diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index a24c40497..a6ed3bda2 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: October 14, 2009 at 14:20:47 GMT |
+Last revised: October 16, 2009 at 09:52:32 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 2101a1c26..a73e38e18 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 763f27ba3..fcfe415d1 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 10e5d2f93..cff30a376 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 00f9b5715..8fbaa9da9 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 f12db8e3d..1aa6a7825 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 3aecc0498..12d15e351 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 d1afa437b..4b27d6bb0 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 eb991eec2..092ee231c 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 51567ac1d..d17fa3a12 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 d22d904eb..324f43d2d 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 da247c49c..3a9d43334 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 f233361ac..36643d269 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 @@ -498,7 +498,7 @@ Probability of getting between 4 and 4 answers right by guessing is 0.2252- + Using Binomial distribution moments
@@ -535,7 +535,7 @@ Skewness is 0.2887- + Quantiles
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 fe6ea7342..806dd6c2b 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 71de5ada3..d8be0e2be 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 d3566caab..a4ce6d7a6 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 811de14a5..b7b7ed17a 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 701f1e253..8f25f771d 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 f44ba04f5..c5df83d3a 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 59827948f..2b6127270 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 d06b41217..1e910c4c7 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 65e57e546..ed41b5438 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 bc2f268bc..38fcc8089 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 4095590fd..0e8513d36 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 3d236038f..fc192c889 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 2c077c334..e15dd0cb4 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 894100f83..71dc64fa1 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-1.41.0
- + 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
@@ -190,7 +190,7 @@- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -209,7 +209,7 @@- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -242,7 +242,7 @@- + Milestone 2: Released September 10th 2006
@@ -283,7 +283,7 @@- + 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 884948ec6..e4c2406a0 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 45cb6b744..f91842d20 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 55b40a4e2..642af99c1 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 f6bbedba3..1d595d2cd 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 336750510..3e6a49fcc 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-1.13 and Cephes
@@ -212,7 +212,7 @@@@ -283,13 +283,13 @@ - - + Comparison to the R and DCDFLIB Statistical Libraries on Windows
@@ -300,7 +300,7 @@ (R-2.9.2 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
@@ -388,7 +388,7 @@
(3.366e-004s)
@@ -820,7 +820,7 @@
(5.987e-007s)
@@ -1052,7 +1052,7 @@
(3.732e-004s)
@@ -1124,7 +1124,7 @@
(2.673e-002s)
@@ -1262,7 +1262,7 @@
(4.411e-004s)
@@ -1549,28 +1549,28 @@- [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
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM, - Ubuntu Linux 8.1 machine, with the test program and R-2.8.1 compiled with - GNU G++ 4.3.2 using -O3. + Ubuntu Linux 9 machine, with the test program and R-2.9.2 compiled with GNU + G++ 4.3.3 using -O3 -DNDEBUG=1.
-Table 52. A Comparison to the R Statistical Library on Linux
+Table 52. A Comparison to the R Statistical Library on Linux
+ @@ -1612,6 +1613,11 @@ R ++ + DCDFLIB +
+@@ -1624,9 +1630,9 @@ @@ -1635,7 +1641,16 @@ -
2.35
+2.09
-
(3.371e-006s)
+(3.189e-006s)
1.00
-
(1.435e-006s)
+(1.526e-006s)
++
+ ++ @@ -1652,18 +1667,27 @@+
+1.19
++
(1.822e-006s)
1.00
-
(1.093e-005s)
+(1.185e-005s)
+ -
31.61 - [1] +
30.51 + [1]
-
(3.455e-004s)
+(3.616e-004s)
++
++ @@ -1678,9 +1702,18 @@+
+2.52
++
(2.989e-005s)
+ -
1.33
+4.41
-
(8.835e-007s)
+(9.175e-007s)
++
++ @@ -1689,7 +1722,7 @@+
+3.59
++
(7.476e-007s)
1.00
-
(6.626e-007s)
+(2.081e-007s)
@@ -1704,9 +1737,9 @@
@@ -1715,7 +1748,16 @@ -
1.73
+1.57
-
(6.532e-006s)
+(6.925e-006s)
1.00
-
(3.777e-006s)
+(4.407e-006s)
++
+ ++ @@ -1730,21 +1772,26 @@+
+7.43
++
(3.274e-005s)
-
1.23
+1.00
-
(1.856e-007s)
+(1.594e-007s)
+ -
1.00
+1.04
-
(1.513e-007s)
+(1.654e-007s)
+ + NA +
+@@ -1756,9 +1803,9 @@ @@ -1767,10 +1814,15 @@ -
1.46
+1.21
-
(2.009e-007s)
+(1.752e-007s)
1.00
-
(1.378e-007s)
+(1.448e-007s)
+
+ + NA +
+@@ -1782,9 +1834,18 @@ + -
1.25
+2.61
-
(1.354e-006s)
+(1.376e-006s)
++
++ @@ -1793,7 +1854,7 @@+
+2.36
++
(1.243e-006s)
1.00
-
(1.087e-006s)
+(5.270e-007s)
@@ -1808,18 +1869,27 @@
-
1.80
+1.00
-
(9.906e-006s)
+(4.252e-006s)
+ -
1.00
+1.34
-
(5.514e-006s)
+(5.700e-006s)
++
++ @@ -1836,19 +1906,24 @@+
+3.47
++
(1.477e-005s)
1.00
-
(1.250e-007s)
+(1.342e-007s)
+ -
1.29
+1.25
-
(1.616e-007s)
+(1.677e-007s)
+ + NA +
+@@ -1860,21 +1935,26 @@ -
1.02
+1.00
-
(9.310e-008s)
+(8.827e-008s)
+ -
1.00
+1.07
-
(9.149e-008s)
+(9.470e-008s)
+ + NA +
+- @@ -1886,96 +1966,132 @@ - -
1.65
--
(2.292e-006s)
--
-- --
-1.00
--
(1.388e-006s)
--
-- -- -- Fisher F Distribution - Quantile -
-- --
-1.78
--
(1.740e-005s)
--
-- --
-1.00
--
(9.787e-006s)
--
-- -- -- Gamma Distribution - CDF -
-- --
-1.48
--
(1.816e-006s)
--
-- --
-1.00
--
(1.230e-006s)
--
-- +- -- Gamma Distribution - Quantile -
-- --
-1.00
--
(8.553e-006s)
--
-- +-
1.62
-
(1.382e-005s)
+(2.324e-006s)
++
++ ++
+1.19
++
(1.711e-006s)
++
++ ++
+1.00
++
(1.437e-006s)
++
++ ++ ++ Fisher F Distribution + Quantile +
++ ++
+1.53
++
(1.577e-005s)
++
++ ++
+1.00
++
(1.033e-005s)
++
++ ++
+2.63
++
(2.719e-005s)
++
++ ++ ++ Gamma Distribution + CDF +
++ ++
+3.18
++
(1.582e-006s)
++
++ ++
+2.63
++
(1.309e-006s)
++
++ ++
+1.00
++
(4.980e-007s)
++
++ + ++ Gamma Distribution + Quantile +
++ ++
+2.19
++
(4.770e-006s)
++
++ ++
+6.94
++
(1.513e-005s)
++
++ @@ -1990,11 +2106,11 @@+
+1.00
++
(2.179e-006s)
@@ -2003,10 +2119,15 @@ -
2.25 - [2] +
2.20 + [2]
-
(3.308e-007s)
+(3.522e-007s)
1.00
-
(1.467e-007s)
+(1.601e-007s)
+
+ + NA +
+@@ -2020,19 +2141,24 @@ 1.00
-
(6.179e-007s)
+(8.279e-007s)
+ -
3.24
+2.57
-
(2.002e-006s)
+(2.125e-006s)
+ + NA +
+@@ -2046,19 +2172,24 @@ 1.00
-
(1.172e-007s)
+(9.398e-008s)
+ -
2.08
+2.75
-
(2.441e-007s)
+(2.588e-007s)
+ + NA +
+@@ -2070,21 +2201,26 @@ -
1.15
+1.00
-
(1.362e-007s)
+(9.893e-008s)
+ -
1.00
+1.30
-
(1.182e-007s)
+(1.285e-007s)
+ + NA +
+@@ -2098,19 +2234,24 @@ 1.00
-
(2.124e-007s)
+(1.831e-007s)
+ -
1.13
+1.39
-
(2.392e-007s)
+(2.539e-007s)
+ + NA +
+@@ -2122,9 +2263,9 @@ @@ -2133,10 +2274,15 @@ -
3.16
+1.10
-
(1.460e-006s)
+(5.551e-007s)
1.00
-
(4.626e-007s)
+(5.037e-007s)
+
+ + NA +
+@@ -2148,9 +2294,9 @@ @@ -2159,7 +2305,16 @@ -
1.27
+1.08
-
(1.665e-006s)
+(1.563e-006s)
1.00
-
(1.308e-006s)
+(1.444e-006s)
++
+ ++ @@ -2176,18 +2331,27 @@+
+1.00
++
(1.444e-006s)
1.00
-
(1.794e-005s)
+(1.700e-005s)
+ -
22.46 - [3] +
25.92 + [3]
-
(4.029e-004s)
+(4.407e-004s)
++
++ @@ -2202,18 +2366,27 @@+
+1.93
++
(3.274e-005s)
-
1.00
+5.06
-
(1.085e-005s)
+(2.841e-005s)
+ -
13.52
+25.01
-
(1.467e-004s)
+(1.405e-004s)
++
++ @@ -2228,20 +2401,29 @@+
+1.00
++
(5.617e-006s)
-
1.00
+8.47
-
(2.031e-003s)
+(1.879e-003s)
+ -
15.65 - [4] +
144.91 + [4]
-
(3.179e-002s)
+(3.214e-002s)
++
++ @@ -2256,9 +2438,18 @@+
+1.00
++
(2.218e-004s)
+ -
7.14
+10.33
-
(6.198e-005s)
+(5.868e-005s)
++
++ @@ -2267,7 +2458,7 @@+
+1.42
++
(8.058e-006s)
1.00
-
(8.678e-006s)
+(5.682e-006s)
@@ -2282,18 +2473,27 @@
-
1.00
+5.64
-
(7.947e-004s)
+(7.869e-004s)
+ -
1.21
+6.63
-
(9.622e-004s)
+(9.256e-004s)
++
++ @@ -2308,9 +2508,9 @@+
+1.00
++
(1.396e-004s)
@@ -2319,10 +2519,15 @@ -
5.70
+4.91
-
(3.461e-005s)
+(3.357e-005s)
1.00
-
(6.069e-006s)
+(6.844e-006s)
+
+ + NA +
+@@ -2334,9 +2539,9 @@ @@ -2344,13 +2549,18 @@ -
1.80
+1.57
-
(9.308e-004s)
+(9.265e-004s)
-
(5.176e-004s)
+(5.916e-004s)
+
+ + NA +
+@@ -2364,6 +2574,15 @@ +1.00
+
(1.074e-007s)
++
++ +
+1.16
+
(1.245e-007s)
@@ -2371,9 +2590,9 @@
@@ -2388,9 +2607,9 @@ -
1.04
+5.36
-
(1.294e-007s)
+(5.762e-007s)
@@ -2400,6 +2619,15 @@ -
1.59
+1.28
-
(2.364e-007s)
+(1.902e-007s)
1.00
(1.490e-007s)
++
+ ++ @@ -2414,9 +2642,18 @@+
+10.35
++
(1.542e-006s)
+ -
1.22
+2.43
-
(1.354e-006s)
+(1.198e-006s)
++
++ @@ -2425,7 +2662,7 @@+
+2.25
++
(1.110e-006s)
1.00
-
(1.110e-006s)
+(4.937e-007s)
@@ -2440,9 +2677,9 @@
@@ -2452,6 +2689,15 @@ -
1.38
+1.11
-
(3.752e-006s)
+(3.032e-006s)
1.00
(2.724e-006s)
++
+ ++ @@ -2466,9 +2712,9 @@+
+4.07
++
(1.110e-005s)
@@ -2477,7 +2723,16 @@ -
2.32
+2.17
-
(2.108e-006s)
+(2.020e-006s)
1.00
-
(9.099e-007s)
+(9.321e-007s)
++
+ ++ @@ -2492,9 +2747,9 @@+
+1.10
++
(1.021e-006s)
@@ -2503,7 +2758,16 @@ -
1.21
+1.18
-
(4.018e-006s)
+(3.972e-006s)
1.00
-
(3.317e-006s)
+(3.364e-006s)
++
+ ++ @@ -2518,21 +2782,26 @@+
+3.89
++
(1.308e-005s)
-
1.04
+1.00
-
(3.955e-007s)
+(3.662e-007s)
+ -
1.00
+1.04
(3.808e-007s)
+ + NA +
+- @@ -2544,46 +2813,51 @@ -
1.06
+1.00
-
(4.472e-007s)
+(4.112e-007s)
+ -
1.00
+1.05
-
(4.215e-007s)
+(4.317e-007s)
+ + NA +
+- [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 85ec923b4..fdfd52224 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 fbd175293..93f29cdfe 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 77edd444e..f0e1d2bc5 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 48847a3d9..656dfba79 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 d39e17d70..3a3819d3a 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 25792c6da..17daaa371 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 0668d2c6d..4b6986f13 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 a556e4f63..7d891b829 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 ece74e3ea..30d1fe1cc 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 6e50540ec..6adb90442 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 f861ce74a..fba8be543 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 56824a075..f14501bd2 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 f2e9372b0..825c8f5d4 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 cdd37c9ad..822988497 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 bf0714691..609e74d20 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 2cfb4e230..16e433254 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 ab15cc48a..655274220 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 c47182483..c70f532c8 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 2834aff74..cf3dcc1bb 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 cc38c2c27..ff2d0af30 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 e4a46089c..6dc0f3078 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 888a1ae72..70d77a9e4 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 9cecf0aad..f084cfda7 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 91aefb8ec..2fc51f3b4 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 231cfc2cc..9d12d3065 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 d2ca9dc4d..ea01767cd 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 84090f6d3..a4395b491 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 4b8f1ea2a..defd23762 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 b18522640..f40dbb6f4 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 85aea8ba0..a240e1237 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 e811773c6..28ca9a41a 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 77932b6cf..7415bccc6 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 e1a81a03e..4c7a768fd 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 990f21430..f124f6bf8 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 b37bb2dc1..797c9bca3 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 428c92118..67b06b5fa 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 49c3ee495..b16714f98 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 bec000a18..0e76ad502 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 7c4090202..18d865321 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 5c0ff5991..a5ba6c0fa 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 2381c8099..a9c712903 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 9f0fec23f..378cf66e4 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 5d01a9970..c2bf8a217 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 fa88dd516..b762aaba5 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 d8885f8ed..a23d94762 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 33764f0d6..c2e8cffb5 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 ea3f420c3..b25549d36 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 cdf7d6858..53bd0707d 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 4bed5a8ab..d6ca2c32a 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 940dee751..2cefdc96a 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 5e53c2949..e513ca60e 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 215938fee..b2f025dd5 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 eefe01269..2c2b4857d 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-1.41.0
- + 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
@@ -189,7 +189,7 @@- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -208,7 +208,7 @@- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -241,7 +241,7 @@- + Milestone 2: Released September 10th 2006
@@ -282,7 +282,7 @@- + 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 9fc72e348..daa31c7c1 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 2d379b170..9ecf7d3d5 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
@@ -78,7 +78,7 @@ }}} // namespaces
- + Description
@@ -178,7 +178,7 @@ a continued fraction for convergence.
- + Implementation
@@ -188,7 +188,7 @@ Lentz, W.J. 1976, Applied Optics, vol. 15, pp. 668-671.
- + Examples
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 bfd6aaf0d..69d0e1ddb 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 18e5a0048..2c910e9b2 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 9c0210d92..5a92f7068 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 d8d801f46..df83112bd 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 3d79325aa..33f38f451 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 a2059f8f3..1a6ba45e5 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
@@ -70,7 +70,7 @@ }}} // namespaces
- + Description
@@ -127,7 +127,7 @@ 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 f0780b73c..8dbfa7422 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 fafddbcc5..9a96b2a9f 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 f9cf1d28e..86b871ef6 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 52389e867..ccb38e8b7 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
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 f6c563bf9..0cabfcfa9 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 44e121d4d..5cdb18e73 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 24772370f..c1c83abae 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 4c5a04950..fae24f44c 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 c3bea018b..210b082f6 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 19dae9089..2b5b81bc4 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 d06e0350a..d4fc5ee93 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> diff --git a/doc/sf_and_dist/performance.qbk b/doc/sf_and_dist/performance.qbk index 46e0ddcc1..5607f8bf3 100644 --- a/doc/sf_and_dist/performance.qbk +++ b/doc/sf_and_dist/performance.qbk @@ -318,51 +318,51 @@ R-2.9.2 compiled in "standalone mode" with MinGW-4.3 [heading Comparison to the R Statistical Library on Linux] -All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM, Ubuntu Linux 8.1 -machine, with the test program and R-2.8.1 compiled with GNU G++ 4.3.2 using -O3. +All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM, Ubuntu Linux 9 +machine, with the test program and R-2.9.2 compiled with GNU G++ 4.3.3 using -O3 -DNDEBUG=1. [table A Comparison to the R Statistical Library on Linux -[[Statistical Function][Boost][R]] -[[__beta_distrib CDF][[perf gcc-4_3_2-dist-beta-cdf..[para 2.35][para (3.371e-006s)]]][[perf gcc-4_3_2-dist-beta-R-cdf..[para *1.00*][para (1.435e-006s)]]]] -[[__beta_distrib Quantile][[perf gcc-4_3_2-dist-beta-quantile..[para *1.00*][para (1.093e-005s)]]][[perf gcc-4_3_2-dist-beta-R-quantile..[para 31.61[footnote 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.]][para (3.455e-004s)]]]] -[[__binomial_distrib CDF][[perf gcc-4_3_2-dist-binomial-cdf..[para 1.33][para (8.835e-007s)]]][[perf gcc-4_3_2-dist-binom-R-cdf..[para *1.00*][para (6.626e-007s)]]]] -[[__binomial_distrib Quantile][[perf gcc-4_3_2-dist-binomial-quantile..[para 1.73][para (6.532e-006s)]]][[perf gcc-4_3_2-dist-binom-R-quantile..[para *1.00*][para (3.777e-006s)]]]] -[[__cauchy_distrib CDF][[perf gcc-4_3_2-dist-cauchy-cdf..[para 1.23][para (1.856e-007s)]]][[perf gcc-4_3_2-dist-cauchy-R-cdf..[para *1.00*][para (1.513e-007s)]]]] -[[__cauchy_distrib Quantile][[perf gcc-4_3_2-dist-cauchy-quantile..[para 1.46][para (2.009e-007s)]]][[perf gcc-4_3_2-dist-cauchy-R-quantile..[para *1.00*][para (1.378e-007s)]]]] -[[__chi_squared_distrib CDF][[perf gcc-4_3_2-dist-chi_squared-cdf..[para 1.25][para (1.354e-006s)]]][[perf gcc-4_3_2-dist-chisq-R-cdf..[para *1.00*][para (1.087e-006s)]]]] -[[__chi_squared_distrib Quantile][[perf gcc-4_3_2-dist-chi_squared-quantile..[para 1.80][para (9.906e-006s)]]][[perf gcc-4_3_2-dist-chisq-R-quantile..[para *1.00*][para (5.514e-006s)]]]] -[[__exp_distrib CDF][[perf gcc-4_3_2-dist-exponential-cdf..[para *1.00*][para (1.250e-007s)]]][[perf gcc-4_3_2-dist-exp-R-cdf..[para 1.29][para (1.616e-007s)]]]] -[[__exp_distrib Quantile][[perf gcc-4_3_2-dist-exponential-quantile..[para 1.02][para (9.310e-008s)]]][[perf gcc-4_3_2-dist-exp-R-quantile..[para *1.00*][para (9.149e-008s)]]]] -[[__F_distrib CDF][[perf gcc-4_3_2-dist-fisher_f-cdf..[para 1.65][para (2.292e-006s)]]][[perf gcc-4_3_2-dist-f-R-cdf..[para *1.00*][para (1.388e-006s)]]]] -[[__F_distrib Quantile][[perf gcc-4_3_2-dist-fisher_f-quantile..[para 1.78][para (1.740e-005s)]]][[perf gcc-4_3_2-dist-f-R-quantile..[para *1.00*][para (9.787e-006s)]]]] -[[__gamma_distrib CDF][[perf gcc-4_3_2-dist-gamma-cdf..[para 1.48][para (1.816e-006s)]]][[perf gcc-4_3_2-dist-gamma-R-cdf..[para *1.00*][para (1.230e-006s)]]]] -[[__gamma_distrib Quantile][[perf gcc-4_3_2-dist-gamma-quantile..[para *1.00*][para (8.553e-006s)]]][[perf gcc-4_3_2-dist-gamma-R-quantile..[para 1.62][para (1.382e-005s)]]]] +[[Statistical Function][Boost][R][DCDFLIB]] +[[__beta_distrib CDF][[perf gcc-4_3_2-dist-beta-cdf..[para 2.09][para (3.189e-006s)]]][[perf gcc-4_3_2-dist-beta-R-cdf..[para *1.00*][para (1.526e-006s)]]][[perf gcc-4_3_2-dist-beta-dcd-cdf..[para 1.19][para (1.822e-006s)]]]] +[[__beta_distrib Quantile][[perf gcc-4_3_2-dist-beta-quantile..[para *1.00*][para (1.185e-005s)]]][[perf gcc-4_3_2-dist-beta-R-quantile..[para 30.51[footnote 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.]][para (3.616e-004s)]]][[perf gcc-4_3_2-dist-beta-dcd-quantile..[para 2.52][para (2.989e-005s)]]]] +[[__binomial_distrib CDF][[perf gcc-4_3_2-dist-binomial-cdf..[para 4.41][para (9.175e-007s)]]][[perf gcc-4_3_2-dist-binom-R-cdf..[para 3.59][para (7.476e-007s)]]][[perf gcc-4_3_2-dist-binomial-dcd-cdf..[para *1.00*][para (2.081e-007s)]]]] +[[__binomial_distrib Quantile][[perf gcc-4_3_2-dist-binomial-quantile..[para 1.57][para (6.925e-006s)]]][[perf gcc-4_3_2-dist-binom-R-quantile..[para *1.00*][para (4.407e-006s)]]][[perf gcc-4_3_2-dist-binomial-dcd-quantile..[para 7.43][para (3.274e-005s)]]]] +[[__cauchy_distrib CDF][[perf gcc-4_3_2-dist-cauchy-cdf..[para *1.00*][para (1.594e-007s)]]][[perf gcc-4_3_2-dist-cauchy-R-cdf..[para 1.04][para (1.654e-007s)]]][NA]] +[[__cauchy_distrib Quantile][[perf gcc-4_3_2-dist-cauchy-quantile..[para 1.21][para (1.752e-007s)]]][[perf gcc-4_3_2-dist-cauchy-R-quantile..[para *1.00*][para (1.448e-007s)]]][NA]] +[[__chi_squared_distrib CDF][[perf gcc-4_3_2-dist-chi_squared-cdf..[para 2.61][para (1.376e-006s)]]][[perf gcc-4_3_2-dist-chisq-R-cdf..[para 2.36][para (1.243e-006s)]]][[perf gcc-4_3_2-dist-chi_squared-dcd-cdf..[para *1.00*][para (5.270e-007s)]]]] +[[__chi_squared_distrib Quantile][[perf gcc-4_3_2-dist-chi_squared-quantile..[para *1.00*][para (4.252e-006s)]]][[perf gcc-4_3_2-dist-chisq-R-quantile..[para 1.34][para (5.700e-006s)]]][[perf gcc-4_3_2-dist-chi_squared-dcd-quantile..[para 3.47][para (1.477e-005s)]]]] +[[__exp_distrib CDF][[perf gcc-4_3_2-dist-exponential-cdf..[para *1.00*][para (1.342e-007s)]]][[perf gcc-4_3_2-dist-exp-R-cdf..[para 1.25][para (1.677e-007s)]]][NA]] +[[__exp_distrib Quantile][[perf gcc-4_3_2-dist-exponential-quantile..[para *1.00*][para (8.827e-008s)]]][[perf gcc-4_3_2-dist-exp-R-quantile..[para 1.07][para (9.470e-008s)]]][NA]] +[[__F_distrib CDF][[perf gcc-4_3_2-dist-fisher_f-cdf..[para 1.62][para (2.324e-006s)]]][[perf gcc-4_3_2-dist-f-R-cdf..[para 1.19][para (1.711e-006s)]]][[perf gcc-4_3_2-dist-f-dcd-cdf..[para *1.00*][para (1.437e-006s)]]]] +[[__F_distrib Quantile][[perf gcc-4_3_2-dist-fisher_f-quantile..[para 1.53][para (1.577e-005s)]]][[perf gcc-4_3_2-dist-f-R-quantile..[para *1.00*][para (1.033e-005s)]]][[perf gcc-4_3_2-dist-f-dcd-quantile..[para 2.63][para (2.719e-005s)]]]] +[[__gamma_distrib CDF][[perf gcc-4_3_2-dist-gamma-cdf..[para 3.18][para (1.582e-006s)]]][[perf gcc-4_3_2-dist-gamma-R-cdf..[para 2.63][para (1.309e-006s)]]][[perf gcc-4_3_2-dist-gam-dcd-cdf..[para *1.00*][para (4.980e-007s)]]]] +[[__gamma_distrib Quantile][[perf gcc-4_3_2-dist-gamma-quantile..[para 2.19][para (4.770e-006s)]]][[perf gcc-4_3_2-dist-gamma-R-quantile..[para 6.94][para (1.513e-005s)]]][[perf gcc-4_3_2-dist-gam-dcd-quantile..[para *1.00*][para (2.179e-006s)]]]] -[[__hypergeometric_distrib CDF][[perf gcc-4_3_2-dist-hypergeometric-cdf..[para 2.25[footnote 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.]][para (3.308e-007s)]]][[perf gcc-4_3_2-dist-hypergeo-R-cdf..[para *1.00*][para (1.467e-007s)]]]] -[[__hypergeometric_distrib Quantile][[perf gcc-4_3_2-dist-hypergeometric-quantile..[para *1.00*][para (6.179e-007s)]]][[perf gcc-4_3_2-dist-hypergeo-R-quantile..[para 3.24][para (2.002e-006s)]]]] -[[__logistic_distrib CDF][[perf gcc-4_3_2-dist-logistic-cdf..[para *1.00*][para (1.172e-007s)]]][[perf gcc-4_3_2-dist-logis-R-cdf..[para 2.08][para (2.441e-007s)]]]] -[[__logistic_distrib Quantile][[perf gcc-4_3_2-dist-logistic-quantile..[para 1.15][para (1.362e-007s)]]][[perf gcc-4_3_2-dist-logis-R-quantile..[para *1.00*][para (1.182e-007s)]]]] +[[__hypergeometric_distrib CDF][[perf gcc-4_3_2-dist-hypergeometric-cdf..[para 2.20[footnote 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.]][para (3.522e-007s)]]][[perf gcc-4_3_2-dist-hypergeo-R-cdf..[para *1.00*][para (1.601e-007s)]]][NA]] +[[__hypergeometric_distrib Quantile][[perf gcc-4_3_2-dist-hypergeometric-quantile..[para *1.00*][para (8.279e-007s)]]][[perf gcc-4_3_2-dist-hypergeo-R-quantile..[para 2.57][para (2.125e-006s)]]][NA]] +[[__logistic_distrib CDF][[perf gcc-4_3_2-dist-logistic-cdf..[para *1.00*][para (9.398e-008s)]]][[perf gcc-4_3_2-dist-logis-R-cdf..[para 2.75][para (2.588e-007s)]]][NA]] +[[__logistic_distrib Quantile][[perf gcc-4_3_2-dist-logistic-quantile..[para *1.00*][para (9.893e-008s)]]][[perf gcc-4_3_2-dist-logis-R-quantile..[para 1.30][para (1.285e-007s)]]][NA]] -[[__lognormal_distrib CDF][[perf gcc-4_3_2-dist-lognormal-cdf..[para *1.00*][para (2.124e-007s)]]][[perf gcc-4_3_2-dist-lnorm-R-cdf..[para 1.13][para (2.392e-007s)]]]] -[[__lognormal_distrib Quantile][[perf gcc-4_3_2-dist-lognormal-quantile..[para 3.16][para (1.460e-006s)]]][[perf gcc-4_3_2-dist-lnorm-R-quantile..[para *1.00*][para (4.626e-007s)]]]] -[[__negative_binomial_distrib CDF][[perf gcc-4_3_2-dist-negative_binomial-cdf..[para 1.27][para (1.665e-006s)]]][[perf gcc-4_3_2-dist-nbinom-R-cdf..[para *1.00*][para (1.308e-006s)]]]] -[[__negative_binomial_distrib Quantile][[perf gcc-4_3_2-dist-negative_binomial-quantile..[para *1.00*][para (1.794e-005s)]]][[perf gcc-4_3_2-dist-nbinom-R-quantile..[para 22.46[footnote 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]][para (4.029e-004s)]]]] +[[__lognormal_distrib CDF][[perf gcc-4_3_2-dist-lognormal-cdf..[para *1.00*][para (1.831e-007s)]]][[perf gcc-4_3_2-dist-lnorm-R-cdf..[para 1.39][para (2.539e-007s)]]][NA]] +[[__lognormal_distrib Quantile][[perf gcc-4_3_2-dist-lognormal-quantile..[para 1.10][para (5.551e-007s)]]][[perf gcc-4_3_2-dist-lnorm-R-quantile..[para *1.00*][para (5.037e-007s)]]][NA]] +[[__negative_binomial_distrib CDF][[perf gcc-4_3_2-dist-negative_binomial-cdf..[para 1.08][para (1.563e-006s)]]][[perf gcc-4_3_2-dist-nbinom-R-cdf..[para *1.00*][para (1.444e-006s)]]][[perf gcc-4_3_2-dist-negative_binomial-dcd-cdf..[para *1.00*][para (1.444e-006s)]]]] +[[__negative_binomial_distrib Quantile][[perf gcc-4_3_2-dist-negative_binomial-quantile..[para *1.00*][para (1.700e-005s)]]][[perf gcc-4_3_2-dist-nbinom-R-quantile..[para 25.92[footnote 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]][para (4.407e-004s)]]][[perf gcc-4_3_2-dist-negative_binomial-dcd-quantile..[para 1.93][para (3.274e-005s)]]]] -[[__non_central_chi_squared_distrib CDF][[perf gcc-4_3_2-dist-non_central_chi_squared-cdf..[para *1.00*][para (1.085e-005s)]]][[perf gcc-4_3_2-dist-nchisq-R-cdf..[para 13.52][para (1.467e-004s)]]]] -[[__non_central_chi_squared_distrib Quantile][[perf gcc-4_3_2-dist-non_central_chi_squared-quantile..[para *1.00*][para (2.031e-003s)]]][[perf gcc-4_3_2-dist-nchisq-R-quantile..[para 15.65[footnote 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.]][para (3.179e-002s)]]]] -[[__non_central_F_distrib CDF][[perf gcc-4_3_2-dist-non_central_f-cdf..[para 7.14][para (6.198e-005s)]]][[perf gcc-4_3_2-dist-nf-R-cdf..[para *1.00*][para (8.678e-006s)]]]] -[[__non_central_F_distrib Quantile][[perf gcc-4_3_2-dist-non_central_f-quantile..[para *1.00*][para (7.947e-004s)]]][[perf gcc-4_3_2-dist-nf-R-quantile..[para 1.21][para (9.622e-004s)]]]] -[[__non_central_t_distrib CDF][[perf gcc-4_3_2-dist-non_central_t-cdf..[para 5.70][para (3.461e-005s)]]][[perf gcc-4_3_2-dist-nt-R-cdf..[para *1.00*][para (6.069e-006s)]]]] -[[__non_central_t_distrib Quantile][[perf gcc-4_3_2-dist-non_central_t-quantile..[para 1.80][para (9.308e-004s)]]][[perf gcc-4_3_2-dist-nt-R-quantile..[para *1.00*[footnote 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.]][para (5.176e-004s)]]]] +[[__non_central_chi_squared_distrib CDF][[perf gcc-4_3_2-dist-non_central_chi_squared-cdf..[para 5.06][para (2.841e-005s)]]][[perf gcc-4_3_2-dist-nchisq-R-cdf..[para 25.01][para (1.405e-004s)]]][[perf gcc-4_3_2-dist-non_central_chi_squared-dcd-cdf..[para *1.00*][para (5.617e-006s)]]]] +[[__non_central_chi_squared_distrib Quantile][[perf gcc-4_3_2-dist-non_central_chi_squared-quantile..[para 8.47][para (1.879e-003s)]]][[perf gcc-4_3_2-dist-nchisq-R-quantile..[para 144.91[footnote 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.]][para (3.214e-002s)]]][[perf gcc-4_3_2-dist-non_central_chi_squared-dcd-quantile..[para *1.00*][para (2.218e-004s)]]]] +[[__non_central_F_distrib CDF][[perf gcc-4_3_2-dist-non_central_f-cdf..[para 10.33][para (5.868e-005s)]]][[perf gcc-4_3_2-dist-nf-R-cdf..[para 1.42][para (8.058e-006s)]]][[perf gcc-4_3_2-dist-fnc-dcd-cdf..[para *1.00*][para (5.682e-006s)]]]] +[[__non_central_F_distrib Quantile][[perf gcc-4_3_2-dist-non_central_f-quantile..[para 5.64][para (7.869e-004s)]]][[perf gcc-4_3_2-dist-nf-R-quantile..[para 6.63][para (9.256e-004s)]]][[perf gcc-4_3_2-dist-fnc-dcd-quantile..[para *1.00*][para (1.396e-004s)]]]] +[[__non_central_t_distrib CDF][[perf gcc-4_3_2-dist-non_central_t-cdf..[para 4.91][para (3.357e-005s)]]][[perf gcc-4_3_2-dist-nt-R-cdf..[para *1.00*][para (6.844e-006s)]]][NA]] +[[__non_central_t_distrib Quantile][[perf gcc-4_3_2-dist-non_central_t-quantile..[para 1.57][para (9.265e-004s)]]][[perf gcc-4_3_2-dist-nt-R-quantile..[para *1.00*[footnote 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.]][para (5.916e-004s)]]][NA]] -[[__normal_distrib CDF][[perf gcc-4_3_2-dist-normal-cdf..[para *1.00*][para (1.245e-007s)]]][[perf gcc-4_3_2-dist-norm-R-cdf..[para 1.04][para (1.294e-007s)]]]] -[[__normal_distrib Quantile][[perf gcc-4_3_2-dist-normal-quantile..[para 1.59][para (2.364e-007s)]]][[perf gcc-4_3_2-dist-norm-R-quantile..[para *1.00*][para (1.490e-007s)]]]] -[[__poisson_distrib CDF][[perf gcc-4_3_2-dist-poisson-cdf..[para 1.22][para (1.354e-006s)]]][[perf gcc-4_3_2-dist-pois-R-cdf..[para *1.00*][para (1.110e-006s)]]]] -[[__poisson_distrib][[perf gcc-4_3_2-dist-poisson-quantile..[para 1.38][para (3.752e-006s)]]][[perf gcc-4_3_2-dist-pois-R-quantile..[para *1.00*][para (2.724e-006s)]]]] -[[__students_t_distrib CDF][[perf gcc-4_3_2-dist-students_t-cdf..[para 2.32][para (2.108e-006s)]]][[perf gcc-4_3_2-dist-t-R-cdf..[para *1.00*][para (9.099e-007s)]]]] -[[__students_t_distrib Quantile][[perf gcc-4_3_2-dist-students_t-quantile..[para 1.21][para (4.018e-006s)]]][[perf gcc-4_3_2-dist-t-R-quantile..[para *1.00*][para (3.317e-006s)]]]] -[[__weibull_distrib CDF][[perf gcc-4_3_2-dist-weibull-cdf..[para 1.04][para (3.955e-007s)]]][[perf gcc-4_3_2-dist-weibull-R-cdf..[para *1.00*][para (3.808e-007s)]]]] -[[__weibull_distrib Quantile][[perf gcc-4_3_2-dist-weibull-quantile..[para 1.06][para (4.472e-007s)]]][[perf gcc-4_3_2-dist-weibull-R-quantile..[para *1.00*][para (4.215e-007s)]]]] +[[__normal_distrib CDF][[perf gcc-4_3_2-dist-normal-cdf..[para *1.00*][para (1.074e-007s)]]][[perf gcc-4_3_2-dist-norm-R-cdf..[para 1.16][para (1.245e-007s)]]][[perf gcc-4_3_2-dist-nor-dcd-cdf..[para 5.36][para (5.762e-007s)]]]] +[[__normal_distrib Quantile][[perf gcc-4_3_2-dist-normal-quantile..[para 1.28][para (1.902e-007s)]]][[perf gcc-4_3_2-dist-norm-R-quantile..[para *1.00*][para (1.490e-007s)]]][[perf gcc-4_3_2-dist-nor-dcd-quantile..[para 10.35][para (1.542e-006s)]]]] +[[__poisson_distrib CDF][[perf gcc-4_3_2-dist-poisson-cdf..[para 2.43][para (1.198e-006s)]]][[perf gcc-4_3_2-dist-pois-R-cdf..[para 2.25][para (1.110e-006s)]]][[perf gcc-4_3_2-dist-poi-dcd-cdf..[para *1.00*][para (4.937e-007s)]]]] +[[__poisson_distrib][[perf gcc-4_3_2-dist-poisson-quantile..[para 1.11][para (3.032e-006s)]]][[perf gcc-4_3_2-dist-pois-R-quantile..[para *1.00*][para (2.724e-006s)]]][[perf gcc-4_3_2-dist-poi-dcd-quantile..[para 4.07][para (1.110e-005s)]]]] +[[__students_t_distrib CDF][[perf gcc-4_3_2-dist-students_t-cdf..[para 2.17][para (2.020e-006s)]]][[perf gcc-4_3_2-dist-t-R-cdf..[para *1.00*][para (9.321e-007s)]]][[perf gcc-4_3_2-dist-t-dcd-cdf..[para 1.10][para (1.021e-006s)]]]] +[[__students_t_distrib Quantile][[perf gcc-4_3_2-dist-students_t-quantile..[para 1.18][para (3.972e-006s)]]][[perf gcc-4_3_2-dist-t-R-quantile..[para *1.00*][para (3.364e-006s)]]][[perf gcc-4_3_2-dist-t-dcd-quantile..[para 3.89][para (1.308e-005s)]]]] +[[__weibull_distrib CDF][[perf gcc-4_3_2-dist-weibull-cdf..[para *1.00*][para (3.662e-007s)]]][[perf gcc-4_3_2-dist-weibull-R-cdf..[para 1.04][para (3.808e-007s)]]][NA]] +[[__weibull_distrib Quantile][[perf gcc-4_3_2-dist-weibull-quantile..[para *1.00*][para (4.112e-007s)]]][[perf gcc-4_3_2-dist-weibull-R-quantile..[para 1.05][para (4.317e-007s)]]][NA]] ] [endsect] @@ -404,3 +404,5 @@ __policy_section you want to test set as the default. + +