mirrors/cpython
1
0
Fork 0
mirror of https://github.com/python/cpython.git synced 2025-09-26 10:19:53 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions 8

Issue #3366: Add lgamma function to math module.

Browse source
This commit is contained in:
Mark Dickinson 2009-12-11 17:29:33 +00:00
parent 5cc4e2a040
commit 9be87bc992
5 changed files with 216 additions and 6 deletions
Download patch file Download diff file Expand all files Collapse all files

57
Modules/mathmodule.c
View file

@ -321,6 +321,60 @@ m_tgamma(double x)
return r;
}
/*
lgamma: natural log of the absolute value of the Gamma function.
For large arguments, Lanczos' formula works extremely well here.
*/
static double
m_lgamma(double x)
{
double r, absx;
/* special cases */
if (!Py_IS_FINITE(x)) {
if (Py_IS_NAN(x))
return x; /* lgamma(nan) = nan */
else
return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
}
/* integer arguments */
if (x == floor(x) && x <= 2.0) {
if (x <= 0.0) {
errno = EDOM; /* lgamma(n) = inf, divide-by-zero for */
return Py_HUGE_VAL; /* integers n <= 0 */
}
else {
return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
}
}
absx = fabs(x);
/* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
if (absx < 1e-20)
return -log(absx);
/* Lanczos' formula */
if (x > 0.0) {
/* we could save a fraction of a ulp in accuracy by having a
second set of numerator coefficients for lanczos_sum that
absorbed the exp(-lanczos_g) term, and throwing out the
lanczos_g subtraction below; it's probably not worth it. */
r = log(lanczos_sum(x)) - lanczos_g +
(x-0.5)*(log(x+lanczos_g-0.5)-1);
}
else {
r = log(pi) - log(fabs(sinpi(absx))) - log(absx) -
(log(lanczos_sum(absx)) - lanczos_g +
(absx-0.5)*(log(absx+lanczos_g-0.5)-1));
}
if (Py_IS_INFINITY(r))
errno = ERANGE;
return r;
}
/*
wrapper for atan2 that deals directly with special cases before
delegating to the platform libm for the remaining cases. This
@ -639,6 +693,8 @@ FUNC1(floor, floor, 0,
"This is the largest integral value <= x.")
FUNC1A(gamma, m_tgamma,
"gamma(x)\n\nGamma function at x.")
FUNC1A(lgamma, m_lgamma,
"lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
FUNC1(log1p, log1p, 1,
"log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
"The result is computed in a way which is accurate for x near zero.")
@ -1375,6 +1431,7 @@ static PyMethodDef math_methods[] = {
{"isinf", math_isinf, METH_O, math_isinf_doc},
{"isnan", math_isnan, METH_O, math_isnan_doc},
{"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
{"lgamma", math_lgamma, METH_O, math_lgamma_doc},
{"log", math_log, METH_VARARGS, math_log_doc},
{"log1p", math_log1p, METH_O, math_log1p_doc},
{"log10", math_log10, METH_O, math_log10_doc},