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

annotate Modules/mathmodule.c @ 80661:94de77bd0b4b 2.7

Issue #16194: document imp.load_dynamic problems when read several extension modules from the same binary object file.

author	Andrew Svetlov <andrew.svetlov@gmail.com>
date	Thu, 29 Nov 2012 19:51:28 +0200
parents	b36cb4602e21
children	f543863f4e43

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 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	76 double y, r;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	77 int n;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	78 /* this function should only ever be called for finite arguments */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	79 assert(Py_IS_FINITE(x));
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	80 y = fmod(fabs(x), 2.0);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	81 n = (int)round(2.0*y);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	82 assert(0 <= n && n <= 4);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	83 switch (n) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	84 case 0:
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	85 r = sin(pi*y);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	86 break;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	87 case 1:
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	88 r = cos(pi*(y-0.5));
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	89 break;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	90 case 2:
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	91 /* N.B. -sin(pi(y-1.0)) is not* equivalent: it would give
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	92 -0.0 instead of 0.0 when y == 1.0. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	93 r = sin(pi*(1.0-y));
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	94 break;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	95 case 3:
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	96 r = -cos(pi*(y-1.5));
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	97 break;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	98 case 4:
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	99 r = sin(pi*(y-2.0));
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	100 break;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	101 default:
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	102 assert(0); /* should never get here */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	103 r = -1.23e200; /* silence gcc warning */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	104 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	105 return copysign(1.0, x)*r;
56268 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] = {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	169 23531376880.410759688572007674451636754734846804940,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	170 42919803642.649098768957899047001988850926355848959,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	171 35711959237.355668049440185451547166705960488635843,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	172 17921034426.037209699919755754458931112671403265390,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	173 6039542586.3520280050642916443072979210699388420708,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	174 1439720407.3117216736632230727949123939715485786772,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	175 248874557.86205415651146038641322942321632125127801,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	176 31426415.585400194380614231628318205362874684987640,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	177 2876370.6289353724412254090516208496135991145378768,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	178 186056.26539522349504029498971604569928220784236328,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	179 8071.6720023658162106380029022722506138218516325024,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	180 210.82427775157934587250973392071336271166969580291,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	181 2.5066282746310002701649081771338373386264310793408
56268 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] = {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	186 0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 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] = {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	192 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	193 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	194 1307674368000.0, 20922789888000.0, 355687428096000.0,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	195 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	196 51090942171709440000.0, 1124000727777607680000.0,
56268 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 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	204 double num = 0.0, den = 0.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	205 int i;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	206 assert(x > 0.0);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	207 /* evaluate the rational function lanczos_sum(x). For large
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	208 x, the obvious algorithm risks overflow, so we instead
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	209 rescale the denominator and numerator of the rational
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	210 function by x**(1-LANCZOS_N) and treat this as a
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	211 rational function in 1/x. This also reduces the error for
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	212 larger x values. The choice of cutoff point (5.0 below) is
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	213 somewhat arbitrary; in tests, smaller cutoff values than
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	214 this resulted in lower accuracy. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	215 if (x < 5.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	216 for (i = LANCZOS_N; --i >= 0; ) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	217 num = num * x + lanczos_num_coeffs[i];
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	218 den = den * x + lanczos_den_coeffs[i];
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	219 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	220 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	221 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	222 for (i = 0; i < LANCZOS_N; i++) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	223 num = num / x + lanczos_num_coeffs[i];
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	224 den = den / x + lanczos_den_coeffs[i];
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	225 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	226 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	227 return num/den;
56268 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 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	233 double absx, r, y, z, sqrtpow;
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	234
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	235 /* special cases */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	236 if (!Py_IS_FINITE(x)) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	237 if (Py_IS_NAN(x) \|\| x > 0.0)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	238 return x; /* tgamma(nan) = nan, tgamma(inf) = inf */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	239 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	240 errno = EDOM;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	241 return Py_NAN; /* tgamma(-inf) = nan, invalid */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	242 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	243 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	244 if (x == 0.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	245 errno = EDOM;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	246 return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	247 }
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	248
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	249 /* integer arguments */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	250 if (x == floor(x)) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	251 if (x < 0.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	252 errno = EDOM; /* tgamma(n) = nan, invalid for */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	253 return Py_NAN; /* negative integers n */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	254 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	255 if (x <= NGAMMA_INTEGRAL)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	256 return gamma_integral[(int)x - 1];
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	257 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	258 absx = fabs(x);
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	259
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	260 /* tiny arguments: tgamma(x) ~ 1/x for x near 0 */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	261 if (absx < 1e-20) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	262 r = 1.0/x;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	263 if (Py_IS_INFINITY(r))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	264 errno = ERANGE;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	265 return r;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	266 }
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	267
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	268 /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	269 x > 200, and underflows to +-0.0 for x < -200, not a negative
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	270 integer. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	271 if (absx > 200.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	272 if (x < 0.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	273 return 0.0/sinpi(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	274 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	275 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	276 errno = ERANGE;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	277 return Py_HUGE_VAL;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	278 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	279 }
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	280
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	281 y = absx + lanczos_g_minus_half;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	282 /* compute error in sum */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	283 if (absx > lanczos_g_minus_half) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	284 /* note: the correction can be foiled by an optimizing
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	285 compiler that (incorrectly) thinks that an expression like
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	286 a + b - a - b can be optimized to 0.0. This shouldn't
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	287 happen in a standards-conforming compiler. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	288 double q = y - absx;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	289 z = q - lanczos_g_minus_half;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	290 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	291 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	292 double q = y - lanczos_g_minus_half;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	293 z = q - absx;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	294 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	295 z = z * lanczos_g / y;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	296 if (x < 0.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	297 r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	298 r -= z * r;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	299 if (absx < 140.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	300 r /= pow(y, absx - 0.5);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	301 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	302 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	303 sqrtpow = pow(y, absx / 2.0 - 0.25);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	304 r /= sqrtpow;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	305 r /= sqrtpow;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	306 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	307 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	308 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	309 r = lanczos_sum(absx) / exp(y);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	310 r += z * r;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	311 if (absx < 140.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	312 r *= pow(y, absx - 0.5);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	313 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	314 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	315 sqrtpow = pow(y, absx / 2.0 - 0.25);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	316 r *= sqrtpow;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	317 r *= sqrtpow;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	318 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	319 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	320 if (Py_IS_INFINITY(r))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	321 errno = ERANGE;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 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 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	333 double r, absx;
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	334
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	335 /* special cases */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	336 if (!Py_IS_FINITE(x)) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	337 if (Py_IS_NAN(x))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	338 return x; /* lgamma(nan) = nan */
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	339 else
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	340 return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	341 }
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	342
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	343 /* integer arguments */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	344 if (x == floor(x) && x <= 2.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	345 if (x <= 0.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	346 errno = EDOM; /* lgamma(n) = inf, divide-by-zero for */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	347 return Py_HUGE_VAL; /* integers n <= 0 */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	348 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	349 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	350 return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	351 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	352 }
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	353
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	354 absx = fabs(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	355 /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	356 if (absx < 1e-20)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	357 return -log(absx);
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	358
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	359 /* Lanczos' formula */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	360 if (x > 0.0) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	361 /* we could save a fraction of a ulp in accuracy by having a
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	362 second set of numerator coefficients for lanczos_sum that
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	363 absorbed the exp(-lanczos_g) term, and throwing out the
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	364 lanczos_g subtraction below; it's probably not worth it. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	365 r = log(lanczos_sum(x)) - lanczos_g +
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	366 (x-0.5)*(log(x+lanczos_g-0.5)-1);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	367 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	368 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	369 r = log(pi) - log(fabs(sinpi(absx))) - log(absx) -
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	370 (log(lanczos_sum(absx)) - lanczos_g +
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	371 (absx-0.5)*(log(absx+lanczos_g-0.5)-1));
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	372 }
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	373 if (Py_IS_INFINITY(r))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	374 errno = ERANGE;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	375 return r;
57655 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 {
62316 cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	431 double x2, acc, fk, result;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	432 int i, saved_errno;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	433
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	434 x2 = x * x;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	435 acc = 0.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	436 fk = (double)ERF_SERIES_TERMS + 0.5;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	437 for (i = 0; i < ERF_SERIES_TERMS; i++) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	438 acc = 2.0 + x2 * acc / fk;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	439 fk -= 1.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	440 }
62316 cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	441 /* Make sure the exp call doesn't affect errno;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	442 see m_erfc_contfrac for more. */
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	443 saved_errno = errno;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	444 result = acc * x * exp(-x2) / sqrtpi;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	445 errno = saved_errno;
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	446 return result;
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	447 }
56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	448
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	449 /*
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	450 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	451
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	452 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	453 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	454 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	455 <= 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	456 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	457
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	458 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	459 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	460 {
62316 cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	461 double x2, a, da, p, p_last, q, q_last, b, result;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	462 int i, saved_errno;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	463
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	464 if (x >= ERFC_CONTFRAC_CUTOFF)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	465 return 0.0;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	466
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	467 x2 = x*x;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	468 a = 0.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	469 da = 0.5;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	470 p = 1.0; p_last = 0.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	471 q = da + x2; q_last = 1.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	472 for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	473 double temp;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	474 a += da;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	475 da += 2.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	476 b = da + x2;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	477 temp = p; p = bp - ap_last; p_last = temp;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	478 temp = q; q = bq - aq_last; q_last = temp;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	479 }
62316 cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	480 /* Issue #8986: On some platforms, exp sets errno on underflow to zero;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	481 save the current errno value so that we can restore it later. */
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	482 saved_errno = errno;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	483 result = p / q * x * exp(-x2) / sqrtpi;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	484 errno = saved_errno;
cff0a923140b Issue #8986: erfc was raising OverflowError on Linux for arguments in Mark Dickinson <dickinsm@gmail.com> parents: 61463 diff changeset	485 return result;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	486 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	487
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	488 /* 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	489
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	490 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	491 m_erf(double x)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	492 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	493 double absx, cf;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	494
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	495 if (Py_IS_NAN(x))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	496 return x;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	497 absx = fabs(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	498 if (absx < ERF_SERIES_CUTOFF)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	499 return m_erf_series(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	500 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	501 cf = m_erfc_contfrac(absx);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	502 return x > 0.0 ? 1.0 - cf : cf - 1.0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	503 }
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	504 }
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	505
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	506 /* 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	507
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	508 static double
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	509 m_erfc(double x)
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	510 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	511 double absx, cf;
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	512
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	513 if (Py_IS_NAN(x))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	514 return x;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	515 absx = fabs(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	516 if (absx < ERF_SERIES_CUTOFF)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	517 return 1.0 - m_erf_series(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	518 else {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	519 cf = m_erfc_contfrac(absx);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	520 return x > 0.0 ? cf : 2.0 - cf;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	521 }
57769 d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	522 }
57655 cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	523
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	524 /*
46507 022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	525 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	526 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	527 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	528 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	529 always follow C99.
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	530 */
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	531
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	532 static double
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	533 m_atan2(double y, double x)
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	534 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	535 if (Py_IS_NAN(x) \|\| Py_IS_NAN(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	536 return Py_NAN;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	537 if (Py_IS_INFINITY(y)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	538 if (Py_IS_INFINITY(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	539 if (copysign(1., x) == 1.)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	540 /* atan2(+-inf, +inf) == +-pi/4 */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	541 return copysign(0.25*Py_MATH_PI, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	542 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	543 /* atan2(+-inf, -inf) == +-pi3/4 /
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	544 return copysign(0.75*Py_MATH_PI, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	545 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	546 /* atan2(+-inf, x) == +-pi/2 for finite x */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	547 return copysign(0.5*Py_MATH_PI, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	548 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	549 if (Py_IS_INFINITY(x) \|\| y == 0.) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	550 if (copysign(1., x) == 1.)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	551 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	552 return copysign(0., y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	553 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	554 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	555 return copysign(Py_MATH_PI, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	556 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	557 return atan2(y, x);
46507 022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	558 }
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	559
022296032d8f math.atan2 is misbehaving on Windows; this patch Mark Dickinson <dickinsm@gmail.com> parents: 46500 diff changeset	560 /*
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	561 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	562 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	563 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	564 the system log/log10.
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	565 */
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	566
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	567 static double
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	568 m_log(double x)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	569 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	570 if (Py_IS_FINITE(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	571 if (x > 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	572 return log(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	573 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	574 if (x == 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	575 return -Py_HUGE_VAL; /* log(0) = -inf */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	576 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	577 return Py_NAN; /* log(-ve) = nan */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	578 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	579 else if (Py_IS_NAN(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	580 return x; /* log(nan) = nan */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	581 else if (x > 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	582 return x; /* log(inf) = inf */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	583 else {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	584 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	585 return Py_NAN; /* log(-inf) = nan */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	586 }
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	587 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	588
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	589 static double
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	590 m_log10(double x)
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	591 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	592 if (Py_IS_FINITE(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	593 if (x > 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	594 return log10(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	595 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	596 if (x == 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	597 return -Py_HUGE_VAL; /* log10(0) = -inf */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	598 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	599 return Py_NAN; /* log10(-ve) = nan */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	600 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	601 else if (Py_IS_NAN(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	602 return x; /* log10(nan) = nan */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	603 else if (x > 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	604 return x; /* log10(inf) = inf */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	605 else {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	606 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	607 return Py_NAN; /* log10(-inf) = nan */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	608 }
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	609 }
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	610
776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	611
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	612 /* 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	613 * 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	614 * 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	615 */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	616 static int
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	617 is_error(double x)
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	618 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	619 int result = 1; /* presumption of guilt */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	620 assert(errno); /* non-zero errno is a precondition for calling */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	621 if (errno == EDOM)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	622 PyErr_SetString(PyExc_ValueError, "math domain error");
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	623
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	624 else if (errno == ERANGE) {
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	625 /* ANSI C generally requires libm functions to set ERANGE
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	626 * on overflow, but also generally allows them to set
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	627 * ERANGE on underflow too. There's no consistency about
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	628 * the latter across platforms.
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	629 * Alas, C99 never requires that errno be set.
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	630 * Here we suppress the underflow errors (libm functions
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	631 * should return a zero on underflow, and +- HUGE_VAL on
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	632 * overflow, so testing the result for zero suffices to
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	633 * distinguish the cases).
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	634 *
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	635 * On some platforms (Ubuntu/ia64) it seems that errno can be
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	636 * set to ERANGE for subnormal results that do not underflow
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	637 * to zero. So to be safe, we'll ignore ERANGE whenever the
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	638 * function result is less than one in absolute value.
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	639 */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	640 if (fabs(x) < 1.0)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	641 result = 0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	642 else
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	643 PyErr_SetString(PyExc_OverflowError,
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	644 "math range error");
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	645 }
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	646 else
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	647 /* Unexpected math error */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	648 PyErr_SetFromErrno(PyExc_ValueError);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	649 return result;
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	650 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	651
50122 776a6cafc21a Merged revisions 67707 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48102 diff changeset	652 /*
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	653 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	654 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	655
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 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	657 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	658 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	659
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 - 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	661 - 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	662 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	663 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	664 - 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	665 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	666 - 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	667 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	668
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 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	670 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	671
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	672 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	673 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	674 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	675 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	676 '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	677 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	678 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	679 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	680 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	682 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	683 math_1(PyObject arg, double (func) (double), int can_overflow)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	684 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	685 double x, r;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	686 x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	687 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	688 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	689 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	690 PyFPE_START_PROTECT("in math_1", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	691 r = (*func)(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	692 PyFPE_END_PROTECT(r);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	693 if (Py_IS_NAN(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	694 if (!Py_IS_NAN(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	695 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	696 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	697 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	698 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	699 else if (Py_IS_INFINITY(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	700 if (Py_IS_FINITE(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	701 errno = can_overflow ? ERANGE : EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	702 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	703 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	704 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	705 if (errno && is_error(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	706 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	707 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	708 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	709 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	710
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	711 /* 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	712 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	713 errno = ERANGE for overflow). */
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	714
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	715 static PyObject *
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	716 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	717 {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	718 double x, r;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	719 x = PyFloat_AsDouble(arg);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	720 if (x == -1.0 && PyErr_Occurred())
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	721 return NULL;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	722 errno = 0;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	723 PyFPE_START_PROTECT("in math_1a", return 0);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	724 r = (*func)(x);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	725 PyFPE_END_PROTECT(r);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	726 if (errno && is_error(r))
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	727 return NULL;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	728 return PyFloat_FromDouble(r);
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	729 }
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	730
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	731 /*
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 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	733 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	734
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 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	736 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	737 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	738
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 - 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	740 - 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	741 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	742 - 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	743 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	744 - 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	745 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	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 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	748 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	749
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	750 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	751 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	752 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	753 '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	754 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	755 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	756 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	757
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	758 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	759 math_2(PyObject args, double (func) (double, double), char *funcname)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	760 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	761 PyObject ox, oy;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	762 double x, y, r;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	763 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	764 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	765 x = PyFloat_AsDouble(ox);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	766 y = PyFloat_AsDouble(oy);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	767 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	768 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	769 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	770 PyFPE_START_PROTECT("in math_2", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	771 r = (*func)(x, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	772 PyFPE_END_PROTECT(r);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	773 if (Py_IS_NAN(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	774 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	775 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	776 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	777 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	778 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	779 else if (Py_IS_INFINITY(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	780 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	781 errno = ERANGE;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	782 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	783 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	784 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	785 if (errno && is_error(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	786 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	787 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	788 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	789 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	790
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	791 #define FUNC1(funcname, func, can_overflow, docstring) \
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	792 static PyObject * math_##funcname(PyObject self, PyObject args) { \
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	793 return math_1(args, func, can_overflow); \
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	794 }\
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	795 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	796
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	797 #define FUNC1A(funcname, func, docstring) \
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	798 static PyObject * math_##funcname(PyObject self, PyObject args) { \
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	799 return math_1a(args, func); \
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	800 }\
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	801 PyDoc_STRVAR(math_##funcname##_doc, docstring);
56268 b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	802
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	803 #define FUNC2(funcname, func, docstring) \
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	804 static PyObject * math_##funcname(PyObject self, PyObject args) { \
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	805 return math_2(args, func, #funcname); \
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	806 }\
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	807 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	808
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	809 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	810 "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	811 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	812 "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	813 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	814 "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	815 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	816 "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	817 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	818 "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	819 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	820 "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	821 "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	822 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	823 "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	824 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	825 "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	826 "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	827 FUNC2(copysign, copysign,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	828 "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	829 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	830 "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	831 FUNC1(cosh, cosh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	832 "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	833 FUNC1A(erf, m_erf,
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	834 "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	835 FUNC1A(erfc, m_erfc,
d350afc337dc Issue #3366: Add error function and complementary error function to Mark Dickinson <dickinsm@gmail.com> parents: 57756 diff changeset	836 "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	837 FUNC1(exp, exp, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	838 "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	839 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	840 "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	841 "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	842 "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	843 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	844 "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	845 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	846 "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	847 "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	848 FUNC1A(gamma, m_tgamma,
b50dd17dfe26 Issue #3366: Add gamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 50243 diff changeset	849 "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	850 FUNC1A(lgamma, m_lgamma,
cb22eaee86c9 Issue #3366: Add lgamma function to math module. Mark Dickinson <dickinsm@gmail.com> parents: 56977 diff changeset	851 "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	852 FUNC1(log1p, m_log1p, 1,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	853 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	854 "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	855 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	856 "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	857 FUNC1(sinh, sinh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	858 "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	859 FUNC1(sqrt, sqrt, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	860 "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	861 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	862 "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	863 FUNC1(tanh, tanh, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	864 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	865
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	866 /* 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	867 <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	868 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	869 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	870 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	871
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	872 Note 1: IEEE 754R floating point semantics are assumed,
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	873 but the current implementation does not re-establish special
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	874 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	875
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	876 Note 2: No provision is made for intermediate overflow handling;
47370 9e6e6b817f32 Fix two typos. Raymond Hettinger <python@rcn.com> parents: 47220 diff changeset	877 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	878 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	879 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	880
47777 c39263e94c33 Fix comment typos Andrew M. Kuchling <amk@amk.ca> parents: 47757 diff changeset	881 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	882 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	883 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	884 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	885 prevents double rounding because any addition or subtraction of two doubles
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	886 can be resolved exactly into double-sized hi and lo values. As long as the
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	887 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	888 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	889 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	890 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	891
47532 6cfa297c6555 Unhappy buildbots. Revert 64052. Long doubles have unexpected effects on some builds. Raymond Hettinger <python@rcn.com> parents: 47531 diff changeset	892 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	893 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	894
48102 b35ce954a392 Replace math.sum with math.fsum in a couple of comments Mark Dickinson <dickinsm@gmail.com> parents: 48101 diff changeset	895 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	896 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	897 accurate summation. Since the partials table is collapsed before
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	898 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	899 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	900 */
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	901
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	902 #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	903
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	904 /* Extend the partials array p[] by doubling its size. */
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	905 static int /* non-zero on error */
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	906 _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	907 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	908 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	909 void *v = NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	910 Py_ssize_t m = *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	911
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	912 m += m; /* double */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	913 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	914 double p = p_ptr;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	915 if (p == ps) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	916 v = PyMem_Malloc(sizeof(double) * m);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	917 if (v != NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	918 memcpy(v, ps, sizeof(double) * n);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	919 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	920 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	921 v = PyMem_Realloc(p, sizeof(double) * m);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	922 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	923 if (v == NULL) { /* size overflow or no memory */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	924 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	925 return 1;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	926 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	927 p_ptr = (double) v;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	928 *m_ptr = m;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	929 return 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	930 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	931
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	932 /* 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	933
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	934 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	935 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	936 for x in iterable:
62494 83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	937 i = 0
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	938 for y in partials:
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	939 if abs(x) < abs(y):
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	940 x, y = y, x
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	941 hi = x + y
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	942 lo = y - (hi - x)
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	943 if lo:
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	944 partials[i] = lo
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	945 i += 1
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	946 x = hi
83ca0ea9ef1f Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61465 diff changeset	947 partials[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	948 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	949
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	950 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	951 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	952 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	953
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	954 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	955 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	956 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	957 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	958
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	959 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	960 */
71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	961
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	962 static PyObject*
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	963 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	964 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	965 PyObject item, iter, *sum = NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	966 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	967 double x, y, t, ps[NUM_PARTIALS], *p = ps;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	968 double xsave, special_sum = 0.0, inf_sum = 0.0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	969 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	970
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	971 iter = PyObject_GetIter(seq);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	972 if (iter == NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	973 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	974
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	975 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	976
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	977 for(;;) { /* for x in iterable */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	978 assert(0 <= n && n <= m);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	979 assert((m == NUM_PARTIALS && p == ps) \|\|
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	980 (m > NUM_PARTIALS && p != 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	981
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	982 item = PyIter_Next(iter);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	983 if (item == NULL) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	984 if (PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	985 goto _fsum_error;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	986 break;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	987 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	988 x = PyFloat_AsDouble(item);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	989 Py_DECREF(item);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	990 if (PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	991 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	992
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	993 xsave = x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	994 for (i = j = 0; j < n; j++) { /* for y in partials */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	995 y = p[j];
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	996 if (fabs(x) < fabs(y)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	997 t = x; x = y; y = t;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	998 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	999 hi = x + y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1000 yr = hi - x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1001 lo = y - yr;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1002 if (lo != 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1003 p[i++] = lo;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1004 x = hi;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1005 }
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1006
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1007 n = i; /* ps[i:] = [x] */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1008 if (x != 0.0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1009 if (! Py_IS_FINITE(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1010 /* a nonfinite x could arise either as
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1011 a result of intermediate overflow, or
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1012 as a result of a nan or inf in the
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1013 summands */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1014 if (Py_IS_FINITE(xsave)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1015 PyErr_SetString(PyExc_OverflowError,
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1016 "intermediate overflow in fsum");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1017 goto _fsum_error;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1018 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1019 if (Py_IS_INFINITY(xsave))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1020 inf_sum += xsave;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1021 special_sum += xsave;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1022 /* reset partials */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1023 n = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1024 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1025 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1026 goto _fsum_error;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1027 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1028 p[n++] = x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1029 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1030 }
47216 2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1031
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1032 if (special_sum != 0.0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1033 if (Py_IS_NAN(inf_sum))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1034 PyErr_SetString(PyExc_ValueError,
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1035 "-inf + inf in fsum");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1036 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1037 sum = PyFloat_FromDouble(special_sum);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1038 goto _fsum_error;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1039 }
48099 b40e13bcb9ea Fix special-value handling for math.sum. Mark Dickinson <dickinsm@gmail.com> parents: 47783 diff changeset	1040
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1041 hi = 0.0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1042 if (n > 0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1043 hi = p[--n];
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1044 /* sum_exact(ps, hi) from the top, stop when the sum becomes
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1045 inexact. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1046 while (n > 0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1047 x = hi;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1048 y = p[--n];
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1049 assert(fabs(y) < fabs(x));
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1050 hi = x + y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1051 yr = hi - x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1052 lo = y - yr;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1053 if (lo != 0.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1054 break;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1055 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1056 /* Make half-even rounding work across multiple partials.
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1057 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1058 digit to two instead of down to zero (the 1e-16 makes the 1
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1059 slightly closer to two). With a potential 1 ULP rounding
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1060 error fixed-up, math.fsum() can guarantee commutativity. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1061 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) \|\|
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1062 (lo > 0.0 && p[n-1] > 0.0))) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1063 y = lo * 2.0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1064 x = hi + y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1065 yr = x - hi;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1066 if (y == yr)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1067 hi = x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1068 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1069 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1070 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	1071
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1072 _fsum_error:
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1073 PyFPE_END_PROTECT(hi)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1074 Py_DECREF(iter);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1075 if (p != ps)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1076 PyMem_Free(p);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1077 return 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	1078 }
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1079
2fffdedb10f8 Issue #2819: Add math.sum, a function that sums a sequence of floats Mark Dickinson <dickinsm@gmail.com> parents: 46797 diff changeset	1080 #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	1081
48101 8d05dda735f8 Rename math.sum to math.fsum Mark Dickinson <dickinsm@gmail.com> parents: 48099 diff changeset	1082 PyDoc_STRVAR(math_fsum_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1083 "fsum(iterable)\n\n\
47220 71deee6b941e Tweak the comments and formatting. Raymond Hettinger <python@rcn.com> parents: 47216 diff changeset	1084 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	1085 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	1086
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1087 static PyObject *
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1088 math_factorial(PyObject self, PyObject arg)
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1089 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1090 long i, x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1091 PyObject result, iobj, *newresult;
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1092
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1093 if (PyFloat_Check(arg)) {
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1094 PyObject *lx;
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1095 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1096 if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1097 PyErr_SetString(PyExc_ValueError,
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1098 "factorial() only accepts integral values");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1099 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1100 }
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1101 lx = PyLong_FromDouble(dx);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1102 if (lx == NULL)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1103 return NULL;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1104 x = PyLong_AsLong(lx);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1105 Py_DECREF(lx);
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1106 }
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1107 else
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1108 x = PyInt_AsLong(arg);
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1109
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1110 if (x == -1 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1111 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1112 if (x < 0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1113 PyErr_SetString(PyExc_ValueError,
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1114 "factorial() not defined for negative values");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1115 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1116 }
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1117
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1118 result = (PyObject *)PyInt_FromLong(1);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1119 if (result == NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1120 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1121 for (i=1 ; i<=x ; i++) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1122 iobj = (PyObject *)PyInt_FromLong(i);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1123 if (iobj == NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1124 goto error;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1125 newresult = PyNumber_Multiply(result, iobj);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1126 Py_DECREF(iobj);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1127 if (newresult == NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1128 goto error;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1129 Py_DECREF(result);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1130 result = newresult;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1131 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1132 return result;
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1133
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1134 error:
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1135 Py_DECREF(result);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1136 return NULL;
47529 6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1137 }
6428c4f1ae09 Issue #2138: Add math.factorial(). Raymond Hettinger <python@rcn.com> parents: 47395 diff changeset	1138
50257 e4675113d10e Merged revisions 67654,67676-67677,67681,67692,67725,67746,67748,67761,67784-67785,67787-67788,67802,67832,67848-67849,67859,67862-67864,67880,67882,67885,67889-67892,67895 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1139 PyDoc_STRVAR(math_factorial_doc,
e4675113d10e Merged revisions 67654,67676-67677,67681,67692,67725,67746,67748,67761,67784-67785,67787-67788,67802,67832,67848-67849,67859,67862-67864,67880,67882,67885,67889-67892,67895 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1140 "factorial(x) -> Integral\n"
e4675113d10e Merged revisions 67654,67676-67677,67681,67692,67725,67746,67748,67761,67784-67785,67787-67788,67802,67832,67848-67849,67859,67862-67864,67880,67882,67885,67889-67892,67895 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1141 "\n"
e4675113d10e Merged revisions 67654,67676-67677,67681,67692,67725,67746,67748,67761,67784-67785,67787-67788,67802,67832,67848-67849,67859,67862-67864,67880,67882,67885,67889-67892,67895 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1142 "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	1143
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1144 static PyObject *
45079 492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1145 math_trunc(PyObject self, PyObject number)
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1146 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1147 return PyObject_CallMethod(number, "__trunc__", NULL);
45079 492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1148 }
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1149
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1150 PyDoc_STRVAR(math_trunc_doc,
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1151 "trunc(x:Real) -> Integral\n"
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1152 "\n"
45102 ce9816f53690 Neaten-up a bit. Raymond Hettinger <python@rcn.com> parents: 45079 diff changeset	1153 "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	1154
492b302aded6 Move __builtins__.trunc() to math.trunc() per Jeffrey Yasskin <jyasskin@gmail.com> parents: 44947 diff changeset	1155 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	1156 math_frexp(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1157 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1158 int i;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1159 double x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1160 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1161 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1162 /* deal with special cases directly, to sidestep platform
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1163 differences */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1164 if (Py_IS_NAN(x) \|\| Py_IS_INFINITY(x) \|\| !x) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1165 i = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1166 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1167 else {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1168 PyFPE_START_PROTECT("in math_frexp", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1169 x = frexp(x, &i);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1170 PyFPE_END_PROTECT(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1171 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1172 return Py_BuildValue("(di)", x, i);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1173 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1174
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1175 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	1176 "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	1177 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1178 "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	1179 "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	1180 "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	1181
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1182 static PyObject *
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1183 math_ldexp(PyObject self, PyObject args)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1184 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1185 double x, r;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1186 PyObject *oexp;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1187 long exp;
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1188 int overflow;
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1189 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1190 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	1191
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1192 if (PyLong_Check(oexp) \|\| PyInt_Check(oexp)) {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1193 /* on overflow, replace exponent with either LONG_MAX
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1194 or LONG_MIN, depending on the sign. */
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1195 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1196 if (exp == -1 && PyErr_Occurred())
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1197 return NULL;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1198 if (overflow)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1199 exp = overflow < 0 ? LONG_MIN : LONG_MAX;
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1200 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1201 else {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1202 PyErr_SetString(PyExc_TypeError,
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1203 "Expected an int or long as second argument "
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1204 "to ldexp.");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1205 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1206 }
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1207
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1208 if (x == 0. \|\| !Py_IS_FINITE(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1209 /* NaNs, zeros and infinities are returned unchanged */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1210 r = x;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1211 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1212 } else if (exp > INT_MAX) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1213 /* overflow */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1214 r = copysign(Py_HUGE_VAL, x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1215 errno = ERANGE;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1216 } else if (exp < INT_MIN) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1217 /* underflow to +-0 */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1218 r = copysign(0., x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1219 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1220 } else {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1221 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1222 PyFPE_START_PROTECT("in math_ldexp", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1223 r = ldexp(x, (int)exp);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1224 PyFPE_END_PROTECT(r);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1225 if (Py_IS_INFINITY(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1226 errno = ERANGE;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1227 }
46797 fd0b894bc90c Issue #2487. math.ldexp(x, n) raised OverflowError when n was large and Mark Dickinson <dickinsm@gmail.com> parents: 46509 diff changeset	1228
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1229 if (errno && is_error(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1230 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1231 return PyFloat_FromDouble(r);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1232 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1233
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1234 PyDoc_STRVAR(math_ldexp_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1235 "ldexp(x, i)\n\n\
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1236 Return x * (2**i).");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1237
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1238 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	1239 math_modf(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1240 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1241 double y, x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1242 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1243 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1244 /* some platforms don't do the right thing for NaNs and
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1245 infinities, so we take care of special cases directly. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1246 if (!Py_IS_FINITE(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1247 if (Py_IS_INFINITY(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1248 return Py_BuildValue("(dd)", copysign(0., x), x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1249 else if (Py_IS_NAN(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1250 return Py_BuildValue("(dd)", x, x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1251 }
46499 80b16595e462 FreeBSD doesn't follow C99 for modf(inf); so add explicit Mark Dickinson <dickinsm@gmail.com> parents: 46490 diff changeset	1252
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1253 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1254 PyFPE_START_PROTECT("in math_modf", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1255 x = modf(x, &y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1256 PyFPE_END_PROTECT(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1257 return Py_BuildValue("(dd)", x, y);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1258 }
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1259
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1260 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	1261 "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	1262 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1263 "Return the fractional and integer parts of x. Both results carry the sign\n"
50257 e4675113d10e Merged revisions 67654,67676-67677,67681,67692,67725,67746,67748,67761,67784-67785,67787-67788,67802,67832,67848-67849,67859,67862-67864,67880,67882,67885,67889-67892,67895 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50122 diff changeset	1264 "of x and are floats.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1265
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	1266 /* 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	1267 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	1268 "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	1269 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	1270 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	1271 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	1272 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	1273 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	1274
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 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	1276 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	1277 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1278 /* If it is long, do it ourselves. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1279 if (PyLong_Check(arg)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1280 double x;
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1281 Py_ssize_t e;
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1282 x = _PyLong_Frexp((PyLongObject *)arg, &e);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1283 if (x == -1.0 && PyErr_Occurred())
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1284 return NULL;
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1285 if (x <= 0.0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1286 PyErr_SetString(PyExc_ValueError,
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1287 "math domain error");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1288 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1289 }
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1290 /* Special case for log(1), to make sure we get an
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1291 exact result there. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1292 if (e == 1 && x == 0.5)
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1293 return PyFloat_FromDouble(0.0);
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1294 /* Value is ~= x * 2*e, so the log ~= log(x) + log(2) e. */
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1295 x = func(x) + func(2.0) * e;
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1296 return PyFloat_FromDouble(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1297 }
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	1298
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1299 /* Else let libm handle it by itself. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1300 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	1301 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1302
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1303 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	1304 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	1305 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1306 PyObject *arg;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1307 PyObject *base = NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1308 PyObject num, den;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1309 PyObject *ans;
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1310
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1311 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1312 return NULL;
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1313
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1314 num = loghelper(arg, m_log, "log");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1315 if (num == NULL \|\| base == NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1316 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	1317
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1318 den = loghelper(base, m_log, "log");
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1319 if (den == NULL) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1320 Py_DECREF(num);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1321 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1322 }
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
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1324 ans = PyNumber_Divide(num, den);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1325 Py_DECREF(num);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1326 Py_DECREF(den);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1327 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	1328 }
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
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1330 PyDoc_STRVAR(math_log_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1331 "log(x[, base])\n\n\
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1332 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	1333 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	1334
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1335 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	1336 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	1337 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1338 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	1339 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1340
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1341 PyDoc_STRVAR(math_log10_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1342 "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	1343
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	1344 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	1345 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	1346 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1347 PyObject ox, oy;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1348 double r, x, y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1349 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1350 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1351 x = PyFloat_AsDouble(ox);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1352 y = PyFloat_AsDouble(oy);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1353 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1354 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1355 /* fmod(x, +/-Inf) returns x for finite x. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1356 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1357 return PyFloat_FromDouble(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1358 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1359 PyFPE_START_PROTECT("in math_fmod", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1360 r = fmod(x, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1361 PyFPE_END_PROTECT(r);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1362 if (Py_IS_NAN(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1363 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1364 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1365 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1366 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1367 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1368 if (errno && is_error(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1369 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1370 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1371 return PyFloat_FromDouble(r);
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	1372 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 PyDoc_STRVAR(math_fmod_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1375 "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	1376 " 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	1377
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 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	1379 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	1380 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1381 PyObject ox, oy;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1382 double r, x, y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1383 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1384 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1385 x = PyFloat_AsDouble(ox);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1386 y = PyFloat_AsDouble(oy);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1387 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1388 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1389 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1390 if (Py_IS_INFINITY(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1391 return PyFloat_FromDouble(fabs(x));
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1392 if (Py_IS_INFINITY(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1393 return PyFloat_FromDouble(fabs(y));
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1394 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1395 PyFPE_START_PROTECT("in math_hypot", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1396 r = hypot(x, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1397 PyFPE_END_PROTECT(r);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1398 if (Py_IS_NAN(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1399 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1400 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1401 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1402 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1403 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1404 else if (Py_IS_INFINITY(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1405 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1406 errno = ERANGE;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1407 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1408 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1409 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1410 if (errno && is_error(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1411 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1412 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1413 return PyFloat_FromDouble(r);
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	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
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 PyDoc_STRVAR(math_hypot_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1417 "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	1418
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 /* 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	1420 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	1421 (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	1422 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	1423 */
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends 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 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	1426 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	1427 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1428 PyObject ox, oy;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1429 double r, x, y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1430 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	1431
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1432 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1433 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1434 x = PyFloat_AsDouble(ox);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1435 y = PyFloat_AsDouble(oy);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1436 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1437 return NULL;
46490 648b4d01cccf Additional special-case handling for math.pow. Mark Dickinson <dickinsm@gmail.com> parents: 46486 diff changeset	1438
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1439 /* deal directly with IEEE specials, to cope with problems on various
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1440 platforms whose semantics don't exactly match C99 */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1441 r = 0.; /* silence compiler warning */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1442 if (!Py_IS_FINITE(x) \|\| !Py_IS_FINITE(y)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1443 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1444 if (Py_IS_NAN(x))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1445 r = y == 0. ? 1. : x; /* NaN*0 = 1 /
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1446 else if (Py_IS_NAN(y))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1447 r = x == 1. ? 1. : y; /* 1*NaN = 1 /
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1448 else if (Py_IS_INFINITY(x)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1449 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1450 if (y > 0.)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1451 r = odd_y ? x : fabs(x);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1452 else if (y == 0.)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1453 r = 1.;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1454 else /* y < 0. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1455 r = odd_y ? copysign(0., x) : 0.;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1456 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1457 else if (Py_IS_INFINITY(y)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1458 if (fabs(x) == 1.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1459 r = 1.;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1460 else if (y > 0. && fabs(x) > 1.0)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1461 r = y;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1462 else if (y < 0. && fabs(x) < 1.0) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1463 r = -y; /* result is +inf */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1464 if (x == 0.) /* 0*-inf: divide-by-zero /
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1465 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1466 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1467 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1468 r = 0.;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1469 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1470 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1471 else {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1472 /* let libm handle finite*finite /
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1473 errno = 0;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1474 PyFPE_START_PROTECT("in math_pow", return 0);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1475 r = pow(x, y);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1476 PyFPE_END_PROTECT(r);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1477 /* a NaN result should arise only from (-ve)**(finite
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1478 non-integer); in this case we want to raise ValueError. */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1479 if (!Py_IS_FINITE(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1480 if (Py_IS_NAN(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1481 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1482 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1483 /*
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1484 an infinite result here arises either from:
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1485 (A) (+/-0.)**negative (-> divide-by-zero)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1486 (B) overflow of x**y with x and y finite
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1487 */
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1488 else if (Py_IS_INFINITY(r)) {
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1489 if (x == 0.)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1490 errno = EDOM;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1491 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1492 errno = ERANGE;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1493 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1494 }
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1495 }
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	1496
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1497 if (errno && is_error(r))
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1498 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1499 else
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1500 return PyFloat_FromDouble(r);
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	1501 }
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1502
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math. Christian Heimes <christian@cheimes.de> parents: 45102 diff changeset	1503 PyDoc_STRVAR(math_pow_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1504 "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	1505
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1506 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	1507 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	1508
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1509 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	1510 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	1511 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1512 double x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1513 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1514 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1515 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	1516 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1517
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1518 PyDoc_STRVAR(math_degrees_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1519 "degrees(x)\n\n\
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1520 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	1521
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1522 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	1523 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	1524 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1525 double x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1526 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1527 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1528 return PyFloat_FromDouble(x * degToRad);
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1529 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1530
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1531 PyDoc_STRVAR(math_radians_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1532 "radians(x)\n\n\
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1533 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	1534
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1535 static PyObject *
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1536 math_isnan(PyObject self, PyObject arg)
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1537 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1538 double x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1539 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1540 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1541 return PyBool_FromLong((long)Py_IS_NAN(x));
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1542 }
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1543
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1544 PyDoc_STRVAR(math_isnan_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1545 "isnan(x) -> bool\n\n\
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1546 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	1547
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1548 static PyObject *
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1549 math_isinf(PyObject self, PyObject arg)
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1550 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1551 double x = PyFloat_AsDouble(arg);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1552 if (x == -1.0 && PyErr_Occurred())
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1553 return NULL;
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1554 return PyBool_FromLong((long)Py_IS_INFINITY(x));
44437 968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1555 }
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1556
968bda81e6c8 Added math.isinf() and math.isnan() Christian Heimes <christian@cheimes.de> parents: 44432 diff changeset	1557 PyDoc_STRVAR(math_isinf_doc,
59829 edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1558 "isinf(x) -> bool\n\n\
edc92bce4d6e Merged revisions 75952-75953,75955,76105,76143,76223,76259,76326,76376-76377 via svnmerge from Georg Brandl <georg@python.org> parents: 50257 diff changeset	1559 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	1560
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1561 static PyMethodDef math_methods[] = {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1562 {"acos", math_acos, METH_O, math_acos_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1563 {"acosh", math_acosh, METH_O, math_acosh_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1564 {"asin", math_asin, METH_O, math_asin_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1565 {"asinh", math_asinh, METH_O, math_asinh_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1566 {"atan", math_atan, METH_O, math_atan_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1567 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1568 {"atanh", math_atanh, METH_O, math_atanh_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1569 {"ceil", math_ceil, METH_O, math_ceil_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1570 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1571 {"cos", math_cos, METH_O, math_cos_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1572 {"cosh", math_cosh, METH_O, math_cosh_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1573 {"degrees", math_degrees, METH_O, math_degrees_doc},
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1574 {"erf", math_erf, METH_O, math_erf_doc},
fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1575 {"erfc", math_erfc, METH_O, math_erfc_doc},
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1576 {"exp", math_exp, METH_O, math_exp_doc},
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1577 {"expm1", math_expm1, METH_O, math_expm1_doc},
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1578 {"fabs", math_fabs, METH_O, math_fabs_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1579 {"factorial", math_factorial, METH_O, math_factorial_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1580 {"floor", math_floor, METH_O, math_floor_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1581 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1582 {"frexp", math_frexp, METH_O, math_frexp_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1583 {"fsum", math_fsum, METH_O, math_fsum_doc},
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1584 {"gamma", math_gamma, METH_O, math_gamma_doc},
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1585 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1586 {"isinf", math_isinf, METH_O, math_isinf_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1587 {"isnan", math_isnan, METH_O, math_isnan_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1588 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
61463 fd25030223b0 Untabify C files. Will watch buildbots. Antoine Pitrou <solipsis@pitrou.net> parents: 58124 diff changeset	1589 {"lgamma", math_lgamma, METH_O, math_lgamma_doc},
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1590 {"log", math_log, METH_VARARGS, math_log_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1591 {"log1p", math_log1p, METH_O, math_log1p_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1592 {"log10", math_log10, METH_O, math_log10_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1593 {"modf", math_modf, METH_O, math_modf_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1594 {"pow", math_pow, METH_VARARGS, math_pow_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1595 {"radians", math_radians, METH_O, math_radians_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1596 {"sin", math_sin, METH_O, math_sin_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1597 {"sinh", math_sinh, METH_O, math_sinh_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1598 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1599 {"tan", math_tan, METH_O, math_tan_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1600 {"tanh", math_tanh, METH_O, math_tanh_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1601 {"trunc", math_trunc, METH_O, math_trunc_doc},
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1602 {NULL, NULL} /* sentinel */
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1603 };
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1604
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1605
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1606 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	1607 "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	1608 "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	1609
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 23832 diff changeset	1610 PyMODINIT_FUNC
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13331 diff changeset	1611 initmath(void)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1612 {
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1613 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	1614
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1615 m = Py_InitModule3("math", math_methods, module_doc);
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1616 if (m == NULL)
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1617 goto finally;
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	1618
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1619 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1620 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	1621
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	1622 finally:
61465 e38335d4df91 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 59829 diff changeset	1623 return;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1624 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 80661:94de77bd0b4b 2.7