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

annotate Modules/mathmodule.c @ 58664:993f703a61ba

Merged revisions 77484,77487,77561,77570,77593,77603,77608,77667,77702-77703,77739,77858,77887,77889 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r77484 | skip.montanaro | 2010-01-13 19:12:34 -0600 (Wed, 13 Jan 2010) | 4 lines Update PyEval_EvalFrame to PyEval_EvalFrameEx. This looks to have been done partially before. Also add a comment describing how this might have to work with different versions of the interpreter. ........ r77487 | ezio.melotti | 2010-01-14 05:34:10 -0600 (Thu, 14 Jan 2010) | 1 line Fixed typo ........ r77561 | georg.brandl | 2010-01-17 02:42:30 -0600 (Sun, 17 Jan 2010) | 1 line #7699: improve datetime docs: straightforward linking to strftime/strptime section, mark classmethods as such. ........ r77570 | georg.brandl | 2010-01-17 06:14:42 -0600 (Sun, 17 Jan 2010) | 1 line Add note about usage of STRINGLIB_EMPTY. ........ r77593 | georg.brandl | 2010-01-17 17:33:53 -0600 (Sun, 17 Jan 2010) | 1 line Fix internal reference. ........ r77603 | benjamin.peterson | 2010-01-18 17:07:56 -0600 (Mon, 18 Jan 2010) | 8 lines data descriptors do not override the class dictionary if __get__ is not defined Adjust documentation and add a test to verify this behavior. See http://mail.python.org/pipermail/python-dev/2010-January/095637.html for discussion. ........ r77608 | gregory.p.smith | 2010-01-19 02:19:03 -0600 (Tue, 19 Jan 2010) | 6 lines Do not compile stubs for the sha2 series hashes in the openssl hashlib module when the openssl version is too old to support them. That leads both compiled code bloat and to unittests attempting to test implementations that don't exist for comparison purposes on such platforms. ........ r77667 | mark.dickinson | 2010-01-21 12:32:27 -0600 (Thu, 21 Jan 2010) | 1 line Add two more test_strtod test values. ........ r77702 | georg.brandl | 2010-01-23 02:43:31 -0600 (Sat, 23 Jan 2010) | 1 line #7762: fix refcount annotation of PyUnicode_Tailmatch(). ........ r77703 | georg.brandl | 2010-01-23 02:47:54 -0600 (Sat, 23 Jan 2010) | 1 line #7725: fix referencing issue. ........ r77739 | benjamin.peterson | 2010-01-24 21:52:52 -0600 (Sun, 24 Jan 2010) | 1 line mention from_float() in error message ........ r77858 | georg.brandl | 2010-01-30 11:57:48 -0600 (Sat, 30 Jan 2010) | 1 line #7802: fix invalid example (heh). ........ r77887 | georg.brandl | 2010-01-31 12:51:49 -0600 (Sun, 31 Jan 2010) | 5 lines Fix-up ftplib documentation: move exception descriptions to toplevel, not inside a class remove attribution in "versionadded" spell and grammar check docstring of FTP_TLS ........ r77889 | michael.foord | 2010-01-31 13:59:26 -0600 (Sun, 31 Jan 2010) | 1 line Minor modification to unittest documentation. ........

author	Benjamin Peterson <benjamin@python.org>
date	Wed, 03 Feb 2010 02:35:45 +0000
parents	9b9adc42c73a
children	cab14be0ada1

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
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	3 /* Here are some comments from Tim Peters, extracted from the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	4 discussion attached to http://bugs.python.org/issue1640. They
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	5 describe the general aims of the math module with respect to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	6 special values, IEEE-754 floating-point exceptions, and Python
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	7 exceptions.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	8
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	9 These are the "spirit of 754" rules:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	10
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	11 1. If the mathematical result is a real number, but of magnitude too
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	12 large to approximate by a machine float, overflow is signaled and the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	13 result is an infinity (with the appropriate sign).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	14
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	15 2. If the mathematical result is a real number, but of magnitude too
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	16 small to approximate by a machine float, underflow is signaled and the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	17 result is a zero (with the appropriate sign).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	18
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	19 3. At a singularity (a value x such that the limit of f(y) as y
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	20 approaches x exists and is an infinity), "divide by zero" is signaled
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	21 and the result is an infinity (with the appropriate sign). This is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	22 complicated a little by that the left-side and right-side limits may
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	23 not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	24 from the positive or negative directions. In that specific case, the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	25 sign of the zero determines the result of 1/0.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	26
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	27 4. At a point where a function has no defined result in the extended
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	28 reals (i.e., the reals plus an infinity or two), invalid operation is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	29 signaled and a NaN is returned.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	30
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	31 And these are what Python has historically /tried/ to do (but not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	32 always successfully, as platform libm behavior varies a lot):
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	33
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	34 For #1, raise OverflowError.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	35
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	36 For #2, return a zero (with the appropriate sign if that happens by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	37 accident ;-)).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	38
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	39 For #3 and #4, raise ValueError. It may have made sense to raise
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	40 Python's ZeroDivisionError in #3, but historically that's only been
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	41 raised for division by zero and mod by zero.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	42
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	43 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	44
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	45 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	46 In general, on an IEEE-754 platform the aim is to follow the C99
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	47 standard, including Annex 'F', whenever possible. Where the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	48 standard recommends raising the 'divide-by-zero' or 'invalid'
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	49 floating-point exceptions, Python should raise a ValueError. Where
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	50 the standard recommends raising 'overflow', Python should raise an
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	51 OverflowError. In all other circumstances a value should be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	52 returned.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	53 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	54
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	55 #include "Python.h"
57758 b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	56 #include "_math.h"
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	57
44943 6547be11f443 Merged revisions 60245-60277 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44499 diff changeset	58 #ifdef _OSF_SOURCE
6547be11f443 Merged revisions 60245-60277 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44499 diff changeset	59 /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
6547be11f443 Merged revisions 60245-60277 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44499 diff changeset	60 extern double copysign(double, double);
6547be11f443 Merged revisions 60245-60277 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44499 diff changeset	61 #endif
6547be11f443 Merged revisions 60245-60277 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44499 diff changeset	62
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	63 /*
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	64 sin(pi*x), giving accurate results for all finite x (especially x
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	65 integral or close to an integer). This is here for use in the
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	66 reflection formula for the gamma function. It conforms to IEEE
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	67 754-2008 for finite arguments, but not for infinities or nans.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	68 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	69
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	70 static const double pi = 3.141592653589793238462643383279502884197;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	71 static const double sqrtpi = 1.772453850905516027298167483341145182798;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	72
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	73 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	74 sinpi(double x)
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	75 {
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	76 double y, r;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	77 int n;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	78 /* this function should only ever be called for finite arguments */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	79 assert(Py_IS_FINITE(x));
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	80 y = fmod(fabs(x), 2.0);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	81 n = (int)round(2.0*y);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	82 assert(0 <= n && n <= 4);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	83 switch (n) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	84 case 0:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	85 r = sin(pi*y);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	86 break;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	87 case 1:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	88 r = cos(pi*(y-0.5));
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	89 break;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	90 case 2:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	91 /* N.B. -sin(pi(y-1.0)) is not* equivalent: it would give
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	92 -0.0 instead of 0.0 when y == 1.0. */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	93 r = sin(pi*(1.0-y));
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	94 break;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	95 case 3:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	96 r = -cos(pi*(y-1.5));
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	97 break;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	98 case 4:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	99 r = sin(pi*(y-2.0));
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	100 break;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	101 default:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	102 assert(0); /* should never get here */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	103 r = -1.23e200; /* silence gcc warning */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	104 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	105 return copysign(1.0, x)*r;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	106 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	107
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	108 /* Implementation of the real gamma function. In extensive but non-exhaustive
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	109 random tests, this function proved accurate to within <= 10 ulps across the
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	110 entire float domain. Note that accuracy may depend on the quality of the
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	111 system math functions, the pow function in particular. Special cases
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	112 follow C99 annex F. The parameters and method are tailored to platforms
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	113 whose double format is the IEEE 754 binary64 format.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	114
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	115 Method: for x > 0.0 we use the Lanczos approximation with parameters N=13
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	116 and g=6.024680040776729583740234375; these parameters are amongst those
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	117 used by the Boost library. Following Boost (again), we re-express the
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	118 Lanczos sum as a rational function, and compute it that way. The
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	119 coefficients below were computed independently using MPFR, and have been
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	120 double-checked against the coefficients in the Boost source code.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	121
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	122 For x < 0.0 we use the reflection formula.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	123
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	124 There's one minor tweak that deserves explanation: Lanczos' formula for
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	125 Gamma(x) involves computing pow(x+g-0.5, x-0.5) / exp(x+g-0.5). For many x
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	126 values, x+g-0.5 can be represented exactly. However, in cases where it
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	127 can't be represented exactly the small error in x+g-0.5 can be magnified
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	128 significantly by the pow and exp calls, especially for large x. A cheap
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	129 correction is to multiply by (1 + e*g/(x+g-0.5)), where e is the error
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	130 involved in the computation of x+g-0.5 (that is, e = computed value of
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	131 x+g-0.5 - exact value of x+g-0.5). Here's the proof:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	132
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	133 Correction factor
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	134 -----------------
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	135 Write x+g-0.5 = y-e, where y is exactly representable as an IEEE 754
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	136 double, and e is tiny. Then:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	137
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 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)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	139 = pow(y, x-0.5)/exp(y) * C,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	140
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	141 where the correction_factor C is given by
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	142
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	143 C = pow(1-e/y, x-0.5) * exp(e)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	144
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 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:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	146
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	147 C ~ (1-(x-0.5)e/y) (1+e) ~ 1 + e*(y-(x-0.5))/y
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	148
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	149 But y-(x-0.5) = g+e, and g+e ~ g. So we get C ~ 1 + e*g/y, and
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	150
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 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),
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	152
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	153 Note that for accuracy, when computing r*C it's better to do
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	154
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	155 r + eg/yr;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	156
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	157 than
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	158
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	159 r * (1 + e*g/y);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	160
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	161 since the addition in the latter throws away most of the bits of
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	162 information in e*g/y.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	163 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	164
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	165 #define LANCZOS_N 13
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	166 static const double lanczos_g = 6.024680040776729583740234375;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	167 static const double lanczos_g_minus_half = 5.524680040776729583740234375;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	168 static const double lanczos_num_coeffs[LANCZOS_N] = {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	169 23531376880.410759688572007674451636754734846804940,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	170 42919803642.649098768957899047001988850926355848959,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	171 35711959237.355668049440185451547166705960488635843,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	172 17921034426.037209699919755754458931112671403265390,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	173 6039542586.3520280050642916443072979210699388420708,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	174 1439720407.3117216736632230727949123939715485786772,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	175 248874557.86205415651146038641322942321632125127801,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	176 31426415.585400194380614231628318205362874684987640,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	177 2876370.6289353724412254090516208496135991145378768,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	178 186056.26539522349504029498971604569928220784236328,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	179 8071.6720023658162106380029022722506138218516325024,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	180 210.82427775157934587250973392071336271166969580291,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	181 2.5066282746310002701649081771338373386264310793408
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	182 };
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	183
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	184 /* denominator is x(x+1)...(x+LANCZOS_N-2) /
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	185 static const double lanczos_den_coeffs[LANCZOS_N] = {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	186 0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 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
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	189 /* gamma values for small positive integers, 1 though NGAMMA_INTEGRAL */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	190 #define NGAMMA_INTEGRAL 23
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	191 static const double gamma_integral[NGAMMA_INTEGRAL] = {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	192 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	193 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	194 1307674368000.0, 20922789888000.0, 355687428096000.0,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	195 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	196 51090942171709440000.0, 1124000727777607680000.0,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	197 };
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	198
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	199 /* Lanczos' sum L_g(x), for positive x */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	200
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	201 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	202 lanczos_sum(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	203 {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	204 double num = 0.0, den = 0.0;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	205 int i;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	206 assert(x > 0.0);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	207 /* evaluate the rational function lanczos_sum(x). For large
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	208 x, the obvious algorithm risks overflow, so we instead
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	209 rescale the denominator and numerator of the rational
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	210 function by x**(1-LANCZOS_N) and treat this as a
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	211 rational function in 1/x. This also reduces the error for
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	212 larger x values. The choice of cutoff point (5.0 below) is
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	213 somewhat arbitrary; in tests, smaller cutoff values than
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	214 this resulted in lower accuracy. */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	215 if (x < 5.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	216 for (i = LANCZOS_N; --i >= 0; ) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	217 num = num * x + lanczos_num_coeffs[i];
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	218 den = den * x + lanczos_den_coeffs[i];
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	219 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	220 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	221 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	222 for (i = 0; i < LANCZOS_N; i++) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	223 num = num / x + lanczos_num_coeffs[i];
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	224 den = den / x + lanczos_den_coeffs[i];
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	225 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	226 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	227 return num/den;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	228 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	229
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	230 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	231 m_tgamma(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	232 {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	233 double absx, r, y, z, sqrtpow;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	234
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	235 /* special cases */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	236 if (!Py_IS_FINITE(x)) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	237 if (Py_IS_NAN(x) \|\| x > 0.0)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	238 return x; /* tgamma(nan) = nan, tgamma(inf) = inf */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	239 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	240 errno = EDOM;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	241 return Py_NAN; /* tgamma(-inf) = nan, invalid */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	242 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	243 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	244 if (x == 0.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	245 errno = EDOM;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	246 return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	247 }
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	248
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	249 /* integer arguments */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	250 if (x == floor(x)) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	251 if (x < 0.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	252 errno = EDOM; /* tgamma(n) = nan, invalid for */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	253 return Py_NAN; /* negative integers n */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	254 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	255 if (x <= NGAMMA_INTEGRAL)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	256 return gamma_integral[(int)x - 1];
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	257 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	258 absx = fabs(x);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	259
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	260 /* tiny arguments: tgamma(x) ~ 1/x for x near 0 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	261 if (absx < 1e-20) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	262 r = 1.0/x;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	263 if (Py_IS_INFINITY(r))
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	264 errno = ERANGE;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	265 return r;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	266 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	267
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	268 /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	269 x > 200, and underflows to +-0.0 for x < -200, not a negative
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	270 integer. */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	271 if (absx > 200.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	272 if (x < 0.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	273 return 0.0/sinpi(x);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	274 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	275 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	276 errno = ERANGE;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	277 return Py_HUGE_VAL;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	278 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	279 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	280
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	281 y = absx + lanczos_g_minus_half;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	282 /* compute error in sum */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	283 if (absx > lanczos_g_minus_half) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	284 /* note: the correction can be foiled by an optimizing
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	285 compiler that (incorrectly) thinks that an expression like
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	286 a + b - a - b can be optimized to 0.0. This shouldn't
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	287 happen in a standards-conforming compiler. */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	288 double q = y - absx;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	289 z = q - lanczos_g_minus_half;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	290 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	291 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	292 double q = y - lanczos_g_minus_half;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	293 z = q - absx;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	294 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	295 z = z * lanczos_g / y;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	296 if (x < 0.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	297 r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	298 r -= z * r;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	299 if (absx < 140.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	300 r /= pow(y, absx - 0.5);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	301 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	302 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	303 sqrtpow = pow(y, absx / 2.0 - 0.25);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	304 r /= sqrtpow;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	305 r /= sqrtpow;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	306 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	307 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	308 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	309 r = lanczos_sum(absx) / exp(y);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	310 r += z * r;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	311 if (absx < 140.0) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	312 r *= pow(y, absx - 0.5);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	313 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	314 else {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	315 sqrtpow = pow(y, absx / 2.0 - 0.25);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	316 r *= sqrtpow;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	317 r *= sqrtpow;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	318 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	319 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	320 if (Py_IS_INFINITY(r))
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	321 errno = ERANGE;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 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
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	325 /*
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	326 lgamma: natural log of the absolute value of the Gamma function.
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	327 For large arguments, Lanczos' formula works extremely well here.
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	328 */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	329
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	330 static double
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	331 m_lgamma(double x)
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	332 {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	333 double r, absx;
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	334
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	335 /* special cases */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	336 if (!Py_IS_FINITE(x)) {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	337 if (Py_IS_NAN(x))
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	338 return x; /* lgamma(nan) = nan */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	339 else
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	340 return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	341 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	342
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	343 /* integer arguments */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	344 if (x == floor(x) && x <= 2.0) {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	345 if (x <= 0.0) {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	346 errno = EDOM; /* lgamma(n) = inf, divide-by-zero for */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	347 return Py_HUGE_VAL; /* integers n <= 0 */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	348 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	349 else {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	350 return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	351 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	352 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	353
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	354 absx = fabs(x);
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	355 /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	356 if (absx < 1e-20)
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	357 return -log(absx);
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	358
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	359 /* Lanczos' formula */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	360 if (x > 0.0) {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	361 /* we could save a fraction of a ulp in accuracy by having a
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	362 second set of numerator coefficients for lanczos_sum that
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	363 absorbed the exp(-lanczos_g) term, and throwing out the
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	364 lanczos_g subtraction below; it's probably not worth it. */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	365 r = log(lanczos_sum(x)) - lanczos_g +
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	366 (x-0.5)*(log(x+lanczos_g-0.5)-1);
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	367 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	368 else {
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	369 r = log(pi) - log(fabs(sinpi(absx))) - log(absx) -
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	370 (log(lanczos_sum(absx)) - lanczos_g +
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	371 (absx-0.5)*(log(absx+lanczos_g-0.5)-1));
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	372 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	373 if (Py_IS_INFINITY(r))
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	374 errno = ERANGE;
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	375 return r;
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	376 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	377
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	378 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	379 Implementations of the error function erf(x) and the complementary error
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	380 function erfc(x).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	381
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	382 Method: following 'Numerical Recipes' by Flannery, Press et. al. (2nd ed.,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	383 Cambridge University Press), we use a series approximation for erf for
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	384 small x, and a continued fraction approximation for erfc(x) for larger x;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	385 combined with the relations erf(-x) = -erf(x) and erfc(x) = 1.0 - erf(x),
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	386 this gives us erf(x) and erfc(x) for all x.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	387
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	388 The series expansion used is:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	389
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	390 erf(x) = xexp(-xx)/sqrt(pi) * [
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	391 2/1 + 4/3 x2 + 8/15 x4 + 16/105 x**6 + ...]
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	392
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	393 The coefficient of x(2k-2) here is 4kfactorial(k)/factorial(2k).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	394 This series converges well for smallish x, but slowly for larger x.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	395
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	396 The continued fraction expansion used is:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	397
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	398 erfc(x) = xexp(-xx)/sqrt(pi) * [1/(0.5 + x2 -) 0.5/(2.5 + x2 - )
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	399 3.0/(4.5 + x2 - ) 7.5/(6.5 + x2 - ) ...]
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	400
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	401 after the first term, the general term has the form:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	402
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	403 k(k-0.5)/(2k+0.5 + x**2 - ...).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	404
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	405 This expansion converges fast for larger x, but convergence becomes
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	406 infinitely slow as x approaches 0.0. The (somewhat naive) continued
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	407 fraction evaluation algorithm used below also risks overflow for large x;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	408 but for large x, erfc(x) == 0.0 to within machine precision. (For
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	409 example, erfc(30.0) is approximately 2.56e-393).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	410
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	411 Parameters: use series expansion for abs(x) < ERF_SERIES_CUTOFF and
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	412 continued fraction expansion for ERF_SERIES_CUTOFF <= abs(x) <
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	413 ERFC_CONTFRAC_CUTOFF. ERFC_SERIES_TERMS and ERFC_CONTFRAC_TERMS are the
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	414 numbers of terms to use for the relevant expansions. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	415
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	416 #define ERF_SERIES_CUTOFF 1.5
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	417 #define ERF_SERIES_TERMS 25
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	418 #define ERFC_CONTFRAC_CUTOFF 30.0
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	419 #define ERFC_CONTFRAC_TERMS 50
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	420
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	421 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	422 Error function, via power series.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	423
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	424 Given a finite float x, return an approximation to erf(x).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	425 Converges reasonably fast for small x.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	426 */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	427
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	428 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	429 m_erf_series(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	430 {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	431 double x2, acc, fk;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	432 int i;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	433
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	434 x2 = x * x;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	435 acc = 0.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	436 fk = (double)ERF_SERIES_TERMS + 0.5;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	437 for (i = 0; i < ERF_SERIES_TERMS; i++) {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	438 acc = 2.0 + x2 * acc / fk;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	439 fk -= 1.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	440 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	441 return acc * x * exp(-x2) / sqrtpi;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	442 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	443
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	444 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	445 Complementary error function, via continued fraction expansion.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	446
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	447 Given a positive float x, return an approximation to erfc(x). Converges
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	448 reasonably fast for x large (say, x > 2.0), and should be safe from
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	449 overflow if x and nterms are not too large. On an IEEE 754 machine, with x
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	450 <= 30.0, we're safe up to nterms = 100. For x >= 30.0, erfc(x) is smaller
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	451 than the smallest representable nonzero float. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	452
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	453 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	454 m_erfc_contfrac(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	455 {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	456 double x2, a, da, p, p_last, q, q_last, b;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	457 int i;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	458
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	459 if (x >= ERFC_CONTFRAC_CUTOFF)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	460 return 0.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	461
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	462 x2 = x*x;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	463 a = 0.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	464 da = 0.5;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	465 p = 1.0; p_last = 0.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	466 q = da + x2; q_last = 1.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	467 for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	468 double temp;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	469 a += da;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	470 da += 2.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	471 b = da + x2;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	472 temp = p; p = bp - ap_last; p_last = temp;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	473 temp = q; q = bq - aq_last; q_last = temp;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	474 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	475 return p / q * x * exp(-x2) / sqrtpi;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	476 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	477
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	478 /* Error function erf(x), for general x */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	479
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	480 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	481 m_erf(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	482 {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	483 double absx, cf;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	484
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	485 if (Py_IS_NAN(x))
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	486 return x;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	487 absx = fabs(x);
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	488 if (absx < ERF_SERIES_CUTOFF)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	489 return m_erf_series(x);
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	490 else {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	491 cf = m_erfc_contfrac(absx);
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	492 return x > 0.0 ? 1.0 - cf : cf - 1.0;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	493 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	494 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	495
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	496 /* Complementary error function erfc(x), for general x. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	497
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	498 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	499 m_erfc(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	500 {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	501 double absx, cf;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	502
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	503 if (Py_IS_NAN(x))
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	504 return x;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	505 absx = fabs(x);
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	506 if (absx < ERF_SERIES_CUTOFF)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	507 return 1.0 - m_erf_series(x);
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	508 else {
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	509 cf = m_erfc_contfrac(absx);
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	510 return x > 0.0 ? cf : 2.0 - cf;
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	511 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	512 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	513
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	514 /*
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	515 wrapper for atan2 that deals directly with special cases before
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	516 delegating to the platform libm for the remaining cases. This
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	517 is necessary to get consistent behaviour across platforms.
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	518 Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	519 always follow C99.
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	520 */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	521
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	522 static double
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	523 m_atan2(double y, double x)
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	524 {
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	525 if (Py_IS_NAN(x) \|\| Py_IS_NAN(y))
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	526 return Py_NAN;
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	527 if (Py_IS_INFINITY(y)) {
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	528 if (Py_IS_INFINITY(x)) {
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	529 if (copysign(1., x) == 1.)
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	530 /* atan2(+-inf, +inf) == +-pi/4 */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	531 return copysign(0.25*Py_MATH_PI, y);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	532 else
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	533 /* atan2(+-inf, -inf) == +-pi3/4 /
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	534 return copysign(0.75*Py_MATH_PI, y);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	535 }
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	536 /* atan2(+-inf, x) == +-pi/2 for finite x */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	537 return copysign(0.5*Py_MATH_PI, y);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	538 }
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	539 if (Py_IS_INFINITY(x) \|\| y == 0.) {
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	540 if (copysign(1., x) == 1.)
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	541 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	542 return copysign(0., y);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	543 else
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	544 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	545 return copysign(Py_MATH_PI, y);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	546 }
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	547 return atan2(y, x);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	548 }
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	549
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	550 /*
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	551 Various platforms (Solaris, OpenBSD) do nonstandard things for log(0),
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	552 log(-ve), log(NaN). Here are wrappers for log and log10 that deal with
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	553 special values directly, passing positive non-special values through to
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	554 the system log/log10.
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	555 */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	556
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	557 static double
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	558 m_log(double x)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	559 {
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	560 if (Py_IS_FINITE(x)) {
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	561 if (x > 0.0)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	562 return log(x);
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	563 errno = EDOM;
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	564 if (x == 0.0)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	565 return -Py_HUGE_VAL; /* log(0) = -inf */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	566 else
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	567 return Py_NAN; /* log(-ve) = nan */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	568 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	569 else if (Py_IS_NAN(x))
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	570 return x; /* log(nan) = nan */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	571 else if (x > 0.0)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	572 return x; /* log(inf) = inf */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	573 else {
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	574 errno = EDOM;
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	575 return Py_NAN; /* log(-inf) = nan */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	576 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	577 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	578
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	579 static double
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	580 m_log10(double x)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	581 {
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	582 if (Py_IS_FINITE(x)) {
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	583 if (x > 0.0)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	584 return log10(x);
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	585 errno = EDOM;
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	586 if (x == 0.0)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	587 return -Py_HUGE_VAL; /* log10(0) = -inf */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	588 else
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	589 return Py_NAN; /* log10(-ve) = nan */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	590 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	591 else if (Py_IS_NAN(x))
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	592 return x; /* log10(nan) = nan */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	593 else if (x > 0.0)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	594 return x; /* log10(inf) = inf */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	595 else {
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	596 errno = EDOM;
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	597 return Py_NAN; /* log10(-inf) = nan */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	598 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	599 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	600
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	601
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	602 /* Call is_error when errno != 0, and where x is the result libm
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	603 * returned. is_error will usually set up an exception and return
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	604 * true (1), but may return false (0) without setting up an exception.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	605 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	606 static int
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	607 is_error(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	608 {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	609 int result = 1; /* presumption of guilt */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	610 assert(errno); /* non-zero errno is a precondition for calling */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	611 if (errno == EDOM)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	612 PyErr_SetString(PyExc_ValueError, "math domain error");
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	613
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	614 else if (errno == ERANGE) {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	615 /* ANSI C generally requires libm functions to set ERANGE
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	616 * on overflow, but also generally allows them to set
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	617 * ERANGE on underflow too. There's no consistency about
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	618 * the latter across platforms.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	619 * Alas, C99 never requires that errno be set.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	620 * Here we suppress the underflow errors (libm functions
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	621 * should return a zero on underflow, and +- HUGE_VAL on
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	622 * overflow, so testing the result for zero suffices to
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	623 * distinguish the cases).
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	624 *
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	625 * On some platforms (Ubuntu/ia64) it seems that errno can be
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	626 * set to ERANGE for subnormal results that do not underflow
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	627 * to zero. So to be safe, we'll ignore ERANGE whenever the
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	628 * function result is less than one in absolute value.
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	629 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	630 if (fabs(x) < 1.0)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	631 result = 0;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	632 else
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	633 PyErr_SetString(PyExc_OverflowError,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	634 "math range error");
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	635 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	636 else
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	637 /* Unexpected math error */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	638 PyErr_SetFromErrno(PyExc_ValueError);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	639 return result;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	640 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	641
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	642 /*
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	643 math_1 is used to wrap a libm function f that takes a double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	644 arguments and returns a double.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	645
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	646 The error reporting follows these rules, which are designed to do
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	647 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	648 platforms.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	649
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	650 - a NaN result from non-NaN inputs causes ValueError to be raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	651 - an infinite result from finite inputs causes OverflowError to be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	652 raised if can_overflow is 1, or raises ValueError if can_overflow
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	653 is 0.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	654 - if the result is finite and errno == EDOM then ValueError is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	655 raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	656 - if the result is finite and nonzero and errno == ERANGE then
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	657 OverflowError is raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	658
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	659 The last rule is used to catch overflow on platforms which follow
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	660 C89 but for which HUGE_VAL is not an infinity.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	661
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	662 For the majority of one-argument functions these rules are enough
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	663 to ensure that Python's functions behave as specified in 'Annex F'
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	664 of the C99 standard, with the 'invalid' and 'divide-by-zero'
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	665 floating-point exceptions mapping to Python's ValueError and the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	666 'overflow' floating-point exception mapping to OverflowError.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	667 math_1 only works for functions that don't have singularities and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	668 the possibility of overflow; fortunately, that covers everything we
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	669 care about right now.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	670 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	671
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	672 static PyObject *
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	673 math_1_to_whatever(PyObject arg, double (func) (double),
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	674 PyObject (from_double_func) (double),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	675 int can_overflow)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	676 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	677 double x, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	678 x = PyFloat_AsDouble(arg);
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	679 if (x == -1.0 && PyErr_Occurred())
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	680 return NULL;
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	681 errno = 0;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	682 PyFPE_START_PROTECT("in math_1", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	683 r = (*func)(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	684 PyFPE_END_PROTECT(r);
46616 3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	685 if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	686 PyErr_SetString(PyExc_ValueError,
48331 a6503ae3e19c Quick fix for test_math failures on Solaris 10 buildbot. For future Mark Dickinson <dickinsm@gmail.com> parents: 48326 diff changeset	687 "math domain error"); /* invalid arg */
46616 3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	688 return NULL;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	689 }
46616 3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	690 if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	691 if (can_overflow)
3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	692 PyErr_SetString(PyExc_OverflowError,
48331 a6503ae3e19c Quick fix for test_math failures on Solaris 10 buildbot. For future Mark Dickinson <dickinsm@gmail.com> parents: 48326 diff changeset	693 "math range error"); /* overflow */
46791 8b67685a8bc3 Revert the temporary change in r62624 Mark Dickinson <dickinsm@gmail.com> parents: 46664 diff changeset	694 else
8b67685a8bc3 Revert the temporary change in r62624 Mark Dickinson <dickinsm@gmail.com> parents: 46664 diff changeset	695 PyErr_SetString(PyExc_ValueError,
48331 a6503ae3e19c Quick fix for test_math failures on Solaris 10 buildbot. For future Mark Dickinson <dickinsm@gmail.com> parents: 48326 diff changeset	696 "math domain error"); /* singularity */
46616 3f2117d3271f Make floating-point exception error messages slightly more verbose: in Mark Dickinson <dickinsm@gmail.com> parents: 46516 diff changeset	697 return NULL;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	698 }
46617 e42fe19ba6fd Whoops. errno should only be tested when the result is finite. Mark Dickinson <dickinsm@gmail.com> parents: 46616 diff changeset	699 if (Py_IS_FINITE(r) && errno && is_error(r))
e42fe19ba6fd Whoops. errno should only be tested when the result is finite. Mark Dickinson <dickinsm@gmail.com> parents: 46616 diff changeset	700 /* this branch unnecessary on most platforms */
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	701 return NULL;
46617 e42fe19ba6fd Whoops. errno should only be tested when the result is finite. Mark Dickinson <dickinsm@gmail.com> parents: 46616 diff changeset	702
e42fe19ba6fd Whoops. errno should only be tested when the result is finite. Mark Dickinson <dickinsm@gmail.com> parents: 46616 diff changeset	703 return (*from_double_func)(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	704 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	705
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	706 /* variant of math_1, to be used when the function being wrapped is known to
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	707 set errno properly (that is, errno = EDOM for invalid or divide-by-zero,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	708 errno = ERANGE for overflow). */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	709
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	710 static PyObject *
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	711 math_1a(PyObject arg, double (func) (double))
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	712 {
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	713 double x, r;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	714 x = PyFloat_AsDouble(arg);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	715 if (x == -1.0 && PyErr_Occurred())
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	716 return NULL;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	717 errno = 0;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	718 PyFPE_START_PROTECT("in math_1a", return 0);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	719 r = (*func)(x);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	720 PyFPE_END_PROTECT(r);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	721 if (errno && is_error(r))
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	722 return NULL;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	723 return PyFloat_FromDouble(r);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	724 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	725
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	726 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	727 math_2 is used to wrap a libm function f that takes two double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	728 arguments and returns a double.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	729
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	730 The error reporting follows these rules, which are designed to do
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	731 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	732 platforms.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	733
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	734 - a NaN result from non-NaN inputs causes ValueError to be raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	735 - an infinite result from finite inputs causes OverflowError to be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	736 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	737 - if the result is finite and errno == EDOM then ValueError is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	738 raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	739 - if the result is finite and nonzero and errno == ERANGE then
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	740 OverflowError is raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	741
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	742 The last rule is used to catch overflow on platforms which follow
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	743 C89 but for which HUGE_VAL is not an infinity.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	744
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	745 For most two-argument functions (copysign, fmod, hypot, atan2)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	746 these rules are enough to ensure that Python's functions behave as
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	747 specified in 'Annex F' of the C99 standard, with the 'invalid' and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	748 'divide-by-zero' floating-point exceptions mapping to Python's
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	749 ValueError and the 'overflow' floating-point exception mapping to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	750 OverflowError.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	751 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	752
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	753 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	754 math_1(PyObject arg, double (func) (double), int can_overflow)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	755 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	756 return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	757 }
31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	758
31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	759 static PyObject *
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	760 math_1_to_int(PyObject arg, double (func) (double), int can_overflow)
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	761 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	762 return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	763 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	764
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	765 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	766 math_2(PyObject args, double (func) (double, double), char *funcname)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	767 {
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	768 PyObject ox, oy;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	769 double x, y, r;
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	770 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	771 return NULL;
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	772 x = PyFloat_AsDouble(ox);
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	773 y = PyFloat_AsDouble(oy);
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	774 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	775 return NULL;
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	776 errno = 0;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	777 PyFPE_START_PROTECT("in math_2", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	778 r = (*func)(x, y);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	779 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	780 if (Py_IS_NAN(r)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	781 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	782 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	783 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	784 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	785 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	786 else if (Py_IS_INFINITY(r)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	787 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	788 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	789 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	790 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	791 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	792 if (errno && is_error(r))
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	793 return NULL;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	794 else
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	795 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	796 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	797
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	798 #define FUNC1(funcname, func, can_overflow, docstring) \
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	799 static PyObject * math_##funcname(PyObject self, PyObject args) { \
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	800 return math_1(args, func, can_overflow); \
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	801 }\
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	802 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	803
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	804 #define FUNC1A(funcname, func, docstring) \
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	805 static PyObject * math_##funcname(PyObject self, PyObject args) { \
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	806 return math_1a(args, func); \
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	807 }\
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	808 PyDoc_STRVAR(math_##funcname##_doc, docstring);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	809
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	810 #define FUNC2(funcname, func, docstring) \
24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	811 static PyObject * math_##funcname(PyObject self, PyObject args) { \
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	812 return math_2(args, func, #funcname); \
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	813 }\
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	814 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	815
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	816 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	817 "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57808 diff changeset	818 FUNC1(acosh, m_acosh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	819 "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	820 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	821 "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57808 diff changeset	822 FUNC1(asinh, m_asinh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	823 "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	824 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	825 "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	826 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	827 "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	828 "Unlike atan(y/x), the signs of both x and y are considered.")
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57808 diff changeset	829 FUNC1(atanh, m_atanh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	830 "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	831
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	832 static PyObject * math_ceil(PyObject self, PyObject number) {
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	833 static PyObject *ceil_str = NULL;
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	834 PyObject *method;
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	835
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	836 if (ceil_str == NULL) {
45029 ef2d3bf8383d Merged revisions 60379-60382 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44999 diff changeset	837 ceil_str = PyUnicode_InternFromString("__ceil__");
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	838 if (ceil_str == NULL)
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	839 return NULL;
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	840 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	841
44351 86a2679dca46 #1629: Renamed Py_Size, Py_Type and Py_Refcnt to Py_SIZE, Py_TYPE and Py_REFCNT. Christian Heimes <christian@cheimes.de> parents: 42754 diff changeset	842 method = _PyType_Lookup(Py_TYPE(number), ceil_str);
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	843 if (method == NULL)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	844 return math_1_to_int(number, ceil, 0);
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	845 else
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	846 return PyObject_CallFunction(method, "O", number);
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	847 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	848
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	849 PyDoc_STRVAR(math_ceil_doc,
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	850 "ceil(x)\n\nReturn the ceiling of x as an int.\n"
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	851 "This is the smallest integral value >= x.");
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	852
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	853 FUNC2(copysign, copysign,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	854 "copysign(x, y)\n\nReturn x with the sign of y.")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	855 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	856 "cos(x)\n\nReturn the cosine of x (measured in radians).")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	857 FUNC1(cosh, cosh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	858 "cosh(x)\n\nReturn the hyperbolic cosine of x.")
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	859 FUNC1A(erf, m_erf,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	860 "erf(x)\n\nError function at x.")
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	861 FUNC1A(erfc, m_erfc,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	862 "erfc(x)\n\nComplementary error function at x.")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	863 FUNC1(exp, exp, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	864 "exp(x)\n\nReturn e raised to the power of x.")
57758 b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	865 FUNC1(expm1, m_expm1, 1,
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	866 "expm1(x)\n\nReturn exp(x)-1.\n"
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	867 "This function avoids the loss of precision involved in the direct "
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	868 "evaluation of exp(x)-1 for small x.")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	869 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	870 "fabs(x)\n\nReturn the absolute value of the float x.")
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	871
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	872 static PyObject * math_floor(PyObject self, PyObject number) {
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	873 static PyObject *floor_str = NULL;
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	874 PyObject *method;
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	875
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	876 if (floor_str == NULL) {
45029 ef2d3bf8383d Merged revisions 60379-60382 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44999 diff changeset	877 floor_str = PyUnicode_InternFromString("__floor__");
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	878 if (floor_str == NULL)
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	879 return NULL;
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	880 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	881
44351 86a2679dca46 #1629: Renamed Py_Size, Py_Type and Py_Refcnt to Py_SIZE, Py_TYPE and Py_REFCNT. Christian Heimes <christian@cheimes.de> parents: 42754 diff changeset	882 method = _PyType_Lookup(Py_TYPE(number), floor_str);
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	883 if (method == NULL)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	884 return math_1_to_int(number, floor, 0);
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	885 else
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	886 return PyObject_CallFunction(method, "O", number);
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	887 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	888
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	889 PyDoc_STRVAR(math_floor_doc,
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	890 "floor(x)\n\nReturn the floor of x as an int.\n"
42754 1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	891 "This is the largest integral value <= x.");
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	892
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	893 FUNC1A(gamma, m_tgamma,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	894 "gamma(x)\n\nGamma function at x.")
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	895 FUNC1A(lgamma, m_lgamma,
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	896 "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57808 diff changeset	897 FUNC1(log1p, m_log1p, 1,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	898 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	899 "The result is computed in a way which is accurate for x near zero.")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	900 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	901 "sin(x)\n\nReturn the sine of x (measured in radians).")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	902 FUNC1(sinh, sinh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	903 "sinh(x)\n\nReturn the hyperbolic sine of x.")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	904 FUNC1(sqrt, sqrt, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	905 "sqrt(x)\n\nReturn the square root of x.")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	906 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	907 "tan(x)\n\nReturn the tangent of x (measured in radians).")
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	908 FUNC1(tanh, tanh, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	909 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	910
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	911 /* Precision summation function as msum() by Raymond Hettinger in
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	912 <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	913 enhanced with the exact partials sum and roundoff from Mark
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	914 Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	915 See those links for more details, proofs and other references.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	916
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	917 Note 1: IEEE 754R floating point semantics are assumed,
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	918 but the current implementation does not re-establish special
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	919 value semantics across iterations (i.e. handling -Inf + Inf).
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	920
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	921 Note 2: No provision is made for intermediate overflow handling;
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	922 therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	923 sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	924 overflow of the first partial sum.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	925
48407 e22deaeb6c1b Merged revisions 64365,64370,64406,64408-64409,64412,64416-64417,64420-64421,64425-64428 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 48331 diff changeset	926 Note 3: The intermediate values lo, yr, and hi are declared volatile so
e22deaeb6c1b Merged revisions 64365,64370,64406,64408-64409,64412,64416-64417,64420-64421,64425-64428 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 48331 diff changeset	927 aggressive compilers won't algebraically reduce lo to always be exactly 0.0.
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	928 Also, the volatile declaration forces the values to be stored in memory as
2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	929 regular doubles instead of extended long precision (80-bit) values. This
48407 e22deaeb6c1b Merged revisions 64365,64370,64406,64408-64409,64412,64416-64417,64420-64421,64425-64428 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 48331 diff changeset	930 prevents double rounding because any addition or subtraction of two doubles
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	931 can be resolved exactly into double-sized hi and lo values. As long as the
2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	932 hi value gets forced into a double before yr and lo are computed, the extra
2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	933 bits in downstream extended precision operations (x87 for example) will be
2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	934 exactly zero and therefore can be losslessly stored back into a double,
2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	935 thereby preventing double rounding.
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	936
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	937 Note 4: A similar implementation is in Modules/cmathmodule.c.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	938 Be sure to update both when making changes.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	939
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	940 Note 5: The signature of math.fsum() differs from __builtin__.sum()
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	941 because the start argument doesn't make sense in the context of
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	942 accurate summation. Since the partials table is collapsed before
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	943 returning a result, sum(seq2, start=sum(seq1)) may not equal the
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	944 accurate result returned by sum(itertools.chain(seq1, seq2)).
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	945 */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	946
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	947 #define NUM_PARTIALS 32 /* initial partials array size, on stack */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	948
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	949 /* Extend the partials array p[] by doubling its size. */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	950 static int /* non-zero on error */
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	951 _fsum_realloc(double **p_ptr, Py_ssize_t n,
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	952 double ps, Py_ssize_t m_ptr)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	953 {
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	954 void *v = NULL;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	955 Py_ssize_t m = *m_ptr;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	956
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	957 m += m; /* double */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	958 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	959 double p = p_ptr;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	960 if (p == ps) {
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	961 v = PyMem_Malloc(sizeof(double) * m);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	962 if (v != NULL)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	963 memcpy(v, ps, sizeof(double) * n);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	964 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	965 else
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	966 v = PyMem_Realloc(p, sizeof(double) * m);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	967 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	968 if (v == NULL) { /* size overflow or no memory */
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	969 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	970 return 1;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	971 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	972 p_ptr = (double) v;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	973 *m_ptr = m;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	974 return 0;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	975 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	976
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	977 /* Full precision summation of a sequence of floats.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	978
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	979 def msum(iterable):
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	980 partials = [] # sorted, non-overlapping partial sums
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	981 for x in iterable:
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	982 i = 0
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	983 for y in partials:
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	984 if abs(x) < abs(y):
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	985 x, y = y, x
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	986 hi = x + y
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	987 lo = y - (hi - x)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	988 if lo:
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	989 partials[i] = lo
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	990 i += 1
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	991 x = hi
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	992 partials[i:] = [x]
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	993 return sum_exact(partials)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	994
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	995 Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	996 are exactly equal to x+y. The inner loop applies hi/lo summation to each
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	997 partial so that the list of partial sums remains exact.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	998
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	999 Sum_exact() adds the partial sums exactly and correctly rounds the final
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1000 result (using the round-half-to-even rule). The items in partials remain
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1001 non-zero, non-special, non-overlapping and strictly increasing in
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1002 magnitude, but possibly not all having the same sign.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1003
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1004 Depends on IEEE 754 arithmetic guarantees and half-even rounding.
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1005 */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1006
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1007 static PyObject*
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1008 math_fsum(PyObject self, PyObject seq)
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1009 {
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1010 PyObject item, iter, *sum = NULL;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1011 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1012 double x, y, t, ps[NUM_PARTIALS], *p = ps;
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1013 double xsave, special_sum = 0.0, inf_sum = 0.0;
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1014 volatile double hi, yr, lo;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1015
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1016 iter = PyObject_GetIter(seq);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1017 if (iter == NULL)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1018 return NULL;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1019
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1020 PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1021
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1022 for(;;) { /* for x in iterable */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1023 assert(0 <= n && n <= m);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1024 assert((m == NUM_PARTIALS && p == ps) \|\|
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1025 (m > NUM_PARTIALS && p != NULL));
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1026
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1027 item = PyIter_Next(iter);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1028 if (item == NULL) {
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1029 if (PyErr_Occurred())
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1030 goto _fsum_error;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1031 break;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1032 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1033 x = PyFloat_AsDouble(item);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1034 Py_DECREF(item);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1035 if (PyErr_Occurred())
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1036 goto _fsum_error;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1037
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1038 xsave = x;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1039 for (i = j = 0; j < n; j++) { /* for y in partials */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1040 y = p[j];
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1041 if (fabs(x) < fabs(y)) {
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1042 t = x; x = y; y = t;
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1043 }
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1044 hi = x + y;
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1045 yr = hi - x;
2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1046 lo = y - yr;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1047 if (lo != 0.0)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1048 p[i++] = lo;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1049 x = hi;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1050 }
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1051
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1052 n = i; /* ps[i:] = [x] */
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1053 if (x != 0.0) {
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1054 if (! Py_IS_FINITE(x)) {
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1055 /* a nonfinite x could arise either as
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1056 a result of intermediate overflow, or
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1057 as a result of a nan or inf in the
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1058 summands */
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1059 if (Py_IS_FINITE(xsave)) {
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1060 PyErr_SetString(PyExc_OverflowError,
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1061 "intermediate overflow in fsum");
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1062 goto _fsum_error;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1063 }
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1064 if (Py_IS_INFINITY(xsave))
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1065 inf_sum += xsave;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1066 special_sum += xsave;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1067 /* reset partials */
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1068 n = 0;
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1069 }
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1070 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1071 goto _fsum_error;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1072 else
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1073 p[n++] = x;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1074 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1075 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1076
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1077 if (special_sum != 0.0) {
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1078 if (Py_IS_NAN(inf_sum))
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1079 PyErr_SetString(PyExc_ValueError,
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1080 "-inf + inf in fsum");
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1081 else
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1082 sum = PyFloat_FromDouble(special_sum);
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1083 goto _fsum_error;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1084 }
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1085
47559 2925b568aacc Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from Georg Brandl <georg@python.org> parents: 47320 diff changeset	1086 hi = 0.0;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1087 if (n > 0) {
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1088 hi = p[--n];
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1089 /* sum_exact(ps, hi) from the top, stop when the sum becomes
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1090 inexact. */
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1091 while (n > 0) {
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1092 x = hi;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1093 y = p[--n];
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1094 assert(fabs(y) < fabs(x));
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1095 hi = x + y;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1096 yr = hi - x;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1097 lo = y - yr;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1098 if (lo != 0.0)
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1099 break;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1100 }
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1101 /* Make half-even rounding work across multiple partials.
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1102 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1103 digit to two instead of down to zero (the 1e-16 makes the 1
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1104 slightly closer to two). With a potential 1 ULP rounding
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1105 error fixed-up, math.fsum() can guarantee commutativity. */
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1106 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) \|\|
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1107 (lo > 0.0 && p[n-1] > 0.0))) {
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1108 y = lo * 2.0;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1109 x = hi + y;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1110 yr = x - hi;
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1111 if (y == yr)
f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1112 hi = x;
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1113 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1114 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1115 sum = PyFloat_FromDouble(hi);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1116
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1117 _fsum_error:
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1118 PyFPE_END_PROTECT(hi)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1119 Py_DECREF(iter);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1120 if (p != ps)
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1121 PyMem_Free(p);
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1122 return sum;
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1123 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1124
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1125 #undef NUM_PARTIALS
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1126
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1127 PyDoc_STRVAR(math_fsum_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1128 "fsum(iterable)\n\n\
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1129 Return an accurate floating point sum of values in the iterable.\n\
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1130 Assumes IEEE-754 floating point arithmetic.");
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1131
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1132 static PyObject *
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1133 math_factorial(PyObject self, PyObject arg)
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1134 {
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1135 long i, x;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1136 PyObject result, iobj, *newresult;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1137
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1138 if (PyFloat_Check(arg)) {
57808 53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1139 PyObject *lx;
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1140 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
57808 53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1141 if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1142 PyErr_SetString(PyExc_ValueError,
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1143 "factorial() only accepts integral values");
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1144 return NULL;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1145 }
57808 53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1146 lx = PyLong_FromDouble(dx);
53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1147 if (lx == NULL)
53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1148 return NULL;
53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1149 x = PyLong_AsLong(lx);
53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1150 Py_DECREF(lx);
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1151 }
57808 53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1152 else
53f21f08af0d Merged revisions 76916 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57770 diff changeset	1153 x = PyLong_AsLong(arg);
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1154
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1155 if (x == -1 && PyErr_Occurred())
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1156 return NULL;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1157 if (x < 0) {
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1158 PyErr_SetString(PyExc_ValueError,
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1159 "factorial() not defined for negative values");
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1160 return NULL;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1161 }
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1162
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1163 result = (PyObject *)PyLong_FromLong(1);
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1164 if (result == NULL)
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1165 return NULL;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1166 for (i=1 ; i<=x ; i++) {
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1167 iobj = (PyObject *)PyLong_FromLong(i);
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1168 if (iobj == NULL)
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1169 goto error;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1170 newresult = PyNumber_Multiply(result, iobj);
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1171 Py_DECREF(iobj);
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1172 if (newresult == NULL)
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1173 goto error;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1174 Py_DECREF(result);
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1175 result = newresult;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1176 }
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1177 return result;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1178
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1179 error:
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1180 Py_DECREF(result);
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1181 return NULL;
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1182 }
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1183
50250 1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1184 PyDoc_STRVAR(math_factorial_doc,
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1185 "factorial(x) -> Integral\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1186 "\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1187 "Find x!. Raise a ValueError if x is negative or non-integral.");
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1188
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1189 static PyObject *
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1190 math_trunc(PyObject self, PyObject number)
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1191 {
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1192 static PyObject *trunc_str = NULL;
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1193 PyObject *trunc;
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1194
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1195 if (Py_TYPE(number)->tp_dict == NULL) {
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1196 if (PyType_Ready(Py_TYPE(number)) < 0)
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1197 return NULL;
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1198 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1199
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1200 if (trunc_str == NULL) {
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1201 trunc_str = PyUnicode_InternFromString("__trunc__");
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1202 if (trunc_str == NULL)
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1203 return NULL;
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1204 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1205
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1206 trunc = _PyType_Lookup(Py_TYPE(number), trunc_str);
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1207 if (trunc == NULL) {
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1208 PyErr_Format(PyExc_TypeError,
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1209 "type %.100s doesn't define __trunc__ method",
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1210 Py_TYPE(number)->tp_name);
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1211 return NULL;
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1212 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1213 return PyObject_CallFunctionObjArgs(trunc, number, NULL);
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1214 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1215
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1216 PyDoc_STRVAR(math_trunc_doc,
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1217 "trunc(x:Real) -> Integral\n"
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1218 "\n"
45134 bdcf40d1b38e Merged revisions 60481,60485,60489-60520,60523-60527,60530-60533,60535-60538,60540-60551 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45082 diff changeset	1219 "Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1220
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1221 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1222 math_frexp(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1223 {
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1224 int i;
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1225 double x = PyFloat_AsDouble(arg);
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1226 if (x == -1.0 && PyErr_Occurred())
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1227 return NULL;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1228 /* deal with special cases directly, to sidestep platform
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1229 differences */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1230 if (Py_IS_NAN(x) \|\| Py_IS_INFINITY(x) \|\| !x) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1231 i = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1232 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1233 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1234 PyFPE_START_PROTECT("in math_frexp", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1235 x = frexp(x, &i);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1236 PyFPE_END_PROTECT(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1237 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1238 return Py_BuildValue("(di)", x, i);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1239 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1240
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1241 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	1242 "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	1243 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1244 "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	1245 "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	1246 "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	1247
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1248 static PyObject *
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1249 math_ldexp(PyObject self, PyObject args)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1250 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1251 double x, r;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1252 PyObject *oexp;
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1253 long exp;
58125 9b9adc42c73a Merged revisions 77275 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 58088 diff changeset	1254 int overflow;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1255 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1256 return NULL;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1257
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1258 if (PyLong_Check(oexp)) {
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1259 /* on overflow, replace exponent with either LONG_MAX
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1260 or LONG_MIN, depending on the sign. */
58125 9b9adc42c73a Merged revisions 77275 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 58088 diff changeset	1261 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
9b9adc42c73a Merged revisions 77275 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 58088 diff changeset	1262 if (exp == -1 && PyErr_Occurred())
9b9adc42c73a Merged revisions 77275 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 58088 diff changeset	1263 return NULL;
9b9adc42c73a Merged revisions 77275 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 58088 diff changeset	1264 if (overflow)
9b9adc42c73a Merged revisions 77275 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 58088 diff changeset	1265 exp = overflow < 0 ? LONG_MIN : LONG_MAX;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1266 }
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1267 else {
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1268 PyErr_SetString(PyExc_TypeError,
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1269 "Expected an int or long as second argument "
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1270 "to ldexp.");
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1271 return NULL;
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1272 }
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1273
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1274 if (x == 0. \|\| !Py_IS_FINITE(x)) {
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1275 /* NaNs, zeros and infinities are returned unchanged */
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1276 r = x;
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1277 errno = 0;
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1278 } else if (exp > INT_MAX) {
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1279 /* overflow */
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1280 r = copysign(Py_HUGE_VAL, x);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1281 errno = ERANGE;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1282 } else if (exp < INT_MIN) {
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1283 /* underflow to +-0 */
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1284 r = copysign(0., x);
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1285 errno = 0;
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1286 } else {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1287 errno = 0;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1288 PyFPE_START_PROTECT("in math_ldexp", return 0);
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1289 r = ldexp(x, (int)exp);
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1290 PyFPE_END_PROTECT(r);
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1291 if (Py_IS_INFINITY(r))
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1292 errno = ERANGE;
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1293 }
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1294
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1295 if (errno && is_error(r))
15170 09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and Tim Peters <tim.peters@gmail.com> parents: 14616 diff changeset	1296 return NULL;
47063 081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46791 diff changeset	1297 return PyFloat_FromDouble(r);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1298 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1299
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1300 PyDoc_STRVAR(math_ldexp_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1301 "ldexp(x, i)\n\n\
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1302 Return x * (2**i).");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1303
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1304 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1305 math_modf(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1306 {
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1307 double y, x = PyFloat_AsDouble(arg);
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1308 if (x == -1.0 && PyErr_Occurred())
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1309 return NULL;
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1310 /* some platforms don't do the right thing for NaNs and
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1311 infinities, so we take care of special cases directly. */
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1312 if (!Py_IS_FINITE(x)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1313 if (Py_IS_INFINITY(x))
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1314 return Py_BuildValue("(dd)", copysign(0., x), x);
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1315 else if (Py_IS_NAN(x))
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1316 return Py_BuildValue("(dd)", x, x);
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1317 }
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1318
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1319 errno = 0;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1320 PyFPE_START_PROTECT("in math_modf", return 0);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1321 x = modf(x, &y);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1322 PyFPE_END_PROTECT(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1323 return Py_BuildValue("(dd)", x, y);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1324 }
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1325
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1326 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	1327 "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	1328 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1329 "Return the fractional and integer parts of x. Both results carry the sign\n"
50250 1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1330 "of x and are floats.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1331
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	1332 /* 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	1333 do that by itself -- loghelper can. func is log or log10, and name is
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1334 "log" or "log10". Note that overflow of the result isn't possible: a long
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1335 can contain no more than INT_MAX * SHIFT bits, so has value certainly less
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1336 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	1337 small enough to fit in an IEEE single. log and log10 are even smaller.
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1338 However, intermediate overflow is possible for a long if the number of bits
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1339 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	1340
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1341 static PyObject*
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1342 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	1343 {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1344 /* If it is long, do it ourselves. */
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1345 if (PyLong_Check(arg)) {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1346 double x;
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1347 Py_ssize_t e;
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1348 x = _PyLong_Frexp((PyLongObject *)arg, &e);
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1349 if (x == -1.0 && PyErr_Occurred())
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1350 return NULL;
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1351 if (x <= 0.0) {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1352 PyErr_SetString(PyExc_ValueError,
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1353 "math domain error");
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1354 return NULL;
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1355 }
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1356 /* Special case for log(1), to make sure we get an
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1357 exact result there. */
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1358 if (e == 1 && x == 0.5)
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1359 return PyFloat_FromDouble(0.0);
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1360 /* Value is ~= x * 2*e, so the log ~= log(x) + log(2) e. */
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1361 x = func(x) + func(2.0) * e;
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1362 return PyFloat_FromDouble(x);
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1363 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1364
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1365 /* Else let libm handle it by itself. */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1366 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	1367 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1368
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1369 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	1370 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	1371 {
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1372 PyObject *arg;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1373 PyObject *base = NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1374 PyObject num, den;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1375 PyObject *ans;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1376
26818 e094a03a80ff SF patch #659536: Use PyArg_UnpackTuple where possible. Raymond Hettinger <python@rcn.com> parents: 26661 diff changeset	1377 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1378 return NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1379
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	1380 num = loghelper(arg, m_log, "log");
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1381 if (num == NULL \|\| base == NULL)
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1382 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	1383
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	1384 den = loghelper(base, m_log, "log");
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1385 if (den == NULL) {
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1386 Py_DECREF(num);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1387 return NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1388 }
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1389
37191 4bfe8afe8f65 Get rid of remnants of integer division Neal Norwitz <nnorwitz@gmail.com> parents: 36324 diff changeset	1390 ans = PyNumber_TrueDivide(num, den);
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1391 Py_DECREF(num);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1392 Py_DECREF(den);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1393 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	1394 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1395
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1396 PyDoc_STRVAR(math_log_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1397 "log(x[, base])\n\n\
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1398 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	1399 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	1400
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1401 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1402 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	1403 {
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	1404 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	1405 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1406
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1407 PyDoc_STRVAR(math_log10_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1408 "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	1409
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1410 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1411 math_fmod(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1412 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1413 PyObject ox, oy;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1414 double r, x, y;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1415 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1416 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1417 x = PyFloat_AsDouble(ox);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1418 y = PyFloat_AsDouble(oy);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1419 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1420 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1421 /* fmod(x, +/-Inf) returns x for finite x. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1422 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1423 return PyFloat_FromDouble(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1424 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1425 PyFPE_START_PROTECT("in math_fmod", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1426 r = fmod(x, y);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1427 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1428 if (Py_IS_NAN(r)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1429 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1430 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1431 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1432 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1433 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1434 if (errno && is_error(r))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1435 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1436 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1437 return PyFloat_FromDouble(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1438 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1439
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1440 PyDoc_STRVAR(math_fmod_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1441 "fmod(x, y)\n\nReturn fmod(x, y), according to platform C."
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1442 " x % y may differ.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1443
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1444 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1445 math_hypot(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1446 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1447 PyObject ox, oy;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1448 double r, x, y;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1449 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1450 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1451 x = PyFloat_AsDouble(ox);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1452 y = PyFloat_AsDouble(oy);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1453 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1454 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1455 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1456 if (Py_IS_INFINITY(x))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1457 return PyFloat_FromDouble(fabs(x));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1458 if (Py_IS_INFINITY(y))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1459 return PyFloat_FromDouble(fabs(y));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1460 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1461 PyFPE_START_PROTECT("in math_hypot", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1462 r = hypot(x, y);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1463 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1464 if (Py_IS_NAN(r)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1465 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1466 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1467 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1468 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1469 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1470 else if (Py_IS_INFINITY(r)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1471 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1472 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1473 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1474 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1475 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1476 if (errno && is_error(r))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1477 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1478 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1479 return PyFloat_FromDouble(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1480 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1481
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1482 PyDoc_STRVAR(math_hypot_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1483 "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(xx + yy).");
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1484
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1485 /* pow can't use math_2, but needs its own wrapper: the problem is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1486 that an infinite result can arise either as a result of overflow
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1487 (in which case OverflowError should be raised) or as a result of
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1488 e.g. 0.**-5. (for which ValueError needs to be raised.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1489 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1490
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1491 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1492 math_pow(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1493 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1494 PyObject ox, oy;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1495 double r, x, y;
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1496 int odd_y;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1497
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1498 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1499 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1500 x = PyFloat_AsDouble(ox);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1501 y = PyFloat_AsDouble(oy);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1502 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1503 return NULL;
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1504
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1505 /* deal directly with IEEE specials, to cope with problems on various
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1506 platforms whose semantics don't exactly match C99 */
46664 031dfe455585 Merged revisions 62425-62429,62434-62436,62441,62444,62446-62448,62450-62455,62463,62465-62466,62469,62474,62476-62478,62480,62485,62492,62497-62498,62500,62507,62513-62514,62516,62521,62531,62535,62545-62546,62548-62551,62553-62559,62569,62574,62577,62593,62595,62604-62606,62608,62616,62626-62627,62636,62638,62644-62645,62647-62648,62651-62653,62656,62661,62663,62680,62686-62687,62696,62699-62703,62711 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46621 diff changeset	1507 r = 0.; /* silence compiler warning */
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1508 if (!Py_IS_FINITE(x) \|\| !Py_IS_FINITE(y)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1509 errno = 0;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1510 if (Py_IS_NAN(x))
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1511 r = y == 0. ? 1. : x; /* NaN*0 = 1 /
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1512 else if (Py_IS_NAN(y))
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1513 r = x == 1. ? 1. : y; /* 1*NaN = 1 /
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1514 else if (Py_IS_INFINITY(x)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1515 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1516 if (y > 0.)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1517 r = odd_y ? x : fabs(x);
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1518 else if (y == 0.)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1519 r = 1.;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1520 else /* y < 0. */
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1521 r = odd_y ? copysign(0., x) : 0.;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1522 }
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1523 else if (Py_IS_INFINITY(y)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1524 if (fabs(x) == 1.0)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1525 r = 1.;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1526 else if (y > 0. && fabs(x) > 1.0)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1527 r = y;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1528 else if (y < 0. && fabs(x) < 1.0) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1529 r = -y; /* result is +inf */
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1530 if (x == 0.) /* 0*-inf: divide-by-zero /
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1531 errno = EDOM;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1532 }
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1533 else
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1534 r = 0.;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1535 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1536 }
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1537 else {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1538 /* let libm handle finite*finite /
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1539 errno = 0;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1540 PyFPE_START_PROTECT("in math_pow", return 0);
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1541 r = pow(x, y);
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1542 PyFPE_END_PROTECT(r);
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1543 /* a NaN result should arise only from (-ve)**(finite
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1544 non-integer); in this case we want to raise ValueError. */
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1545 if (!Py_IS_FINITE(r)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1546 if (Py_IS_NAN(r)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1547 errno = EDOM;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1548 }
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1549 /*
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1550 an infinite result here arises either from:
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1551 (A) (+/-0.)**negative (-> divide-by-zero)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1552 (B) overflow of x**y with x and y finite
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1553 */
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1554 else if (Py_IS_INFINITY(r)) {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1555 if (x == 0.)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1556 errno = EDOM;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1557 else
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1558 errno = ERANGE;
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1559 }
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1560 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1561 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1562
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1563 if (errno && is_error(r))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1564 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1565 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1566 return PyFloat_FromDouble(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1567 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1568
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1569 PyDoc_STRVAR(math_pow_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1570 "pow(x, y)\n\nReturn x**y (x to the power of y).");
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1571
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1572 static const double degToRad = Py_MATH_PI / 180.0;
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1573 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	1574
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1575 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1576 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	1577 {
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1578 double x = PyFloat_AsDouble(arg);
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1579 if (x == -1.0 && PyErr_Occurred())
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1580 return NULL;
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1581 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	1582 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1583
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1584 PyDoc_STRVAR(math_degrees_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1585 "degrees(x)\n\n\
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1586 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	1587
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1588 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1589 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	1590 {
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1591 double x = PyFloat_AsDouble(arg);
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1592 if (x == -1.0 && PyErr_Occurred())
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1593 return NULL;
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1594 return PyFloat_FromDouble(x * degToRad);
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1595 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1596
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1597 PyDoc_STRVAR(math_radians_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1598 "radians(x)\n\n\
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1599 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	1600
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1601 static PyObject *
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1602 math_isnan(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1603 {
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1604 double x = PyFloat_AsDouble(arg);
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1605 if (x == -1.0 && PyErr_Occurred())
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1606 return NULL;
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1607 return PyBool_FromLong((long)Py_IS_NAN(x));
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1608 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1609
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1610 PyDoc_STRVAR(math_isnan_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1611 "isnan(x) -> bool\n\n\
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1612 Check if float x is not a number (NaN).");
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1613
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1614 static PyObject *
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1615 math_isinf(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1616 {
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1617 double x = PyFloat_AsDouble(arg);
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1618 if (x == -1.0 && PyErr_Occurred())
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1619 return NULL;
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1620 return PyBool_FromLong((long)Py_IS_INFINITY(x));
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1621 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1622
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1623 PyDoc_STRVAR(math_isinf_doc,
57209 b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1624 "isinf(x) -> bool\n\n\
b354c1b6b476 Merged revisions 75149,75260-75263,75265-75267,75292,75300,75376,75405,75429-75433,75437,75445,75501,75551,75572,75589-75591,75657,75742,75868,75952-75957,76057,76105,76139,76143,76162,76223 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 56270 diff changeset	1625 Check if float x is infinite (positive or negative).");
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1626
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1627 static PyMethodDef math_methods[] = {
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1628 {"acos", math_acos, METH_O, math_acos_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1629 {"acosh", math_acosh, METH_O, math_acosh_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1630 {"asin", math_asin, METH_O, math_asin_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1631 {"asinh", math_asinh, METH_O, math_asinh_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1632 {"atan", math_atan, METH_O, math_atan_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1633 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1634 {"atanh", math_atanh, METH_O, math_atanh_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1635 {"ceil", math_ceil, METH_O, math_ceil_doc},
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1636 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1637 {"cos", math_cos, METH_O, math_cos_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1638 {"cosh", math_cosh, METH_O, math_cosh_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1639 {"degrees", math_degrees, METH_O, math_degrees_doc},
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	1640 {"erf", math_erf, METH_O, math_erf_doc},
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	1641 {"erfc", math_erfc, METH_O, math_erfc_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1642 {"exp", math_exp, METH_O, math_exp_doc},
57758 b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	1643 {"expm1", math_expm1, METH_O, math_expm1_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1644 {"fabs", math_fabs, METH_O, math_fabs_doc},
47562 bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from Georg Brandl <georg@python.org> parents: 47559 diff changeset	1645 {"factorial", math_factorial, METH_O, math_factorial_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1646 {"floor", math_floor, METH_O, math_floor_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1647 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1648 {"frexp", math_frexp, METH_O, math_frexp_doc},
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1649 {"fsum", math_fsum, METH_O, math_fsum_doc},
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	1650 {"gamma", math_gamma, METH_O, math_gamma_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1651 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1652 {"isinf", math_isinf, METH_O, math_isinf_doc},
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1653 {"isnan", math_isnan, METH_O, math_isnan_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1654 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	1655 {"lgamma", math_lgamma, METH_O, math_lgamma_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1656 {"log", math_log, METH_VARARGS, math_log_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1657 {"log1p", math_log1p, METH_O, math_log1p_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1658 {"log10", math_log10, METH_O, math_log10_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1659 {"modf", math_modf, METH_O, math_modf_doc},
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1660 {"pow", math_pow, METH_VARARGS, math_pow_doc},
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1661 {"radians", math_radians, METH_O, math_radians_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1662 {"sin", math_sin, METH_O, math_sin_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1663 {"sinh", math_sinh, METH_O, math_sinh_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1664 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1665 {"tan", math_tan, METH_O, math_tan_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1666 {"tanh", math_tanh, METH_O, math_tanh_doc},
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1667 {"trunc", math_trunc, METH_O, math_trunc_doc},
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1668 {NULL, NULL} /* sentinel */
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1669 };
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1670
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1671
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1672 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	1673 "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	1674 "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	1675
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1676
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1677 static struct PyModuleDef mathmodule = {
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1678 PyModuleDef_HEAD_INIT,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1679 "math",
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1680 module_doc,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1681 -1,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1682 math_methods,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1683 NULL,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1684 NULL,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1685 NULL,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1686 NULL
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1687 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1688
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 23832 diff changeset	1689 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1690 PyInit_math(void)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1691 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1692 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	1693
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1694 m = PyModule_Create(&mathmodule);
36324 1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 34872 diff changeset	1695 if (m == NULL)
1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 34872 diff changeset	1696 goto finally;
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	1697
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1698 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1699 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	1700
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1701 finally:
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1702 return m;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1703 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 58664:993f703a61ba