Mirror
/
cpython
mirror of https://github.com/python/cpython
4
1
Fork 0
Code Issues Releases Wiki Activity

Issue #3366: Add lgamma function to math module.

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
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
Doc/library/math.rst
View File

@ -318,6 +318,14 @@ Special functions
.. versionadded:: 2.7
.. function:: lgamma(x)
Return the natural logarithm of the absolute value of the Gamma
function at *x*.
.. versionadded:: 2.7
Constants
---------

105
Lib/test/math_testcases.txt
View File

@ -47,6 +47,111 @@
-- MPFR homepage at http://www.mpfr.org for more information about the
-- MPFR project.
---------------------------------------------------------
-- lgamma: log of absolute value of the gamma function --
---------------------------------------------------------
-- special values
lgam0000 lgamma 0.0 -> inf divide-by-zero
lgam0001 lgamma -0.0 -> inf divide-by-zero
lgam0002 lgamma inf -> inf
lgam0003 lgamma -inf -> inf
lgam0004 lgamma nan -> nan
-- negative integers
lgam0010 lgamma -1 -> inf divide-by-zero
lgam0011 lgamma -2 -> inf divide-by-zero
lgam0012 lgamma -1e16 -> inf divide-by-zero
lgam0013 lgamma -1e300 -> inf divide-by-zero
lgam0014 lgamma -1.79e308 -> inf divide-by-zero
-- small positive integers give factorials
lgam0020 lgamma 1 -> 0.0
lgam0021 lgamma 2 -> 0.0
lgam0022 lgamma 3 -> 0.69314718055994529
lgam0023 lgamma 4 -> 1.791759469228055
lgam0024 lgamma 5 -> 3.1780538303479458
lgam0025 lgamma 6 -> 4.7874917427820458
-- half integers
lgam0030 lgamma 0.5 -> 0.57236494292470008
lgam0031 lgamma 1.5 -> -0.12078223763524522
lgam0032 lgamma 2.5 -> 0.28468287047291918
lgam0033 lgamma 3.5 -> 1.2009736023470743
lgam0034 lgamma -0.5 -> 1.2655121234846454
lgam0035 lgamma -1.5 -> 0.86004701537648098
lgam0036 lgamma -2.5 -> -0.056243716497674054
lgam0037 lgamma -3.5 -> -1.309006684993042
-- values near 0
lgam0040 lgamma 0.1 -> 2.252712651734206
lgam0041 lgamma 0.01 -> 4.5994798780420219
lgam0042 lgamma 1e-8 -> 18.420680738180209
lgam0043 lgamma 1e-16 -> 36.841361487904734
lgam0044 lgamma 1e-30 -> 69.077552789821368
lgam0045 lgamma 1e-160 -> 368.41361487904732
lgam0046 lgamma 1e-308 -> 709.19620864216608
lgam0047 lgamma 5.6e-309 -> 709.77602713741896
lgam0048 lgamma 5.5e-309 -> 709.79404564292167
lgam0049 lgamma 1e-309 -> 711.49879373516012
lgam0050 lgamma 1e-323 -> 743.74692474082133
lgam0051 lgamma 5e-324 -> 744.44007192138122
lgam0060 lgamma -0.1 -> 2.3689613327287886
lgam0061 lgamma -0.01 -> 4.6110249927528013
lgam0062 lgamma -1e-8 -> 18.420680749724522
lgam0063 lgamma -1e-16 -> 36.841361487904734
lgam0064 lgamma -1e-30 -> 69.077552789821368
lgam0065 lgamma -1e-160 -> 368.41361487904732
lgam0066 lgamma -1e-308 -> 709.19620864216608
lgam0067 lgamma -5.6e-309 -> 709.77602713741896
lgam0068 lgamma -5.5e-309 -> 709.79404564292167
lgam0069 lgamma -1e-309 -> 711.49879373516012
lgam0070 lgamma -1e-323 -> 743.74692474082133
lgam0071 lgamma -5e-324 -> 744.44007192138122
-- values near negative integers
lgam0080 lgamma -0.99999999999999989 -> 36.736800569677101
lgam0081 lgamma -1.0000000000000002 -> 36.043653389117154
lgam0082 lgamma -1.9999999999999998 -> 35.350506208557213
lgam0083 lgamma -2.0000000000000004 -> 34.657359027997266
lgam0084 lgamma -100.00000000000001 -> -331.85460524980607
lgam0085 lgamma -99.999999999999986 -> -331.85460524980596
-- large inputs
lgam0100 lgamma 170 -> 701.43726380873704
lgam0101 lgamma 171 -> 706.57306224578736
lgam0102 lgamma 171.624 -> 709.78077443669895
lgam0103 lgamma 171.625 -> 709.78591682948365
lgam0104 lgamma 172 -> 711.71472580228999
lgam0105 lgamma 2000 -> 13198.923448054265
lgam0106 lgamma 2.55998332785163e305 -> 1.7976931348623099e+308
lgam0107 lgamma 2.55998332785164e305 -> inf overflow
lgam0108 lgamma 1.7e308 -> inf overflow
-- inputs for which gamma(x) is tiny
lgam0120 lgamma -100.5 -> -364.90096830942736
lgam0121 lgamma -160.5 -> -656.88005261126432
lgam0122 lgamma -170.5 -> -707.99843314507882
lgam0123 lgamma -171.5 -> -713.14301641168481
lgam0124 lgamma -176.5 -> -738.95247590846486
lgam0125 lgamma -177.5 -> -744.13144651738037
lgam0126 lgamma -178.5 -> -749.3160351186001
lgam0130 lgamma -1000.5 -> -5914.4377011168517
lgam0131 lgamma -30000.5 -> -279278.6629959144
lgam0132 lgamma -4503599627370495.5 -> -1.5782258434492883e+17
-- results close to 0: positive argument ...
lgam0150 lgamma 0.99999999999999989 -> 6.4083812134800075e-17
lgam0151 lgamma 1.0000000000000002 -> -1.2816762426960008e-16
lgam0152 lgamma 1.9999999999999998 -> -9.3876980655431170e-17
lgam0153 lgamma 2.0000000000000004 -> 1.8775396131086244e-16
-- ... and negative argument
lgam0160 lgamma -2.7476826467 -> -5.2477408147689136e-11
lgam0161 lgamma -2.457024738 -> 3.3464637541912932e-10
---------------------------
-- gamma: Gamma function --
---------------------------

50
Lib/test/test_math.py
View File

@ -48,6 +48,36 @@ def to_ulps(x):
n = ~(n+2**63)
return n
def ulps_check(expected, got, ulps=20):
"""Given non-NaN floats `expected` and `got`,
check that they're equal to within the given number of ulps.
Returns None on success and an error message on failure."""
ulps_error = to_ulps(got) - to_ulps(expected)
if abs(ulps_error) <= ulps:
return None
return "error = {} ulps; permitted error = {} ulps".format(ulps_error,
ulps)
def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323):
"""Determine whether non-NaN floats a and b are equal to within a
(small) rounding error. The default values for rel_err and
abs_err are chosen to be suitable for platforms where a float is
represented by an IEEE 754 double. They allow an error of between
9 and 19 ulps."""
# need to special case infinities, since inf - inf gives nan
if math.isinf(expected) and got == expected:
return None
error = got - expected
permitted_error = max(abs_err, rel_err * abs(expected))
if abs(error) < permitted_error:
return None
return "error = {}; permitted error = {}".format(error,
permitted_error)
def parse_mtestfile(fname):
"""Parse a file with test values
@ -952,13 +982,23 @@ class MathTests(unittest.TestCase):
except OverflowError:
got = 'OverflowError'
diff_ulps = None
accuracy_failure = None
if isinstance(got, float) and isinstance(expected, float):
if math.isnan(expected) and math.isnan(got):
continue
if not math.isnan(expected) and not math.isnan(got):
diff_ulps = to_ulps(expected) - to_ulps(got)
if abs(diff_ulps) <= ALLOWED_ERROR:
# we use different closeness criteria for
# different functions.
if fn == 'gamma':
accuracy_failure = ulps_check(expected, got, 20)
elif fn == 'lgamma':
accuracy_failure = acc_check(expected, got,
rel_err = 5e-15,
abs_err = 5e-15)
else:
raise ValueError("don't know how to check accuracy "
"for this function")
if accuracy_failure is None:
continue
if isinstance(got, str) and isinstance(expected, str):
@ -966,8 +1006,8 @@ class MathTests(unittest.TestCase):
continue
fail_msg = fail_fmt.format(id, fn, arg, expected, got)
if diff_ulps is not None:
fail_msg += ' ({} ulps)'.format(diff_ulps)
if accuracy_failure is not None:
fail_msg += ' ({})'.format(accuracy_failure)
failures.append(fail_msg)
if failures:

2
Misc/NEWS
View File

@ -1654,7 +1654,7 @@ Extension Modules
- Issue #7078: Set struct.__doc__ from _struct.__doc__.
- Issue #3366: Add gamma function to math module.
- Issue #3366: Add gamma, lgamma functions to math module.
- Issue #6823: Allow time.strftime() to accept a tuple with a isdst field
outside of the range of [-1, 1] by normalizing the value to within that

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},