std.internal.math.gammafunction

Implementation of the gamma and beta functions, and their integrals.
License
Boost License 1.0.
Copyright
Based on the CEPHES math library, which is
Copyright (C) 1994 Stephen L. Moshier (moshier@world.std.com).
Authors
Stephen L. Moshier (original C code). Conversion to D by Don Clugston

Functions 20

private fnreal largestNaNPayload(real first, real[] rest ...) pure nothrow @safe @nogc

private fnreal gammaStirling(real x) pure nothrow @safe @nogc

private fnreal igammaTemmeLarge(real a, real x, bool compl) pure nothrow @safe @nogc

fnreal gamma(real x) pure nothrow @safe @nogcThe Gamma function, (x)

fnreal logGamma(real x) pure nothrow @safe @nogcNatural logarithm of gamma function.

fnreal sgnGamma(in real x) pure nothrow @safe @nogcsgn((x))

private fnreal betaLarge(in real x, in real y) pure nothrow @safe @nogc

fnreal beta(in real x, in real y) pure nothrow @safe @nogcB(x,y)

private fnreal logBeta(real x, in real y) pure nothrow @safe @nogc

fnreal betaIncomplete(real aa, real bb, real xx ) pure nothrow @safe @nogcIncomplete beta integral

fnreal betaIncompleteInv(real aa, real bb, real yy0 ) pure nothrow @safe @nogcInverse of incomplete beta integral

private fnreal betaDistExpansion1(real a, real b, real x ) pure nothrow @safe @nogc

private fnreal betaDistExpansion2(real a, real b, real x ) pure nothrow @safe @nogc

private fnreal betaDistPowerSeries(real a, real b, real x ) pure nothrow @safe @nogc

fnreal gammaIncomplete(real a, real x ) pure nothrow @safe @nogcIncomplete gamma integral and its complement

fnreal gammaIncompleteCompl(real a, real x ) pure nothrow @safe @nogcditto

fnreal gammaIncompleteComplInv(real a, real p) pure nothrow @safe @nogcInverse of complemented incomplete gamma integral

fnreal digamma(real x) pure nothrow @safe @nogcDigamma function

fnreal logmdigamma(real x) pure nothrow @safe @nogcLog Minus Digamma function

fnreal logmdigammaInverse(real y) pure nothrow @safe @nogcInverse of the Log Minus Digamma function

private enumvarSQRT2PI = 2.50662827463100050242E0L

private varreal EULERGAMMA = 0.57721_56649_01532_86060_65120_90082_40243_10421_59335_93992L

private varreal[8] GammaNumeratorCoeffs

private varreal[9] GammaDenominatorCoeffs

private varreal[9] GammaSmallCoeffs

private varreal[9] GammaSmallNegCoeffs

private varreal[7] logGammaStirlingCoeffs

private varreal[7] logGammaNumerator

private varreal[8] logGammaDenominator

private enumvarLN_GAMMA_STIRLING_LB = 13.0L

private enumvarBETA_BIG = 9.223372036854775808e18L

private enumvarBETA_BIGINV = 1.084202172485504434007e-19L

varreal [7] Bn_n