diff --git a/doc/sf_and_dist/error_handling.qbk b/doc/sf_and_dist/error_handling.qbk index 7ac906b71..b7ce6f84e 100644 --- a/doc/sf_and_dist/error_handling.qbk +++ b/doc/sf_and_dist/error_handling.qbk @@ -27,7 +27,7 @@ The kinds of errors that can be raised are: the function.]] [[Denormalisation Error][Occurs when the returned result would be a denormalised value.]] [[Rounding Error][Occurs when the argument to one of the rounding functions __trunc, - __round and __modf can not be represented as an integer type, is is + __round and __modf can not be represented as an integer type, is outide the range of the result type.]] [[Evaluation Error][Occurs when an internal error occured that prevented the result from being evaluated: this should never occur, but if it does, then diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index a86cce756..ac86ee0d0 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: July 15, 2010 at 16:56:47 GMT |
+Last revised: August 07, 2010 at 16:25:25 GMT |
@@ -99,7 +99,7 @@ functions divided by large powers into single (simpler) expressions.
Table 53. Optimal choices for N and g when computing with guard digits (source: +
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 3702db923..368a0ef0e 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.
@@ -596,7 +596,7 @@ 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 27674652f..abbace075 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
@@ -636,7 +636,7 @@ examples are available illustrating the use of the binomial distribution.
@@ -646,7 +646,7 @@ please refer to these functions for information on accuracy.
@@ -157,7 +157,7 @@ have very low error rates.
@@ -273,7 +273,7 @@
@@ -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 a32d2c2f3..638f74452 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 5d4304064..6550c8f56 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 3e5905b73..67776d9a9 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 e28e22562..36285b1d3 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
@@ -81,7 +81,7 @@
@@ -141,7 +141,7 @@ 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.
@@ -616,7 +616,7 @@ 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 2877b1a27..b47dffc74 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 d0ed879d1..6bdcd0c69 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 537f92db4..be306d507 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 16f560bbb..84458802a 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> @@ -275,7 +275,7 @@- + Cumulative Hazard Function
@@ -303,7 +303,7 @@- + mean
template<class RealType, class Policy> @@ -318,7 +318,7 @@ distribution).- + median
template<class RealType, class Policy> @@ -328,7 +328,7 @@ Returns the median of the distribution dist.- + mode
template<class RealType, Policy> @@ -342,7 +342,7 @@ if the distribution does not have a defined mode.- + Probability Density Function
@@ -371,7 +371,7 @@![]()
- + range
template<class RealType, class Policy> @@ -381,7 +381,7 @@ Returns the valid range of the random variable over distribution dist.- + Quantile
template <class RealType, class Policy> @@ -410,7 +410,7 @@![]()
- + Quantile from the complement of the probability.
@@ -456,7 +456,7 @@![]()
- + Standard Deviation
@@ -471,7 +471,7 @@ if the distribution does not have a defined standard deviation.- + support
template<class RealType, class Policy> @@ -488,7 +488,7 @@ where the pdf is zero, and the cdf zero or unity.- + Variance
template <class RealType, class Policy> @@ -502,7 +502,7 @@ if the distribution does not have a defined variance.- + Skewness
template <class RealType, class Policy> @@ -516,7 +516,7 @@ if the distribution does not have a defined skewness.- + Kurtosis
template <class RealType, class Policy> @@ -558,7 +558,7 @@ 'Proper' kurtosis can have a value from zero to + infinity.- + Kurtosis excess
@@ -593,7 +593,7 @@ The kurtosis excess of a normal distribution is zero.- + P and Q
@@ -603,7 +603,7 @@ returned by these functions.
- + Percent Point Function
@@ -612,7 +612,7 @@ the Quantile.- + Inverse CDF Function.
@@ -621,7 +621,7 @@ Quantile.- + Inverse Survival Function.
@@ -629,7 +629,7 @@ The inverse of the survival function, is the same as computing the quantile from the complement of the probability.- + Probability Mass Function
@@ -643,7 +643,7 @@ applies to continuous distributions.- + Lower Critical Value.
@@ -653,7 +653,7 @@ the Quantile.- + Upper Critical Value.
@@ -664,7 +664,7 @@ 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 998316c8b..fcbe7364a 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 ca1d0243a..a16f276e4 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 69482986a..a4892c8e8 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 ec6ff6abe..acbc35208 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 03dbd9189..766d96c15 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 ebc157093..56e5ab7be 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 73818ec1b..a8b155fc4 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 98ff95819..24ed0a639 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 0434e02b5..3b327ac1b 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 29e21958a..b5e1c1f5e 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 d9a5ceab1..b7c71137c 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 3835195af..0c91117ea 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 2e20dc758..cba2bd111 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
@@ -549,7 +549,7 @@
-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 bc3541854..fd11ae394 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 f1979ac52..b8416560d 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
@@ -80,7 +80,7 @@ Occurs when the argument to one of the rounding functions trunc, round and modf can not - be represented as an integer type, is is outide the range of the result + be represented as an integer type, is outide the range of the result type.Evaluation Error @@ -134,7 +134,7 @@ the default action for each error shown in bold:-Table 1. Possible Actions for Domain Errors
+Table 1. Possible Actions for Domain Errors
@@ -209,7 +209,7 @@ -Table 2. Possible Actions for Pole Errors
+Table 2. Possible Actions for Pole Errors
@@ -284,7 +284,7 @@ -Table 3. Possible Actions for Overflow Errors
+Table 3. Possible Actions for Overflow Errors
@@ -359,7 +359,7 @@ -Table 4. Possible Actions for Underflow Errors
+Table 4. Possible Actions for Underflow Errors
@@ -434,7 +434,7 @@ -Table 5. Possible Actions for Denorm Errors
+Table 5. Possible Actions for Denorm Errors
@@ -509,7 +509,7 @@ -Table 6. Possible Actions for Rounding Errors
+Table 6. Possible Actions for Rounding Errors
@@ -584,7 +584,7 @@ -Table 7. Possible Actions for Internal Evaluation Errors
+Table 7. Possible Actions for Internal Evaluation Errors
@@ -659,7 +659,7 @@ -Table 8. Possible Actions for Indeterminate Result Errors
+Table 8. Possible Actions for Indeterminate Result Errors
@@ -735,7 +735,7 @@ - + Rationale
- + Finding More Information
@@ -776,7 +776,7 @@ The various kind of errors are described in more detail below.- + Domain Errors
@@ -848,7 +848,7 @@ for more details.- + Evaluation at a pole
@@ -887,7 +887,7 @@ for more details.- + Numeric Overflow
@@ -912,7 +912,7 @@ doesn't support infinities, the maximum value for the type is returned.- + Numeric Underflow
@@ -935,7 +935,7 @@ anstd::underflow_errorC++ exception.- + Denormalisation Errors
@@ -958,7 +958,7 @@ throws anstd::underflow_errorC++ exception.- + Evaluation Errors
@@ -995,7 +995,7 @@ for more details.- + Indeterminate Result Errors
@@ -1022,7 +1022,7 @@ the result of 00 is 1, even though the result is actually mathematically indeterminate.- + Rounding Errors
@@ -1062,7 +1062,7 @@ 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 1fc7034c8..4d7afecb1 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 @@ -31,19 +31,26 @@- + Boost-1.44.0
-
- +
+++
- Fixed incorrect range and support for Rayleigh distribution. -
- + Fixed numerical error in the quantile of the Student's T distribution: + the function was returning garbage values for non-integer degrees of + freedom between 2 and 3. +
+- + 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
@@ -204,7 +211,7 @@- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -223,7 +230,7 @@- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -256,7 +263,7 @@- + Milestone 2: Released September 10th 2006
@@ -297,7 +304,7 @@- + 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 41189fb92..95c7fbe19 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 447c76ac3..6ed6262e7 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 4544ce504..962828b19 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 0d6b53c06..df93e5ac2 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 daa179d71..6e08fb568 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
@@ -344,7 +344,7 @@@@ -423,7 +423,7 @@ -
17.89[2]
+17.89[2]
(4.248e-005s)
@@ -548,11 +548,11 @@
- - + Comparison to the R and DCDFLIB Statistical Libraries on Windows
@@ -574,7 +574,7 @@ (R-2.9.2 appears not to be buildable with Visual C++).-Table 51. A Comparison to the R Statistical Library on Windows XP
+Table 51. A Comparison to the R Statistical Library on Windows XP
@@ -659,7 +659,7 @@ -
67.66[1]
+67.66[1]
(3.366e-004s)
@@ -1089,7 +1089,7 @@
-
3.60[2]
+3.60[2]
(5.987e-007s)
@@ -1319,7 +1319,7 @@
-
43.43[3]
+43.43[3]
(3.732e-004s)
@@ -1389,7 +1389,7 @@
-
393.90[4]
+393.90[4]
(2.673e-002s)
@@ -1525,7 +1525,7 @@
-
1.00[5]
+1.00[5]
(4.411e-004s)
@@ -1811,28 +1811,28 @@
- [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
@@ -1851,7 +1851,7 @@ G++ 4.3.3 using -O3 -DNDEBUG=1.-Table 52. A Comparison to the R Statistical Library on Linux
+Table 52. A Comparison to the R Statistical Library on Linux
@@ -1936,7 +1936,7 @@ -
30.51[1]
+30.51[1]
(3.616e-004s)
@@ -2366,7 +2366,7 @@
-
2.20[2]
+2.20[2]
(3.522e-007s)
@@ -2596,7 +2596,7 @@
-
25.92[3]
+25.92[3]
(4.407e-004s)
@@ -2666,7 +2666,7 @@
-
144.91[4]
+144.91[4]
(3.214e-002s)
@@ -2802,7 +2802,7 @@
-
1.00[5]
+1.00[5]
(5.916e-004s)
@@ -3088,28 +3088,28 @@
- [1] +
-[1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.
[2] +
-[2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.
[3] +
-[3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases
[4] +
-[4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.
[5] +
[5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html index 48d7d8bfe..933244c62 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 5fcdae49e..25ac7c3b8 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html @@ -238,7 +238,7 @@ highly vectorisable processors in the future. -Table 49. A Comparison of Polynomial Evaluation Methods
+Table 49. A Comparison of Polynomial Evaluation Methods
@@ -638,7 +638,7 @@ tutorial. -Table 50. Performance Comparison with and Without Internal Promotion to long +
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 19f162422..53bf8e4a3 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 b7d459145..54d3524aa 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
@@ -689,7 +689,7 @@- + 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 30af99787..0b4c08808 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 5c491b51d..d175218fa 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 f87a1c174..f18062339 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 71f629e22..c8911fdf1 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 dd0404342..cfaa08640 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 88caa4e70..ee8fd216e 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 7d8ded2f4..d53a88b60 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 d4198c5c9..04936a678 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 First Kind
+Table 41. Errors Rates in the Elliptic Integrals of the First Kind
@@ -235,7 +235,7 @@ - + Testing
@@ -245,7 +245,7 @@ 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 a0b4f0631..bc2d80d62 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 Second Kind
+Table 42. Errors Rates in the Elliptic Integrals of the Second Kind
@@ -235,7 +235,7 @@ - + Testing
@@ -245,7 +245,7 @@ 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 67a9e6d0d..7dccd19d1 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 Third Kind
+Table 43. Errors Rates in the Elliptic Integrals of the Third Kind
@@ -241,7 +241,7 @@ - + Testing
@@ -251,7 +251,7 @@ this implementation.
- + Implementation
@@ -288,7 +288,7 @@ Π(n, φ+mπ, k) = Π(n, φ, k) + 2mΠ(n, k) ; n <= 1
- Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1] + Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1]
are used to move φ to the range [0, π/2]. @@ -308,7 +308,7 @@
-[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 9f0c1c449..9d8277a04 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
@@ -259,7 +259,7 @@ to verify their correctness: see the above Carlson paper for details.
- + Accuracy
@@ -270,7 +270,7 @@ All values are relative errors in units of epsilon.
-Table 40. Errors Rates in the Carlson Elliptic Integrals
+Table 40. Errors Rates in the Carlson Elliptic Integrals
@@ -413,7 +413,7 @@ - + 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 8a439bcee..cd3e96110 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 @@ -49,14 +49,14 @@ Elliptic integral.
- + Notation
All variables are real numbers unless otherwise noted.
- + Definition
@@ -245,7 +245,7 @@
- + Duplication Theorem
@@ -257,7 +257,7 @@![]()
- + Carlson's Formulas
@@ -275,7 +275,7 @@![]()
- + Numerical Algorithms
@@ -289,7 +289,7 @@ 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 92fbf5181..3843cf267 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
@@ -252,7 +252,7 @@ a minimax rational approximation rescaled so that it is evaluated over [-1,1]. Note that while the rational approximation over [0,6] converges rapidly to the minimax solution it is rather ill-conditioned in practice. - Cody and Thacher [2] experienced the same issue and converted the polynomials into + Cody and Thacher [2] experienced the same issue and converted the polynomials into Chebeshev form to ensure stable computation. By experiment we found that the polynomials are just as stable in polynomial as Chebyshev form, provided they are computed over the interval [-1,1]. @@ -282,7 +282,7 @@
-[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 the exponential 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 c9fcd1d28..3706d1885 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 da48cf4a7..df82d4ad5 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 e91c09ed1..74112d228 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 7334fb9c5..d3ef6c478 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 5af3fe5bf..5c1a2a404 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 cd61ad3d5..70093fe54 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 a774cc4fb..b354ada76 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 b60db5d3f..b684c32ed 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 b14767590..bb5b83eb8 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 a13215279..ca899205a 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 7e2f3404a..7c50afb97 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
@@ -232,7 +232,7 @@ double result = pow<-5>(base);- + Acknowledgements
@@ -243,7 +243,7 @@ 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 d0681b470..e0d3ace06 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 2fe8780fc..2f34023ec 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 4b1c0e163..b6b2e8126 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 fbee54eda..c635ca2b3 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 01e60e712..9a7467df3 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 8cfb12771..1b355ca53 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 9f1e5e0be..df8361614 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 282dafc9c..5886959ef 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
@@ -163,7 +163,7 @@
![]()
- + Accuracy
@@ -182,7 +182,7 @@ with the wider exponent range of the long double types.
-Table 23. Errors In the Function ibeta(a,b,x)
+Table 23. Errors In the Function ibeta(a,b,x)
@@ -369,7 +369,7 @@ -Table 24. Errors In the Function ibetac(a,b,x)
+Table 24. Errors In the Function ibetac(a,b,x)
@@ -536,7 +536,7 @@ -Table 25. Errors In the Function beta(a, b, x)
+Table 25. Errors In the Function beta(a, b, x)
@@ -703,7 +703,7 @@ -Table 26. Errors In the Function betac(a,b,x)
+Table 26. Errors In the Function betac(a,b,x)
@@ -870,7 +870,7 @@ - + Testing
@@ -888,7 +888,7 @@ 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 d04d0bea3..4b88ff0b5 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 188d1ac3c..0f11be7cf 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 d28dc1a4d..6be08b728 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 e48fa47b7..7916b0fc5 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 ec31e5fea..cbff74dc0 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 b975ef675..867cba1df 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, b)
+Table 17. Errors In the Function tgamma_ratio(a, b)
@@ -327,7 +327,7 @@ - + Testing
@@ -336,7 +336,7 @@ 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 240fc1f2f..0013598ea 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 b7236c316..ab038ef69 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 bb319aa4d..085c6ded9 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 6daf27ff3..24b1d08da 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 69e78664a..1b97e526a 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 413512ac7..0390a7ee4 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 Polynomial
+Table 33. Peak Errors In the Associated Laguerre Polynomial
@@ -427,7 +427,7 @@ is very close to a root. - + Testing
@@ -437,7 +437,7 @@ 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 27c280c4c..09b1c94fa 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 P Function
+Table 30. Peak Errors In the Associated Legendre P Function
@@ -531,7 +531,7 @@ -Table 31. Peak Errors In the Legendre Q Function
+Table 31. Peak Errors In the Legendre Q Function
@@ -673,7 +673,7 @@ given here. - + Testing
@@ -683,7 +683,7 @@ 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 446ce9edf..0e6da214b 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 abaaa0264..2de987eca 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 2d24d4a38..495fe93ef 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
@@ -549,7 +549,7 @@
-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 b7f74f816..d9f4148a9 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -30,19 +30,26 @@ - + Boost-1.44.0
-
- +
+++
- Fixed incorrect range and support for Rayleigh distribution. -
- + Fixed numerical error in the quantile of the Student's T distribution: + the function was returning garbage values for non-integer degrees of + freedom between 2 and 3. +
+- + 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
@@ -203,7 +210,7 @@- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -222,7 +229,7 @@- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -255,7 +262,7 @@- + Milestone 2: Released September 10th 2006
@@ -296,7 +303,7 @@- + 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 96da98b1f..a3536f511 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 @@ b (medium priority).
- + Inverse Gamma
- @@ -67,7 +67,7 @@ is good enough (Medium Priority).
- + Polynomials
- @@ -77,7 +77,7 @@ not (Low Priority).
- + Elliptic Integrals
@@ -130,7 +130,7 @@
- + Inverse Hyperbolic Functions
@@ -140,7 +140,7 @@ This is probably only an issue for very high precision types (Low Priority).- + Statistical distributions
@@ -149,7 +149,7 @@ 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 939b944ef..18cd4b3e2 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 98a1913c8..ed041c020 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 dcc10c9e2..511fa5893 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
@@ -89,7 +89,7 @@ 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 302e971b3..653ccff72 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 06cf71192..0df4fa00a 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 8082c4e5c..ef1be57a7 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
@@ -561,7 +561,7 @@ 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 636b77aa1..1d28d6bf3 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 e4cdd6ff9..68739928e 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> @@ -157,7 +157,7 @@ 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 735d952d3..08a523cd4 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 37b7b7dff..eed7c2c8b 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 a7321061e..b456c8c3b 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
@@ -1035,7 +1035,7 @@- + 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 73c9951d8..97a00a7b7 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 659cdf9ac..ff3536c85 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 a3f63878b..dee27673f 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 16484a681..e41b1af04 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 2a9d88655..fbb76dbb6 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 a95c000ce..56ff426f3 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 31a3099fa..3a618a027 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/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index defae090b..567e7f7ee 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -3,6 +3,8 @@ [h4 Boost-1.44.0] * Fixed incorrect range and support for Rayleigh distribution. +* Fixed numerical error in the quantile of the Student's T distribution: the function was +returning garbage values for non-integer degrees of freedom between 2 and 3. [h4 Boost-1.41.0] diff --git a/include/boost/math/special_functions/detail/t_distribution_inv.hpp b/include/boost/math/special_functions/detail/t_distribution_inv.hpp index a58935f4e..3cfa68770 100644 --- a/include/boost/math/special_functions/detail/t_distribution_inv.hpp +++ b/include/boost/math/special_functions/detail/t_distribution_inv.hpp @@ -143,8 +143,8 @@ T inverse_students_t_body_series(T df, T u, const Policy& pol) // Figure out what the coefficients are, note these depend // only on the degrees of freedom (Eq 57 of Shaw): // - c[2] = 0.16666666666666666667 + 0.16666666666666666667 / df; T in = 1 / df; + c[2] = 0.16666666666666666667 + 0.16666666666666666667 * in; c[3] = (0.0083333333333333333333 * in + 0.066666666666666666667) * in + 0.058333333333333333333; @@ -152,7 +152,7 @@ T inverse_students_t_body_series(T df, T u, const Policy& pol) + 0.0017857142857142857143) * in + 0.026785714285714285714) * in + 0.025198412698412698413; - c[5] = (((2.7557319223985890653e10-6 * in + c[5] = (((2.7557319223985890653e-6 * in + 0.00037477954144620811287) * in - 0.0011078042328042328042) * in + 0.010559964726631393298) * in diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 8997d87c5..720afe4c4 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -40,8 +40,11 @@ project../../.. ../../regex/build//boost_regex shared: BOOST_REGEX_DYN_LINK=1 - # Sunpro has problems building regex as a shared lib: + # Sunpro and cygwin/Mingw have problems building regex as a shared lib: sun:static + gcc-mw:static + gcc-mingw:static + gcc-cygwin:static BOOST_ALL_NO_LIB=1 BOOST_UBLAS_UNSUPPORTED_COMPILER=0 . diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index c6bf8b94a..b3ac8c709 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -255,6 +255,98 @@ void test_spots(RealType) static_cast (-6.96455673428326), // t tolerance); + // + // Some special tests to exercise the double-precision approximations + // to the quantile: + // + // tolerance is 50 eps expressed as a persent: + // + tolerance = boost::math::tools::epsilon () * 5000; + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (2.00390625L), // degrees_of_freedom. + static_cast (0.5625L)), // probability. + static_cast (0.178133131573788108465134803511798566L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (1L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-10.1531703876088604621071476634194722L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (1L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (2.41421356237309504880168872421390942L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (2L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-3.81000381000571500952501666878143315L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (2L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.60356745147454630810732088527854144L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (4L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-2.56208431914409044861223047927635034L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (4L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.34439755550909142430681981315923574L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (6L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-2.28348667906973065861212495010082952L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (6L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.27334930914664286821103236660071906L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (8L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-2.16296475406014719458642055768894376L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (8L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.24031826078267310637634677726479038L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (10L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-2.09596136475109350926340169211429572L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (10L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.2212553950039221407185188573696834L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (2.125L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-3.62246031671091980110493455859296532L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (2.125L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.56905270993307293450392958697861969L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (3L), // degrees_of_freedom. + static_cast (0.03125L)), // probability. + static_cast (-2.90004411882995814036141778367917946L), // t. + tolerance); + BOOST_CHECK_CLOSE(boost::math::quantile( + students_t_distribution (3L), // degrees_of_freedom. + static_cast (0.875L)), // probability. + static_cast (1.42262528146180931868169289781115099L), // t. + tolerance); // Student's t pdf tests. // for PDF checks, use 100 eps tolerance expressed as a percent: