cpython-lru_cache-weakref: Modules/mathmodule.c annotate

annotate Modules/mathmodule.c @ 58765:2ba7677bfa95 legacy-trunk

testCopysign was defined twice in test_math; combine the definitions

author	Mark Dickinson <dickinsm@gmail.com>
date	Sat, 06 Feb 2010 23:11:25 +0000
parents	0f8a58792563
children	fd25030223b0

rev	line source
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1 /* Math module -- standard C math library functions, pi and e */
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	2
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	3 /* Here are some comments from Tim Peters, extracted from the
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	4 discussion attached to http://bugs.python.org/issue1640. They
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	5 describe the general aims of the math module with respect to
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	6 special values, IEEE-754 floating-point exceptions, and Python
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	7 exceptions.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	8
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	9 These are the "spirit of 754" rules:
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	10
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	11 1. If the mathematical result is a real number, but of magnitude too
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	12 large to approximate by a machine float, overflow is signaled and the
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	13 result is an infinity (with the appropriate sign).
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	14
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	15 2. If the mathematical result is a real number, but of magnitude too
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	16 small to approximate by a machine float, underflow is signaled and the
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	17 result is a zero (with the appropriate sign).
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	18
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	19 3. At a singularity (a value x such that the limit of f(y) as y
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	20 approaches x exists and is an infinity), "divide by zero" is signaled
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	21 and the result is an infinity (with the appropriate sign). This is
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	22 complicated a little by that the left-side and right-side limits may
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	23 not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	24 from the positive or negative directions. In that specific case, the
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	25 sign of the zero determines the result of 1/0.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	26
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	27 4. At a point where a function has no defined result in the extended
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	28 reals (i.e., the reals plus an infinity or two), invalid operation is
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	29 signaled and a NaN is returned.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	30
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	31 And these are what Python has historically /tried/ to do (but not
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	32 always successfully, as platform libm behavior varies a lot):
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	33
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	34 For #1, raise OverflowError.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	35
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	36 For #2, return a zero (with the appropriate sign if that happens by
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	37 accident ;-)).
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	38
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	39 For #3 and #4, raise ValueError. It may have made sense to raise
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	40 Python's ZeroDivisionError in #3, but historically that's only been
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	41 raised for division by zero and mod by zero.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	42
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	43 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	44
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	45 /*
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	46 In general, on an IEEE-754 platform the aim is to follow the C99
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	47 standard, including Annex 'F', whenever possible. Where the
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	48 standard recommends raising the 'divide-by-zero' or 'invalid'
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	49 floating-point exceptions, Python should raise a ValueError. Where
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	50 the standard recommends raising 'overflow', Python should raise an
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	51 OverflowError. In all other circumstances a value should be
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	52 returned.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	53 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	54
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	55 #include "Python.h"
57756 b206ad8cf5bf Issue #3366: Add expm1 function to math module. Thanks Eric Smith for Mark Dickinson <dickinsm@gmail.com> parents: 57655 diff changeset	56 #include "_math.h"
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	57
44940 12099143724f Add prototypes to get the mathmodule.c to compile on OSF1 5.1 (Tru64) Neal Norwitz <nnorwitz@gmail.com> parents: 44488 diff changeset	58 #ifdef _OSF_SOURCE
12099143724f Add prototypes to get the mathmodule.c to compile on OSF1 5.1 (Tru64) Neal Norwitz <nnorwitz@gmail.com> parents: 44488 diff changeset	59 /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
12099143724f Add prototypes to get the mathmodule.c to compile on OSF1 5.1 (Tru64) Neal Norwitz <nnorwitz@gmail.com> parents: 44488 diff changeset	60 extern double copysign(double, double);
12099143724f Add prototypes to get the mathmodule.c to compile on OSF1 5.1 (Tru64) Neal Norwitz <nnorwitz@gmail.com> parents: 44488 diff changeset	61 #endif
12099143724f Add prototypes to get the mathmodule.c to compile on OSF1 5.1 (Tru64) Neal Norwitz <nnorwitz@gmail.com> parents: 44488 diff changeset	62
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	63 /*
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	64 sin(pi*x), giving accurate results for all finite x (especially x
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	65 integral or close to an integer). This is here for use in the
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	66 reflection formula for the gamma function. It conforms to IEEE
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	67 754-2008 for finite arguments, but not for infinities or nans.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	68 */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	69
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	70 static const double pi = 3.141592653589793238462643383279502884197;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	71 static const double sqrtpi = 1.772453850905516027298167483341145182798;
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	72
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	73 static double
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	74 sinpi(double x)
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	75 {
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	76 double y, r;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	77 int n;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	78 /* this function should only ever be called for finite arguments */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	79 assert(Py_IS_FINITE(x));
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	80 y = fmod(fabs(x), 2.0);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	81 n = (int)round(2.0*y);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	82 assert(0 <= n && n <= 4);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	83 switch (n) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	84 case 0:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	85 r = sin(pi*y);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	86 break;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	87 case 1:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	88 r = cos(pi*(y-0.5));
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	89 break;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	90 case 2:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	91 /* N.B. -sin(pi(y-1.0)) is not* equivalent: it would give
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	92 -0.0 instead of 0.0 when y == 1.0. */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	93 r = sin(pi*(1.0-y));
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	94 break;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	95 case 3:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	96 r = -cos(pi*(y-1.5));
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	97 break;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	98 case 4:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	99 r = sin(pi*(y-2.0));
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	100 break;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	101 default:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	102 assert(0); /* should never get here */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	103 r = -1.23e200; /* silence gcc warning */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	104 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	105 return copysign(1.0, x)*r;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	106 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	107
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	108 /* Implementation of the real gamma function. In extensive but non-exhaustive
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	109 random tests, this function proved accurate to within <= 10 ulps across the
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	110 entire float domain. Note that accuracy may depend on the quality of the
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	111 system math functions, the pow function in particular. Special cases
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	112 follow C99 annex F. The parameters and method are tailored to platforms
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	113 whose double format is the IEEE 754 binary64 format.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	114
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	115 Method: for x > 0.0 we use the Lanczos approximation with parameters N=13
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	116 and g=6.024680040776729583740234375; these parameters are amongst those
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	117 used by the Boost library. Following Boost (again), we re-express the
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	118 Lanczos sum as a rational function, and compute it that way. The
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	119 coefficients below were computed independently using MPFR, and have been
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	120 double-checked against the coefficients in the Boost source code.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	121
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	122 For x < 0.0 we use the reflection formula.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	123
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	124 There's one minor tweak that deserves explanation: Lanczos' formula for
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	125 Gamma(x) involves computing pow(x+g-0.5, x-0.5) / exp(x+g-0.5). For many x
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	126 values, x+g-0.5 can be represented exactly. However, in cases where it
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	127 can't be represented exactly the small error in x+g-0.5 can be magnified
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	128 significantly by the pow and exp calls, especially for large x. A cheap
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	129 correction is to multiply by (1 + e*g/(x+g-0.5)), where e is the error
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	130 involved in the computation of x+g-0.5 (that is, e = computed value of
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	131 x+g-0.5 - exact value of x+g-0.5). Here's the proof:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	132
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	133 Correction factor
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	134 -----------------
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	135 Write x+g-0.5 = y-e, where y is exactly representable as an IEEE 754
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	136 double, and e is tiny. Then:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	137
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	138 pow(x+g-0.5,x-0.5)/exp(x+g-0.5) = pow(y-e, x-0.5)/exp(y-e)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	139 = pow(y, x-0.5)/exp(y) * C,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	140
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	141 where the correction_factor C is given by
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	142
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	143 C = pow(1-e/y, x-0.5) * exp(e)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	144
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	145 Since e is tiny, pow(1-e/y, x-0.5) ~ 1-(x-0.5)*e/y, and exp(x) ~ 1+e, so:
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	146
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	147 C ~ (1-(x-0.5)e/y) (1+e) ~ 1 + e*(y-(x-0.5))/y
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	148
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	149 But y-(x-0.5) = g+e, and g+e ~ g. So we get C ~ 1 + e*g/y, and
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	150
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	151 pow(x+g-0.5,x-0.5)/exp(x+g-0.5) ~ pow(y, x-0.5)/exp(y) * (1 + e*g/y),
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	152
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	153 Note that for accuracy, when computing r*C it's better to do
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	154
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	155 r + eg/yr;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	156
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	157 than
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	158
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	159 r * (1 + e*g/y);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	160
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	161 since the addition in the latter throws away most of the bits of
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	162 information in e*g/y.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	163 */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	164
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	165 #define LANCZOS_N 13
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	166 static const double lanczos_g = 6.024680040776729583740234375;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	167 static const double lanczos_g_minus_half = 5.524680040776729583740234375;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	168 static const double lanczos_num_coeffs[LANCZOS_N] = {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	169 23531376880.410759688572007674451636754734846804940,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	170 42919803642.649098768957899047001988850926355848959,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	171 35711959237.355668049440185451547166705960488635843,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	172 17921034426.037209699919755754458931112671403265390,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	173 6039542586.3520280050642916443072979210699388420708,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	174 1439720407.3117216736632230727949123939715485786772,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	175 248874557.86205415651146038641322942321632125127801,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	176 31426415.585400194380614231628318205362874684987640,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	177 2876370.6289353724412254090516208496135991145378768,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	178 186056.26539522349504029498971604569928220784236328,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	179 8071.6720023658162106380029022722506138218516325024,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	180 210.82427775157934587250973392071336271166969580291,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	181 2.5066282746310002701649081771338373386264310793408
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	182 };
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	183
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	184 /* denominator is x(x+1)...(x+LANCZOS_N-2) /
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	185 static const double lanczos_den_coeffs[LANCZOS_N] = {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	186 0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	187 13339535.0, 2637558.0, 357423.0, 32670.0, 1925.0, 66.0, 1.0};
19750 35b6a1d0b1e0 Rework the way we try to check for libm overflow, given that C99 no longer Tim Peters <tim.peters@gmail.com> parents: 19730 diff changeset	188
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	189 /* gamma values for small positive integers, 1 though NGAMMA_INTEGRAL */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	190 #define NGAMMA_INTEGRAL 23
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	191 static const double gamma_integral[NGAMMA_INTEGRAL] = {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	192 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	193 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	194 1307674368000.0, 20922789888000.0, 355687428096000.0,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	195 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	196 51090942171709440000.0, 1124000727777607680000.0,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	197 };
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	198
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	199 /* Lanczos' sum L_g(x), for positive x */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	200
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	201 static double
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	202 lanczos_sum(double x)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	203 {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	204 double num = 0.0, den = 0.0;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	205 int i;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	206 assert(x > 0.0);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	207 /* evaluate the rational function lanczos_sum(x). For large
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	208 x, the obvious algorithm risks overflow, so we instead
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	209 rescale the denominator and numerator of the rational
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	210 function by x**(1-LANCZOS_N) and treat this as a
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	211 rational function in 1/x. This also reduces the error for
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	212 larger x values. The choice of cutoff point (5.0 below) is
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	213 somewhat arbitrary; in tests, smaller cutoff values than
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	214 this resulted in lower accuracy. */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	215 if (x < 5.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	216 for (i = LANCZOS_N; --i >= 0; ) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	217 num = num * x + lanczos_num_coeffs[i];
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	218 den = den * x + lanczos_den_coeffs[i];
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	219 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	220 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	221 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	222 for (i = 0; i < LANCZOS_N; i++) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	223 num = num / x + lanczos_num_coeffs[i];
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	224 den = den / x + lanczos_den_coeffs[i];
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	225 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	226 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	227 return num/den;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	228 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	229
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	230 static double
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	231 m_tgamma(double x)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	232 {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	233 double absx, r, y, z, sqrtpow;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	234
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	235 /* special cases */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	236 if (!Py_IS_FINITE(x)) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	237 if (Py_IS_NAN(x) \|\| x > 0.0)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	238 return x; /* tgamma(nan) = nan, tgamma(inf) = inf */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	239 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	240 errno = EDOM;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	241 return Py_NAN; /* tgamma(-inf) = nan, invalid */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	242 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	243 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	244 if (x == 0.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	245 errno = EDOM;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	246 return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	247 }
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	248
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	249 /* integer arguments */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	250 if (x == floor(x)) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	251 if (x < 0.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	252 errno = EDOM; /* tgamma(n) = nan, invalid for */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	253 return Py_NAN; /* negative integers n */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	254 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	255 if (x <= NGAMMA_INTEGRAL)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	256 return gamma_integral[(int)x - 1];
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	257 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	258 absx = fabs(x);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	259
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	260 /* tiny arguments: tgamma(x) ~ 1/x for x near 0 */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	261 if (absx < 1e-20) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	262 r = 1.0/x;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	263 if (Py_IS_INFINITY(r))
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	264 errno = ERANGE;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	265 return r;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	266 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	267
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	268 /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	269 x > 200, and underflows to +-0.0 for x < -200, not a negative
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	270 integer. */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	271 if (absx > 200.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	272 if (x < 0.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	273 return 0.0/sinpi(x);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	274 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	275 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	276 errno = ERANGE;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	277 return Py_HUGE_VAL;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	278 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	279 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	280
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	281 y = absx + lanczos_g_minus_half;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	282 /* compute error in sum */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	283 if (absx > lanczos_g_minus_half) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	284 /* note: the correction can be foiled by an optimizing
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	285 compiler that (incorrectly) thinks that an expression like
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	286 a + b - a - b can be optimized to 0.0. This shouldn't
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	287 happen in a standards-conforming compiler. */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	288 double q = y - absx;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	289 z = q - lanczos_g_minus_half;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	290 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	291 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	292 double q = y - lanczos_g_minus_half;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	293 z = q - absx;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	294 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	295 z = z * lanczos_g / y;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	296 if (x < 0.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	297 r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	298 r -= z * r;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	299 if (absx < 140.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	300 r /= pow(y, absx - 0.5);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	301 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	302 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	303 sqrtpow = pow(y, absx / 2.0 - 0.25);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	304 r /= sqrtpow;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	305 r /= sqrtpow;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	306 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	307 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	308 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	309 r = lanczos_sum(absx) / exp(y);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	310 r += z * r;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	311 if (absx < 140.0) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	312 r *= pow(y, absx - 0.5);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	313 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	314 else {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	315 sqrtpow = pow(y, absx / 2.0 - 0.25);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	316 r *= sqrtpow;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	317 r *= sqrtpow;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	318 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	319 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	320 if (Py_IS_INFINITY(r))
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	321 errno = ERANGE;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	322 return r;
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	323 }
56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	324
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	325 /*
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	326 lgamma: natural log of the absolute value of the Gamma function.
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	327 For large arguments, Lanczos' formula works extremely well here.
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	328 */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	329
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	330 static double
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	331 m_lgamma(double x)
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	332 {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	333 double r, absx;
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	334
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	335 /* special cases */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	336 if (!Py_IS_FINITE(x)) {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	337 if (Py_IS_NAN(x))
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	338 return x; /* lgamma(nan) = nan */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	339 else
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	340 return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	341 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	342
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	343 /* integer arguments */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	344 if (x == floor(x) && x <= 2.0) {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	345 if (x <= 0.0) {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	346 errno = EDOM; /* lgamma(n) = inf, divide-by-zero for */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	347 return Py_HUGE_VAL; /* integers n <= 0 */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	348 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	349 else {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	350 return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	351 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	352 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	353
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	354 absx = fabs(x);
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	355 /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	356 if (absx < 1e-20)
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	357 return -log(absx);
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	358
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	359 /* Lanczos' formula */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	360 if (x > 0.0) {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	361 /* we could save a fraction of a ulp in accuracy by having a
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	362 second set of numerator coefficients for lanczos_sum that
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	363 absorbed the exp(-lanczos_g) term, and throwing out the
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	364 lanczos_g subtraction below; it's probably not worth it. */
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	365 r = log(lanczos_sum(x)) - lanczos_g +
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	366 (x-0.5)*(log(x+lanczos_g-0.5)-1);
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	367 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	368 else {
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	369 r = log(pi) - log(fabs(sinpi(absx))) - log(absx) -
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	370 (log(lanczos_sum(absx)) - lanczos_g +
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	371 (absx-0.5)*(log(absx+lanczos_g-0.5)-1));
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	372 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	373 if (Py_IS_INFINITY(r))
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	374 errno = ERANGE;
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	375 return r;
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	376 }
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	377
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	378 /*
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	379 Implementations of the error function erf(x) and the complementary error
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	380 function erfc(x).
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	381
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	382 Method: following 'Numerical Recipes' by Flannery, Press et. al. (2nd ed.,
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	383 Cambridge University Press), we use a series approximation for erf for
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	384 small x, and a continued fraction approximation for erfc(x) for larger x;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	385 combined with the relations erf(-x) = -erf(x) and erfc(x) = 1.0 - erf(x),
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	386 this gives us erf(x) and erfc(x) for all x.
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	387
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	388 The series expansion used is:
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	389
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	390 erf(x) = xexp(-xx)/sqrt(pi) * [
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	391 2/1 + 4/3 x2 + 8/15 x4 + 16/105 x**6 + ...]
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	392
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	393 The coefficient of x(2k-2) here is 4kfactorial(k)/factorial(2k).
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	394 This series converges well for smallish x, but slowly for larger x.
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	395
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	396 The continued fraction expansion used is:
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	397
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	398 erfc(x) = xexp(-xx)/sqrt(pi) * [1/(0.5 + x2 -) 0.5/(2.5 + x2 - )
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	399 3.0/(4.5 + x2 - ) 7.5/(6.5 + x2 - ) ...]
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	400
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	401 after the first term, the general term has the form:
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	402
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	403 k(k-0.5)/(2k+0.5 + x**2 - ...).
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	404
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	405 This expansion converges fast for larger x, but convergence becomes
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	406 infinitely slow as x approaches 0.0. The (somewhat naive) continued
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	407 fraction evaluation algorithm used below also risks overflow for large x;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	408 but for large x, erfc(x) == 0.0 to within machine precision. (For
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	409 example, erfc(30.0) is approximately 2.56e-393).
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	410
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	411 Parameters: use series expansion for abs(x) < ERF_SERIES_CUTOFF and
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	412 continued fraction expansion for ERF_SERIES_CUTOFF <= abs(x) <
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	413 ERFC_CONTFRAC_CUTOFF. ERFC_SERIES_TERMS and ERFC_CONTFRAC_TERMS are the
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	414 numbers of terms to use for the relevant expansions. */
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	415
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	416 #define ERF_SERIES_CUTOFF 1.5
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	417 #define ERF_SERIES_TERMS 25
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	418 #define ERFC_CONTFRAC_CUTOFF 30.0
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	419 #define ERFC_CONTFRAC_TERMS 50
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	420
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	421 /*
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	422 Error function, via power series.
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	423
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	424 Given a finite float x, return an approximation to erf(x).
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	425 Converges reasonably fast for small x.
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	426 */
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	427
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	428 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	429 m_erf_series(double x)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	430 {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	431 double x2, acc, fk;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	432 int i;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	433
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	434 x2 = x * x;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	435 acc = 0.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	436 fk = (double)ERF_SERIES_TERMS + 0.5;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	437 for (i = 0; i < ERF_SERIES_TERMS; i++) {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	438 acc = 2.0 + x2 * acc / fk;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	439 fk -= 1.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	440 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	441 return acc * x * exp(-x2) / sqrtpi;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	442 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	443
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	444 /*
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	445 Complementary error function, via continued fraction expansion.
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	446
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	447 Given a positive float x, return an approximation to erfc(x). Converges
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	448 reasonably fast for x large (say, x > 2.0), and should be safe from
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	449 overflow if x and nterms are not too large. On an IEEE 754 machine, with x
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	450 <= 30.0, we're safe up to nterms = 100. For x >= 30.0, erfc(x) is smaller
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	451 than the smallest representable nonzero float. */
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	452
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	453 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	454 m_erfc_contfrac(double x)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	455 {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	456 double x2, a, da, p, p_last, q, q_last, b;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	457 int i;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	458
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	459 if (x >= ERFC_CONTFRAC_CUTOFF)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	460 return 0.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	461
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	462 x2 = x*x;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	463 a = 0.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	464 da = 0.5;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	465 p = 1.0; p_last = 0.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	466 q = da + x2; q_last = 1.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	467 for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	468 double temp;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	469 a += da;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	470 da += 2.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	471 b = da + x2;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	472 temp = p; p = bp - ap_last; p_last = temp;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	473 temp = q; q = bq - aq_last; q_last = temp;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	474 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	475 return p / q * x * exp(-x2) / sqrtpi;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	476 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	477
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	478 /* Error function erf(x), for general x */
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	479
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	480 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	481 m_erf(double x)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	482 {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	483 double absx, cf;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	484
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	485 if (Py_IS_NAN(x))
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	486 return x;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	487 absx = fabs(x);
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	488 if (absx < ERF_SERIES_CUTOFF)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	489 return m_erf_series(x);
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	490 else {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	491 cf = m_erfc_contfrac(absx);
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	492 return x > 0.0 ? 1.0 - cf : cf - 1.0;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	493 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	494 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	495
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	496 /* Complementary error function erfc(x), for general x. */
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	497
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	498 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	499 m_erfc(double x)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	500 {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	501 double absx, cf;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	502
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	503 if (Py_IS_NAN(x))
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	504 return x;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	505 absx = fabs(x);
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	506 if (absx < ERF_SERIES_CUTOFF)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	507 return 1.0 - m_erf_series(x);
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	508 else {
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	509 cf = m_erfc_contfrac(absx);
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	510 return x > 0.0 ? cf : 2.0 - cf;
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	511 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	512 }
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	513
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	514 /*
46507 022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	515 wrapper for atan2 that deals directly with special cases before
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	516 delegating to the platform libm for the remaining cases. This
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	517 is necessary to get consistent behaviour across platforms.
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	518 Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	519 always follow C99.
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	520 */
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	521
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	522 static double
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	523 m_atan2(double y, double x)
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	524 {
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	525 if (Py_IS_NAN(x) \|\| Py_IS_NAN(y))
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	526 return Py_NAN;
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	527 if (Py_IS_INFINITY(y)) {
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	528 if (Py_IS_INFINITY(x)) {
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	529 if (copysign(1., x) == 1.)
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	530 /* atan2(+-inf, +inf) == +-pi/4 */
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	531 return copysign(0.25*Py_MATH_PI, y);
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	532 else
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	533 /* atan2(+-inf, -inf) == +-pi3/4 /
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	534 return copysign(0.75*Py_MATH_PI, y);
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	535 }
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	536 /* atan2(+-inf, x) == +-pi/2 for finite x */
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	537 return copysign(0.5*Py_MATH_PI, y);
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	538 }
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	539 if (Py_IS_INFINITY(x) \|\| y == 0.) {
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	540 if (copysign(1., x) == 1.)
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	541 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	542 return copysign(0., y);
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	543 else
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	544 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	545 return copysign(Py_MATH_PI, y);
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	546 }
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	547 return atan2(y, x);
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	548 }
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	549
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	550 /*
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	551 Various platforms (Solaris, OpenBSD) do nonstandard things for log(0),
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	552 log(-ve), log(NaN). Here are wrappers for log and log10 that deal with
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	553 special values directly, passing positive non-special values through to
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	554 the system log/log10.
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	555 */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	556
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	557 static double
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	558 m_log(double x)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	559 {
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	560 if (Py_IS_FINITE(x)) {
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	561 if (x > 0.0)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	562 return log(x);
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	563 errno = EDOM;
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	564 if (x == 0.0)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	565 return -Py_HUGE_VAL; /* log(0) = -inf */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	566 else
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	567 return Py_NAN; /* log(-ve) = nan */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	568 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	569 else if (Py_IS_NAN(x))
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	570 return x; /* log(nan) = nan */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	571 else if (x > 0.0)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	572 return x; /* log(inf) = inf */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	573 else {
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	574 errno = EDOM;
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	575 return Py_NAN; /* log(-inf) = nan */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	576 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	577 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	578
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	579 static double
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	580 m_log10(double x)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	581 {
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	582 if (Py_IS_FINITE(x)) {
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	583 if (x > 0.0)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	584 return log10(x);
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	585 errno = EDOM;
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	586 if (x == 0.0)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	587 return -Py_HUGE_VAL; /* log10(0) = -inf */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	588 else
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	589 return Py_NAN; /* log10(-ve) = nan */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	590 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	591 else if (Py_IS_NAN(x))
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	592 return x; /* log10(nan) = nan */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	593 else if (x > 0.0)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	594 return x; /* log10(inf) = inf */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	595 else {
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	596 errno = EDOM;
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	597 return Py_NAN; /* log10(-inf) = nan */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	598 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	599 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	600
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	601
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	602 /* Call is_error when errno != 0, and where x is the result libm
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	603 * returned. is_error will usually set up an exception and return
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	604 * true (1), but may return false (0) without setting up an exception.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	605 */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	606 static int
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	607 is_error(double x)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	608 {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	609 int result = 1; /* presumption of guilt */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	610 assert(errno); /* non-zero errno is a precondition for calling */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	611 if (errno == EDOM)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	612 PyErr_SetString(PyExc_ValueError, "math domain error");
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	613
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	614 else if (errno == ERANGE) {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	615 /* ANSI C generally requires libm functions to set ERANGE
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	616 * on overflow, but also generally allows them to set
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	617 * ERANGE on underflow too. There's no consistency about
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	618 * the latter across platforms.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	619 * Alas, C99 never requires that errno be set.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	620 * Here we suppress the underflow errors (libm functions
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	621 * should return a zero on underflow, and +- HUGE_VAL on
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	622 * overflow, so testing the result for zero suffices to
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	623 * distinguish the cases).
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	624 *
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	625 * On some platforms (Ubuntu/ia64) it seems that errno can be
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	626 * set to ERANGE for subnormal results that do not underflow
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	627 * to zero. So to be safe, we'll ignore ERANGE whenever the
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	628 * function result is less than one in absolute value.
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	629 */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	630 if (fabs(x) < 1.0)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	631 result = 0;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	632 else
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	633 PyErr_SetString(PyExc_OverflowError,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	634 "math range error");
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	635 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	636 else
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	637 /* Unexpected math error */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	638 PyErr_SetFromErrno(PyExc_ValueError);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	639 return result;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	640 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	641
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	642 /*
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	643 math_1 is used to wrap a libm function f that takes a double
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	644 arguments and returns a double.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	645
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	646 The error reporting follows these rules, which are designed to do
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	647 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	648 platforms.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	649
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	650 - a NaN result from non-NaN inputs causes ValueError to be raised
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	651 - an infinite result from finite inputs causes OverflowError to be
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	652 raised if can_overflow is 1, or raises ValueError if can_overflow
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	653 is 0.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	654 - if the result is finite and errno == EDOM then ValueError is
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	655 raised
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	656 - if the result is finite and nonzero and errno == ERANGE then
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	657 OverflowError is raised
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	658
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	659 The last rule is used to catch overflow on platforms which follow
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	660 C89 but for which HUGE_VAL is not an infinity.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	661
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	662 For the majority of one-argument functions these rules are enough
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	663 to ensure that Python's functions behave as specified in 'Annex F'
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	664 of the C99 standard, with the 'invalid' and 'divide-by-zero'
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	665 floating-point exceptions mapping to Python's ValueError and the
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	666 'overflow' floating-point exception mapping to OverflowError.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	667 math_1 only works for functions that don't have singularities and
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	668 the possibility of overflow; fortunately, that covers everything we
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	669 care about right now.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	670 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	671
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	672 static PyObject *
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	673 math_1(PyObject arg, double (func) (double), int can_overflow)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	674 {
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	675 double x, r;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	676 x = PyFloat_AsDouble(arg);
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	677 if (x == -1.0 && PyErr_Occurred())
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	678 return NULL;
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	679 errno = 0;
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	680 PyFPE_START_PROTECT("in math_1", return 0);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	681 r = (*func)(x);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	682 PyFPE_END_PROTECT(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	683 if (Py_IS_NAN(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	684 if (!Py_IS_NAN(x))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	685 errno = EDOM;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	686 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	687 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	688 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	689 else if (Py_IS_INFINITY(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	690 if (Py_IS_FINITE(x))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	691 errno = can_overflow ? ERANGE : EDOM;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	692 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	693 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	694 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	695 if (errno && is_error(r))
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	696 return NULL;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	697 else
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	698 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	699 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	700
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	701 /* variant of math_1, to be used when the function being wrapped is known to
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	702 set errno properly (that is, errno = EDOM for invalid or divide-by-zero,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	703 errno = ERANGE for overflow). */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	704
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	705 static PyObject *
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	706 math_1a(PyObject arg, double (func) (double))
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	707 {
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	708 double x, r;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	709 x = PyFloat_AsDouble(arg);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	710 if (x == -1.0 && PyErr_Occurred())
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	711 return NULL;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	712 errno = 0;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	713 PyFPE_START_PROTECT("in math_1a", return 0);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	714 r = (*func)(x);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	715 PyFPE_END_PROTECT(r);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	716 if (errno && is_error(r))
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	717 return NULL;
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	718 return PyFloat_FromDouble(r);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	719 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	720
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	721 /*
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	722 math_2 is used to wrap a libm function f that takes two double
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	723 arguments and returns a double.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	724
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	725 The error reporting follows these rules, which are designed to do
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	726 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	727 platforms.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	728
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	729 - a NaN result from non-NaN inputs causes ValueError to be raised
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	730 - an infinite result from finite inputs causes OverflowError to be
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	731 raised.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	732 - if the result is finite and errno == EDOM then ValueError is
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	733 raised
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	734 - if the result is finite and nonzero and errno == ERANGE then
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	735 OverflowError is raised
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	736
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	737 The last rule is used to catch overflow on platforms which follow
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	738 C89 but for which HUGE_VAL is not an infinity.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	739
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	740 For most two-argument functions (copysign, fmod, hypot, atan2)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	741 these rules are enough to ensure that Python's functions behave as
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	742 specified in 'Annex F' of the C99 standard, with the 'invalid' and
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	743 'divide-by-zero' floating-point exceptions mapping to Python's
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	744 ValueError and the 'overflow' floating-point exception mapping to
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	745 OverflowError.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	746 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	747
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	748 static PyObject *
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	749 math_2(PyObject args, double (func) (double, double), char *funcname)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	750 {
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	751 PyObject ox, oy;
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	752 double x, y, r;
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	753 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	754 return NULL;
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	755 x = PyFloat_AsDouble(ox);
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	756 y = PyFloat_AsDouble(oy);
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	757 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	758 return NULL;
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	759 errno = 0;
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	760 PyFPE_START_PROTECT("in math_2", return 0);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	761 r = (*func)(x, y);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	762 PyFPE_END_PROTECT(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	763 if (Py_IS_NAN(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	764 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	765 errno = EDOM;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	766 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	767 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	768 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	769 else if (Py_IS_INFINITY(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	770 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	771 errno = ERANGE;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	772 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	773 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	774 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	775 if (errno && is_error(r))
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	776 return NULL;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	777 else
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	778 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	779 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	780
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	781 #define FUNC1(funcname, func, can_overflow, docstring) \
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	782 static PyObject * math_##funcname(PyObject self, PyObject args) { \
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	783 return math_1(args, func, can_overflow); \
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	784 }\
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	785 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	786
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	787 #define FUNC1A(funcname, func, docstring) \
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	788 static PyObject * math_##funcname(PyObject self, PyObject args) { \
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	789 return math_1a(args, func); \
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	790 }\
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	791 PyDoc_STRVAR(math_##funcname##_doc, docstring);
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	792
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	793 #define FUNC2(funcname, func, docstring) \
24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	794 static PyObject * math_##funcname(PyObject self, PyObject args) { \
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	795 return math_2(args, func, #funcname); \
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	796 }\
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	797 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	798
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	799 FUNC1(acos, acos, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	800 "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
57864 7f5cbc28f433 Issue #7518: Move substitute definitions of C99 math functions from Mark Dickinson <dickinsm@gmail.com> parents: 57807 diff changeset	801 FUNC1(acosh, m_acosh, 0,
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	802 "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	803 FUNC1(asin, asin, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	804 "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
57864 7f5cbc28f433 Issue #7518: Move substitute definitions of C99 math functions from Mark Dickinson <dickinsm@gmail.com> parents: 57807 diff changeset	805 FUNC1(asinh, m_asinh, 0,
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	806 "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	807 FUNC1(atan, atan, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	808 "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
46507 022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	809 FUNC2(atan2, m_atan2,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	810 "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	811 "Unlike atan(y/x), the signs of both x and y are considered.")
57864 7f5cbc28f433 Issue #7518: Move substitute definitions of C99 math functions from Mark Dickinson <dickinsm@gmail.com> parents: 57807 diff changeset	812 FUNC1(atanh, m_atanh, 0,
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	813 "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	814 FUNC1(ceil, ceil, 0,
44488 94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44453 diff changeset	815 "ceil(x)\n\nReturn the ceiling of x as a float.\n"
94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44453 diff changeset	816 "This is the smallest integral value >= x.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	817 FUNC2(copysign, copysign,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	818 "copysign(x, y)\n\nReturn x with the sign of y.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	819 FUNC1(cos, cos, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	820 "cos(x)\n\nReturn the cosine of x (measured in radians).")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	821 FUNC1(cosh, cosh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	822 "cosh(x)\n\nReturn the hyperbolic cosine of x.")
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	823 FUNC1A(erf, m_erf,
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	824 "erf(x)\n\nError function at x.")
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	825 FUNC1A(erfc, m_erfc,
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	826 "erfc(x)\n\nComplementary error function at x.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	827 FUNC1(exp, exp, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	828 "exp(x)\n\nReturn e raised to the power of x.")
57756 b206ad8cf5bf Issue #3366: Add expm1 function to math module. Thanks Eric Smith for Mark Dickinson <dickinsm@gmail.com> parents: 57655 diff changeset	829 FUNC1(expm1, m_expm1, 1,
b206ad8cf5bf Issue #3366: Add expm1 function to math module. Thanks Eric Smith for Mark Dickinson <dickinsm@gmail.com> parents: 57655 diff changeset	830 "expm1(x)\n\nReturn exp(x)-1.\n"
b206ad8cf5bf Issue #3366: Add expm1 function to math module. Thanks Eric Smith for Mark Dickinson <dickinsm@gmail.com> parents: 57655 diff changeset	831 "This function avoids the loss of precision involved in the direct "
b206ad8cf5bf Issue #3366: Add expm1 function to math module. Thanks Eric Smith for Mark Dickinson <dickinsm@gmail.com> parents: 57655 diff changeset	832 "evaluation of exp(x)-1 for small x.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	833 FUNC1(fabs, fabs, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	834 "fabs(x)\n\nReturn the absolute value of the float x.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	835 FUNC1(floor, floor, 0,
44488 94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44453 diff changeset	836 "floor(x)\n\nReturn the floor of x as a float.\n"
94eeaeeb3ce9 Continue rolling back pep-3141 changes that changed behavior from 2.5. This Jeffrey Yasskin <jyasskin@gmail.com> parents: 44453 diff changeset	837 "This is the largest integral value <= x.")
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	838 FUNC1A(gamma, m_tgamma,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	839 "gamma(x)\n\nGamma function at x.")
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	840 FUNC1A(lgamma, m_lgamma,
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	841 "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
57864 7f5cbc28f433 Issue #7518: Move substitute definitions of C99 math functions from Mark Dickinson <dickinsm@gmail.com> parents: 57807 diff changeset	842 FUNC1(log1p, m_log1p, 1,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	843 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	844 "The result is computed in a way which is accurate for x near zero.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	845 FUNC1(sin, sin, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	846 "sin(x)\n\nReturn the sine of x (measured in radians).")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	847 FUNC1(sinh, sinh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	848 "sinh(x)\n\nReturn the hyperbolic sine of x.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	849 FUNC1(sqrt, sqrt, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	850 "sqrt(x)\n\nReturn the square root of x.")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	851 FUNC1(tan, tan, 0,
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	852 "tan(x)\n\nReturn the tangent of x (measured in radians).")
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	853 FUNC1(tanh, tanh, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	854 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	855
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	856 /* Precision summation function as msum() by Raymond Hettinger in
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	857 <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	858 enhanced with the exact partials sum and roundoff from Mark
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	859 Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	860 See those links for more details, proofs and other references.
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	861
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	862 Note 1: IEEE 754R floating point semantics are assumed,
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	863 but the current implementation does not re-establish special
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	864 value semantics across iterations (i.e. handling -Inf + Inf).
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	865
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	866 Note 2: No provision is made for intermediate overflow handling;
47370 9e6e6b817f32 Fix two typos. Raymond Hettinger <python@rcn.com> parents: 47220 diff changeset	867 therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	868 sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	869 overflow of the first partial sum.
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	870
47777 c39263e94c33 Fix comment typos Andrew M. Kuchling <amk@amk.ca> parents: 47757 diff changeset	871 Note 3: The intermediate values lo, yr, and hi are declared volatile so
47783 a7186fee7596 Fix another typo in math_sum comment Mark Dickinson <dickinsm@gmail.com> parents: 47777 diff changeset	872 aggressive compilers won't algebraically reduce lo to always be exactly 0.0.
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	873 Also, the volatile declaration forces the values to be stored in memory as
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	874 regular doubles instead of extended long precision (80-bit) values. This
47777 c39263e94c33 Fix comment typos Andrew M. Kuchling <amk@amk.ca> parents: 47757 diff changeset	875 prevents double rounding because any addition or subtraction of two doubles
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	876 can be resolved exactly into double-sized hi and lo values. As long as the
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	877 hi value gets forced into a double before yr and lo are computed, the extra
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	878 bits in downstream extended precision operations (x87 for example) will be
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	879 exactly zero and therefore can be losslessly stored back into a double,
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	880 thereby preventing double rounding.
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	881
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	882 Note 4: A similar implementation is in Modules/cmathmodule.c.
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	883 Be sure to update both when making changes.
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	884
48102 b35ce954a392 Replace math.sum with math.fsum in a couple of comments Mark Dickinson <dickinsm@gmail.com> parents: 48101 diff changeset	885 Note 5: The signature of math.fsum() differs from __builtin__.sum()
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	886 because the start argument doesn't make sense in the context of
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	887 accurate summation. Since the partials table is collapsed before
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	888 returning a result, sum(seq2, start=sum(seq1)) may not equal the
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	889 accurate result returned by sum(itertools.chain(seq1, seq2)).
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	890 */
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	891
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	892 #define NUM_PARTIALS 32 /* initial partials array size, on stack */
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	893
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	894 /* Extend the partials array p[] by doubling its size. */
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	895 static int /* non-zero on error */
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	896 _fsum_realloc(double **p_ptr, Py_ssize_t n,
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	897 double ps, Py_ssize_t m_ptr)
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	898 {
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	899 void *v = NULL;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	900 Py_ssize_t m = *m_ptr;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	901
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	902 m += m; /* double */
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	903 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	904 double p = p_ptr;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	905 if (p == ps) {
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	906 v = PyMem_Malloc(sizeof(double) * m);
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	907 if (v != NULL)
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	908 memcpy(v, ps, sizeof(double) * n);
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	909 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	910 else
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	911 v = PyMem_Realloc(p, sizeof(double) * m);
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	912 }
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	913 if (v == NULL) { /* size overflow or no memory */
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	914 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	915 return 1;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	916 }
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	917 p_ptr = (double) v;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	918 *m_ptr = m;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	919 return 0;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	920 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	921
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	922 /* Full precision summation of a sequence of floats.
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	923
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	924 def msum(iterable):
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	925 partials = [] # sorted, non-overlapping partial sums
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	926 for x in iterable:
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	927 i = 0
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	928 for y in partials:
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	929 if abs(x) < abs(y):
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	930 x, y = y, x
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	931 hi = x + y
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	932 lo = y - (hi - x)
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	933 if lo:
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	934 partials[i] = lo
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	935 i += 1
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	936 x = hi
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	937 partials[i:] = [x]
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	938 return sum_exact(partials)
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	939
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	940 Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	941 are exactly equal to x+y. The inner loop applies hi/lo summation to each
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	942 partial so that the list of partial sums remains exact.
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	943
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	944 Sum_exact() adds the partial sums exactly and correctly rounds the final
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	945 result (using the round-half-to-even rule). The items in partials remain
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	946 non-zero, non-special, non-overlapping and strictly increasing in
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	947 magnitude, but possibly not all having the same sign.
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	948
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	949 Depends on IEEE 754 arithmetic guarantees and half-even rounding.
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	950 */
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	951
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	952 static PyObject*
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	953 math_fsum(PyObject self, PyObject seq)
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	954 {
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	955 PyObject item, iter, *sum = NULL;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	956 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	957 double x, y, t, ps[NUM_PARTIALS], *p = ps;
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	958 double xsave, special_sum = 0.0, inf_sum = 0.0;
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	959 volatile double hi, yr, lo;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	960
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	961 iter = PyObject_GetIter(seq);
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	962 if (iter == NULL)
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	963 return NULL;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	964
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	965 PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	966
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	967 for(;;) { /* for x in iterable */
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	968 assert(0 <= n && n <= m);
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	969 assert((m == NUM_PARTIALS && p == ps) \|\|
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	970 (m > NUM_PARTIALS && p != NULL));
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	971
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	972 item = PyIter_Next(iter);
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	973 if (item == NULL) {
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	974 if (PyErr_Occurred())
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	975 goto _fsum_error;
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	976 break;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	977 }
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	978 x = PyFloat_AsDouble(item);
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	979 Py_DECREF(item);
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	980 if (PyErr_Occurred())
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	981 goto _fsum_error;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	982
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	983 xsave = x;
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	984 for (i = j = 0; j < n; j++) { /* for y in partials */
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	985 y = p[j];
47395 bba29f462bcc * Mark intermedidate computes values (hi, lo, yr) as volatile. Raymond Hettinger <python@rcn.com> parents: 47370 diff changeset	986 if (fabs(x) < fabs(y)) {
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	987 t = x; x = y; y = t;
47395 bba29f462bcc * Mark intermedidate computes values (hi, lo, yr) as volatile. Raymond Hettinger <python@rcn.com> parents: 47370 diff changeset	988 }
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	989 hi = x + y;
47395 bba29f462bcc * Mark intermedidate computes values (hi, lo, yr) as volatile. Raymond Hettinger <python@rcn.com> parents: 47370 diff changeset	990 yr = hi - x;
bba29f462bcc * Mark intermedidate computes values (hi, lo, yr) as volatile. Raymond Hettinger <python@rcn.com> parents: 47370 diff changeset	991 lo = y - yr;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	992 if (lo != 0.0)
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	993 p[i++] = lo;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	994 x = hi;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	995 }
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	996
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	997 n = i; /* ps[i:] = [x] */
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	998 if (x != 0.0) {
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	999 if (! Py_IS_FINITE(x)) {
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1000 /* a nonfinite x could arise either as
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1001 a result of intermediate overflow, or
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1002 as a result of a nan or inf in the
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1003 summands */
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1004 if (Py_IS_FINITE(xsave)) {
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1005 PyErr_SetString(PyExc_OverflowError,
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1006 "intermediate overflow in fsum");
8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1007 goto _fsum_error;
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1008 }
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1009 if (Py_IS_INFINITY(xsave))
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1010 inf_sum += xsave;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1011 special_sum += xsave;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1012 /* reset partials */
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1013 n = 0;
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1014 }
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1015 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1016 goto _fsum_error;
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1017 else
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1018 p[n++] = x;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1019 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1020 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1021
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1022 if (special_sum != 0.0) {
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1023 if (Py_IS_NAN(inf_sum))
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1024 PyErr_SetString(PyExc_ValueError,
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1025 "-inf + inf in fsum");
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1026 else
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1027 sum = PyFloat_FromDouble(special_sum);
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1028 goto _fsum_error;
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1029 }
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1030
47395 bba29f462bcc * Mark intermedidate computes values (hi, lo, yr) as volatile. Raymond Hettinger <python@rcn.com> parents: 47370 diff changeset	1031 hi = 0.0;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1032 if (n > 0) {
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1033 hi = p[--n];
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1034 /* sum_exact(ps, hi) from the top, stop when the sum becomes
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1035 inexact. */
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1036 while (n > 0) {
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1037 x = hi;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1038 y = p[--n];
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1039 assert(fabs(y) < fabs(x));
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1040 hi = x + y;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1041 yr = hi - x;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1042 lo = y - yr;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1043 if (lo != 0.0)
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1044 break;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1045 }
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1046 /* Make half-even rounding work across multiple partials.
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1047 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1048 digit to two instead of down to zero (the 1e-16 makes the 1
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1049 slightly closer to two). With a potential 1 ULP rounding
48102 b35ce954a392 Replace math.sum with math.fsum in a couple of comments Mark Dickinson <dickinsm@gmail.com> parents: 48101 diff changeset	1050 error fixed-up, math.fsum() can guarantee commutativity. */
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1051 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) \|\|
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1052 (lo > 0.0 && p[n-1] > 0.0))) {
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1053 y = lo * 2.0;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1054 x = hi + y;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1055 yr = x - hi;
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1056 if (y == yr)
b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1057 hi = x;
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1058 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1059 }
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	1060 sum = PyFloat_FromDouble(hi);
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1061
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1062 _fsum_error:
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1063 PyFPE_END_PROTECT(hi)
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1064 Py_DECREF(iter);
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1065 if (p != ps)
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1066 PyMem_Free(p);
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1067 return sum;
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1068 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1069
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1070 #undef NUM_PARTIALS
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1071
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1072 PyDoc_STRVAR(math_fsum_doc,
56974 c6d62340aebf Use the correct function name in docstring. Georg Brandl <georg@python.org> parents: 56268 diff changeset	1073 "fsum(iterable)\n\n\
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	1074 Return an accurate floating point sum of values in the iterable.\n\
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	1075 Assumes IEEE-754 floating point arithmetic.");
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1076
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1077 static PyObject *
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1078 math_factorial(PyObject self, PyObject arg)
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1079 {
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1080 long i, x;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1081 PyObject result, iobj, *newresult;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1082
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1083 if (PyFloat_Check(arg)) {
57807 5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1084 PyObject *lx;
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1085 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
57807 5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1086 if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1087 PyErr_SetString(PyExc_ValueError,
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1088 "factorial() only accepts integral values");
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1089 return NULL;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1090 }
57807 5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1091 lx = PyLong_FromDouble(dx);
5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1092 if (lx == NULL)
5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1093 return NULL;
5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1094 x = PyLong_AsLong(lx);
5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1095 Py_DECREF(lx);
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1096 }
57807 5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1097 else
5ccc5d4068c1 math.factorial depends on PyLong_AsLong correctly converting floats; rewrite Mark Dickinson <dickinsm@gmail.com> parents: 57769 diff changeset	1098 x = PyInt_AsLong(arg);
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1099
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1100 if (x == -1 && PyErr_Occurred())
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1101 return NULL;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1102 if (x < 0) {
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1103 PyErr_SetString(PyExc_ValueError,
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1104 "factorial() not defined for negative values");
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1105 return NULL;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1106 }
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1107
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1108 result = (PyObject *)PyInt_FromLong(1);
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1109 if (result == NULL)
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1110 return NULL;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1111 for (i=1 ; i<=x ; i++) {
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1112 iobj = (PyObject *)PyInt_FromLong(i);
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1113 if (iobj == NULL)
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1114 goto error;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1115 newresult = PyNumber_Multiply(result, iobj);
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1116 Py_DECREF(iobj);
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1117 if (newresult == NULL)
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1118 goto error;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1119 Py_DECREF(result);
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1120 result = newresult;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1121 }
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1122 return result;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1123
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1124 error:
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1125 Py_DECREF(result);
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1126 return NULL;
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1127 }
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1128
50236 670204cf23e2 beef up docstring Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1129 PyDoc_STRVAR(math_factorial_doc,
670204cf23e2 beef up docstring Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1130 "factorial(x) -> Integral\n"
670204cf23e2 beef up docstring Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1131 "\n"
670204cf23e2 beef up docstring Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1132 "Find x!. Raise a ValueError if x is negative or non-integral.");
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1133
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1134 static PyObject *
45079 492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1135 math_trunc(PyObject self, PyObject number)
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1136 {
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1137 return PyObject_CallMethod(number, "__trunc__", NULL);
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1138 }
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1139
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1140 PyDoc_STRVAR(math_trunc_doc,
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1141 "trunc(x:Real) -> Integral\n"
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1142 "\n"
45102 ce9816f53690 Neaten-up a bit. Raymond Hettinger <python@rcn.com> parents: 45079 diff changeset	1143 "Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
45079 492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1144
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1145 static PyObject *
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1146 math_frexp(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1147 {
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1148 int i;
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1149 double x = PyFloat_AsDouble(arg);
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1150 if (x == -1.0 && PyErr_Occurred())
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1151 return NULL;
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1152 /* deal with special cases directly, to sidestep platform
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1153 differences */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1154 if (Py_IS_NAN(x) \|\| Py_IS_INFINITY(x) \|\| !x) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1155 i = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1156 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1157 else {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1158 PyFPE_START_PROTECT("in math_frexp", return 0);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1159 x = frexp(x, &i);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1160 PyFPE_END_PROTECT(x);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1161 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1162 return Py_BuildValue("(di)", x, i);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1163 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1164
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1165 PyDoc_STRVAR(math_frexp_doc,
19712 b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1166 "frexp(x)\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1167 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1168 "Return the mantissa and exponent of x, as pair (m, e).\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1169 "m is a float and e is an int, such that x = m * 2.**e.\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1170 "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1171
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1172 static PyObject *
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1173 math_ldexp(PyObject self, PyObject args)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1174 {
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1175 double x, r;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1176 PyObject *oexp;
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1177 long exp;
58124 0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1178 int overflow;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1179 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1180 return NULL;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1181
58124 0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1182 if (PyLong_Check(oexp) \|\| PyInt_Check(oexp)) {
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1183 /* on overflow, replace exponent with either LONG_MAX
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1184 or LONG_MIN, depending on the sign. */
58124 0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1185 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1186 if (exp == -1 && PyErr_Occurred())
0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1187 return NULL;
0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1188 if (overflow)
0f8a58792563 Make use of PyLong_AsLongAndOverflow in math_ldexp. Mark Dickinson <dickinsm@gmail.com> parents: 58085 diff changeset	1189 exp = overflow < 0 ? LONG_MIN : LONG_MAX;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1190 }
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1191 else {
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1192 PyErr_SetString(PyExc_TypeError,
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1193 "Expected an int or long as second argument "
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1194 "to ldexp.");
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1195 return NULL;
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1196 }
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1197
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1198 if (x == 0. \|\| !Py_IS_FINITE(x)) {
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1199 /* NaNs, zeros and infinities are returned unchanged */
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1200 r = x;
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1201 errno = 0;
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1202 } else if (exp > INT_MAX) {
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1203 /* overflow */
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1204 r = copysign(Py_HUGE_VAL, x);
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1205 errno = ERANGE;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1206 } else if (exp < INT_MIN) {
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1207 /* underflow to +-0 */
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1208 r = copysign(0., x);
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1209 errno = 0;
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1210 } else {
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1211 errno = 0;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1212 PyFPE_START_PROTECT("in math_ldexp", return 0);
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1213 r = ldexp(x, (int)exp);
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1214 PyFPE_END_PROTECT(r);
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1215 if (Py_IS_INFINITY(r))
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1216 errno = ERANGE;
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1217 }
fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1218
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1219 if (errno && is_error(r))
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	1220 return NULL;
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1221 return PyFloat_FromDouble(r);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1222 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1223
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1224 PyDoc_STRVAR(math_ldexp_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1225 "ldexp(x, i)\n\n\
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1226 Return x * (2**i).");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1227
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1228 static PyObject *
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1229 math_modf(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1230 {
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1231 double y, x = PyFloat_AsDouble(arg);
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1232 if (x == -1.0 && PyErr_Occurred())
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1233 return NULL;
46499 80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1234 /* some platforms don't do the right thing for NaNs and
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1235 infinities, so we take care of special cases directly. */
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1236 if (!Py_IS_FINITE(x)) {
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1237 if (Py_IS_INFINITY(x))
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1238 return Py_BuildValue("(dd)", copysign(0., x), x);
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1239 else if (Py_IS_NAN(x))
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1240 return Py_BuildValue("(dd)", x, x);
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1241 }
80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1242
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1243 errno = 0;
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1244 PyFPE_START_PROTECT("in math_modf", return 0);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1245 x = modf(x, &y);
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1246 PyFPE_END_PROTECT(x);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1247 return Py_BuildValue("(dd)", x, y);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1248 }
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1249
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1250 PyDoc_STRVAR(math_modf_doc,
19712 b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1251 "modf(x)\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1252 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1253 "Return the fractional and integer parts of x. Both results carry the sign\n"
50243 589edf615adb remove redundant sentence Benjamin Peterson <benjamin@python.org> parents: 50236 diff changeset	1254 "of x and are floats.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1255
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1256 /* A decent logarithm is easy to compute even for huge longs, but libm can't
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1257 do that by itself -- loghelper can. func is log or log10, and name is
58085 27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1258 "log" or "log10". Note that overflow of the result isn't possible: a long
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1259 can contain no more than INT_MAX * SHIFT bits, so has value certainly less
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1260 than 2(264 * 216) == 2280, and log2 of that is 280, which is
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1261 small enough to fit in an IEEE single. log and log10 are even smaller.
58085 27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1262 However, intermediate overflow is possible for a long if the number of bits
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1263 in that long is larger than PY_SSIZE_T_MAX. */
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1264
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1265 static PyObject*
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1266 loghelper(PyObject* arg, double (func)(double), char funcname)
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1267 {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1268 /* If it is long, do it ourselves. */
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1269 if (PyLong_Check(arg)) {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1270 double x;
58085 27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1271 Py_ssize_t e;
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1272 x = _PyLong_Frexp((PyLongObject *)arg, &e);
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1273 if (x == -1.0 && PyErr_Occurred())
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1274 return NULL;
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1275 if (x <= 0.0) {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1276 PyErr_SetString(PyExc_ValueError,
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1277 "math domain error");
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1278 return NULL;
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1279 }
58085 27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1280 /* Special case for log(1), to make sure we get an
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1281 exact result there. */
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1282 if (e == 1 && x == 0.5)
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1283 return PyFloat_FromDouble(0.0);
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1284 /* Value is ~= x * 2*e, so the log ~= log(x) + log(2) e. */
27c946ff76a3 Refactor some longobject internals: PyLong_AsDouble and _PyLong_AsScaledDouble Mark Dickinson <dickinsm@gmail.com> parents: 57864 diff changeset	1285 x = func(x) + func(2.0) * e;
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1286 return PyFloat_FromDouble(x);
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1287 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1288
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1289 /* Else let libm handle it by itself. */
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1290 return math_1(arg, func, 0);
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1291 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1292
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1293 static PyObject *
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1294 math_log(PyObject self, PyObject args)
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1295 {
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1296 PyObject *arg;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1297 PyObject *base = NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1298 PyObject num, den;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1299 PyObject *ans;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1300
26818 e094a03a80ff SF patch #659536: Use PyArg_UnpackTuple where possible. Raymond Hettinger <python@rcn.com> parents: 26661 diff changeset	1301 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1302 return NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1303
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	1304 num = loghelper(arg, m_log, "log");
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1305 if (num == NULL \|\| base == NULL)
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1306 return num;
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1307
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	1308 den = loghelper(base, m_log, "log");
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1309 if (den == NULL) {
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1310 Py_DECREF(num);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1311 return NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1312 }
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1313
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1314 ans = PyNumber_Divide(num, den);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1315 Py_DECREF(num);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1316 Py_DECREF(den);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1317 return ans;
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1318 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1319
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1320 PyDoc_STRVAR(math_log_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1321 "log(x[, base])\n\n\
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1322 Return the logarithm of x to the given base.\n\
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1323 If the base not specified, returns the natural logarithm (base e) of x.");
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1324
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1325 static PyObject *
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1326 math_log10(PyObject self, PyObject arg)
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1327 {
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	1328 return loghelper(arg, m_log10, "log10");
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1329 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1330
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1331 PyDoc_STRVAR(math_log10_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1332 "log10(x)\n\nReturn the base 10 logarithm of x.");
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1333
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1334 static PyObject *
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1335 math_fmod(PyObject self, PyObject args)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1336 {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1337 PyObject ox, oy;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1338 double r, x, y;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1339 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1340 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1341 x = PyFloat_AsDouble(ox);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1342 y = PyFloat_AsDouble(oy);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1343 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1344 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1345 /* fmod(x, +/-Inf) returns x for finite x. */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1346 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1347 return PyFloat_FromDouble(x);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1348 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1349 PyFPE_START_PROTECT("in math_fmod", return 0);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1350 r = fmod(x, y);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1351 PyFPE_END_PROTECT(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1352 if (Py_IS_NAN(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1353 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1354 errno = EDOM;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1355 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1356 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1357 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1358 if (errno && is_error(r))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1359 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1360 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1361 return PyFloat_FromDouble(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1362 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1363
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1364 PyDoc_STRVAR(math_fmod_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1365 "fmod(x, y)\n\nReturn fmod(x, y), according to platform C."
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1366 " x % y may differ.");
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1367
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1368 static PyObject *
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1369 math_hypot(PyObject self, PyObject args)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1370 {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1371 PyObject ox, oy;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1372 double r, x, y;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1373 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1374 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1375 x = PyFloat_AsDouble(ox);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1376 y = PyFloat_AsDouble(oy);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1377 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1378 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1379 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1380 if (Py_IS_INFINITY(x))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1381 return PyFloat_FromDouble(fabs(x));
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1382 if (Py_IS_INFINITY(y))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1383 return PyFloat_FromDouble(fabs(y));
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1384 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1385 PyFPE_START_PROTECT("in math_hypot", return 0);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1386 r = hypot(x, y);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1387 PyFPE_END_PROTECT(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1388 if (Py_IS_NAN(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1389 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1390 errno = EDOM;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1391 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1392 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1393 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1394 else if (Py_IS_INFINITY(r)) {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1395 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1396 errno = ERANGE;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1397 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1398 errno = 0;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1399 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1400 if (errno && is_error(r))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1401 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1402 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1403 return PyFloat_FromDouble(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1404 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1405
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1406 PyDoc_STRVAR(math_hypot_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1407 "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(xx + yy).");
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1408
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1409 /* pow can't use math_2, but needs its own wrapper: the problem is
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1410 that an infinite result can arise either as a result of overflow
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1411 (in which case OverflowError should be raised) or as a result of
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1412 e.g. 0.**-5. (for which ValueError needs to be raised.)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1413 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1414
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1415 static PyObject *
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1416 math_pow(PyObject self, PyObject args)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1417 {
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1418 PyObject ox, oy;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1419 double r, x, y;
46500 a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1420 int odd_y;
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1421
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1422 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1423 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1424 x = PyFloat_AsDouble(ox);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1425 y = PyFloat_AsDouble(oy);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1426 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1427 return NULL;
46490 648b4d01cccf Additional special-case handling for math.pow. Mark Dickinson <dickinsm@gmail.com> parents: 46486 diff changeset	1428
46500 a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1429 /* deal directly with IEEE specials, to cope with problems on various
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1430 platforms whose semantics don't exactly match C99 */
46509 052fd8f1ca37 Silence 'r may be used uninitialized' compiler warning. Mark Dickinson <dickinsm@gmail.com> parents: 46507 diff changeset	1431 r = 0.; /* silence compiler warning */
46500 a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1432 if (!Py_IS_FINITE(x) \|\| !Py_IS_FINITE(y)) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1433 errno = 0;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1434 if (Py_IS_NAN(x))
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1435 r = y == 0. ? 1. : x; /* NaN*0 = 1 /
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1436 else if (Py_IS_NAN(y))
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1437 r = x == 1. ? 1. : y; /* 1*NaN = 1 /
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1438 else if (Py_IS_INFINITY(x)) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1439 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1440 if (y > 0.)
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1441 r = odd_y ? x : fabs(x);
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1442 else if (y == 0.)
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1443 r = 1.;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1444 else /* y < 0. */
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1445 r = odd_y ? copysign(0., x) : 0.;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1446 }
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1447 else if (Py_IS_INFINITY(y)) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1448 if (fabs(x) == 1.0)
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1449 r = 1.;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1450 else if (y > 0. && fabs(x) > 1.0)
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1451 r = y;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1452 else if (y < 0. && fabs(x) < 1.0) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1453 r = -y; /* result is +inf */
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1454 if (x == 0.) /* 0*-inf: divide-by-zero /
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1455 errno = EDOM;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1456 }
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1457 else
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1458 r = 0.;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1459 }
46486 82d85a05923b Additional tests for math.pow, and extra special-case Mark Dickinson <dickinsm@gmail.com> parents: 46473 diff changeset	1460 }
46500 a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1461 else {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1462 /* let libm handle finite*finite /
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1463 errno = 0;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1464 PyFPE_START_PROTECT("in math_pow", return 0);
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1465 r = pow(x, y);
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1466 PyFPE_END_PROTECT(r);
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1467 /* a NaN result should arise only from (-ve)**(finite
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1468 non-integer); in this case we want to raise ValueError. */
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1469 if (!Py_IS_FINITE(r)) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1470 if (Py_IS_NAN(r)) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1471 errno = EDOM;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1472 }
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1473 /*
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1474 an infinite result here arises either from:
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1475 (A) (+/-0.)**negative (-> divide-by-zero)
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1476 (B) overflow of x**y with x and y finite
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1477 */
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1478 else if (Py_IS_INFINITY(r)) {
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1479 if (x == 0.)
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1480 errno = EDOM;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1481 else
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1482 errno = ERANGE;
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1483 }
a20def0101de Yet more explicit special case handling to make Mark Dickinson <dickinsm@gmail.com> parents: 46499 diff changeset	1484 }
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1485 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1486
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1487 if (errno && is_error(r))
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1488 return NULL;
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1489 else
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1490 return PyFloat_FromDouble(r);
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1491 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1492
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1493 PyDoc_STRVAR(math_pow_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1494 "pow(x, y)\n\nReturn x**y (x to the power of y).");
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1495
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1496 static const double degToRad = Py_MATH_PI / 180.0;
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1497 static const double radToDeg = 180.0 / Py_MATH_PI;
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1498
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1499 static PyObject *
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1500 math_degrees(PyObject self, PyObject arg)
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1501 {
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1502 double x = PyFloat_AsDouble(arg);
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1503 if (x == -1.0 && PyErr_Occurred())
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1504 return NULL;
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1505 return PyFloat_FromDouble(x * radToDeg);
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1506 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1507
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1508 PyDoc_STRVAR(math_degrees_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1509 "degrees(x)\n\n\
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1510 Convert angle x from radians to degrees.");
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1511
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1512 static PyObject *
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1513 math_radians(PyObject self, PyObject arg)
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1514 {
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1515 double x = PyFloat_AsDouble(arg);
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1516 if (x == -1.0 && PyErr_Occurred())
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1517 return NULL;
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1518 return PyFloat_FromDouble(x * degToRad);
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1519 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1520
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1521 PyDoc_STRVAR(math_radians_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1522 "radians(x)\n\n\
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1523 Convert angle x from degrees to radians.");
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1524
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1525 static PyObject *
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1526 math_isnan(PyObject self, PyObject arg)
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1527 {
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1528 double x = PyFloat_AsDouble(arg);
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1529 if (x == -1.0 && PyErr_Occurred())
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1530 return NULL;
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1531 return PyBool_FromLong((long)Py_IS_NAN(x));
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1532 }
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1533
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1534 PyDoc_STRVAR(math_isnan_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1535 "isnan(x) -> bool\n\n\
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1536 Check if float x is not a number (NaN).");
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1537
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1538 static PyObject *
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1539 math_isinf(PyObject self, PyObject arg)
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1540 {
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1541 double x = PyFloat_AsDouble(arg);
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1542 if (x == -1.0 && PyErr_Occurred())
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1543 return NULL;
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1544 return PyBool_FromLong((long)Py_IS_INFINITY(x));
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1545 }
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1546
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1547 PyDoc_STRVAR(math_isinf_doc,
56977 7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1548 "isinf(x) -> bool\n\n\
7e02371aa506 Use a single style for all the docstrings in the math module. Georg Brandl <georg@python.org> parents: 56974 diff changeset	1549 Check if float x is infinite (positive or negative).");
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1550
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1551 static PyMethodDef math_methods[] = {
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1552 {"acos", math_acos, METH_O, math_acos_doc},
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1553 {"acosh", math_acosh, METH_O, math_acosh_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1554 {"asin", math_asin, METH_O, math_asin_doc},
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1555 {"asinh", math_asinh, METH_O, math_asinh_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1556 {"atan", math_atan, METH_O, math_atan_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1557 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1558 {"atanh", math_atanh, METH_O, math_atanh_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1559 {"ceil", math_ceil, METH_O, math_ceil_doc},
44440 6208b17d0dbe Added copysign(x, y) function to the math module Christian Heimes <christian@cheimes.de> parents: 44437 diff changeset	1560 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1561 {"cos", math_cos, METH_O, math_cos_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1562 {"cosh", math_cosh, METH_O, math_cosh_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1563 {"degrees", math_degrees, METH_O, math_degrees_doc},
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	1564 {"erf", math_erf, METH_O, math_erf_doc},
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	1565 {"erfc", math_erfc, METH_O, math_erfc_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1566 {"exp", math_exp, METH_O, math_exp_doc},
57756 b206ad8cf5bf Issue #3366: Add expm1 function to math module. Thanks Eric Smith for Mark Dickinson <dickinsm@gmail.com> parents: 57655 diff changeset	1567 {"expm1", math_expm1, METH_O, math_expm1_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1568 {"fabs", math_fabs, METH_O, math_fabs_doc},
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1569 {"factorial", math_factorial, METH_O, math_factorial_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1570 {"floor", math_floor, METH_O, math_floor_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1571 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1572 {"frexp", math_frexp, METH_O, math_frexp_doc},
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1573 {"fsum", math_fsum, METH_O, math_fsum_doc},
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	1574 {"gamma", math_gamma, METH_O, math_gamma_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1575 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1576 {"isinf", math_isinf, METH_O, math_isinf_doc},
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1577 {"isnan", math_isnan, METH_O, math_isnan_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1578 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	1579 {"lgamma", math_lgamma, METH_O, math_lgamma_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1580 {"log", math_log, METH_VARARGS, math_log_doc},
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1581 {"log1p", math_log1p, METH_O, math_log1p_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1582 {"log10", math_log10, METH_O, math_log10_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1583 {"modf", math_modf, METH_O, math_modf_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1584 {"pow", math_pow, METH_VARARGS, math_pow_doc},
40362 271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1585 {"radians", math_radians, METH_O, math_radians_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1586 {"sin", math_sin, METH_O, math_sin_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1587 {"sinh", math_sinh, METH_O, math_sinh_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1588 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1589 {"tan", math_tan, METH_O, math_tan_doc},
271133981e63 Speed up function calls into the math module by using METH_O. Neal Norwitz <nnorwitz@gmail.com> parents: 38491 diff changeset	1590 {"tanh", math_tanh, METH_O, math_tanh_doc},
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1591 {"trunc", math_trunc, METH_O, math_trunc_doc},
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1592 {NULL, NULL} /* sentinel */
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1593 };
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1594
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1595
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1596 PyDoc_STRVAR(module_doc,
19712 b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1597 "This module is always available. It provides access to the\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1598 "mathematical functions defined by the C standard.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1599
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 23832 diff changeset	1600 PyMODINIT_FUNC
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13331 diff changeset	1601 initmath(void)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1602 {
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1603 PyObject *m;
19048 e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from Tim Peters <tim.peters@gmail.com> parents: 18066 diff changeset	1604
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1605 m = Py_InitModule3("math", math_methods, module_doc);
36324 1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 34872 diff changeset	1606 if (m == NULL)
1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 34872 diff changeset	1607 goto finally;
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	1608
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1609 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1610 PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	1611
46473 5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1612 finally:
14346 5397fdf88ec2 Do the absolute minimal amount of modifications to eradicate Barry Warsaw <barry@python.org> parents: 13912 diff changeset	1613 return;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1614 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 58765:2ba7677bfa95 legacy-trunk