diff --git a/doc/sf_and_dist/concepts.qbk b/doc/sf_and_dist/concepts.qbk index 775345154..227141afa 100644 --- a/doc/sf_and_dist/concepts.qbk +++ b/doc/sf_and_dist/concepts.qbk @@ -238,8 +238,9 @@ In addition, for efficient and accurate results, a __lanczos is highly desirable You may be able to adapt an existing approximation from [@../../../../../boost/math/special_functions/lanczos.hpp boost/math/special_functions/lanczos.hpp] or -[@../../../tools/ntl_rr_lanczos.hpp libs/math/tools/ntl_rr_lanczos.hpp]: -you will need change +[@../../../../../boost/math/bindings/detail/big_lanczos.hpp +boost/math/bindings/detail/big_lanczos.hpp]: +in the former case you will need change static_cast's to lexical_cast's, and the constants to /strings/ (in order to ensure the coefficients aren't truncated to long double) and then specialise `lanczos_traits` for type T. Otherwise you may have to hack @@ -420,3 +421,4 @@ there too.) + diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 3c32df895..715c030d8 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -53,7 +53,7 @@ Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg
Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -488,7 +488,7 @@Last revised: May 21, 2009 at 16:48:36 GMT |
+Last revised: July 23, 2009 at 12:24:16 GMT |
@@ -98,7 +98,7 @@ functions divided by large powers into single (simpler) expressions.
Table 53. Optimal choices for N and g when computing with +
Table 53. Optimal choices for N and g when computing with guard digits (source: Pugh)
@@ -250,7 +250,7 @@
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html index 6153e4bfe..22c237222 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html @@ -28,7 +28,7 @@ Algorithms
@@ -136,7 +136,7 @@ and so should have errors within an epsilon or two.
@@ -327,7 +327,7 @@
beta_distribution(RealType alpha, RealType beta); @@ -165,7 +165,7 @@ yellow in the graph above).- + Parameter Accessors
@@ -189,7 +189,7 @@ assert(mybeta.beta() == 5.); // mybeta.beta() returns 5
cdf(beta_distribution<RealType>(alpha, beta), x) == probability.
@@ -277,7 +277,7 @@ from presumed-known mean and variance. statistical inference.
@@ -315,7 +315,7 @@ from presumed-known mean and variance. please refer to these functions for information on accuracy.
@@ -597,7 +597,7 @@ from presumed-known mean and variance.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index 47fc0b1d3..bd33c1e44 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -167,12 +167,12 @@
binomial_distribution(RealType n, RealType p); @@ -189,7 +189,7 @@ otherwise calls domain_error.- + Accessors
RealType success_fraction() const; @@ -205,7 +205,7 @@ was constructed.- + Lower Bound on the Success Fraction
@@ -311,7 +311,7 @@ limits illustrated in the case of the binomial. Biometrika 26 404-413.- + Upper Bound on the Success Fraction
@@ -389,7 +389,7 @@
Table 11. Meaning of the non-member accessors
+Table 11. Meaning of the non-member accessors
@@ -635,7 +635,7 @@ examples are available illustrating the use of the binomial distribution.
@@ -645,7 +645,7 @@ please refer to these functions for information on accuracy.
@@ -160,7 +160,7 @@ have very low error rates.
@@ -276,7 +276,7 @@
@@ -204,7 +204,7 @@ independent, normally distributed random are available illustrating the use of the Chi Squared Distribution.
@@ -212,7 +212,7 @@ independent, normally distributed random gamma functions: please refer to the accuracy data for those functions.
@@ -379,7 +379,7 @@ independent, normally distributed random
@@ -122,7 +122,7 @@ should have very low error rates.
@@ -283,7 +283,7 @@
@@ -154,7 +154,7 @@ very low error rates.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html
index 8b50e3756..c63b0916e 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html
@@ -80,7 +80,7 @@
@@ -134,7 +134,7 @@ are available illustrating the use of the F Distribution.
@@ -143,7 +143,7 @@ refer to those functions for accuracy data.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html index 63f002417..8f2848270 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html @@ -137,7 +137,7 @@ than a dedicated Erlang Distribution.
@@ -194,7 +194,7 @@ refer to the accuracy data for those functions for more information.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html
index 965398713..9e205db03 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html
@@ -102,7 +102,7 @@
@@ -211,7 +211,7 @@ meaningless for N >= 1015.
@@ -223,7 +223,7 @@ this implementation and NTL::RR.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html
index f459e64c4..58e4abc97 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html
@@ -87,7 +87,7 @@
@@ -147,7 +147,7 @@ log and exp functions and as such should have very small errors.
@@ -140,7 +140,7 @@ as special cases if RealType error can be guarenteed.
@@ -613,7 +613,7 @@ please refer to these functions for information on accuracy.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html
index 894e1d5a8..3b0bdb5c2 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html
@@ -79,7 +79,7 @@
@@ -139,7 +139,7 @@ function, and as such should have very low error rates.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html
index edb9e825c..1d92ab560 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html
@@ -87,12 +87,12 @@
@@ -151,7 +151,7 @@ zero) see also why complements?.
@@ -319,7 +319,7 @@
@@ -171,7 +171,7 @@ using an iterative method with a lower tolerance to avoid excessive computation.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html
index 070f35c18..f4768dbdd 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html
@@ -86,7 +86,7 @@
@@ -151,7 +151,7 @@ using NTL RR type with 150-bit accuracy, about 50 decimal digits.
@@ -320,7 +320,7 @@
@@ -202,7 +202,7 @@ are available illustrating the use of the Student's t distribution.
@@ -211,7 +211,7 @@ inverses, refer to accuracy data on those functions for more information.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html
index 27aeb6b99..1ce8bc7d1 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html
@@ -128,7 +128,7 @@
@@ -193,7 +193,7 @@ with arguments nearing the extremes of zero and unity.
@@ -378,7 +378,7 @@ Calculate and plot probability distributions
@@ -173,7 +173,7 @@ and so should have errors within an epsilon or two.
@@ -337,7 +337,7 @@
@@ -170,7 +170,7 @@ as such should have very low error rates.
@@ -337,7 +337,7 @@
template <class RealType, class Policy> @@ -267,7 +267,7 @@- + Cumulative Hazard Function
@@ -295,7 +295,7 @@- + mean
template<class RealType, class Policy> @@ -310,7 +310,7 @@ distribution).- + median
template<class RealType, class Policy> @@ -320,7 +320,7 @@ Returns the median of the distribution dist.- + mode
template<class RealType, Policy> @@ -334,7 +334,7 @@ if the distribution does not have a defined mode.- + Probability Density Function
@@ -363,7 +363,7 @@![]()
- + range
template<class RealType, class Policy> @@ -373,7 +373,7 @@ Returns the valid range of the random variable over distribution dist.- + Quantile
template <class RealType, class Policy> @@ -402,7 +402,7 @@![]()
- + Quantile from the complement of the probability.
@@ -448,7 +448,7 @@![]()
- + Standard Deviation
@@ -463,7 +463,7 @@ if the distribution does not have a defined standard deviation.- + support
template<class RealType, class Policy> @@ -480,7 +480,7 @@ where the pdf is zero, and the cdf zero or unity.- + Variance
template <class RealType, class Policy> @@ -494,7 +494,7 @@ if the distribution does not have a defined variance.- + Skewness
template <class RealType, class Policy> @@ -508,7 +508,7 @@ if the distribution does not have a defined skewness.- + Kurtosis
template <class RealType, class Policy> @@ -550,7 +550,7 @@ 'Proper' kurtosis can have a value from zero to + infinity.- + Kurtosis excess
@@ -585,7 +585,7 @@ The kurtosis excess of a normal distribution is zero.- + P and Q
@@ -595,7 +595,7 @@ returned by these functions.
- + Percent Point Function
@@ -604,7 +604,7 @@ the Quantile.- + Inverse CDF Function.
@@ -613,7 +613,7 @@ Quantile.- + Inverse Survival Function.
@@ -621,7 +621,7 @@ The inverse of the survival function, is the same as computing the quantile from the complement of the probability.- + Probability Mass Function
@@ -635,7 +635,7 @@ applies to continuous distributions.- + Lower Critical Value.
@@ -645,7 +645,7 @@ the Quantile.- + Upper Critical Value.
@@ -656,7 +656,7 @@ complement of the probability.- + Survival Function
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/future.html b/doc/sf_and_dist/html/math_toolkit/dist/future.html index 4add68b4a..8c3ac12e7 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/future.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/future.html @@ -27,7 +27,7 @@ Extras/Future Directions- + Adding Additional Location and Scale Parameters
@@ -55,7 +55,7 @@ functions.- + An "any_distribution" class
@@ -84,7 +84,7 @@ use case: this needs more investigation.- + Higher Level Hypothesis Tests
@@ -104,7 +104,7 @@ expected_mean.- + Integration With Statistical Accumulators
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html index 43d1240e1..8b1e45d24 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html @@ -497,7 +497,7 @@ Probability of getting between 4 and 4 answers right by guessing is 0.2252- + Using Binomial distribution moments
@@ -534,7 +534,7 @@ Skewness is 0.2887- + Quantiles
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html index 5050a5f47..98cd5b7e5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html @@ -139,7 +139,7 @@ _____________________________________________ is between 0.00551 and 0.00729.
- + Confidence intervals as a function of the number of observations
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html index 84581ef29..34ea68232 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html @@ -332,7 +332,7 @@ error C3861: 'mybetad0': identifier not found- + Default arguments to distribution constructors.
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html index f2a4d59ce..5d0fe75e2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html @@ -177,7 +177,7 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999- + Controlling Error Handling from find_location
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html index 2d75d3c5d..4b1e2b701 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html @@ -62,7 +62,7 @@- + Using find_location and find_scale to meet dispensing and measurement specifications
@@ -246,7 +246,7 @@- + Using Cauchy-Lorentz instead of normal distribution
@@ -397,7 +397,7 @@- + Changing the scale or standard deviation
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html index 761bd8fc3..47c8ce54f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html @@ -179,7 +179,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999- + Controlling how Errors from find_scale are handled
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html index 656cf4105..b9a6bfb81 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html @@ -32,7 +32,7 @@ illustrates their use.- + Traditional Tables
@@ -278,7 +278,7 @@
- + Standard deviations either side of the Mean
@@ -346,12 +346,12 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
- + Some simple examples
- + Life of light bulbs
@@ -435,7 +435,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
- + How many onions?
@@ -494,7 +494,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
- + Packing beef
@@ -703,7 +703,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
- + Length of bolts
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html index 9730af29f..16775e840 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html @@ -27,7 +27,7 @@ C99 C Functions- + Supported C99 Functions
@@ -138,7 +138,7 @@ acosh(2); // integer argument is treated as a double, returns double.- + Quick Reference
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html index 19e2c8051..e3d8326cf 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html @@ -285,7 +285,7 @@
- + Usage Recomendations
- + Supported C99 Functions
@@ -440,7 +440,7 @@- + Supported TR1 Functions
@@ -579,7 +579,7 @@- + Currently Unsupported C99 Functions
@@ -650,7 +650,7 @@- + Currently Unsupported TR1 Functions
diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html index 9385ef853..e1f25b34c 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html @@ -28,7 +28,7 @@ Reference- + Supported TR1 Functions
@@ -163,7 +163,7 @@ expint(2); // integer argument is treated as a double, returns double.- + Quick Reference
// [5.2.1.1] associated Laguerre polynomials: @@ -494,7 +494,7 @@ for the full template (header only) version of this function.- + Currently Unsupported TR1 Functions
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html index 09a814f85..2acc3dc74 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html @@ -28,7 +28,7 @@ the Library and its Examples and Tests- + Building the Library
@@ -93,7 +93,7 @@ building the sources. Boost.Build will do this automatically when appropriate.- + Building the Examples
@@ -104,7 +104,7 @@ the Boost headers are in your compilers #include search path.- + Building the Tests
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html index b23656b29..442ea7ace 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html @@ -37,7 +37,7 @@
-Table 9. Supported/Tested Compilers
+Table 9. Supported/Tested Compilers
@@ -540,7 +540,7 @@
-Table 10. Unsupported Compilers
+Table 10. Unsupported Compilers
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html index 59425b920..96143f08e 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html @@ -28,7 +28,7 @@ File Structure - + boost/math
@@ -73,7 +73,7 @@- + boost/libs
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html index 352242091..8a99e9e98 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html @@ -27,7 +27,7 @@ Error Handling- + Quick Reference
@@ -132,7 +132,7 @@ the default action for each error shown in bold:-Table 1. Possible Actions for Domain Errors
+Table 1. Possible Actions for Domain Errors
@@ -207,7 +207,7 @@ -Table 2. Possible Actions for Pole Errors
+Table 2. Possible Actions for Pole Errors
@@ -282,7 +282,7 @@ -Table 3. Possible Actions for Overflow Errors
+Table 3. Possible Actions for Overflow Errors
@@ -357,7 +357,7 @@ -Table 4. Possible Actions for Underflow Errors
+Table 4. Possible Actions for Underflow Errors
@@ -432,7 +432,7 @@ -Table 5. Possible Actions for Denorm Errors
+Table 5. Possible Actions for Denorm Errors
@@ -507,7 +507,7 @@ -Table 6. Possible Actions for Rounding Errors
+Table 6. Possible Actions for Rounding Errors
@@ -582,7 +582,7 @@ -Table 7. Possible Actions for Internal Evaluation +
Table 7. Possible Actions for Internal Evaluation Errors
@@ -659,7 +659,7 @@
-Table 8. Possible Actions for Indeterminate Result +
Table 8. Possible Actions for Indeterminate Result Errors
@@ -737,7 +737,7 @@
- + Rationale
- + Finding More Information
@@ -778,7 +778,7 @@ The various kind of errors are described in more detail below.- + Domain Errors
@@ -871,7 +871,7 @@ for more details.- + Evaluation at a pole
@@ -910,7 +910,7 @@ for more details.- + Numeric Overflow
@@ -935,7 +935,7 @@ doesn't support infinities, the maximum value for the type is returned.- + Numeric Underflow
@@ -958,7 +958,7 @@ anstd::underflow_errorC++ exception.- + Denormalisation Errors
@@ -981,7 +981,7 @@ throws anstd::underflow_errorC++ exception.- + Evaluation Errors
@@ -1018,7 +1018,7 @@ for more details.- + Indeterminate Result Errors
@@ -1045,7 +1045,7 @@ the result of 00 is 1, even though the result is actually mathematically indeterminate.- + Rounding Errors
@@ -1085,7 +1085,7 @@ for more details.- + Errors from typecasts
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index aeb6b28a1..d7fa66390 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -31,7 +31,7 @@- + Boost-1.40.0
- + Boost-1.38.0
- + Boost-1.37.0
- + Boost-1.36.0
- + Boost-1.35.0: Post Review First Official Release
@@ -177,7 +177,7 @@- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -196,7 +196,7 @@- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -229,7 +229,7 @@- + Milestone 2: Released September 10th 2006
@@ -270,7 +270,7 @@- + Milestone 1: Released March 31st 2006
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html index 69a3c7528..3ae45c476 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html @@ -30,7 +30,7 @@ This library is divided into three interconnected parts:- + Statistical Distributions
@@ -56,7 +56,7 @@ tests.- + Mathematical Special Functions
@@ -83,7 +83,7 @@ double.- + Implementation Toolkit
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index d1841146c..6f9428a95 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -31,7 +31,7 @@ as handy shortcuts for common navigation tasks.- + Shortcuts
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html index d813769ad..0a15cac5f 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html @@ -286,7 +286,7 @@- + Usage Recomendations
@@ -338,7 +338,7 @@- + Supported C99 Functions
@@ -442,7 +442,7 @@- + Supported TR1 Functions
@@ -581,7 +581,7 @@- + Currently Unsupported C99 Functions
@@ -652,7 +652,7 @@- + Currently Unsupported TR1 Functions
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html index 317ebc2ac..ffb51e580 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html @@ -35,7 +35,7 @@ in this respect).-Table 48. Performance Comparison of Various Windows Compilers
+Table 48. Performance Comparison of Various Windows Compilers
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html index 56ccae198..7d772f1be 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html @@ -46,7 +46,7 @@ - + Comparison to GSL-1.9 and Cephes
@@ -213,7 +213,7 @@@@ -284,13 +284,13 @@ - - + Comparison to the R Statistical Library on Windows
@@ -301,7 +301,7 @@ (R-2.8.1 appears not to be buildable with Visual C++).-Table 51. A Comparison to the R Statistical Library on Windows +
Table 51. A Comparison to the R Statistical Library on Windows XP
@@ -374,7 +374,7 @@
(3.347e-004s)
@@ -705,7 +705,7 @@
(2.583e-007s)
@@ -898,7 +898,7 @@
(3.704e-004s)
@@ -952,7 +952,7 @@
(2.671e-002s)
@@ -1058,7 +1058,7 @@
(4.432e-004s)
@@ -1276,28 +1276,28 @@- [1] +
-[1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.
[2] +
-[2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.
[3] +
-[3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases
- + Comparison to the R Statistical Library on Linux
@@ -1316,7 +1316,7 @@ GNU G++ 4.3.2 using -O3.-Table 52. A Comparison to the R Statistical Library on Linux
+Table 52. A Comparison to the R Statistical Library on Linux
@@ -1387,7 +1387,7 @@
(3.455e-004s)
@@ -1718,7 +1718,7 @@
(3.308e-007s)
@@ -1911,7 +1911,7 @@
(4.029e-004s)
@@ -1965,7 +1965,7 @@
(3.179e-002s)
@@ -2071,7 +2071,7 @@
(5.176e-004s)
@@ -2289,28 +2289,28 @@- [1] +
-[1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.
[2] +
-[2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.
[3] +
-[3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases
[4] +
-[4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.
[5] +
[5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html index 347aa4de8..ab6aaaf6e 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html @@ -33,7 +33,7 @@ penalty for using the library in debug mode can be quite large.
-Table 47. Performance Comparison of Release and Debug Settings
+Table 47. Performance Comparison of Release and Debug Settings
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html index f82cd993e..58f962761 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html @@ -234,7 +234,7 @@ highly vectorisable processors in the future. -Table 49. A Comparison of Polynomial Evaluation Methods
+Table 49. A Comparison of Polynomial Evaluation Methods
@@ -634,7 +634,7 @@ tutorial. -Table 50. Performance Comparison with and Without Internal +
Table 50. Performance Comparison with and Without Internal Promotion to long double
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html index 9f58b5cf2..ab840bf88 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html @@ -55,7 +55,7 @@ can take have the following meanings:
- + real
@@ -93,7 +93,7 @@ = 68.1584.
- + integer_round_outwards
@@ -151,7 +151,7 @@ in each tail.
- + integer_round_inwards
@@ -214,7 +214,7 @@ in each tail.
- + integer_round_down
@@ -222,7 +222,7 @@ or a lower quantile.
- + integer_round_up
@@ -230,7 +230,7 @@ a lower quantile.
- + integer_round_nearest
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html index 36ce1132d..f93f5031b 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html @@ -39,7 +39,7 @@
- + Available Actions When an Error is Raised
@@ -62,7 +62,7 @@ The various enumerated values have the following meanings:- + throw_on_error
@@ -174,7 +174,7 @@
- + errno_on_error
@@ -287,7 +287,7 @@
- + ignore_error
@@ -400,7 +400,7 @@
- + user_error
@@ -449,7 +449,7 @@ here.
- + Kinds of Error Raised
@@ -688,7 +688,7 @@- + Examples
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html index 8dc080952..e47829829 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html @@ -84,7 +84,7 @@
- + Examples
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html index a250e2a6e..e97ac63d8 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html @@ -61,7 +61,7 @@ then you can do so by defining various macros in boost/math/tools/user.hpp.
- + BOOST_MATH_DOMAIN_ERROR_POLICY
@@ -71,7 +71,7 @@
ignore_errororuser_error.- + BOOST_MATH_POLE_ERROR_POLICY
@@ -81,7 +81,7 @@
ignore_errororuser_error.- + BOOST_MATH_OVERFLOW_ERROR_POLICY
@@ -91,7 +91,7 @@
ignore_errororuser_error.- + BOOST_MATH_ROUNDING_ERROR_POLICY
@@ -101,7 +101,7 @@
ignore_errororuser_error.- + BOOST_MATH_EVALUATION_ERROR_POLICY
@@ -111,7 +111,7 @@
ignore_errororuser_error.- + BOOST_MATH_UNDERFLOW_ERROR_POLICY
@@ -121,7 +121,7 @@
ignore_errororuser_error.- + BOOST_MATH_DENORM_ERROR_POLICY
@@ -131,7 +131,7 @@
ignore_errororuser_error.- + BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY
@@ -142,7 +142,7 @@
ignore_errororuser_error.- + BOOST_MATH_DIGITS10_POLICY
@@ -153,7 +153,7 @@ recommended that you change this from the default.
- + BOOST_MATH_PROMOTE_FLOAT_POLICY
@@ -165,7 +165,7 @@ off.
- + BOOST_MATH_PROMOTE_DOUBLE_POLICY
@@ -177,7 +177,7 @@ off.
- + BOOST_MATH_DISCRETE_QUANTILE_POLICY
@@ -188,7 +188,7 @@ Defaults to
integer_round_outwards.- + BOOST_MATH_ASSERT_UNDEFINED_POLICY
@@ -201,7 +201,7 @@ whether or not a particular property is well defined.
- + BOOST_MATH_MAX_SERIES_ITERATION_POLICY
@@ -210,7 +210,7 @@ Defaults to 1000000.
- + BOOST_MATH_MAX_ROOT_ITERATION_POLICY
@@ -219,7 +219,7 @@ Defaults to 200.
- + Example
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html index 591179444..7fa115b9f 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html @@ -177,7 +177,7 @@ base your comparisons on CDF's instead.
- + Other Rounding Policies are Available
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html index dd4ad5258..87853772b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html @@ -28,7 +28,7 @@ of the First and Second Kinds- + Synopsis
template <class T1, class T2> @@ -44,7 +44,7 @@ calculated-result-type cyl_neumann(T1 v, T2 x, const Policy&);- + Description
@@ -110,7 +110,7 @@
![]()
- + Testing
@@ -119,7 +119,7 @@ (with all the special case handling removed).
- + Accuracy
@@ -135,7 +135,7 @@ zero error. All values are relative errors in units of epsilon.
-Table 37. Errors Rates in cyl_neumann
+Table 37. Errors Rates in cyl_neumann
@@ -494,7 +494,7 @@ were found. - + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html index 6622030c7..30522ee24 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html @@ -28,7 +28,7 @@ Overview
- + Ordinary Bessel Functions
@@ -103,7 +103,7 @@ and is known as either a Bessel![]()
- + Modified Bessel Functions
@@ -167,7 +167,7 @@ respectively:![]()
- + Spherical Bessel Functions
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html index f54071b55..8feaeb7f2 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html @@ -28,7 +28,7 @@ Functions of the First and Second Kinds- + Synopsis
template <class T1, class T2> @@ -44,7 +44,7 @@ calculated-result-type cyl_bessel_k(T1 v, T2 x, const Policy&);- + Description
@@ -109,7 +109,7 @@
![]()
- + Testing
@@ -118,7 +118,7 @@ (with all the special case handling removed).
- + Accuracy
@@ -129,7 +129,7 @@ zero error. All values are relative errors in units of epsilon.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html index bbd010a4e..36d15d07c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html @@ -28,7 +28,7 @@ Bessel Functions of the First and Second Kinds
- + Synopsis
template <class T1, class T2> @@ -44,7 +44,7 @@ calculated-result-type sph_neumann(unsigned v, T2 x, const Policy&);- + Description
@@ -97,7 +97,7 @@ for small x:
![]()
- + Testing
@@ -106,7 +106,7 @@ for small x: implementation (with all the special case handling removed).
- + Accuracy
@@ -116,7 +116,7 @@ for small x: refer to these functions for accuracy data.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html index cf68e3224..71e1f81ad 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html @@ -28,7 +28,7 @@ of the First Kind - Legendre Form
- + Synopsis
@@ -55,7 +55,7 @@ }} // namespaces
- + Description
@@ -123,7 +123,7 @@
- + Accuracy
@@ -134,7 +134,7 @@ All values are relative errors in units of epsilon.
-Table 41. Errors Rates in the Elliptic Integrals of the +
Table 41. Errors Rates in the Elliptic Integrals of the First Kind
@@ -237,7 +237,7 @@
- + Testing
@@ -247,7 +247,7 @@ this implementation.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html index cbab8e3dd..bfccb7685 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html @@ -28,7 +28,7 @@ of the Second Kind - Legendre Form
- + Synopsis
@@ -55,7 +55,7 @@ }} // namespaces
- + Description
@@ -123,7 +123,7 @@
- + Accuracy
@@ -134,7 +134,7 @@ All values are relative errors in units of epsilon.
-Table 42. Errors Rates in the Elliptic Integrals of the +
Table 42. Errors Rates in the Elliptic Integrals of the Second Kind
@@ -237,7 +237,7 @@
- + Testing
@@ -247,7 +247,7 @@ this implementation.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html index 031c267c5..e5f340428 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html @@ -28,7 +28,7 @@ of the Third Kind - Legendre Form
- + Synopsis
@@ -55,7 +55,7 @@ }} // namespaces
- + Description
@@ -129,7 +129,7 @@
- + Accuracy
@@ -140,7 +140,7 @@ All values are relative errors in units of epsilon.
-Table 43. Errors Rates in the Elliptic Integrals of the +
Table 43. Errors Rates in the Elliptic Integrals of the Third Kind
@@ -243,7 +243,7 @@
- + Testing
@@ -253,7 +253,7 @@ this implementation.
- + Implementation
@@ -291,7 +291,7 @@
Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 - [1] + [1]
are used to move φ to the range [0, π/2]. @@ -311,7 +311,7 @@
-[1] +
[1] I haven't been able to find a literature reference for this relation, but it appears to be the convention used by Mathematica. Intuitively the first 2 * m * Π(n, k) terms cancel out as the diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html index 457782c23..a12b55383 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html @@ -28,7 +28,7 @@ Integrals - Carlson Form
- + Synopsis
@@ -100,7 +100,7 @@ }} // namespaces
- + Description
@@ -236,7 +236,7 @@
![]()
- + Testing
@@ -265,7 +265,7 @@ to verify their correctness: see the above Carlson paper for details.
- + Accuracy
@@ -276,7 +276,7 @@ All values are relative errors in units of epsilon.
-Table 40. Errors Rates in the Carlson Elliptic Integrals
+Table 40. Errors Rates in the Carlson Elliptic Integrals
@@ -419,7 +419,7 @@ - + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html index db615911b..7f7b6c8da 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html @@ -61,14 +61,14 @@ Elliptic integral.
- + Notation
All variables are real numbers unless otherwise noted.
- + Definition
@@ -257,7 +257,7 @@
- + Duplication Theorem
@@ -269,7 +269,7 @@![]()
- + Carlson's Formulas
@@ -287,7 +287,7 @@![]()
- + Numerical Algorithms
@@ -301,7 +301,7 @@ integrals with satisfactory precisions.- + References
diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 6cf049841..2fea71827 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -28,7 +28,7 @@ Integral Ei
- + Synopsis
@@ -63,7 +63,7 @@
- + Description
template <class T> @@ -83,7 +83,7 @@![]()
- + Accuracy
@@ -95,7 +95,7 @@ error.
-Table 46. Errors In the Function expint(z)
+Table 46. Errors In the Function expint(z)
@@ -207,7 +207,7 @@ slightly over the range [4,6]. - + Testing
@@ -222,7 +222,7 @@ check.
- + Implementation
@@ -253,7 +253,7 @@ [-1,1]. Note that while the rational approximation over [0,6] converges rapidly to the minimax solution it is rather ill-conditioned in practice. Cody and Thacher - [2] + [2] experienced the same issue and converted the polynomials into Chebeshev form to ensure stable computation. By experiment we found that the polynomials are just as stable in polynomial as Chebyshev form, provided @@ -284,7 +284,7 @@
-[2] +
[2] W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649, and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html index a6305c5d7..32077bf69 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html @@ -28,7 +28,7 @@ Integral En
- + Synopsis
@@ -63,7 +63,7 @@
- + Description
template <class T> @@ -83,7 +83,7 @@![]()
- + Accuracy
@@ -94,7 +94,7 @@ the one shown will have effectively zero error.
-Table 45. Errors In the Function expint(n, z)
+Table 45. Errors In the Function expint(n, z)
@@ -225,7 +225,7 @@ - + Testing
@@ -240,7 +240,7 @@ check.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html index bc4e333f5..b3978d095 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html @@ -65,7 +65,7 @@ if the result is too large to represent in type T.
- + Accuracy
@@ -74,14 +74,14 @@ function for larger arguments.
- + Testing
The spot tests for the binomial coefficients use data generated by functions.wolfram.com.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html index 900e491fe..e9b5a00d7 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html @@ -64,7 +64,7 @@ of i! is possible.
- + Accuracy
@@ -72,14 +72,14 @@ so error rates should be no more than a couple of epsilon higher.
- + Testing
The spot tests for the double factorial use data generated by functions.wolfram.com.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html index 7b33c18b3..c8bb12226 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html @@ -27,7 +27,7 @@ Factorial
- + Synopsis
@@ -54,7 +54,7 @@ }} // namespaces
- + Description
template <class T> @@ -112,7 +112,7 @@ the size of further tables that depend on the factorials.- + Accuracy
@@ -121,7 +121,7 @@ will be the same as for tgamma.
- + Testing
@@ -130,7 +130,7 @@ function handle those cases already.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html index 2f56d975b..817cadc97 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html @@ -76,7 +76,7 @@ the type of the result is T.
- + Accuracy
@@ -84,14 +84,14 @@ function.
- + Testing
The spot tests for the falling factorials use data generated by functions.wolfram.com.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html index 51c475df8..0e483412d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html @@ -80,7 +80,7 @@ the type of the result is T.
- + Accuracy
@@ -88,14 +88,14 @@ function.
- + Testing
The spot tests for the rising factorials use data generated by functions.wolfram.com.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html index 1ff752499..447ec719a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html @@ -67,14 +67,14 @@
![]()
- + Accuracy
Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
- + Testing
@@ -90,7 +90,7 @@ to at least 50 decimal digits.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html index 8a2966918..12afba680 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html @@ -62,14 +62,14 @@
- + Accuracy
Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
- + Testing
@@ -85,7 +85,7 @@ to at least 50 decimal digits.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html index faf56f95c..e25acad0e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html @@ -76,14 +76,14 @@ denoting
![]()
- + Accuracy
Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
- + Testing
@@ -99,7 +99,7 @@ denoting to at least 50 decimal digits.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html index 5def3a00e..5ea45631c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html @@ -71,7 +71,7 @@
![]()
- + Accuracy
@@ -79,7 +79,7 @@ should have approximately 2 epsilon accuracy.
- + Testing
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html index 2601cca3c..5f415e817 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html @@ -32,7 +32,7 @@ computes the compile-time integral power of a run-time base.
- + Synopsis
@@ -49,7 +49,7 @@ }}
- + Rationale and Usage
@@ -91,7 +91,7 @@ Only 3 different products were actually computed.- + Return Type
- + Policies
@@ -126,7 +126,7 @@
- + Error Handling
@@ -231,7 +231,7 @@ double result = pow<-5>(base);- + Acknowledgements
@@ -242,7 +242,7 @@ improving the implementation.
- + References
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html index 328186bde..4ac35c660 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html @@ -80,7 +80,7 @@
![]()
- + Accuracy
@@ -88,7 +88,7 @@ should have approximately 1 epsilon accuracy.
- + Testing
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html index 59c6a7494..b922d73bd 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html @@ -58,7 +58,7 @@ in such a representable.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html index 298e1f0be..1ef376c70 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html @@ -93,7 +93,7 @@
![]()
- + Accuracy
@@ -101,7 +101,7 @@ should have approximately 1 epsilon accuracy.
- + Testing
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html index 2b39cbe5a..5c7eca575 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html @@ -74,14 +74,14 @@
![]()
- + Accuracy
Should have approximately 2-3 epsilon accuracy.
- + Testing
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html index 46520a3c7..192abe710 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html @@ -76,7 +76,7 @@
![]()
- + Accuracy
@@ -84,7 +84,7 @@ should have approximately 3 epsilon accuracy.
- + Testing
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html index 0558a85fc..edeb135d7 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html @@ -28,7 +28,7 @@ of the Incomplete Beta Function
- + Synopsis
@@ -49,7 +49,7 @@ }} // namespaces
- + Description
@@ -76,14 +76,14 @@
- + Accuracy
Almost identical to the incomplete beta function ibeta.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html index e4d8909e2..dad1c4436 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html @@ -27,7 +27,7 @@ Beta
- + Synopsis
@@ -48,7 +48,7 @@ }} // namespaces
- + Description
@@ -86,7 +86,7 @@ type calculation rules when T1 and T2 are different types.
- + Accuracy
@@ -98,7 +98,7 @@ zero error.
-Table 22. Peak Errors In the Beta Function
+Table 22. Peak Errors In the Beta Function
@@ -244,7 +244,7 @@ very small. - + Testing
@@ -253,7 +253,7 @@ at 1000-bit precision.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html index b770f36a1..11f9356b4 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html @@ -28,7 +28,7 @@ Beta Functions
- + Synopsis
@@ -67,7 +67,7 @@ }} // namespaces
- + Description
@@ -153,7 +153,7 @@
![]()
- + Accuracy
@@ -172,7 +172,7 @@ with the wider exponent range of the long double types.
-Table 23. Errors In the Function ibeta(a,b,x)
+Table 23. Errors In the Function ibeta(a,b,x)
@@ -359,7 +359,7 @@ -Table 24. Errors In the Function ibetac(a,b,x)
+Table 24. Errors In the Function ibetac(a,b,x)
@@ -526,7 +526,7 @@ -Table 25. Errors In the Function beta(a, b, x)
+Table 25. Errors In the Function beta(a, b, x)
@@ -693,7 +693,7 @@ -Table 26. Errors In the Function betac(a,b,x)
+Table 26. Errors In the Function betac(a,b,x)
@@ -860,7 +860,7 @@ - + Testing
@@ -878,7 +878,7 @@ have test data that is fully independent of the code.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html index 7b748d9cd..0857d246a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html @@ -87,7 +87,7 @@ }} // namespaces
- + Description
@@ -323,7 +323,7 @@
- + Accuracy
@@ -335,7 +335,7 @@ or
1.- + Testing
- + Implementation of ibeta_inv and ibetac_inv
@@ -527,7 +527,7 @@ rapidly converges on the true value.- + Implementation of inverses on the a and b parameters
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html index be06a03b4..bb43fcd2a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html @@ -28,7 +28,7 @@ Functions- + Synopsis
@@ -69,7 +69,7 @@
- + Description
template <class T> @@ -106,7 +106,7 @@![]()
- + Accuracy
@@ -119,7 +119,7 @@ the one shown will have effectively zero error.
-Table 27. Errors In the Function erf(z)
+Table 27. Errors In the Function erf(z)
@@ -325,7 +325,7 @@ -Table 28. Errors In the Function erfc(z)
+Table 28. Errors In the Function erfc(z)
@@ -531,7 +531,7 @@ - + Testing
@@ -546,7 +546,7 @@ check.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html index 8d60e8ef4..f1b1d2e0a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html @@ -28,7 +28,7 @@ Inverses
- + Synopsis
@@ -69,7 +69,7 @@
- + Description
template <class T> @@ -103,7 +103,7 @@![]()
- + Accuracy
@@ -113,7 +113,7 @@ error functions.
- + Testing
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html index 3c4b3c6fc..d7b9ac491 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html @@ -27,7 +27,7 @@ Digamma
- + Synopsis
@@ -48,7 +48,7 @@ }} // namespaces
- + Description
@@ -82,7 +82,7 @@ T otherwise.
- + Accuracy
@@ -270,7 +270,7 @@ absolute error will remain very low.
- + Testing
@@ -280,7 +280,7 @@ see below).
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html index a7ba1302a..f2e43ecdb 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html @@ -28,7 +28,7 @@ of the Incomplete Gamma Function
- + Synopsis
@@ -49,7 +49,7 @@ }} // namespaces
- + Description
@@ -80,7 +80,7 @@ otherwise the return type is simply T1.
- + Accuracy
@@ -88,7 +88,7 @@ refer to the documentation for that function for more information.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html index f3beab88e..f97fa8813 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html @@ -51,7 +51,7 @@ }} // namespaces
- + Description
template <class T1, class T2> @@ -117,7 +117,7 @@![]()
- + Accuracy
@@ -127,7 +127,7 @@ effectively zero error.
-Table 16. Errors In the Function tgamma_delta_ratio(a, delta)
+Table 16. Errors In the Function tgamma_delta_ratio(a, delta)
@@ -230,7 +230,7 @@ -Table 17. Errors In the Function tgamma_ratio(a, +
Table 17. Errors In the Function tgamma_ratio(a, b)
@@ -329,7 +329,7 @@
- + Testing
@@ -338,7 +338,7 @@ a deliberately naive calculation of Γ(x)/Γ(y).
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html index de0fda5db..914cac89a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html @@ -28,7 +28,7 @@ Functions
- + Synopsis
@@ -67,7 +67,7 @@ }} // namespaces
- + Description
@@ -160,7 +160,7 @@
![]()
- + Accuracy
@@ -185,7 +185,7 @@ All values are in units of epsilon.
-Table 18. Errors In the Function gamma_p(a,z)
+Table 18. Errors In the Function gamma_p(a,z)
@@ -372,7 +372,7 @@ -Table 19. Errors In the Function gamma_q(a,z)
+Table 19. Errors In the Function gamma_q(a,z)
@@ -558,7 +558,7 @@ -Table 20. Errors In the Function tgamma_lower(a,z)
+Table 20. Errors In the Function tgamma_lower(a,z)
@@ -693,7 +693,7 @@ -Table 21. Errors In the Function tgamma(a,z)
+Table 21. Errors In the Function tgamma(a,z)
@@ -828,7 +828,7 @@ - + Testing
@@ -844,7 +844,7 @@ fraction (see below) is unstable for small a and z.
- + Implementation
@@ -1013,7 +1013,7 @@ by Temme (see references below).
- + References
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html index e452f696d..fb2081b09 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html @@ -28,7 +28,7 @@ Gamma Function Inverses
- + Synopsis
@@ -67,7 +67,7 @@ }} // namespaces
- + Description
@@ -173,7 +173,7 @@ 0.
- + Accuracy
@@ -187,7 +187,7 @@ functions.
- + Testing
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html index b49685890..8ffce1fab 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html @@ -27,7 +27,7 @@ Log Gamma
- + Synopsis
@@ -54,7 +54,7 @@ }} // namespaces
- + Description
@@ -98,7 +98,7 @@ T otherwise.
- + Accuracy
@@ -349,7 +349,7 @@
- + Testing
@@ -360,7 +360,7 @@ Random tests in key problem areas are also used.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html index 462a29b65..ccd9245e3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html @@ -27,7 +27,7 @@ Gamma
- + Synopsis
@@ -54,7 +54,7 @@ }} // namespaces
- + Description
template <class T> @@ -129,7 +129,7 @@
- + Accuracy
@@ -384,7 +384,7 @@
- + Testing
@@ -399,7 +399,7 @@ a lanczos approximation accurate to around 100 decimal digits.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html index 7370dc406..938c45539 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html @@ -27,7 +27,7 @@ Hermite Polynomials
- + Synopsis
@@ -51,7 +51,7 @@ }} // namespaces
- + Description
- + Accuracy
@@ -146,7 +146,7 @@ zero error.
-Table 34. Peak Errors In the Hermite Polynomial
+Table 34. Peak Errors In the Hermite Polynomial
@@ -253,7 +253,7 @@ is very close to a root. - + Testing
@@ -263,7 +263,7 @@ precision.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html index f84df71de..6c912b656 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html @@ -28,7 +28,7 @@ Associated) Polynomials
- + Synopsis
@@ -62,7 +62,7 @@ }} // namespaces
- + Description
- + Accuracy
@@ -220,7 +220,7 @@ zero error.
-Table 32. Peak Errors In the Laguerre Polynomial
+Table 32. Peak Errors In the Laguerre Polynomial
@@ -320,7 +320,7 @@ -Table 33. Peak Errors In the Associated Laguerre +
Table 33. Peak Errors In the Associated Laguerre Polynomial
@@ -429,7 +429,7 @@ is very close to a root.
- + Testing
@@ -439,7 +439,7 @@ precision.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html index 918fac92d..808d1e896 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html @@ -28,7 +28,7 @@ Associated) Polynomials
- + Synopsis
@@ -84,7 +84,7 @@
- + Description
template <class T> @@ -292,7 +292,7 @@- + Accuracy
@@ -302,7 +302,7 @@ zero error.
-Table 29. Peak Errors In the Legendre P Function
+Table 29. Peak Errors In the Legendre P Function
@@ -431,7 +431,7 @@ -Table 30. Peak Errors In the Associated Legendre +
Table 30. Peak Errors In the Associated Legendre P Function
@@ -533,7 +533,7 @@
-Table 31. Peak Errors In the Legendre Q Function
+Table 31. Peak Errors In the Legendre Q Function
@@ -675,7 +675,7 @@ given here. - + Testing
@@ -685,7 +685,7 @@ precision.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html index 7663202c6..bb003b886 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html @@ -27,7 +27,7 @@ Spherical Harmonics
- + Synopsis
@@ -60,7 +60,7 @@ }} // namespaces
- + Description
@@ -155,7 +155,7 @@
![]()
- + Accuracy
@@ -170,7 +170,7 @@ All values are in units of epsilon.
-Table 35. Peak Errors In the Sperical Harmonic Functions
+Table 35. Peak Errors In the Sperical Harmonic Functions
@@ -276,7 +276,7 @@ arbitrarily large when the function is very close to a root. - + Testing
@@ -286,7 +286,7 @@ precision.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index a1af950f8..58ba1d936 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -27,7 +27,7 @@ Riemann Zeta Function
- + Synopsis
@@ -62,7 +62,7 @@
- + Description
template <class T> @@ -85,7 +85,7 @@![]()
- + Accuracy
@@ -97,7 +97,7 @@ shown will have effectively zero error.
-Table 44. Errors In the Function zeta(z)
+Table 44. Errors In the Function zeta(z)
@@ -234,7 +234,7 @@ - + Testing
@@ -249,7 +249,7 @@ check.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/status/compilers.html b/doc/sf_and_dist/html/math_toolkit/status/compilers.html index 1779c123e..ae2bab119 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/compilers.html +++ b/doc/sf_and_dist/html/math_toolkit/status/compilers.html @@ -37,7 +37,7 @@
-Table 55. Supported/Tested Compilers
+Table 55. Supported/Tested Compilers
@@ -540,7 +540,7 @@
-Table 56. Unsupported Compilers
+Table 56. Unsupported Compilers
diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index b8a55bccd..c6f62607a 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -30,7 +30,7 @@ - + Boost-1.40.0
- + Boost-1.38.0
- + Boost-1.37.0
- + Boost-1.36.0
- + Boost-1.35.0: Post Review First Official Release
@@ -176,7 +176,7 @@- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -195,7 +195,7 @@- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -228,7 +228,7 @@- + Milestone 2: Released September 10th 2006
@@ -269,7 +269,7 @@- + Milestone 1: Released March 31st 2006
diff --git a/doc/sf_and_dist/html/math_toolkit/status/issues.html b/doc/sf_and_dist/html/math_toolkit/status/issues.html index fd96c056a..07137ab59 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/issues.html +++ b/doc/sf_and_dist/html/math_toolkit/status/issues.html @@ -43,7 +43,7 @@ with it.- + tgamma
- @@ -51,7 +51,7 @@ be optimized any further? (low priority)
- + Incomplete Beta
- @@ -59,7 +59,7 @@ (medium priority).
- + Inverse Gamma
- @@ -67,7 +67,7 @@ is good enough (Medium Priority).
- + Polynomials
- @@ -77,7 +77,7 @@ not (Low Priority).
- + Elliptic Integrals
@@ -127,7 +127,7 @@
- + Inverse Hyperbolic Functions
@@ -137,7 +137,7 @@ is probably only an issue for very high precision types (Low Priority).- + Statistical distributions
@@ -146,7 +146,7 @@ for very large degrees of freedom?- + Feature Requests
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html index ad254c32e..ace5207c3 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html @@ -28,7 +28,7 @@ Evaluation
- + Synopsis
@@ -59,7 +59,7 @@ }}} // namespaces
- + Description
@@ -157,7 +157,7 @@ a continued fraction for convergence.
- + Implementation
@@ -167,7 +167,7 @@ Lentz, W.J. 1976, Applied Optics, vol. 15, pp. 668-671.
- + Examples
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html index 69108fc0d..e3c33e14b 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html @@ -28,7 +28,7 @@ Constants
- + Synopsis
@@ -59,7 +59,7 @@ }}} // namespaces
- + Description
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html index 4945a4543..3405e6a02 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html @@ -28,7 +28,7 @@ Minima
- + synopsis
@@ -45,7 +45,7 @@ std::pair<T, T> brent_find_minima(F f, T min, T max, int bits, boost::uintmax_t& max_iter);
- + Description
@@ -88,7 +88,7 @@ the abscissa at the minima and the value of f(x) at the minima.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html index c5cfe65dd..82dcec72b 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html @@ -28,7 +28,7 @@ and Rational Function Evaluation
- + synopsis
@@ -79,7 +79,7 @@ V evaluate_rational(const T* num, const U* denom, V z, unsigned count);
- + Description
@@ -193,7 +193,7 @@ evaluation with compile-time array sizes may offer slightly better performance.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html index 2d5e77cf4..f3dea3e33 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html @@ -28,7 +28,7 @@ With Derivatives
- + Synopsis
@@ -61,7 +61,7 @@ }}} // namespaces
- + Description
- + Newton Raphson Method
@@ -196,7 +196,7 @@
- + Halley's Method
@@ -220,7 +220,7 @@
- + Schroeder's Method
@@ -244,7 +244,7 @@ iteration.- + Example
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html index ffdbfb77f..0ea6456e2 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html @@ -28,7 +28,7 @@ Without Derivatives
- + Synopsis
@@ -141,7 +141,7 @@ }}} // namespaces
- + Description
@@ -559,7 +559,7 @@ as soon as both ends of the interval round to the same nearest integer.
- + Implementation
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html index 35b41126a..793077ab3 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html @@ -28,7 +28,7 @@ Series Evaluation
- + Synopsis
@@ -61,7 +61,7 @@ }}} // namespaces
- + Description
@@ -117,7 +117,7 @@ summation in this way.
- + Example
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html index 61b30759e..bf3075624 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html @@ -28,7 +28,7 @@ Error and Testing
- + Synopsis
@@ -45,7 +45,7 @@ test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);
- + Description
template <class T> @@ -165,7 +165,7 @@ is mainly a debugging/development aid (and a good place for a breakpoint).- + Example
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html index 5258ac73b..263ddd965 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html @@ -27,7 +27,7 @@ Polynomials
- + Synopsis
@@ -103,7 +103,7 @@ }}} // namespaces
- + Description
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html index 5444e34f5..89df81caa 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html @@ -46,7 +46,7 @@
- + Synopsis
namespace boost{ namespace math{ namespace tools{ @@ -147,7 +147,7 @@ }}} // namespaces- + Description
- + Example 1: Output Data for Graph Plotting
@@ -211,7 +211,7 @@![]()
- + Example 2: Creating Test Data
@@ -375,7 +375,7 @@ used by default as it's rather hard on the compiler when the table is large.- + Example 3: Profiling a Continued Fraction for Convergence and Accuracy
@@ -481,7 +481,7 @@ of a and z.- + reference
diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html index 97568e753..3bfee7dbf 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html @@ -42,7 +42,7 @@ behaves just like a built in floating point type.
- + Basic Arithmetic Requirements
@@ -1034,7 +1034,7 @@- + Standard Library Support Requirements
@@ -1337,11 +1337,11 @@ In addition, for efficient and accurate results, a Lanczos approximation is highly desirable. You may be able to adapt an existing approximation from boost/math/special_functions/lanczos.hpp - or libs/math/tools/ntl_rr_lanczos.hpp: - you will need change static_cast's to lexical_cast's, and the constants to - strings (in order to ensure the coefficients aren't - truncated to long double) and then specialiselanczos_traits- for type T. Otherwise you may have to hack libs/math/tools/lanczos_generator.cpp + or boost/math/bindings/detail/big_lanczos.hpp: + in the former case you will need change static_cast's to lexical_cast's, + and the constants to strings (in order to ensure the + coefficients aren't truncated to long double) and then specialiselanczos_traitsfor type T. Otherwise you + may have to hack libs/math/tools/lanczos_generator.cpp to find a suitable approximation for your RealType. The code will still compile if you don't do this, but both accuracy and efficiency will be greatly compromised in any function that makes use of the gamma/beta/erf family of functions. diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html index 9d157dd0f..fd93c4054 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html @@ -28,7 +28,7 @@ Infinities and NaN's- + Synopsis
#define FP_ZERO /* implementation specific value */ @@ -58,7 +58,7 @@ to use these functions.- + Description
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html index 6c7ed0f10..3dd5b83fc 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html @@ -32,7 +32,7 @@ number of ULP.
- + Synopsis
@@ -50,7 +50,7 @@ }} // namespaces
- + Description - float_advance
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html index e24159e58..52e4fada7 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html @@ -34,7 +34,7 @@ different.- + Synopsis
@@ -52,7 +52,7 @@ }} // namespaces
- + Description - float_distance
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html index 940a751fe..213cc3596 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html @@ -28,7 +28,7 @@ the Next Greater Representable Value (float_next)- + Synopsis
@@ -46,7 +46,7 @@ }} // namespaces
- + Description - float_next
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html index ccbc5d86b..f67cabbb3 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html @@ -28,7 +28,7 @@ the Next Smaller Representable Value (float_prior)- + Synopsis
@@ -46,7 +46,7 @@ }} // namespaces
- + Description - float_prior
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html index 03c59b775..a8300a16c 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html @@ -28,7 +28,7 @@ Next Representable Value in a Specific Direction (nextafter)- + Synopsis
@@ -46,7 +46,7 @@ }} // namespaces
- + Description - nextafter
@@ -76,7 +76,7 @@ returns an overflow_error.- + Examples - nextafter
diff --git a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html index 2b6ca25af..301d01a60 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html @@ -28,7 +28,7 @@ Functions- + Synopsis
@@ -52,7 +52,7 @@ }} // namespaces
- + Description
template<class T>