs.
+None of the methods proposed met many users' essential requirement to allow writing simply `pi` rather than `pi()`.
+Many science and engineering equations look difficult to read when because function call brackets can be confused
+with the many other brackets often needed.  All the methods then proposed of avoiding the brackets failed to meet all needs,
+often on grounds of complexity and lack of applicability to various realistic scenarios.
+
+So the simple namespace method, proposed on its own, but rejected at the first review,
+has been added to allow users to have convenient access to float, double and long double values,
+but combined with template struct and functions to allow simultaneous use
+with other non-built-in floating-point types.
+
+[h4 Why do the constants (internally) have a struct rather than a simple function?]
+
+A function mechanism was provided by in previous versions of Boost.Math.
+
+The new mechanism is to permit partial specialization. See Custom Specializing a constant above.
+It should also allow use with other packages like [@http://www.ttmath.org/ ttmath Bignum C++ library.]
+
+[h4 Where can I find other high precision constants?]
+
+# Constants with very high precision and good accuracy (>40 decimal digits)
+from Simon Plouffe's web based collection [@http://pi.lacim.uqam.ca/eng/].
+# [@https://oeis.org/ The On-Line Encyclopedia of Integer Sequences (OEIS)]
+# Checks using  printed text optically scanned values and converted from:
+D. E. Knuth, Art of Computer Programming, Appendix A, Table 1, Vol 1, ISBN 0 201 89683 4 (1997)
+# M. Abrahamovitz & I. E. Stegun, National Bureau of Standards, Handbook of Mathematical Functions,
+a reference source for formulae now superceded by
+# Frank W. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark, NIST Handbook of Mathemetical Functions, Cambridge University Press, ISBN 978-0-521-14063-8, 2010. 
+# John F Hart, Computer Approximations, Kreiger (1978) ISBN 0 88275 642 7.
+# Some values from Cephes Mathematical Library, Stephen L. Moshier
+and CALC100 100 decimal digit Complex Variable Calculator Program, a DOS utility.
+# Xavier Gourdon, Pascal Sebah, 50 decimal digits constants at [@http://numbers.computation.free.fr/Constants/constants.html Number, constants and computation].
+
+[h4 Where are Physical Constants?]
+
+Not here in this Boost.Math collection, because physical constants:
+
+* Are measurements.
+* Are not truly constant and keeping changing as mensuration technology improves.
+* Have a instrinsic uncertainty.
+* Mathematical constants are stored and represented at varying precision, but should never be inaccurate.
+
+Some physical constants may be available in Boost.Units.
+
+[endsect] [/section:FAQ FAQ]
+
+[endsect]
+
+
+

doc/sf_and_dist/credits.qbk

@@ -64,6 +64,8 @@ Thanks to Mark Coleman and Georgi Boshnakov for spot test values
 from __Mathematica, and of course,
 to Eric Weissten for nurturing __Mathworld, an invaluable resource. 
 
+The Skew-normal distribution and Owen's t function were written by Benjamin Sobotta.
+
 Plots of the functions and distributions were prepared in
 [@http://www.w3.org/ W3C] standard
 [@http://www.svg.org/ Scalable Vector Graphic (SVG)] format

doc/sf_and_dist/dist_reference.qbk

@@ -30,6 +30,7 @@
 [include distributions/pareto.qbk]
 [include distributions/poisson.qbk]
 [include distributions/rayleigh.qbk]
+[include distributions/skew_normal.qbk]
 [include distributions/students_t.qbk]
 [include distributions/triangular.qbk]
 [include distributions/uniform.qbk]

doc/sf_and_dist/distributions/normal.qbk

@@ -35,13 +35,22 @@ is known as the ['Standard Normal Distribution].
 
 Given mean [mu][space]and standard deviation [sigma][space]it has the PDF:
 
-[equation normal_ref1]
+[space] [equation normal_ref1]
 
 The variation the PDF with its parameters is illustrated
 in the following graph:
 
 [graph normal_pdf]
 
+The cumulative distribution function is given by
+
+[space] [equation normal_cdf]
+
+and illustrated by this graph
+
+[graph normal_cdf]
+
+
 [h4 Member Functions]
 
    normal_distribution(RealType mean = 0, RealType sd = 1);
@@ -94,6 +103,7 @@ and /s/ is its standard deviation.
 [[quantile from the complement][Using the relation: x = m + s * sqrt(2) * __erfc_inv(2*p)]]
 [[mean and standard deviation][The same as `dist.mean()` and `dist.standard_deviation()`]]
 [[mode][The same as the mean.]]
+[[median][The same as the mean.]]
 [[skewness][0]]
 [[kurtosis][3]]
 [[kurtosis excess][0]]
@@ -102,7 +112,7 @@ and /s/ is its standard deviation.
 [endsect][/section:normal_dist Normal]
 
 [/ normal.qbk
-  Copyright 2006, 2007 John Maddock and Paul A. Bristow.
+  Copyright 2006, 2007, 2012 John Maddock and Paul A. Bristow.
   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).

doc/sf_and_dist/distributions/skew_normal.qbk

@@ -0,0 +1,193 @@
+[section:skew_normal_dist Skew Normal Distribution]
+
+``#include <boost/math/distributions/skew_normal.hpp>``
+
+   namespace boost{ namespace math{ 
+      
+   template <class RealType = double, 
+             class ``__Policy``   = ``__policy_class`` >
+   class skew_normal_distribution;
+   
+   typedef skew_normal_distribution<> normal;
+   
+   template <class RealType, class ``__Policy``>
+   class skew_normal_distribution
+   {
+   public:
+      typedef RealType value_type;
+      typedef Policy   policy_type;
+      // Constructor:
+      skew_normal_distribution(RealType location = 0, RealType scale = 1, RealType shape = 0);
+      // Accessors:
+      RealType location()const; // mean if normal.
+      RealType scale()const; // width, standard deviation if normal.
+      RealType shape()const; // The distribution is right skewed if shape > 0 and is left skewed if shape < 0.
+                             // The distribution is normal if shape is zero.
+   };
+   
+   }} // namespaces
+   
+The skew normal distribution is a variant of the most well known
+Gaussian statistical distribution.  
+
+The skew normal distribution with shape zero resembles the
+[@http://en.wikipedia.org/wiki/Normal_distribution Normal Distribution],
+hence the latter can be regarded as a special case of the more generic skew normal distribution.
+
+If the standard (mean = 0, scale = 1) normal distribution probability density function is 
+
+[space][space][equation normal01_pdf]
+
+and the cumulative distribution function
+
+[space][space][equation normal01_cdf]
+
+then the [@http://en.wikipedia.org/wiki/Probability_density_function PDF]
+of the [@http://en.wikipedia.org/wiki/Skew_normal_distribution skew normal distribution]
+with shape parameter [alpha], defined by O'Hagan and Leonhard (1976) is
+
+[space][space][equation skew_normal_pdf0]
+
+Given [@http://en.wikipedia.org/wiki/Location_parameter location] [xi],
+[@http://en.wikipedia.org/wiki/Scale_parameter scale] [omega],
+and [@http://en.wikipedia.org/wiki/Shape_parameter shape] [alpha],
+it can be 
+[@http://en.wikipedia.org/wiki/Skew_normal_distribution transformed],
+to the form:
+
+[space][space][equation skew_normal_pdf]
+
+and [@http://en.wikipedia.org/wiki/Cumulative_distribution_function CDF]:
+
+[space][space][equation skew_normal_cdf]
+
+where ['T(h,a)] is Owen's T function, and ['[Phi](x)] is the normal distribution.
+
+The variation the PDF and CDF with its parameters is illustrated
+in the following graphs:
+
+[graph skew_normal_pdf]
+[graph skew_normal_cdf]
+
+[h4 Member Functions]
+
+   skew_normal_distribution(RealType location = 0, RealType scale = 1, RealType shape = 0);
+   
+Constructs a skew_normal distribution with location [xi],
+scale [omega] and shape [alpha].
+
+Requires scale > 0, otherwise __domain_error is called.
+
+   RealType location()const;   
+   
+returns the location [xi] of this distribution,
+   
+   RealType scale()const;
+
+returns the scale [omega] of this distribution,
+   
+   RealType shape()const;
+
+returns the shape [alpha] of this distribution.
+     
+(Location and scale function match other similar distributions,
+allowing the functions `find_location` and `find_scale` to be used generically).
+
+[note While the shape parameter may be chosen arbitrarily (finite),
+the resulting [*skewness] of the distribution is in fact limited to about (-1, 1);
+strictly, the interval is (-0.9952717, 0.9952717).
+
+A parameter [delta] is related to the shape [alpha] by
+[delta] = [alpha] / (1 + [alpha][pow2]),
+and used in the expression for skewness
+[equation skew_normal_skewness]
+] [/note]
+
+[h4 References]
+
+* [@http://azzalini.stat.unipd.it/SN/ Skew-Normal Probability Distribution] for many links and bibliography.
+* [@http://azzalini.stat.unipd.it/SN/Intro/intro.html A very brief introduction to the skew-normal distribution]
+by Adelchi Azzalini (2005-11-2).
+* See a [@http://www.tri.org.au/azzalini.html skew-normal function animation].
+
+[h4 Non-member Accessors]
+
+All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
+that are generic to all distributions are supported: __usual_accessors.
+
+The domain of the random variable is ['-[max_value], +[min_value]].
+Infinite values are not supported.
+
+There are no [@http://en.wikipedia.org/wiki/Closed-form_expression closed-form expression]
+known for the mode and median, but these are computed for the
+
+* mode - by finding the maximum of the PDF.
+* median - by computing `quantile(1/2)`.
+
+The maximum of the PDF is sought through searching the root of f'(x)=0.
+
+Both involve iterative methods that will have lower accuracy than other estimates.
+
+[h4 Testing]
+
+__R using library(sn) described at
+[@http://azzalini.stat.unipd.it/SN/  Skew-Normal Probability Distribution],
+and at [@http://cran.r-project.org/web/packages/sn/sn.pd R skew-normal(sn) package].
+
+Package sn provides functions related to the skew-normal (SN)
+and the skew-t (ST) probability distributions,
+both for the univariate and for the the multivariate case,
+including regression models. 
+
+__Mathematica was also used to generate some more accurate spot test data.
+
+[h4 Accuracy]
+
+The skew_normal distribution with shape = zero is implemented as a special case,
+equivalent to the normal distribution in terms of the
+[link math_toolkit.special.sf_erf.error_function error function], 
+and therefore should have excellent accuracy.
+
+The PDF and mean, variance, skewness and kurtosis are also accurately evaluated using
+[@http://en.wikipedia.org/wiki/Analytical_expression analytical expressions].
+The CDF requires [@http://en.wikipedia.org/wiki/Owen%27s_T_function Owen's T function]
+that is evaluated using a Boost C++ __owens_t implementation of the algorithms of
+M. Patefield and D. Tandy, Journal of Statistical Software, 5(5), 1-25 (2000);
+the complicated accuracy of this function is discussed in detail at __owens_t.
+
+The median and mode are calculated by iterative root finding, and both will be less accurate.
+
+[h4 Implementation]
+
+In the following table, [xi] is the location of the distribution,
+and [omega] is its scale, and [alpha] is its shape.
+
+[table
+[[Function][Implementation Notes]]
+[[pdf][Using:[equation skew_normal_pdf] ]]
+[[cdf][Using: [equation skew_normal_cdf]\n
+where ['T(h,a)] is Owen's T function, and ['[Phi](x)] is the normal distribution. ]]
+[[cdf complement][Using: complement of normal distribution + 2 * Owens_t]]
+[[quantile][Maximum of the pdf is sought through searching the root of f'(x)=0]]
+[[quantile from the complement][-quantile(SN(-location [xi], scale [omega], -shape[alpha]), p)]]
+[[location][location [xi]]]
+[[scale][scale [omega]]]
+[[shape][shape [alpha]]]
+[[median][quantile(1/2)]]
+[[mean][[equation skew_normal_mean]]]
+[[mode][Maximum of the pdf is sought through searching the root of f'(x)=0]]
+[[variance][[equation skew_normal_variance] ]]
+[[skewness][[equation skew_normal_skewness] ]]
+[[kurtosis][kurtosis excess-3]]
+[[kurtosis excess] [ [equation skew_normal_kurt_ex] ]]
+] [/table]
+
+[endsect] [/section:skew_normal_dist skew_Normal]
+
+[/ skew_normal.qbk
+  Copyright 2012 Bejamin Sobotta, John Maddock and Paul A. Bristow.
+  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).
+]
+

doc/sf_and_dist/equations/hankel1.mml

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+        <mrow>
+          <mo>-</mo>
+          <mi>&#x03BD;</mi>
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+      <mo>&#x2062;</mo>
+      <mrow>
+        <msub>
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+    </mrow>
+  </mrow>
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+

doc/sf_and_dist/equations/hankel2.mml

@@ -0,0 +1,152 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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+    <mrow>
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+        <msub>
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+          <mi>&#x03BD;</mi>
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doc/sf_and_dist/equations/skew_normal_pdf0.svg

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doc/sf_and_dist/fp_facets.qbk

@@ -338,7 +338,7 @@ and also string representations used by other programming languages.
 [h5 signed_zero]
 
 If the `signed_zero` flag is used with `nonfinite_num_put`,
-then the facet will distinguish between positive and negative zero.
+then the facet will always distinguish between positive and negative zero.
 It will format positive zero as "0" or "+0" and negative zero as "-0".
 The string representation of positive zero can be controlled
 with the `showpos` and `noshowpos` manipulators.
@@ -348,6 +348,16 @@ The input facet `nonfinite_num_get` always parses "0" and "+0"
 as positive zero and "-0" as negative zero,
 as do most implementations of `std::num_get`.
 
+[note If the `signed_zero` flag is not set (the default), then a negative zero value
+will be displayed on output in whatever way the platform normally handles it.
+For most platforms, this it will format positive zero as "0" or "+0" and negative zero as "-0".
+But setting the `signed_zero` flag may be more portable.]
+
+[tip A negative zero value can be portably produced using the changesign function
+`(changesign)(static_cast<ValType>(0))` where `ValType` is `float`, `double` or `long double`,
+ or a User-Defined floating-point type (UDT) provided that this UDT has a sign
+and that the changesign function is implemented.]
+
 [h5 trap_infinity]
 
 If the `trap_infinity` flag is used with `nonfinite_num_put`,
@@ -361,6 +371,7 @@ If the `trap_infinity` flag is used with `nonfinite_num_get`,
 then the facet will set the `fail bit` of the stream when an attempt is made
 to parse a string that represents positive or negative infinity.
 
+
 (See Design Rationale below for a discussion of this inconsistency.)
 
 [h5 trap_nan]
@@ -502,6 +513,9 @@ Example [@../../../example/nonfinite_loopback_ok.cpp] shows loopback works OK.
 Example [@../../../example/nonfinite_num_facet.cpp] shows output and re-input
 of various finite and nonfinite values.
 
+A simple example of trapping nonfinite output is at
+[@../../../example/nonfinite_num_facet_trap.cpp nonfinite_num_facet_trap.cpp].
+
 A very basic example of using Boost.Archive is at
 [@../../../example/nonfinite_serialization_archives.cpp].
 

doc/sf_and_dist/graphs/dist_graphs.cpp

@@ -10,7 +10,7 @@
     \author John Maddock and Paul A. Bristow
   */
 //  Copyright John Maddock 2008.
-//  Copyright Paul A. Bristow 2008, 2009
+//  Copyright Paul A. Bristow 2008, 2009, 2012
 //  Use, modification and distribution are subject to 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)
@@ -499,6 +499,26 @@ int main()
    rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(10), "&#x3C3;=10");
    rayleigh_cdf_plotter.plot("Rayleigh Distribution CDF", "rayleigh_cdf.svg");
 
+   distribution_plotter<boost::math::skew_normal_distribution<> >
+      skew_normal_plotter;
+   skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,0), "{0,1,0}");
+   skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,1), "{0,1,1}");
+   skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,4), "{0,1,4}");
+   skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,20), "{0,1,20}");
+   skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,-2), "{0,1,-2}");
+   skew_normal_plotter.add(boost::math::skew_normal_distribution<>(-2,0.5,-1), "{-2,0.5,-1}");
+   skew_normal_plotter.plot("Skew Normal Distribution PDF", "skew_normal_pdf.svg");
+
+   distribution_plotter<boost::math::skew_normal_distribution<> >
+      skew_normal_cdf_plotter(false);
+   skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,0), "{0,1,0}");
+   skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,1), "{0,1,1}");
+   skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,4), "{0,1,4}");
+   skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,20), "{0,1,20}");
+   skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,-2), "{0,1,-2}");
+   skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(-2,0.5,-1), "{-2,0.5,-1}");
+   skew_normal_cdf_plotter.plot("Skew Normal Distribution CDF", "skew_normal_cdf.svg");
+
    distribution_plotter<boost::math::triangular_distribution<> >
       triangular_plotter;
    triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
@@ -622,4 +642,4 @@ int main()
    hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(450, 50, 500), "N=500, r=50, n=450");
    hypergeometric_plotter2.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_2.svg");
 
-}
+} // int main()

doc/sf_and_dist/graphs/owens_integration_area.svg

@@ -0,0 +1,121 @@
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+
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+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:xlink="http://www.w3.org/1999/xlink"
+   version="1.1"
+   width="744.09448"
+   height="1052.3622"
+   id="svg2">
+  <defs
+     id="defs4" />
+  <metadata
+     id="metadata7">
+    <rdf:RDF>
+      <cc:Work
+         rdf:about="">
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <dc:title></dc:title>
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+  </metadata>
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+</svg>

doc/sf_and_dist/graphs/skew_normal_cdf.svg

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+xmlns ="http://www.w3.org/2000/svg"
+>
+<!-- SVG plot written using Boost.Plot program (Creator Jacob Voytko) --> 
+<!-- Use, modification and distribution of Boost.Plot subject to the --> 
+<!-- Boost Software License, Version 1.0.--> 
+<!-- (See accompanying file LICENSE_1_0.txt --> 
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+
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doc/sf_and_dist/hankel.qbk

@@ -0,0 +1,136 @@
+
+[section:hankel Hankel Functions]
+[section:cyl_hankel Cyclic Hankel Functions]
+
+[h4 Synopsis]
+
+   template <class T1, class T2>
+   std::complex<``__sf_result``> cyl_hankel_1(T1 v, T2 x);
+
+   template <class T1, class T2, class ``__Policy``>
+   std::complex<``__sf_result``> cyl_hankel_1(T1 v, T2 x, const ``__Policy``&);
+
+   template <class T1, class T2>
+   std::complex<``__sf_result``> cyl_hankel_2(T1 v, T2 x);
+   
+   template <class T1, class T2, class ``__Policy``>
+   std::complex<``__sf_result``> cyl_hankel_2(T1 v, T2 x, const ``__Policy``&);
+   
+   
+[h4 Description]
+
+The functions __cyl_hankel_1 and __cyl_hankel_2 return the result of the
+[@http://dlmf.nist.gov/10.2#P3 Hankel functions] of the first and second kind respectively:
+
+[:['cyl_hankel_1(v, x) = H[sub v][super (1)](x) = J[sub v](x) + i Y[sub v](x)]]
+
+[:['cyl_hankel_2(v, x) = H[sub v][super (2)](x) = J[sub v](x) - i Y[sub v](x)]]
+
+where:
+
+['J[sub v](x)] is the Bessel function of the first kind, and ['Y[sub v](x)] is the Bessel function of the second kind.
+
+The return type of these functions is computed using the __arg_pomotion_rules
+when T1 and T2 are different types.  The functions are also optimised for the
+relatively common case that T1 is an integer.
+
+[optional_policy]
+
+Note that while the arguments to these functions are real values, the results are complex.
+That means that the functions can only be instantiated on types `float`, `double` and `long double`.
+The functions have also been extended to operate over the whole range of ['v] and ['x] 
+(unlike __cyl_bessel_j and __cyl_neumann).
+
+[h4 Performance]
+
+These functions are generally more efficient than two separate calls to the underlying Bessel
+functions as internally Bessel J and Y can be computed simultaneously.
+
+[h4 Testing]
+
+There are just a few spot tests to exercise all the special case handling - the bulk of the testing is done
+on the Bessel functions upon which these are based.
+
+[h4 Accuracy]
+
+Refer to __cyl_bessel_j and __cyl_neumann.
+
+[h4 Implementation]
+
+For ['x < 0] the following reflection formulae are used:
+
+[@http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/16/01/01/ [equation hankel1]]
+
+[@http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/ [equation hankel2]]
+
+[@http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/ [equation hankel3]]
+
+Otherwise the implementation is trivially in terms of the Bessel J and Y functions.
+
+Note however, that the Hankel functions compute the Bessel J and Y functions simultaneously,
+and therefore a single Hankel function call is more efficient than two Bessel function calls.
+The one exception is when ['v] is a small positive integer, in which case the usual Bessel function
+routines for integer order are used.
+
+[endsect]
+
+
+[section:sph_hankel Spherical Hankel Functions]
+
+[h4 Synopsis]
+
+   template <class T1, class T2>
+   std::complex<``__sf_result``> sph_hankel_1(T1 v, T2 x);
+
+   template <class T1, class T2, class ``__Policy``>
+   std::complex<``__sf_result``> sph_hankel_1(T1 v, T2 x, const ``__Policy``&);
+
+   template <class T1, class T2>
+   std::complex<``__sf_result``> sph_hankel_2(T1 v, T2 x);
+   
+   template <class T1, class T2, class ``__Policy``>
+   std::complex<``__sf_result``> sph_hankel_2(T1 v, T2 x, const ``__Policy``&);
+   
+   
+[h4 Description]
+
+The functions __sph_hankel_1 and __sph_hankel_2 return the result of the
+[@http://dlmf.nist.gov/10.47#P1 spherical Hankel functions] of the first and second kind respectively:
+
+[equation hankel4]
+
+[equation hankel5]
+
+The return type of these functions is computed using the __arg_pomotion_rules
+when T1 and T2 are different types.  The functions are also optimised for the
+relatively common case that T1 is an integer.
+
+[optional_policy]
+
+Note that while the arguments to these functions are real values, the results are complex.
+That means that the functions can only be instantiated on types `float`, `double` and `long double`.
+The functions have also been extended to operate over the whole range of ['v] and ['x] 
+(unlike __cyl_bessel_j and __cyl_neumann).
+
+[h4 Testing]
+
+There are just a few spot tests to exercise all the special case handling - the bulk of the testing is done
+on the Bessel functions upon which these are based.
+
+[h4 Accuracy]
+
+Refer to __cyl_bessel_j and __cyl_neumann.
+
+[h4 Implementation]
+
+These functions are trivially implemented in terms of __cyl_hankel_1 and __cyl_hankel_2.
+
+[endsect]
+[endsect]
+
+[/ 
+  Copyright 2012 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).
+]

doc/sf_and_dist/html/index.html

@@ -48,9 +48,12 @@
 <div class="author"><h3 class="author">
 <span class="firstname">Thijs</span> <span class="surname">van den Berg</span>
 </h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">Benjamin</span> <span class="surname">Sobotta</span>
+</h3></div>
 </div></div>
 <div><p class="copyright">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg</p></div>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta</p></div>
 <div><div class="legalnotice">
 <a name="math_toolkit.legal"></a><p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
@@ -67,6 +70,8 @@
 <dd><dl>
 <dt><span class="section"><a href="math_toolkit/main_overview/intro.html">About the Math Toolkit</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/main_overview/navigation.html">Navigation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/conventions.html">Document Conventions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/hints.html">Other Hints and tips</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/main_overview/directories.html">Directory and
       File Structure</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/main_overview/namespaces.html">Namespaces</a></span></dt>
@@ -201,6 +206,8 @@
           Distribution</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/rayleigh.html">Rayleigh
           Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/skew_normal_dist.html">Skew
+          Normal Distribution</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/students_t_dist.html">Students
           t Distribution</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/triangular_dist.html">Triangular
@@ -280,6 +287,13 @@
 <dt><span class="section"><a href="math_toolkit/special/bessel/sph_bessel.html">Spherical Bessel
         Functions of the First and Second Kinds</a></span></dt>
 </dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/hankel.html">Hankel Functions</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/hankel/cyl_hankel.html">Cyclic Hankel
+        Functions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/hankel/sph_hankel.html">Spherical Hankel
+        Functions</a></span></dt>
+</dl></dd>
 <dt><span class="section"><a href="math_toolkit/special/ellint.html">Elliptic Integrals</a></span></dt>
 <dd><dl>
 <dt><span class="section"><a href="math_toolkit/special/ellint/ellint_intro.html">Elliptic
@@ -330,6 +344,7 @@
 <dt><span class="section"><a href="math_toolkit/special/inv_hyper/asinh.html">asinh</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/special/inv_hyper/atanh.html">atanh</a></span></dt>
 </dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/owens_t.html">Owen's T function</a></span></dt>
 </dl></dd>
 <dt><span class="section"><a href="math_toolkit/utils.html">Floating Point Utilities</a></span></dt>
 <dd><dl>
@@ -377,14 +392,27 @@
 <dt><span class="section"><a href="math_toolkit/extern_c/tr1_ref.html">TR1 C Functions Quick
       Reference</a></span></dt>
 </dl></dd>
-<dt><span class="section"><a href="math_toolkit/toolkit.html">Tools, Constants and Internal Details</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants.html">Mathematical Constants</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/constants/intro.html">Introduction</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants/tutorial.html">Tutorial</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/constants/tutorial/non_templ.html">Use in non-template
+        code</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants/tutorial/templ.html">Use in template
+        code</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants/tutorial/user_def.html">Use With
+        User Defined Types</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/constants/constants.html">The Mathematical Constants</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants/new_const.html">Defining New Constants</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/constants/FAQ.html">FAQs</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/toolkit.html">Tools and Internal Details</a></span></dt>
 <dd><dl>
 <dt><span class="section"><a href="math_toolkit/toolkit/internals_overview.html">Overview</a></span></dt>
-<dt><span class="section"><a href="math_toolkit/toolkit/internals1.html">Utilities - Constants
-      &amp; Tools</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1.html">Utilities &amp; Tools</a></span></dt>
 <dd><dl>
-<dt><span class="section"><a href="math_toolkit/toolkit/internals1/constants.html">Numeric
-        Constants</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/toolkit/internals1/series_evaluation.html">Series
         Evaluation</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/toolkit/internals1/cf.html">Continued Fraction
@@ -499,11 +527,11 @@
 <dt><span class="section"><a href="math_toolkit/status/issues.html">Known Issues, and TODO List</a></span></dt>
 <dt><span class="section"><a href="math_toolkit/status/credits.html">Credits and Acknowledgements</a></span></dt>
 </dl></dd>
-<dt><span class="section"><a href="index/s12.html">Function Index</a></span></dt>
-<dt><span class="section"><a href="index/s13.html">Class Index</a></span></dt>
-<dt><span class="section"><a href="index/s14.html">Typedef Index</a></span></dt>
-<dt><span class="section"><a href="index/s15.html">Macro Index</a></span></dt>
-<dt><span class="section"><a href="index/s16.html">Index</a></span></dt>
+<dt><span class="section"><a href="index/s13.html">Function Index</a></span></dt>
+<dt><span class="section"><a href="index/s14.html">Class Index</a></span></dt>
+<dt><span class="section"><a href="index/s15.html">Typedef Index</a></span></dt>
+<dt><span class="section"><a href="index/s16.html">Macro Index</a></span></dt>
+<dt><span class="section"><a href="index/s17.html">Index</a></span></dt>
 </dl>
 </div>
 <p>
@@ -513,7 +541,7 @@
   </p>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: January 09, 2012 at 12:12:07 GMT</small></p></td>
+<td align="left"><p><small>Last revised: April 29, 2012 at 16:45:52 GMT</small></p></td>
 <td align="right"><div class="copyright-footer"></div></td>
 </tr></table>
 <hr>

doc/sf_and_dist/html/index/s14.html

@@ -1,13 +1,13 @@
 <html>
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
-<title>Typedef Index</title>
+<title>Class Index</title>
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 <meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
 <link rel="home" href="../index.html" title="Math Toolkit">
 <link rel="up" href="../index.html" title="Math Toolkit">
-<link rel="prev" href="s13.html" title="Class Index">
-<link rel="next" href="s15.html" title="Macro Index">
+<link rel="prev" href="s13.html" title="Function Index">
+<link rel="next" href="s15.html" title="Typedef Index">
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@@ -22,373 +22,216 @@
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 <a accesskey="p" href="s13.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s15.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
 </div>
-<div class="section id1492041">
+<div class="section id1324922">
 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1492041"></a>Typedef Index</h2></div></div></div>
-<p><a class="link" href="s14.html#idx_id_46">A</a> <a class="link" href="s14.html#idx_id_47">B</a> <a class="link" href="s14.html#idx_id_48">C</a> <a class="link" href="s14.html#idx_id_49">D</a> <a class="link" href="s14.html#idx_id_50">E</a> <a class="link" href="s14.html#idx_id_51">F</a> <a class="link" href="s14.html#idx_id_52">G</a> <a class="link" href="s14.html#idx_id_53">H</a> <a class="link" href="s14.html#idx_id_54">I</a> <a class="link" href="s14.html#idx_id_56">L</a> <a class="link" href="s14.html#idx_id_58">N</a> <a class="link" href="s14.html#idx_id_59">O</a> <a class="link" href="s14.html#idx_id_60">P</a> <a class="link" href="s14.html#idx_id_62">R</a> <a class="link" href="s14.html#idx_id_63">S</a> <a class="link" href="s14.html#idx_id_64">T</a> <a class="link" href="s14.html#idx_id_65">U</a> <a class="link" href="s14.html#idx_id_66">V</a> <a class="link" href="s14.html#idx_id_67">W</a></p>
+<a name="id1324922"></a>Class Index</h2></div></div></div>
+<p><a class="link" href="s14.html#idx_id_24">B</a> <a class="link" href="s14.html#idx_id_25">C</a> <a class="link" href="s14.html#idx_id_26">D</a> <a class="link" href="s14.html#idx_id_27">E</a> <a class="link" href="s14.html#idx_id_28">F</a> <a class="link" href="s14.html#idx_id_29">G</a> <a class="link" href="s14.html#idx_id_30">H</a> <a class="link" href="s14.html#idx_id_31">I</a> <a class="link" href="s14.html#idx_id_33">L</a> <a class="link" href="s14.html#idx_id_34">M</a> <a class="link" href="s14.html#idx_id_35">N</a> <a class="link" href="s14.html#idx_id_37">P</a> <a class="link" href="s14.html#idx_id_39">R</a> <a class="link" href="s14.html#idx_id_40">S</a> <a class="link" href="s14.html#idx_id_41">T</a> <a class="link" href="s14.html#idx_id_42">U</a> <a class="link" href="s14.html#idx_id_44">W</a></p>
 <div class="variablelist"><dl>
 <dt>
-<a name="idx_id_46"></a><span class="term">A</span>
+<a name="idx_id_24"></a><span class="term">B</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-0">bernoulli_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-0">beta_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-0">binomial_distribution</span></a></p></li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_25"></a><span class="term">C</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">cauchy_distribution</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-0">chi_squared_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">construction_traits</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/constants/tutorial/user_def.html" title="Use With User Defined Types"><span class="index-entry-level-1">Use With User Defined Types</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_26"></a><span class="term">D</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">assert_undefined_type</span></p>
+<p><span class="index-entry-level-0">default_policy</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
 </li></ul></div></dd>
 <dt>
-<a name="idx_id_47"></a><span class="term">B</span>
+<a name="idx_id_27"></a><span class="term">E</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">bernoulli</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">eps_tolerance</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748"><span class="index-entry-level-1">Root Finding Without Derivatives: Bisection, Bracket and TOMS748</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">beta</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">equal_ceil</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748"><span class="index-entry-level-1">Root Finding Without Derivatives: Bisection, Bracket and TOMS748</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">binomial</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">equal_floor</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748"><span class="index-entry-level-1">Root Finding Without Derivatives: Bisection, Bracket and TOMS748</span></a></p></li></ul></div>
 </li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">equal_nearest_integer</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748"><span class="index-entry-level-1">Root Finding Without Derivatives: Bisection, Bracket and TOMS748</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-0">exponential_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-0">extreme_value_distribution</span></a></p></li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_48"></a><span class="term">C</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">cauchy</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example"><span class="index-entry-level-1">Find Location (Mean) Example</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example"><span class="index-entry-level-1">Find mean and standard deviation example</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope"><span class="index-entry-level-1">Setting Polices at Namespace Scope</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope"><span class="index-entry-level-1">Setting Policies at Namespace or Translation Unit Scope</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">chi_squared</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-1">Chi Squared Distribution</span></a></p></li></ul></div>
-</li>
-</ul></div></dd>
-<dt>
-<a name="idx_id_49"></a><span class="term">D</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">denorm_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">discrete_quantile_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">domain_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">double_t</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/c99.html" title="C99 C Functions"><span class="index-entry-level-1">C99 C Functions</span></a></p></li>
-</ul></div>
-</li>
-</ul></div></dd>
-<dt>
-<a name="idx_id_50"></a><span class="term">E</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">evaluation_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">exponential</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-1">Exponential Distribution</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">extreme_value</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-1">Extreme Value Distribution</span></a></p></li></ul></div>
-</li>
-</ul></div></dd>
-<dt>
-<a name="idx_id_51"></a><span class="term">F</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">fisher_f</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution"><span class="index-entry-level-1">F Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis"><span class="index-entry-level-1">Setting Policies for Distributions on an Ad Hoc Basis</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">float_t</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/c99.html" title="C99 C Functions"><span class="index-entry-level-1">C99 C Functions</span></a></p></li>
-</ul></div>
-</li>
-</ul></div></dd>
-<dt>
-<a name="idx_id_52"></a><span class="term">G</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">gamma</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-1">Inverse Gamma Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope"><span class="index-entry-level-1">Setting Policies at Namespace or Translation Unit Scope</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">geometric</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-1">Geometric Distribution</span></a></p></li></ul></div>
-</li>
-</ul></div></dd>
-<dt>
-<a name="idx_id_53"></a><span class="term">H</span>
+<a name="idx_id_28"></a><span class="term">F</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">hypergeometric</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-1">Hypergeometric Distribution</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">fisher_f_distribution</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution"><span class="index-entry-level-1">F Distribution</span></a></p></li></ul></div>
 </li></ul></div></dd>
 <dt>
-<a name="idx_id_54"></a><span class="term">I</span>
+<a name="idx_id_29"></a><span class="term">G</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">indeterminate_result_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">gamma_distribution</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li></ul></div>
 </li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-0">geometric_distribution</span></a></p></li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_30"></a><span class="term">H</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-0">hypergeometric_distribution</span></a></p></li></ul></div></dd>
+<dt>
+<a name="idx_id_31"></a><span class="term">I</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-0">inverse_chi_squared_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-0">inverse_gamma_distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">inverse_chi_squared</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-1">Inverse Chi Squared Distribution</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">inverse_gaussian</span></p>
+<p><span class="index-entry-level-0">inverse_gaussian_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution"><span class="index-entry-level-1">Inverse Gaussian (or Inverse Normal) Distribution</span></a></p></li></ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_56"></a><span class="term">L</span>
+<a name="idx_id_33"></a><span class="term">L</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-0">laplace_distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">laplace</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-1">Laplace Distribution</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">log1p_series</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation"><span class="index-entry-level-1">Series Evaluation</span></a></p></li></ul></div>
 </li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-0">logistic_distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">logistic</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">lognormal</span></p>
+<p><span class="index-entry-level-0">lognormal_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution"><span class="index-entry-level-1">Log Normal Distribution</span></a></p></li></ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_58"></a><span class="term">N</span>
+<a name="idx_id_34"></a><span class="term">M</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">max_factorial</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial"><span class="index-entry-level-1">Factorial</span></a></p></li></ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_35"></a><span class="term">N</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-0">negative_binomial_distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">negative_binomial</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example"><span class="index-entry-level-1">Distribution Construction Example</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
-</ul></div>
+<p><span class="index-entry-level-0">nonfinite_num_get</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"><span class="index-entry-level-1">Facets for Floating-Point Infinities and NaNs</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">non_central_beta</span></p>
+<p><span class="index-entry-level-0">nonfinite_num_put</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"><span class="index-entry-level-1">Facets for Floating-Point Infinities and NaNs</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">non_central_beta_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">non_central_chi_squared</span></p>
+<p><span class="index-entry-level-0">non_central_chi_squared_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">non_central_f</span></p>
+<p><span class="index-entry-level-0">non_central_f_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution"><span class="index-entry-level-1">Noncentral F Distribution</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">non_central_t</span></p>
+<p><span class="index-entry-level-0">non_central_t_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution"><span class="index-entry-level-1">Noncentral T Distribution</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">normal</span></p>
+<p><span class="index-entry-level-0">normalise</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">normal_distribution</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_37"></a><span class="term">P</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution"><span class="index-entry-level-0">pareto_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-0">poisson_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">promote_args</span></p>
 <div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/geometric_eg.html" title="Geometric Distribution Examples"><span class="index-entry-level-1">Geometric Distribution Examples</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers"><span class="index-entry-level-1">Calling User Defined Error Handlers</span></a></p></li>
 <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope"><span class="index-entry-level-1">Setting Policies at Namespace or Translation Unit Scope</span></a></p></li>
 </ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_59"></a><span class="term">O</span>
+<a name="idx_id_39"></a><span class="term">R</span>
 </dt>
-<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">overflow_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li></ul></div></dd>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution"><span class="index-entry-level-0">rayleigh_distribution</span></a></p></li></ul></div></dd>
 <dt>
-<a name="idx_id_60"></a><span class="term">P</span>
+<a name="idx_id_40"></a><span class="term">S</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/skew_normal_dist.html" title="Skew Normal Distribution"><span class="index-entry-level-0">skew_normal_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution"><span class="index-entry-level-0">students_t_distribution</span></a></p></li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_41"></a><span class="term">T</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">pareto</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution"><span class="index-entry-level-1">Pareto Distribution</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">test_data</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions"><span class="index-entry-level-1">Graphing, Profiling, and Generating Test Data for Special Functions</span></a></p></li></ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">poisson</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-1">Poisson Distribution</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">pole_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">policy_type</span></p>
+<p><span class="index-entry-level-0">triangular_distribution</span></p>
 <div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-1">Chi Squared Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-1">Exponential Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-1">Geometric Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-1">Hypergeometric Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-1">Inverse Chi Squared Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-1">Inverse Gamma Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution"><span class="index-entry-level-1">Inverse Gaussian (or Inverse Normal) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-1">Laplace Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution"><span class="index-entry-level-1">Log Normal Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution"><span class="index-entry-level-1">Noncentral F Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution"><span class="index-entry-level-1">Noncentral T Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-1">Poisson Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution"><span class="index-entry-level-1">Rayleigh Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution"><span class="index-entry-level-1">Students t Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-1">Weibull Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></strong></span></p></li>
 </ul></div>
 </li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">precision_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">promote_double_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">promote_float_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_62"></a><span class="term">R</span>
+<a name="idx_id_42"></a><span class="term">U</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution"><span class="index-entry-level-0">uniform_distribution</span></a></p></li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">rayleigh</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution"><span class="index-entry-level-1">Rayleigh Distribution</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">rounding_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">upper_incomplete_gamma_fract</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions"><span class="index-entry-level-1">Graphing, Profiling, and Generating Test Data for Special Functions</span></a></p></li></ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_63"></a><span class="term">S</span>
+<a name="idx_id_44"></a><span class="term">W</span>
 </dt>
-<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">students_t</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces"><span class="index-entry-level-1">Namespaces</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution"><span class="index-entry-level-1">Students t Distribution</span></a></p></li>
-</ul></div>
-</li></ul></div></dd>
-<dt>
-<a name="idx_id_64"></a><span class="term">T</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">triangular</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></p></li></ul></div>
-</li></ul></div></dd>
-<dt>
-<a name="idx_id_65"></a><span class="term">U</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">underflow_error_type</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">uniform</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution"><span class="index-entry-level-1">Uniform Distribution</span></a></p></li></ul></div>
-</li>
-</ul></div></dd>
-<dt>
-<a name="idx_id_66"></a><span class="term">V</span>
-</dt>
-<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">value_type</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-1">Chi Squared Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-1">Exponential Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-1">Extreme Value Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution"><span class="index-entry-level-1">F Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-1">Geometric Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions"><span class="index-entry-level-1">Graphing, Profiling, and Generating Test Data for Special Functions</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-1">Hypergeometric Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-1">Inverse Chi Squared Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-1">Inverse Gamma Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution"><span class="index-entry-level-1">Inverse Gaussian (or Inverse Normal) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-1">Laplace Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution"><span class="index-entry-level-1">Log Normal Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution"><span class="index-entry-level-1">Noncentral F Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution"><span class="index-entry-level-1">Noncentral T Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution"><span class="index-entry-level-1">Pareto Distribution</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-1">Poisson Distribution</span></a></p></li>
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-<dt>
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-<p><span class="index-entry-level-0">weibull</span></p>
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-</li></ul></div></dd>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-0">weibull_distribution</span></a></p></li></ul></div></dd>
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-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">assert_undefined_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
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-<p><span class="index-entry-level-0">BOOST_MATH_MAX_POLY_ORDER</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_tuning" title="Table&#160;12.&#160;Boost.Math Tuning"><span class="index-entry-level-1">Boost.Math Tuning</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros"><span class="index-entry-level-1">Performance Tuning Macros</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies"><span class="index-entry-level-1">Iteration Limits Policies</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies"><span class="index-entry-level-1">Iteration Limits Policies</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_macros" title="Table&#160;11.&#160;Boost.Math Macros"><span class="index-entry-level-1">Boost.Math Macros</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_macros" title="Table&#160;11.&#160;Boost.Math Macros"><span class="index-entry-level-1">Boost.Math Macros</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/compilers_overview.html#math_toolkit.main_overview.compilers_overview.supported_tested_compilers" title="Table&#160;9.&#160;Supported/Tested Compilers"><span class="index-entry-level-1">Supported/Tested Compilers</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_NO_REAL_CONCEPT_TESTS</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_macros" title="Table&#160;11.&#160;Boost.Math Macros"><span class="index-entry-level-1">Boost.Math Macros</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_OVERFLOW_ERROR_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults"><span class="index-entry-level-1">Changing the Policy Defaults</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/special/powers/ct_pow.html" title="Compile Time Power of a Runtime Base"><span class="index-entry-level-1">Compile Time Power of a Runtime Base</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example"><span class="index-entry-level-1">Error Handling Example</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/geometric_eg.html" title="Geometric Distribution Examples"><span class="index-entry-level-1">Geometric Distribution Examples</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example."><span class="index-entry-level-1">Negative Binomial Sales Quota Example.</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_POLE_ERROR_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_POLY_METHOD</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_tuning" title="Table&#160;12.&#160;Boost.Math Tuning"><span class="index-entry-level-1">Boost.Math Tuning</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros"><span class="index-entry-level-1">Performance Tuning Macros</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_PROMOTE_DOUBLE_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros"><span class="index-entry-level-1">Performance Tuning Macros</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_PROMOTE_FLOAT_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_RATIONAL_METHOD</span></p>
-<div class="index"><ul class="index" type="none" compact>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_tuning" title="Table&#160;12.&#160;Boost.Math Tuning"><span class="index-entry-level-1">Boost.Math Tuning</span></a></p></li>
-<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros"><span class="index-entry-level-1">Performance Tuning Macros</span></a></p></li>
-</ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_ROUNDING_ERROR_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_SMALL_CONSTANT</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_macros" title="Table&#160;11.&#160;Boost.Math Macros"><span class="index-entry-level-1">Boost.Math Macros</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_STD_USING</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_macros" title="Table&#160;11.&#160;Boost.Math Macros"><span class="index-entry-level-1">Boost.Math Macros</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_UNDERFLOW_ERROR_POLICY</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults"><span class="index-entry-level-1">Using Macros to Change the Policy Defaults</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">BOOST_MATH_USE_C99</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/config_macros.html#math_toolkit.main_overview.config_macros.boost_math_macros" title="Table&#160;11.&#160;Boost.Math Macros"><span class="index-entry-level-1">Boost.Math Macros</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">binomial</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li></ul></div>
 </li>
 </ul></div></dd>
 <dt>
-<a name="idx_id_74"></a><span class="term">F</span>
+<a name="idx_id_48"></a><span class="term">C</span>
 </dt>
 <dd><div class="index"><ul class="index" type="none" compact>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">FP_INFINITE</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fpclass.html" title="Floating-Point Classification: Infinities and NaNs"><span class="index-entry-level-1">Floating-Point Classification: Infinities and NaNs</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">cauchy</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example"><span class="index-entry-level-1">Find Location (Mean) Example</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example"><span class="index-entry-level-1">Find mean and standard deviation example</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope"><span class="index-entry-level-1">Setting Polices at Namespace Scope</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope"><span class="index-entry-level-1">Setting Policies at Namespace or Translation Unit Scope</span></a></p></li>
+</ul></div>
 </li>
 <li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">FP_NAN</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fpclass.html" title="Floating-Point Classification: Infinities and NaNs"><span class="index-entry-level-1">Floating-Point Classification: Infinities and NaNs</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">FP_NORMAL</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fpclass.html" title="Floating-Point Classification: Infinities and NaNs"><span class="index-entry-level-1">Floating-Point Classification: Infinities and NaNs</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">FP_SUBNORMAL</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fpclass.html" title="Floating-Point Classification: Infinities and NaNs"><span class="index-entry-level-1">Floating-Point Classification: Infinities and NaNs</span></a></p></li></ul></div>
-</li>
-<li class="listitem" style="list-style-type: none">
-<p><span class="index-entry-level-0">FP_ZERO</span></p>
-<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/utils/fpclass.html" title="Floating-Point Classification: Infinities and NaNs"><span class="index-entry-level-1">Floating-Point Classification: Infinities and NaNs</span></a></p></li></ul></div>
+<p><span class="index-entry-level-0">chi_squared</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-1">Chi Squared Distribution</span></a></p></li></ul></div>
 </li>
 </ul></div></dd>
+<dt>
+<a name="idx_id_49"></a><span class="term">D</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">denorm_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">discrete_quantile_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">domain_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">double_t</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/c99.html" title="C99 C Functions"><span class="index-entry-level-1">C99 C Functions</span></a></p></li>
+</ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_50"></a><span class="term">E</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">evaluation_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">exponential</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-1">Exponential Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">extreme_value</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-1">Extreme Value Distribution</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_51"></a><span class="term">F</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">fisher_f</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution"><span class="index-entry-level-1">F Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis"><span class="index-entry-level-1">Setting Policies for Distributions on an Ad Hoc Basis</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">float_t</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/extern_c/c99.html" title="C99 C Functions"><span class="index-entry-level-1">C99 C Functions</span></a></p></li>
+</ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_52"></a><span class="term">G</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">gamma</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-1">Inverse Gamma Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope"><span class="index-entry-level-1">Setting Policies at Namespace or Translation Unit Scope</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">geometric</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-1">Geometric Distribution</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_53"></a><span class="term">H</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">hypergeometric</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-1">Hypergeometric Distribution</span></a></p></li></ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_54"></a><span class="term">I</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">indeterminate_result_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">inverse_chi_squared</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-1">Inverse Chi Squared Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">inverse_gaussian</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution"><span class="index-entry-level-1">Inverse Gaussian (or Inverse Normal) Distribution</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_56"></a><span class="term">L</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">laplace</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-1">Laplace Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">logistic</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">lognormal</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution"><span class="index-entry-level-1">Log Normal Distribution</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_58"></a><span class="term">N</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">negative_binomial</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example"><span class="index-entry-level-1">Distribution Construction Example</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">non_central_beta</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">non_central_chi_squared</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">non_central_f</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution"><span class="index-entry-level-1">Noncentral F Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">non_central_t</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution"><span class="index-entry-level-1">Noncentral T Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">normal</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/geometric_eg.html" title="Geometric Distribution Examples"><span class="index-entry-level-1">Geometric Distribution Examples</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope"><span class="index-entry-level-1">Setting Policies at Namespace or Translation Unit Scope</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/skew_normal_dist.html" title="Skew Normal Distribution"><span class="index-entry-level-1">Skew Normal Distribution</span></a></p></li>
+</ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_59"></a><span class="term">O</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">overflow_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_60"></a><span class="term">P</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">pareto</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution"><span class="index-entry-level-1">Pareto Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">poisson</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-1">Poisson Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">pole_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">policy_type</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-1">Chi Squared Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-1">Exponential Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-1">Geometric Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-1">Hypergeometric Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-1">Inverse Chi Squared Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-1">Inverse Gamma Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution"><span class="index-entry-level-1">Inverse Gaussian (or Inverse Normal) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-1">Laplace Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution"><span class="index-entry-level-1">Log Normal Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution"><span class="index-entry-level-1">Noncentral F Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution"><span class="index-entry-level-1">Noncentral T Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-1">Poisson Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution"><span class="index-entry-level-1">Rayleigh Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/skew_normal_dist.html" title="Skew Normal Distribution"><span class="index-entry-level-1">Skew Normal Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution"><span class="index-entry-level-1">Students t Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-1">Weibull Distribution</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">precision_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">promote_double_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">promote_float_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_62"></a><span class="term">R</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">rayleigh</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution"><span class="index-entry-level-1">Rayleigh Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">rounding_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_63"></a><span class="term">S</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">students_t</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces"><span class="index-entry-level-1">Namespaces</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution"><span class="index-entry-level-1">Students t Distribution</span></a></p></li>
+</ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_64"></a><span class="term">T</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">triangular</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></p></li></ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_65"></a><span class="term">U</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">underflow_error_type</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">uniform</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution"><span class="index-entry-level-1">Uniform Distribution</span></a></p></li></ul></div>
+</li>
+</ul></div></dd>
+<dt>
+<a name="idx_id_66"></a><span class="term">V</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">value_type</span></p>
+<div class="index"><ul class="index" type="none" compact>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution"><span class="index-entry-level-1">Cauchy-Lorentz Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution"><span class="index-entry-level-1">Chi Squared Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution"><span class="index-entry-level-1">Exponential Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution"><span class="index-entry-level-1">Extreme Value Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution"><span class="index-entry-level-1">F Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution"><span class="index-entry-level-1">Gamma (and Erlang) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/geometric_dist.html" title="Geometric Distribution"><span class="index-entry-level-1">Geometric Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions"><span class="index-entry-level-1">Graphing, Profiling, and Generating Test Data for Special Functions</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution"><span class="index-entry-level-1">Hypergeometric Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution"><span class="index-entry-level-1">Inverse Chi Squared Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution"><span class="index-entry-level-1">Inverse Gamma Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution"><span class="index-entry-level-1">Inverse Gaussian (or Inverse Normal) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/laplace_dist.html" title="Laplace Distribution"><span class="index-entry-level-1">Laplace Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution"><span class="index-entry-level-1">Log Normal Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution"><span class="index-entry-level-1">Logistic Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution"><span class="index-entry-level-1">Negative Binomial Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution"><span class="index-entry-level-1">Noncentral Beta Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution"><span class="index-entry-level-1">Noncentral Chi-Squared Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution"><span class="index-entry-level-1">Noncentral F Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution"><span class="index-entry-level-1">Noncentral T Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution"><span class="index-entry-level-1">Normal (Gaussian) Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution"><span class="index-entry-level-1">Pareto Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution"><span class="index-entry-level-1">Poisson Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/toolkit/internals2/polynomials.html" title="Polynomials"><span class="index-entry-level-1">Polynomials</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution"><span class="index-entry-level-1">Rayleigh Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/skew_normal_dist.html" title="Skew Normal Distribution"><span class="index-entry-level-1">Skew Normal Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution"><span class="index-entry-level-1">Students t Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution"><span class="index-entry-level-1">Uniform Distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-1">Weibull Distribution</span></a></p></li>
+</ul></div>
+</li></ul></div></dd>
+<dt>
+<a name="idx_id_67"></a><span class="term">W</span>
+</dt>
+<dd><div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">weibull</span></p>
+<div class="index"><ul class="index" type="none" compact><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-1">Weibull Distribution</span></a></p></li></ul></div>
+</li></ul></div></dd>
 </dl></div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/backgrounders.html

@@ -38,7 +38,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html

@@ -608,20 +608,25 @@
 </pre>
 <p>
         Note that unlike the sample config file supplied with SVGMath, this does
-        not make use of the Mathematica 7 font as this lacks sufficient Unicode information
-        for it to be used with either SVGMath or XEP "as is".
+        not make use of the <a href="http://support.wolfram.com/technotes/fonts/windows/latestfonts.html" target="_top">Mathematica
+        7 font</a> as this lacks sufficient Unicode information for it to be
+        used with either SVGMath or XEP "as is".
       </p>
 <p>
         Also note that the SVG files in the repository are almost certainly Windows-specific
         since they reference various Windows Fonts.
       </p>
 <p>
-        PNG files can be created from the SVG's using <a href="http://xmlgraphics.apache.org/batik/tools/rasterizer.html" target="_top">Batik</a>
+        PNG files can be created from the SVGs using <a href="http://xmlgraphics.apache.org/batik/tools/rasterizer.html" target="_top">Batik</a>
         and a command such as:
       </p>
 <pre class="programlisting">java -jar 'C:\download\open\batik-1.7\batik-rasterizer.jar' -dpi 120 *.svg</pre>
 <p>
-        Or using Inkscape and a command such as:
+        Or using Inkscape (File, Export bitmap, Drawing tab, bitmap size (default
+        size, 100 dpi), Filename (default). png)
+      </p>
+<p>
+        or Using Cygwin, a command such as:
       </p>
 <pre class="programlisting">for file in *.svg; do
   /cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file);
@@ -751,7 +756,7 @@ done</pre>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html

@@ -228,7 +228,7 @@
         computing to float precision with double precision arithmetic.
       </p>
 <div class="table">
-<a name="math_toolkit.backgrounders.lanczos.optimal_choices_for_n_and_g_when_computing_with_guard_digits__source__pugh_"></a><p class="title"><b>Table&#160;57.&#160;Optimal choices for N and g when computing with guard digits (source:
+<a name="math_toolkit.backgrounders.lanczos.optimal_choices_for_n_and_g_when_computing_with_guard_digits__source__pugh_"></a><p class="title"><b>Table&#160;58.&#160;Optimal choices for N and g when computing with guard digits (source:
         Pugh)</b></p>
 <div class="table-contents"><table class="table" summary="Optimal choices for N and g when computing with guard digits (source:
         Pugh)">
@@ -371,7 +371,7 @@
         exactly matches the machine epsilon for the type in question.
       </p>
 <div class="table">
-<a name="math_toolkit.backgrounders.lanczos.optimum_value_for_n_and_g_when_computing_at_fixed_precision"></a><p class="title"><b>Table&#160;58.&#160;Optimum value for N and g when computing at fixed precision</b></p>
+<a name="math_toolkit.backgrounders.lanczos.optimum_value_for_n_and_g_when_computing_at_fixed_precision"></a><p class="title"><b>Table&#160;59.&#160;Optimum value for N and g when computing at fixed precision</b></p>
 <div class="table-contents"><table class="table" summary="Optimum value for N and g when computing at fixed precision">
 <colgroup>
 <col>
@@ -560,7 +560,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html

@@ -203,7 +203,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html

@@ -107,7 +107,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html

@@ -528,7 +528,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/constants.html

@@ -0,0 +1,59 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Mathematical Constants</title>
+<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">
+<link rel="next" href="constants/intro.html" title="Introduction">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="extern_c/tr1_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="constants/intro.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section math_toolkit_constants">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.constants"></a><a class="link" href="constants.html" title="Mathematical Constants">Mathematical Constants</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="constants/intro.html">Introduction</a></span></dt>
+<dt><span class="section"><a href="constants/tutorial.html">Tutorial</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="constants/tutorial/non_templ.html">Use in non-template
+        code</a></span></dt>
+<dt><span class="section"><a href="constants/tutorial/templ.html">Use in template
+        code</a></span></dt>
+<dt><span class="section"><a href="constants/tutorial/user_def.html">Use With
+        User Defined Types</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="constants/constants.html">The Mathematical Constants</a></span></dt>
+<dt><span class="section"><a href="constants/new_const.html">Defining New Constants</a></span></dt>
+<dt><span class="section"><a href="constants/FAQ.html">FAQs</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="extern_c/tr1_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="constants/intro.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

doc/sf_and_dist/html/math_toolkit/constants/FAQ.html

@@ -0,0 +1,480 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>FAQs</title>
+<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../constants.html" title="Mathematical Constants">
+<link rel="prev" href="new_const.html" title="Defining New Constants">
+<link rel="next" href="../toolkit.html" title="Tools and Internal Details">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="new_const.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../toolkit.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section math_toolkit_constants_FAQ">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.constants.FAQ"></a><a class="link" href="FAQ.html" title="FAQs">FAQs</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.constants.FAQ.h0"></a>
+        <span><a name="math_toolkit.constants.FAQ.why_are__emphasis_these__emphasis__constants_chosen_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.why_are__emphasis_these__emphasis__constants_chosen_">Why
+        are <span class="emphasis"><em>these</em></span> Constants Chosen?</a>
+      </h5>
+<p>
+        It is, of course, impossible to please everyone with a list like this.
+      </p>
+<p>
+        Some of the criteria we have used are:
+      </p>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+            Used in Boost.Math.
+          </li>
+<li class="listitem">
+            Commonly used.
+          </li>
+<li class="listitem">
+            Expensive to compute.
+          </li>
+<li class="listitem">
+            Requested by users.
+          </li>
+<li class="listitem">
+            <a href="http://en.wikipedia.org/wiki/Mathematical_constant" target="_top">Used
+            in science and mathematics.</a>
+          </li>
+<li class="listitem">
+            No integer values (because so cheap to construct).<br> (You can easily
+            define your own if found convenient, for example: <code class="computeroutput"><span class="identifier">FPT</span>
+            <span class="identifier">one</span> <span class="special">=</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">FPT</span><span class="special">&gt;(</span><span class="number">42</span><span class="special">);</span></code>).
+          </li>
+</ul></div>
+<h5>
+<a name="math_toolkit.constants.FAQ.h1"></a>
+        <span><a name="math_toolkit.constants.FAQ.how_are_constants_named_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.how_are_constants_named_">How
+        are constants named?</a>
+      </h5>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+            Not macros, so no upper case.
+          </li>
+<li class="listitem">
+            All lower case (following C++ standard names).
+          </li>
+<li class="listitem">
+            No CamelCase.
+          </li>
+<li class="listitem">
+            Underscore as _ delimiter between words.
+          </li>
+<li class="listitem">
+            Numbers spelt as words rather than decimal digits (except following pow).
+          </li>
+<li class="listitem">
+            Abbreviation conventions:
+            <div class="itemizedlist"><ul class="itemizedlist" type="circle">
+<li class="listitem">
+                  root for square root.
+                </li>
+<li class="listitem">
+                  cbrt for cube root.
+                </li>
+<li class="listitem">
+                  pow for pow function using decimal digits like pow23 for n<sup>2/3</sup>.
+                </li>
+<li class="listitem">
+                  div for divided by or operator /.
+                </li>
+<li class="listitem">
+                  minus for operator -, plus for operator +.
+                </li>
+<li class="listitem">
+                  sqr for squared.
+                </li>
+<li class="listitem">
+                  cubed for cubed n<sup>3</sup>.
+                </li>
+<li class="listitem">
+                  words for greek, like &#960;, &#950; and &#915;.
+                </li>
+<li class="listitem">
+                  words like half, third, three_quarters, sixth for fractions. (Digit(s)
+                  can get muddled).
+                </li>
+<li class="listitem">
+                  log10 for log<sub>10</sub>
+                </li>
+<li class="listitem">
+                  ln for log<sub>e</sub>
+                </li>
+</ul></div>
+          </li>
+</ul></div>
+<h5>
+<a name="math_toolkit.constants.FAQ.h2"></a>
+        <span><a name="math_toolkit.constants.FAQ.how_are_the_constants_derived_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.how_are_the_constants_derived_">How are
+        the constants derived?</a>
+      </h5>
+<p>
+        The constants have all been calculated using high-precision software working
+        with up to 300-bit precision giving about 100 decimal digits. (The precision
+        can be arbitrarily chosen and is limited only by compute time).
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h3"></a>
+        <span><a name="math_toolkit.constants.FAQ.how_accurate_are_the_constants_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.how_accurate_are_the_constants_">How
+        Accurate are the constants?</a>
+      </h5>
+<p>
+        The minimum accuracy chosen (100 decimal digits) exceeds the accuracy of
+        reasonably-foreseeable floating-point hardware (256-bit) and should meet
+        most high-precision computations.
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h4"></a>
+        <span><a name="math_toolkit.constants.FAQ.how_are_the_constants_tested_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.how_are_the_constants_tested_">How are
+        the constants tested?</a>
+      </h5>
+<div class="orderedlist"><ol class="orderedlist" type="1">
+<li class="listitem">
+            Comparison using Boost.Test BOOST_CHECK_CLOSE_FRACTION using long double
+            literals, with at least 35 decimal digits, enough to be accurate for
+            all long double implementations. The tolerance is usually twice <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span>
+            <span class="identifier">epsilon</span></code>.
+          </li>
+<li class="listitem">
+            Comparison with calculation at long double precision. This often requires
+            a slightly higher tolerance than two epsilon because of computational
+            noise from round-off etc, especially when trig and other functions are
+            called.
+          </li>
+<li class="listitem">
+            Comparison with independent published values, for example, using <a href="http://oeis.org/" target="_top">The On-Line Encyclopedia of Integer Sequences
+            (OEIS)</a> again using at least 35 decimal digits strings.
+          </li>
+<li class="listitem">
+            Comparison with independely calculated values using arbitrary precision
+            tools like <a href="http://www.wolfram.com/mathematica/" target="_top">Mathematica</a>,
+            again using at least 35 decimal digits literal strings.
+          </li>
+</ol></div>
+<div class="warning"><table border="0" summary="Warning">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../../doc/src/images/warning.png"></td>
+<th align="left">Warning</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          We have not yet been able to <span class="bold"><strong>check</strong></span> that
+          <span class="bold"><strong>all</strong></span> constants are accurate at the full
+          arbitrary precision, at present 100 decimal digits. But certain key values
+          like <code class="computeroutput"><span class="identifier">e</span></code> and <code class="computeroutput"><span class="identifier">pi</span></code> appear to be accurate and internal
+          consistencies suggest that others are this accurate too.
+        </p></td></tr>
+</table></div>
+<h5>
+<a name="math_toolkit.constants.FAQ.h5"></a>
+        <span><a name="math_toolkit.constants.FAQ.why_is_portability_important_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.why_is_portability_important_">Why is
+        Portability important?</a>
+      </h5>
+<p>
+        Code written using math constants is easily portable even when using different
+        floating-point types with differing precision.
+      </p>
+<p>
+        It is a mistake to expect that results of computations will be <span class="bold"><strong>identical</strong></span>, but you can achieve the <span class="bold"><strong>best
+        accuracy possible for the floating-point type in use</strong></span>.
+      </p>
+<p>
+        This has no extra cost to the user, but reduces irritating, and often confusing
+        and very hard-to-trace effects, caused by the intrinsically limited precision
+        of floating-point calculations.
+      </p>
+<p>
+        A harmless symptom of this limit is a spurious least-significant digit; at
+        worst, slightly inaccurate constants sometimes cause iterating algorithms
+        to diverge wildly because internal comparisons just fail.
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h6"></a>
+        <span><a name="math_toolkit.constants.FAQ.what_is_the_internal_format_of_the_constants__and_why_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.what_is_the_internal_format_of_the_constants__and_why_">What
+        is the Internal Format of the constants, and why?</a>
+      </h5>
+<p>
+        See <a class="link" href="tutorial.html" title="Tutorial">tutorial</a> above
+        for normal use, but this FAQ explains the internal details used for the constants.
+      </p>
+<p>
+        Constants are stored as 100 decimal digit values. However, some compilers
+        do not accept decimal digits strings as long as this. So the constant is
+        split into two parts, with the first containing at least 128-bit long double
+        precision (35 decimal digits), and for consistency should be in scientific
+        format with a signed exponent.
+      </p>
+<p>
+        The second part is the value of the constant expressed as a string literal,
+        accurate to at least 100 decimal digits (in practice that means at least
+        102 digits). Again for consistency use scientific format with a signed exponent.
+      </p>
+<p>
+        For types with precision greater than a long double, then if T is constructible
+        <code class="computeroutput"><span class="identifier">T</span> </code>is constructible from a
+        <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code> then it's directly constructed from the
+        string, otherwise we fall back on lexical_cast to convert to type <code class="computeroutput"><span class="identifier">T</span></code>. (Using a string is necessary because
+        you can't use a numeric constant since even a <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code> might not have enough digits).
+      </p>
+<p>
+        So, for example, a constant like pi is internally defined as
+      </p>
+<pre class="programlisting"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">pi</span><span class="special">,</span> <span class="number">3.141592653589793238462643383279502884e+00</span><span class="special">,</span> <span class="string">"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00"</span><span class="special">);</span>
+</pre>
+<p>
+        In this case the significand is 109 decimal digits, ensuring 100 decimal
+        digits are exact, and exponent is zero.
+      </p>
+<p>
+        See <a class="link" href="new_const.html" title="Defining New Constants">defining new constants</a>
+        to calculate new constants.
+      </p>
+<p>
+        A macro definition like this can be pasted into user code where convenient,
+        or into <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> if
+        it is to be added to the Boost.Math library.
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h7"></a>
+        <span><a name="math_toolkit.constants.FAQ.what_floating_point_types_could_i_use_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.what_floating_point_types_could_i_use_">What
+        Floating-point Types could I use?</a>
+      </h5>
+<p>
+        Apart from the built-in floating-point types <code class="computeroutput"><span class="keyword">float</span></code>,
+        <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code>, there are several arbitrary
+        precision floating-point classes available, but most are not licensed for
+        commercial use.
+      </p>
+<h6>
+<a name="math_toolkit.constants.FAQ.h8"></a>
+        <span><a name="math_toolkit.constants.FAQ.boost_multiprecision_by_christopher_kormanyos"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.boost_multiprecision_by_christopher_kormanyos">Boost.Multiprecision
+        by Christopher Kormanyos</a>
+      </h6>
+<p>
+        This work is based on an earlier work called e-float: Algorithm 910: A Portable
+        C++ Multiple-Precision System for Special-Function Calculations, in ACM TOMS,
+        {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. <a href="http://doi.acm.org/10.1145/1916461.1916469" target="_top">http://doi.acm.org/10.1145/1916461.1916469</a>
+        <a href="https://svn.boost.org/svn/boost/sandbox/e_float/" target="_top">e_float</a>
+        but is now re-factored and available under the Boost license in the Boost-sandbox
+        at <a href="https://svn.boost.org/svn/boost/sandbox/multiprecision/" target="_top">multiprecision</a>
+        where it is being refined and prepared for review.
+      </p>
+<h6>
+<a name="math_toolkit.constants.FAQ.h9"></a>
+        <span><a name="math_toolkit.constants.FAQ.boost_cpp_float_by_john_maddock_using_expression_templates"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.boost_cpp_float_by_john_maddock_using_expression_templates">Boost.cpp_float
+        by John Maddock using Expression Templates</a>
+      </h6>
+<p>
+        <a href="https://svn.boost.org/svn/boost/sandbox/big_number/" target="_top">Big Number</a>
+        which is a reworking of <a href="https://svn.boost.org/svn/boost/sandbox/e_float/" target="_top">e_float</a>
+        by Christopher Kormanyos to use expression templates for faster execution.
+      </p>
+<h6>
+<a name="math_toolkit.constants.FAQ.h10"></a>
+        <span><a name="math_toolkit.constants.FAQ.ntl_class_quad_float"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.ntl_class_quad_float">NTL
+        class quad_float</a>
+      </h6>
+<p>
+        <a href="http://shoup.net/ntl/" target="_top">NTL</a> by Victor Shoup has fixed
+        and arbitrary high precision fixed and floating-point types. However none
+        of these are licenced for commercial use.
+      </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">/</span><span class="identifier">quad_float</span><span class="special">.</span><span class="identifier">h</span><span class="special">&gt;</span> <span class="comment">// quad precision 106-bit, about 32 decimal digits.</span>
+<span class="keyword">using</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">to_quad_float</span><span class="special">;</span> <span class="comment">// Less precise than arbitrary precision NTL::RR.</span>
+</pre>
+<p>
+        NTL class <code class="computeroutput"><span class="identifier">quad_float</span></code>, which
+        gives a form of quadruple precision, 106-bit significand (but without an
+        extended exponent range.) With an IEC559/IEEE 754 compatible processor, for
+        example Intel X86 family, with 64-bit double, and 53-bit significand, using
+        the significands of <span class="bold"><strong>two</strong></span> 64-bit doubles,
+        if <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">digits10</span></code> is 16, then we get about twice
+        the precision, so <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">quad_float</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">()</span></code>
+        should be 32. (the default <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RR</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">()</span></code> should be about 40). (which seems to agree
+        with experiments). We output constants (including some noisy bits, an approximation
+        to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RR</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">()</span></code>)
+        by adding 2 extra decimal digits, so using <code class="computeroutput"><span class="identifier">quad_float</span><span class="special">::</span><span class="identifier">SetOutputPrecision</span><span class="special">(</span><span class="number">32</span> <span class="special">+</span>
+        <span class="number">2</span><span class="special">);</span></code>
+      </p>
+<p>
+        Apple Mac/Darwin uses a similar <span class="emphasis"><em>doubledouble</em></span> 106-bit
+        for its built-in <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
+        type.
+      </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          The precision of all <code class="computeroutput"><span class="identifier">doubledouble</span></code>
+          floating-point types is rather odd and values given are only approximate.
+        </p></td></tr>
+</table></div>
+<h6>
+<a name="math_toolkit.constants.FAQ.h11"></a>
+        <span><a name="math_toolkit.constants.FAQ.ntl_class_rr"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.ntl_class_rr">NTL
+        class RR</a>
+      </h6>
+<p>
+        Arbitrary precision floating point with NTL class RR, default is 150 bit
+        (about 50 decimal digits) used here with 300 bit to output 100 decimal digits,
+        enough for many practical non-'number-theoretic' C++ applications.
+      </p>
+<p>
+        NTL is <span class="bold"><strong>not licenced for commercial use</strong></span>.
+      </p>
+<p>
+        This class is used in Boost.Math and an option when using big_number projects
+        to calculate new math constants.
+      </p>
+<h6>
+<a name="math_toolkit.constants.FAQ.h12"></a>
+        <span><a name="math_toolkit.constants.FAQ.gmp_and_mpfr"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.gmp_and_mpfr">GMP
+        and MPFR</a>
+      </h6>
+<p>
+        <a href="../../gmplib.org" target="_top">GMP</a> and <a href="http://www.mpfr.org/" target="_top">MPFR</a>
+        have also been used to compute constants, but are licensed under the <a href="http://www.gnu.org/copyleft/lesser.html" target="_top">Lesser GPL license</a>
+        and are <span class="bold"><strong>not licensed for commercial use</strong></span>.
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h13"></a>
+        <span><a name="math_toolkit.constants.FAQ.what_happened_to_a_previous_collection_of_constants_proposed_for_boost_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.what_happened_to_a_previous_collection_of_constants_proposed_for_boost_">What
+        happened to a previous collection of constants proposed for Boost?</a>
+      </h5>
+<p>
+        A review concluded that the way in which the constants were presented did
+        not meet many peoples needs. None of the methods proposed met many users'
+        essential requirement to allow writing simply <code class="computeroutput"><span class="identifier">pi</span></code>
+        rather than <code class="computeroutput"><span class="identifier">pi</span><span class="special">()</span></code>.
+        Many science and engineering equations look difficult to read when because
+        function call brackets can be confused with the many other brackets often
+        needed. All the methods then proposed of avoiding the brackets failed to
+        meet all needs, often on grounds of complexity and lack of applicability
+        to various realistic scenarios.
+      </p>
+<p>
+        So the simple namespace method, proposed on its own, but rejected at the
+        first review, has been added to allow users to have convenient access to
+        float, double and long double values, but combined with template struct and
+        functions to allow simultaneous use with other non-built-in floating-point
+        types.
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h14"></a>
+        <span><a name="math_toolkit.constants.FAQ.why_do_the_constants__internally__have_a_struct_rather_than_a_simple_function_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.why_do_the_constants__internally__have_a_struct_rather_than_a_simple_function_">Why
+        do the constants (internally) have a struct rather than a simple function?</a>
+      </h5>
+<p>
+        A function mechanism was provided by in previous versions of Boost.Math.
+      </p>
+<p>
+        The new mechanism is to permit partial specialization. See Custom Specializing
+        a constant above. It should also allow use with other packages like <a href="http://www.ttmath.org/" target="_top">ttmath Bignum C++ library.</a>
+      </p>
+<h5>
+<a name="math_toolkit.constants.FAQ.h15"></a>
+        <span><a name="math_toolkit.constants.FAQ.where_can_i_find_other_high_precision_constants_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.where_can_i_find_other_high_precision_constants_">Where
+        can I find other high precision constants?</a>
+      </h5>
+<div class="orderedlist"><ol class="orderedlist" type="1">
+<li class="listitem">
+            Constants with very high precision and good accuracy (&gt;40 decimal
+            digits) from Simon Plouffe's web based collection <a href="http://pi.lacim.uqam.ca/eng/" target="_top">http://pi.lacim.uqam.ca/eng/</a>.
+          </li>
+<li class="listitem">
+            <a href="https://oeis.org/" target="_top">The On-Line Encyclopedia of Integer Sequences
+            (OEIS)</a>
+          </li>
+<li class="listitem">
+            Checks using printed text optically scanned values and converted from:
+            D. E. Knuth, Art of Computer Programming, Appendix A, Table 1, Vol 1,
+            ISBN 0 201 89683 4 (1997)
+          </li>
+<li class="listitem">
+            M. Abrahamovitz &amp; I. E. Stegun, National Bureau of Standards, Handbook
+            of Mathematical Functions, a reference source for formulae now superceded
+            by
+          </li>
+<li class="listitem">
+            Frank W. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark,
+            NIST Handbook of Mathemetical Functions, Cambridge University Press,
+            ISBN 978-0-521-14063-8, 2010.
+          </li>
+<li class="listitem">
+            John F Hart, Computer Approximations, Kreiger (1978) ISBN 0 88275 642
+            7.
+          </li>
+<li class="listitem">
+            Some values from Cephes Mathematical Library, Stephen L. Moshier and
+            CALC100 100 decimal digit Complex Variable Calculator Program, a DOS
+            utility.
+          </li>
+<li class="listitem">
+            Xavier Gourdon, Pascal Sebah, 50 decimal digits constants at <a href="http://numbers.computation.free.fr/Constants/constants.html" target="_top">Number,
+            constants and computation</a>.
+          </li>
+</ol></div>
+<h5>
+<a name="math_toolkit.constants.FAQ.h16"></a>
+        <span><a name="math_toolkit.constants.FAQ.where_are_physical_constants_"></a></span><a class="link" href="FAQ.html#math_toolkit.constants.FAQ.where_are_physical_constants_">Where
+        are Physical Constants?</a>
+      </h5>
+<p>
+        Not here in this Boost.Math collection, because physical constants:
+      </p>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+            Are measurements.
+          </li>
+<li class="listitem">
+            Are not truly constant and keeping changing as mensuration technology
+            improves.
+          </li>
+<li class="listitem">
+            Have a instrinsic uncertainty.
+          </li>
+<li class="listitem">
+            Mathematical constants are stored and represented at varying precision,
+            but should never be inaccurate.
+          </li>
+</ul></div>
+<p>
+        Some physical constants may be available in Boost.Units.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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doc/sf_and_dist/html/math_toolkit/constants/intro.html

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+<html>
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+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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+</div>
+<div class="section math_toolkit_constants_intro">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.constants.intro"></a><a class="link" href="intro.html" title="Introduction">Introduction</a>
+</h3></div></div></div>
+<p>
+        Boost.Math provides a collection of mathematical constants.
+      </p>
+<h5>
+<a name="math_toolkit.constants.intro.h0"></a>
+        <span><a name="math_toolkit.constants.intro.why_use_boost_math_mathematical_constants_"></a></span><a class="link" href="intro.html#math_toolkit.constants.intro.why_use_boost_math_mathematical_constants_">Why
+        use Boost.Math mathematical constants?</a>
+      </h5>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+            Readable. For the very many jobs just using built-in like <code class="computeroutput"><span class="keyword">double</span></code>, you can just write expressions
+            like
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">area</span> <span class="special">=</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span></pre>
+            (If that's all you want, jump direct to <a class="link" href="tutorial/non_templ.html" title="Use in non-template code">use
+            in non-template code</a>!)
+          </li>
+<li class="listitem">
+            Effortless - avoiding a search of reference sources.
+          </li>
+<li class="listitem">
+            Usable with both builtin floating point types, and user-defined, possibly
+            extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter
+            case the constants are computed to the necessary precision and then cached.
+          </li>
+<li class="listitem">
+            Accurate - ensuring that the values are as accurate as possible for the
+            chosen floating-point type
+            <div class="itemizedlist"><ul class="itemizedlist" type="circle">
+<li class="listitem">
+                  No loss of accuracy from repeated rounding of intermediate computations.
+                </li>
+<li class="listitem">
+                  Result is computed with higher precision and only rounded once.
+                </li>
+<li class="listitem">
+                  Less risk of inaccurate result from functions pow, trig and log
+                  at <a href="http://en.wikipedia.org/wiki/Corner_case" target="_top">corner
+                  cases</a>.
+                </li>
+<li class="listitem">
+                  Less risk of <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">cancellation
+                  error</a>.
+                </li>
+</ul></div>
+          </li>
+<li class="listitem">
+            Faster - can avoid (re-)calculation at runtime. This can be significant
+            if:
+            <div class="itemizedlist"><ul class="itemizedlist" type="circle">
+<li class="listitem">
+                  Functions pow, trig or log are used.
+                </li>
+<li class="listitem">
+                  Inside an inner loop.
+                </li>
+<li class="listitem">
+                  Using a high-precision UDT.
+                </li>
+<li class="listitem">
+                  Compiler optimizations possible with built-in types, especially
+                  <code class="computeroutput"><span class="keyword">double</span></code>, are not available.
+                </li>
+</ul></div>
+          </li>
+<li class="listitem">
+            Portable - as possible between different systems using different floating-point
+            precisions: see <a class="link" href="tutorial/templ.html" title="Use in template code">use
+            in template code</a>.
+          </li>
+<li class="listitem">
+            Tested - by comparison with other published sources, or separately computed
+            at long double precision.
+          </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../constants.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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+</html>

doc/sf_and_dist/html/math_toolkit/constants/new_const.html

@@ -0,0 +1,267 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Defining New Constants</title>
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+<link rel="home" href="../../index.html" title="Math Toolkit">
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="constants.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="FAQ.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section math_toolkit_constants_new_const">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.constants.new_const"></a><a class="link" href="new_const.html" title="Defining New Constants">Defining New Constants</a>
+</h3></div></div></div>
+<p>
+        The library provides some helper code to assist in defining new constants;
+        the process for defining a constant called <code class="computeroutput"><span class="identifier">my_constant</span></code>
+        goes like this:
+      </p>
+<p>
+        1. <span class="bold"><strong>Define a function that calculates the value of the
+        constant</strong></span>. This should be a template function, and be placed in
+        <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">calculate_constants</span><span class="special">.</span><span class="identifier">hpp</span></code> if
+        the constant is to be added to this library, or else defined at the top of
+        your source file if not.
+      </p>
+<p>
+        The function should look like this:
+      </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
+<span class="identifier">Real</span> <span class="identifier">constant_my_constant</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">compute</span><span class="special">(</span><span class="identifier">BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC</span><span class="special">(</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;))</span>
+<span class="special">{</span>
+  <span class="keyword">int</span> <span class="identifier">required_precision</span> <span class="special">=</span> <span class="identifier">N</span> <span class="special">?</span> <span class="identifier">N</span> <span class="special">:</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;();</span>
+  <span class="identifier">Real</span> <span class="identifier">result</span> <span class="special">=</span> <span class="comment">/* value computed to required_precision bits */</span> <span class="special">;</span>
+  <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
+<span class="special">}</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces</span>
+</pre>
+<p>
+        Then define a placeholder for the constant itself:
+      </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{</span>
+
+<span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">my_constant</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span> <span class="string">"0"</span><span class="special">);</span>
+
+<span class="special">}}}</span>
+</pre>
+<p>
+        For example, to calculate &#960;/2, add to <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">calculate_constants</span><span class="special">.</span><span class="identifier">hpp</span></code>
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">constant_half_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">compute</span><span class="special">(</span><span class="identifier">BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC</span><span class="special">(</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;))</span>
+<span class="special">{</span>
+   <span class="identifier">BOOST_MATH_STD_USING</span>
+   <span class="keyword">return</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;()</span> <span class="special">/</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="number">2</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+<p>
+        Then to <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> add:
+      </p>
+<pre class="programlisting"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">half_pi</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span> <span class="string">"0"</span><span class="special">);</span>  <span class="comment">// Actual values are temporary, we'll replace them later.</span>
+</pre>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          Previously defined constants like pi and e can be used, but by <span class="bold"><strong>not simply calling</strong></span> <code class="computeroutput"><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</span></code>; specifying the precision via the
+          policy <code class="computeroutput"><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;()</span></code> is essential to ensure full accuracy.
+        </p></td></tr>
+</table></div>
+<div class="warning"><table border="0" summary="Warning">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../../doc/src/images/warning.png"></td>
+<th align="left">Warning</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          Newly defined constants can only be used once they are included in <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code>. So if you add <code class="computeroutput"><span class="keyword">template</span>
+          <span class="special">&lt;</span><span class="keyword">class</span>
+          <span class="identifier">T</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">constant_my_constant</span><span class="special">{...}</span></code>,
+          then you cannot define <code class="computeroutput"><span class="identifier">constant_my_constant</span></code>
+          until you add the temporary <code class="computeroutput"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">my_constant</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span>
+          <span class="string">"0"</span><span class="special">)</span></code>.
+          Failing to do this will result in surprising compile errors:
+</p>
+<pre class="programlisting"><span class="identifier">error</span> <span class="identifier">C2143</span><span class="special">:</span> <span class="identifier">syntax</span> <span class="identifier">error</span> <span class="special">:</span> <span class="identifier">missing</span> <span class="char">';'</span> <span class="identifier">before</span> <span class="char">'&lt;'</span>
+<span class="identifier">error</span> <span class="identifier">C2433</span><span class="special">:</span> <span class="char">'constant_root_two_div_pi'</span> <span class="special">:</span> <span class="char">'inline'</span> <span class="keyword">not</span> <span class="identifier">permitted</span> <span class="identifier">on</span> <span class="identifier">data</span> <span class="identifier">declarations</span>
+<span class="identifier">error</span> <span class="identifier">C2888</span><span class="special">:</span> <span class="char">'T constant_root_two_div_pi'</span> <span class="special">:</span> <span class="identifier">symbol</span> <span class="identifier">cannot</span> <span class="identifier">be</span> <span class="identifier">defined</span> <span class="identifier">within</span> <span class="keyword">namespace</span> <span class="char">'detail'</span>
+<span class="identifier">error</span> <span class="identifier">C2988</span><span class="special">:</span> <span class="identifier">unrecognizable</span> <span class="keyword">template</span> <span class="identifier">declaration</span><span class="special">/</span><span class="identifier">definition</span>
+</pre>
+<p>
+        </p>
+</td></tr>
+</table></div>
+<p>
+        2. <span class="bold"><strong>You will need an arbitrary precision type to use
+        to calculate the value</strong></span>. This library currently supports either
+        <code class="computeroutput"><span class="identifier">cpp_float</span></code>, <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code>
+        or <code class="computeroutput"><span class="identifier">mpfr_class</span></code> used via the
+        bindings in <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">bindings</span></code>.
+        The default is to use <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code> unless
+        you define an alternate macro, for example, <code class="computeroutput"><span class="identifier">USE_MPFR</span></code>
+        or <code class="computeroutput"><span class="identifier">USE_CPP_FLOAT</span></code> at the start
+        of your program.
+      </p>
+<p>
+        3. It is necessary to link to the Boost.Regex library, and probably to your
+        chosen arbitrary precision type library.
+      </p>
+<p>
+        4. The complete program to generate the constant <code class="computeroutput"><span class="identifier">half_pi</span></code>
+        using function <code class="computeroutput"><span class="identifier">calculate_half_pi</span></code>
+        is then:
+      </p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">USE_CPP_FLOAT</span> <span class="comment">// If required.</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">generate</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">BOOST_CONSTANTS_GENERATE</span><span class="special">(</span><span class="identifier">half_pi</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+<p>
+        The output from the program is a snippet of C++ code (actually a macro call)
+        that can be cut and pasted into <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> or else into your own code, for example:
+      </p>
+<pre class="programlisting">BOOST_DEFINE_MATH_CONSTANT(half_pi, 1.570796326794896619231321691639751442e+00, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404326e+00");
+</pre>
+<p>
+        This macro BOOST_DEFINE_MATH_CONSTANT inserts a C++ struct code snippet that
+        declares the <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code> versions of the constant, plus
+        a decimal digit string representation correct to 100 decimal digits, and
+        all the meta-programming machinery needed to select between them.
+      </p>
+<p>
+        The result of an expanded macro for Pi is shown below.
+      </p>
+<p>
+</p>
+<pre class="programlisting"><span class="comment">// Preprocessed pi constant, annotated.</span>
+
+<span class="keyword">namespace</span> <span class="identifier">boost</span>
+<span class="special">{</span>
+  <span class="keyword">namespace</span> <span class="identifier">math</span>
+  <span class="special">{</span>
+    <span class="keyword">namespace</span> <span class="identifier">constants</span>
+    <span class="special">{</span>
+      <span class="keyword">namespace</span> <span class="identifier">detail</span>
+      <span class="special">{</span>
+        <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">struct</span> <span class="identifier">constant_pi</span>
+        <span class="special">{</span>
+          <span class="keyword">private</span><span class="special">:</span>
+            <span class="comment">// Default implementations from string of decimal digits:</span>
+            <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get_from_string</span><span class="special">()</span>
+            <span class="special">{</span>
+            <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">result</span>
+               <span class="special">=</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">convert_from_string</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="string">"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00"</span><span class="special">,</span>
+               <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_convertible</span><span class="special">&lt;</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*,</span> <span class="identifier">T</span><span class="special">&gt;());</span>
+              <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
+            <span class="special">}</span>
+            <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="keyword">static</span> <span class="identifier">T</span> <span class="identifier">compute</span><span class="special">();</span>
+
+          <span class="keyword">public</span><span class="special">:</span>
+            <span class="comment">// Default implementations from string of decimal digits:</span>
+            <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_string</span><span class="special">&gt;&amp;)</span>
+            <span class="special">{</span>
+              <span class="identifier">constant_initializer</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="special">&amp;</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">get_from_string</span> <span class="special">&gt;::</span><span class="identifier">do_nothing</span><span class="special">();</span>
+              <span class="keyword">return</span> <span class="identifier">get_from_string</span><span class="special">();</span>
+            <span class="special">}</span>
+            <span class="comment">// Float, double and long double versions:</span>
+            <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_float</span><span class="special">&gt;)</span>
+            <span class="special">{</span>
+              <span class="keyword">return</span> <span class="number">3.141592653589793238462643383279502884e+00F</span><span class="special">;</span>
+            <span class="special">}</span>
+            <span class="keyword">static</span> <span class="keyword">inline</span>  <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_double</span><span class="special">&gt;&amp;)</span>
+            <span class="special">{</span>
+              <span class="keyword">return</span> <span class="number">3.141592653589793238462643383279502884e+00</span><span class="special">;</span>
+            <span class="special">}</span>
+            <span class="keyword">static</span> <span class="keyword">inline</span>  <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_long_double</span><span class="special">&gt;&amp;)</span>
+            <span class="special">{</span>
+              <span class="keyword">return</span> <span class="number">3.141592653589793238462643383279502884e+00L</span><span class="special">;</span>
+            <span class="special">}</span>
+            <span class="comment">// For very high precision that is nonetheless can be calculated at compile time:</span>
+            <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">n</span><span class="special">)</span>
+            <span class="special">{</span>
+              <span class="identifier">constant_initializer2</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">N</span><span class="special">,</span> <span class="special">&amp;</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="keyword">template</span> <span class="identifier">compute</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">do_nothing</span><span class="special">();</span>
+              <span class="keyword">return</span> <span class="identifier">compute</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;();</span>
+            <span class="special">}</span>
+            <span class="comment">//For true arbitrary precision, which may well vary at runtime.</span>
+            <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;&amp;)</span>
+            <span class="special">{</span>
+              <span class="keyword">return</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</span> <span class="special">&gt;</span> <span class="identifier">max_string_digits</span> <span class="special">?</span> <span class="identifier">compute</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;()</span> <span class="special">:</span> <span class="identifier">get</span><span class="special">(</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_string</span><span class="special">&gt;());</span>
+            <span class="special">}</span>
+         <span class="special">};</span> <span class="comment">// template &lt;class T&gt; struct constant_pi</span>
+      <span class="special">}</span> <span class="comment">//  namespace detail</span>
+
+      <span class="comment">// The actual forwarding function (including policy to control precision).</span>
+      <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">(</span> <span class="special">)</span>
+      <span class="special">{</span>
+        <span class="keyword">return</span> <span class="identifier">detail</span><span class="special">::</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">get</span><span class="special">(</span><span class="keyword">typename</span> <span class="identifier">construction_traits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Policy</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">());</span>
+      <span class="special">}</span>
+      <span class="comment">// The actual forwarding function (using default policy to control precision).</span>
+      <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">inline</span>  <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">()</span>
+      <span class="special">{</span>
+        <span class="keyword">return</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;</span> <span class="special">&gt;()</span>
+      <span class="special">}</span>
+    <span class="special">}</span> <span class="comment">//     namespace constants</span>
+
+    <span class="comment">// Namespace specific versions, for the three built-in floats:</span>
+    <span class="keyword">namespace</span> <span class="identifier">float_constants</span>
+    <span class="special">{</span>
+      <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.141592653589793238462643383279502884e+00F</span><span class="special">;</span>
+    <span class="special">}</span>
+    <span class="keyword">namespace</span> <span class="identifier">double_constants</span>
+    <span class="special">{</span>
+      <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.141592653589793238462643383279502884e+00</span><span class="special">;</span>
+    <span class="special">}</span>
+    <span class="keyword">namespace</span> <span class="identifier">long_double_constants</span>
+    <span class="special">{</span>
+      <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.141592653589793238462643383279502884e+00L</span><span class="special">;</span>
+    <span class="special">}</span>
+    <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{;</span>
+    <span class="special">}</span> <span class="comment">// namespace constants</span>
+  <span class="special">}</span> <span class="comment">// namespace math</span>
+<span class="special">}</span> <span class="comment">// namespace boost</span>
+</pre>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
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+</div>
+<div class="section math_toolkit_constants_tutorial">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.constants.tutorial"></a><a class="link" href="tutorial.html" title="Tutorial">Tutorial</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="tutorial/non_templ.html">Use in non-template
+        code</a></span></dt>
+<dt><span class="section"><a href="tutorial/templ.html">Use in template
+        code</a></span></dt>
+<dt><span class="section"><a href="tutorial/user_def.html">Use With
+        User Defined Types</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
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+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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+</div>
+<div class="section math_toolkit_constants_tutorial_non_templ">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.constants.tutorial.non_templ"></a><a class="link" href="non_templ.html" title="Use in non-template code">Use in non-template
+        code</a>
+</h4></div></div></div>
+<p>
+          When using the math constants at your chosen fixed precision in non-template
+          code, you can simply add a <code class="computeroutput"><span class="keyword">using</span></code>
+          declaration, for example, <code class="computeroutput"><span class="keyword">using</span>
+          <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_constants</span></code>, to make the constants
+          of the correct precision for your code visible in the current scope, and
+          then use each constant <span class="emphasis"><em>as a simple variable</em></span>:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">double</span> <span class="identifier">area</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">r</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_constants</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Had our function been written as taking a <code class="computeroutput"><span class="keyword">float</span></code>
+          rather than a <code class="computeroutput"><span class="keyword">double</span></code>, we could
+          have written instead:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">float</span> <span class="identifier">area</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">r</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">float_constants</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Likewise, constants that are suitable for use at <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code> precision are available in
+          the namespace <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">long_double_constants</span></code>.
+        </p>
+<p>
+          You can see the full list of available constants at <a class="link" href="../constants.html" title="The Mathematical Constants">math_toolkit.constants.constants</a>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
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+<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="non_templ.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="user_def.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section math_toolkit_constants_tutorial_templ">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.constants.tutorial.templ"></a><a class="link" href="templ.html" title="Use in template code">Use in template
+        code</a>
+</h4></div></div></div>
+<p>
+          When using the constants inside a function template, we need to ensure
+          that we use a constant of the correct precision for our template parameters.
+          We can do this by calling the function-template versions, <code class="computeroutput"><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">FPType</span><span class="special">&gt;()</span></code>,
+          of the constants like this:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
+<span class="identifier">Real</span> <span class="identifier">area</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">r</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;()</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Although this syntax is a little less "cute" than the non-template
+          version, the code is no less efficient (at least for the built-in types
+          <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>
+          and <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>)
+          : the function template versions of the constants are simple inline functions
+          that return a constant of the correct precision for the type used. In addition,
+          these functions are declared <code class="computeroutput"><span class="identifier">constexp</span></code>
+          for those compilers that support this, allowing the result to be used in
+          constant-expressions provided the template argument is a literal type.
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../../doc/src/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            Keep in mind the difference between the variable version, just <code class="computeroutput"><span class="identifier">pi</span></code>, and the template-function version:
+            the template-function requires both a &lt;<em class="replaceable"><code>floating-point-type</code></em>&gt;
+            and function call <code class="computeroutput"><span class="special">()</span></code> brackets,
+            for example: <code class="computeroutput"><span class="identifier">pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;()</span></code>.
+            You cannot write <code class="computeroutput"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">pi</span><span class="special">&lt;&gt;()</span></code>,
+            nor <code class="computeroutput"><span class="keyword">double</span> <span class="identifier">p</span>
+            <span class="special">=</span> <span class="identifier">pi</span><span class="special">()</span></code>.
+          </p></td></tr>
+</table></div>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            You can always use <span class="bold"><strong>both</strong></span> variable and
+            template-function versions <span class="bold"><strong>provided calls are fully
+            qualified</strong></span>, for example:
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">my_pi1</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;();</span>
+<span class="keyword">double</span> <span class="identifier">my_pi2</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span>
+</pre>
+<p>
+          </p>
+</td></tr>
+</table></div>
+<div class="warning"><table border="0" summary="Warning">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../../../doc/src/images/warning.png"></td>
+<th align="left">Warning</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            It may be tempting to simply define
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_constants</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">;</span>
+</pre>
+<p>
+            but if you do define two namespaces, this will, of course, create ambiguity!
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">my_pi</span> <span class="special">=</span> <span class="identifier">pi</span><span class="special">();</span> <span class="comment">// error C2872: 'pi' : ambiguous symbol</span>
+<span class="keyword">double</span> <span class="identifier">my_pi2</span> <span class="special">=</span> <span class="identifier">pi</span><span class="special">;</span> <span class="comment">// Context does not allow for disambiguation of overloaded function</span>
+</pre>
+<p>
+            Although the mistake above is fairly obvious, it is also not too difficult
+            to do this accidentally, or worse, create it in someone elses code.
+          </p>
+<p>
+            Therefore is it prudent to avoid this risk by <span class="bold"><strong>localising
+            the scope of such definitions</strong></span>, as shown above.
+          </p>
+</td></tr>
+</table></div>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../../doc/src/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            Be very careful with the type provided as parameter. For example, providing
+            an <span class="bold"><strong>integer</strong></span> instead of a floating-point
+            type can be disastrous (a C++ feature).
+          </p>
+<p>
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Area = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">area</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Area = 12!!!</span></pre>
+<p>
+          </p>
+<p>
+            You should get a compiler warning
+          </p>
+<pre class="programlisting">warning : 'return' : conversion from 'double' to 'int', possible loss of data
+</pre>
+<p>
+            Failure to heed this warning can lead to very wrong answers!
+          </p>
+<p>
+            You can also avoid this by being explicit about the type of <code class="computeroutput"><span class="identifier">Area</span></code>.
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Area = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">area</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Area = 12.566371</span></pre>
+<p>
+          </p>
+</td></tr>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="non_templ.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="user_def.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,313 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Use With User Defined Types</title>
+<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
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+<link rel="next" href="../constants.html" title="The Mathematical Constants">
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+</div>
+<div class="section math_toolkit_constants_tutorial_user_def">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.constants.tutorial.user_def"></a><a class="link" href="user_def.html" title="Use With User Defined Types">Use With
+        User Defined Types</a>
+</h4></div></div></div>
+<p>
+          The syntax for using the function-call constants with user-defined types
+          is the same as it is in the template class, which is to say we use:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">UserDefinedType</span><span class="special">&gt;();</span>
+</pre>
+<p>
+          However, since the precision of the user-defined type may be much greater
+          than that of the built-in floating pointer types, how the value returned
+          is created is as follows:
+        </p>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+              If the precision of the type is known at compile time:
+              <div class="itemizedlist"><ul class="itemizedlist" type="circle">
+<li class="listitem">
+                    If the precision is less than or equal to that of a <code class="computeroutput"><span class="keyword">float</span></code> and the type is constructable
+                    from a <code class="computeroutput"><span class="keyword">float</span></code> then
+                    our code returns a <code class="computeroutput"><span class="keyword">float</span></code>
+                    literal. If the user-defined type is a literal type then the
+                    function call that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
+                  </li>
+<li class="listitem">
+                    If the precision is less than or equal to that of a <code class="computeroutput"><span class="keyword">double</span></code> and the type is constructable
+                    from a <code class="computeroutput"><span class="keyword">double</span></code> then
+                    our code returns a <code class="computeroutput"><span class="keyword">double</span></code>
+                    literal. If the user-defined type is a literal type then the
+                    function call that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
+                  </li>
+<li class="listitem">
+                    If the precision is less than or equal to that of a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
+                    and the type is constructable from a <code class="computeroutput"><span class="keyword">long</span>
+                    <span class="keyword">double</span></code> then our code returns
+                    a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
+                    literal. If the user-defined type is a literal type then the
+                    function call that returns the constant will be a <code class="computeroutput"><span class="identifier">constexp</span></code>.
+                  </li>
+<li class="listitem">
+                    If the precision is less than 100 decimal digits, then the constant
+                    will be constructed (just the once, then cached in a thread-safe
+                    manner) from a string representation of the constant.
+                  </li>
+<li class="listitem">
+                    Otherwise the value is computed (just once, then cached in a
+                    thread-safe manner).
+                  </li>
+</ul></div>
+            </li>
+<li class="listitem">
+              If the precision is unknown at compile time then:
+              <div class="itemizedlist"><ul class="itemizedlist" type="circle">
+<li class="listitem">
+                    If the runtime precision (obtained from a call to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</span></code>)
+                    is less than 100 decimal digits, then the constant is constructed
+                    "on the fly" from the string representation of the
+                    constant.
+                  </li>
+<li class="listitem">
+                    Otherwise the value is constructed "on the fly" by
+                    calculating then value of the constant using the current default
+                    precision of the type. Note that this can make use of the constants
+                    rather expensive.
+                  </li>
+</ul></div>
+            </li>
+</ul></div>
+<p>
+          In addition, it is possible to pass a <code class="computeroutput"><span class="identifier">Policy</span></code>
+          type as a second template argument, and use this to control the precision:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="number">80</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">my_policy_type</span><span class="special">;</span>
+<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">MyType</span><span class="special">,</span> <span class="identifier">my_policy_type</span><span class="special">&gt;();</span>
+</pre>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            Boost.Math doesn't know how to control the internal precision of <code class="computeroutput"><span class="identifier">MyType</span></code>, the policy just controls how
+            the selection process above is carried out, and the calculation precision
+            if the result is computed.
+          </p></td></tr>
+</table></div>
+<p>
+          It is also possible to control which method is used to construct the constant
+          by specialising the traits class <code class="computeroutput"><span class="identifier">construction_traits</span></code>:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constant</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">construction_traits</span>
+<span class="special">{</span>
+   <span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces</span>
+</pre>
+<p>
+          Where <span class="emphasis"><em>N</em></span> takes one of the following values:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    <span class="emphasis"><em>N</em></span>
+                  </p>
+                </th>
+<th>
+                  <p>
+                    Meaning
+                  </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    0
+                  </p>
+                </td>
+<td>
+                  <p>
+                    The precision is unavailable at compile time; either construct
+                    from a decimal digit string or calculate on the fly depending
+                    upon the runtime precision.
+                  </p>
+                </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    1
+                  </p>
+                </td>
+<td>
+                  <p>
+                    Return a float precision constant.
+                  </p>
+                </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    2
+                  </p>
+                </td>
+<td>
+                  <p>
+                    Return a double precision constant.
+                  </p>
+                </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    3
+                  </p>
+                </td>
+<td>
+                  <p>
+                    Return a long double precision constant.
+                  </p>
+                </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    4
+                  </p>
+                </td>
+<td>
+                  <p>
+                    Construct the result from the string representation, and cache
+                    the result.
+                  </p>
+                </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    Any other value <span class="emphasis"><em>N</em></span>
+                  </p>
+                </td>
+<td>
+                  <p>
+                    Sets the compile time precision to <span class="emphasis"><em>N</em></span> bits.
+                  </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<h6>
+<a name="math_toolkit.constants.tutorial.user_def.h0"></a>
+          <span><a name="math_toolkit.constants.tutorial.user_def.custom_specializing_a_constant"></a></span><a class="link" href="user_def.html#math_toolkit.constants.tutorial.user_def.custom_specializing_a_constant">Custom
+          Specializing a constant</a>
+        </h6>
+<p>
+          In addition, for user-defined types that need special handling, it's possible
+          to [partially-] specialize the internal structure used by each constant.
+          For example, suppose we're using the C++ wrapper around MPFR <code class="computeroutput"><span class="identifier">mpfr_class</span></code>: this has its own representation
+          of Pi which we may well wish to use in place of the above mechanism. We
+          can achieve this by specialising the class template <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">detail</span><span class="special">::</span><span class="identifier">constant_pi</span></code>:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span>
+
+<span class="keyword">template</span><span class="special">&lt;&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">mpfr_class</span><span class="special">&gt;</span>
+<span class="special">{</span>
+   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
+   <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;&amp;)</span>
+   <span class="special">{</span>
+      <span class="comment">// The template param N is one of the values in the table above,</span>
+      <span class="comment">// we can either handle all cases in one as is the case here,</span>
+      <span class="comment">// or overload "get" for the different options.</span>
+      <span class="identifier">mpfr_class</span> <span class="identifier">result</span><span class="special">;</span>
+      <span class="identifier">mpfr_const_pi</span><span class="special">(</span><span class="identifier">result</span><span class="special">.</span><span class="identifier">get_mpfr_t</span><span class="special">(),</span> <span class="identifier">GMP_RNDN</span><span class="special">);</span>
+      <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
+   <span class="special">}</span>
+<span class="special">};</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h6>
+<a name="math_toolkit.constants.tutorial.user_def.h1"></a>
+          <span><a name="math_toolkit.constants.tutorial.user_def.diagnosing_what_meta_programmed_code_is_doing"></a></span><a class="link" href="user_def.html#math_toolkit.constants.tutorial.user_def.diagnosing_what_meta_programmed_code_is_doing">Diagnosing
+          what meta-programmed code is doing</a>
+        </h6>
+<p>
+          Finally, since it can be tricky to diagnose what meta-programmed code is
+          doing, there is a diagnostic routine that prints information about how
+          this library will handle a specific type, it can be used like this:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">info</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">print_info_on_type</span><span class="special">&lt;</span><span class="identifier">MyType</span><span class="special">&gt;();</span>
+<span class="special">}</span>
+</pre>
+<p>
+          If you wish, you can also pass an optional std::ostream argument to the
+          <code class="computeroutput"><span class="identifier">print_info_on_type</span></code> function.
+          Typical output for a user-defined type looks like this:
+        </p>
+<pre class="programlisting">Information on the Implementation and Handling of
+Mathematical Constants for Type class boost::math::concepts::real_concept
+
+Checking for std::numeric_limits&lt;class boost::math::concepts::real_concept&gt; specialisation: no
+boost::math::policies::precision&lt;class boost::math::concepts::real_concept, Policy&gt;
+reports that there is no compile type precision available.
+boost::math::tools::digits&lt;class boost::math::concepts::real_concept&gt;()
+reports that the current runtime precision is
+53 binary digits.
+No compile time precision is available, the construction method
+will be decided at runtime and results will not be cached
+- this may lead to poor runtime performance.
+Current runtime precision indicates that
+the constant will be constructed from a string on each call.
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="templ.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../constants.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

doc/sf_and_dist/html/math_toolkit/dist.html

@@ -190,6 +190,8 @@
           Distribution</a></span></dt>
 <dt><span class="section"><a href="dist/dist_ref/dists/rayleigh.html">Rayleigh
           Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/skew_normal_dist.html">Skew
+          Normal Distribution</a></span></dt>
 <dt><span class="section"><a href="dist/dist_ref/dists/students_t_dist.html">Students
           t Distribution</a></span></dt>
 <dt><span class="section"><a href="dist/dist_ref/dists/triangular_dist.html">Triangular
@@ -208,7 +210,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html

@@ -81,6 +81,8 @@
           Distribution</a></span></dt>
 <dt><span class="section"><a href="dist_ref/dists/rayleigh.html">Rayleigh
           Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/skew_normal_dist.html">Skew
+          Normal Distribution</a></span></dt>
 <dt><span class="section"><a href="dist_ref/dists/students_t_dist.html">Students
           t Distribution</a></span></dt>
 <dt><span class="section"><a href="dist_ref/dists/triangular_dist.html">Triangular
@@ -97,7 +99,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html

@@ -129,7 +129,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html

@@ -77,6 +77,8 @@
           Distribution</a></span></dt>
 <dt><span class="section"><a href="dists/rayleigh.html">Rayleigh
           Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/skew_normal_dist.html">Skew
+          Normal Distribution</a></span></dt>
 <dt><span class="section"><a href="dists/students_t_dist.html">Students
           t Distribution</a></span></dt>
 <dt><span class="section"><a href="dists/triangular_dist.html">Triangular
@@ -90,7 +92,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html

@@ -343,7 +343,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html

@@ -612,7 +612,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html

@@ -904,7 +904,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html

@@ -294,7 +294,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html

@@ -400,7 +400,7 @@ independent, normally distributed random
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html

@@ -318,7 +318,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html

@@ -320,7 +320,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>

doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html

@@ -427,7 +427,7 @@
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
-      Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
+      Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>