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

annotate Modules/mathmodule.c @ 66410:dcb60bf26dce

information on Issue #9846

author	Łukasz Langa <lukasz@langa.pl>
date	Tue, 23 Nov 2010 00:19:53 +0000
parents	a9349fd3d0f7
children	3c9232a684ae

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;
62843 e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	72 static const double logpi = 1.144729885849400174143427351353058711647;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	73
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	74 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	75 sinpi(double x)
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	76 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	77 double y, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	78 int n;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	79 /* this function should only ever be called for finite arguments */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	80 assert(Py_IS_FINITE(x));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	81 y = fmod(fabs(x), 2.0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	82 n = (int)round(2.0*y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	83 assert(0 <= n && n <= 4);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	84 switch (n) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	85 case 0:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	86 r = sin(pi*y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	87 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	88 case 1:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	89 r = cos(pi*(y-0.5));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	90 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	91 case 2:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	92 /* N.B. -sin(pi(y-1.0)) is not* equivalent: it would give
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	93 -0.0 instead of 0.0 when y == 1.0. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	94 r = sin(pi*(1.0-y));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	95 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	96 case 3:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	97 r = -cos(pi*(y-1.5));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	98 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	99 case 4:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	100 r = sin(pi*(y-2.0));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	101 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	102 default:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	103 assert(0); /* should never get here */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	104 r = -1.23e200; /* silence gcc warning */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	105 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	106 return copysign(1.0, x)*r;
56270 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
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	109 /* 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	110 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	111 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	112 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	113 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	114 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	115
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	116 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	117 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	118 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	119 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	120 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	121 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	122
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	123 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	124
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	125 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	126 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	127 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	128 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	129 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	130 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	131 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	132 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	133
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	134 Correction factor
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	135 -----------------
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	136 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	137 double, and e is tiny. Then:
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	138
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	139 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	140 = pow(y, x-0.5)/exp(y) * C,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	141
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	142 where the correction_factor C is given by
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	143
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	144 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	145
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	146 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	147
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	148 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	149
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	150 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	151
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	152 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	153
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	154 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	155
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	156 r + eg/yr;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	157
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	158 than
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	159
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	160 r * (1 + e*g/y);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	161
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	162 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	163 information in e*g/y.
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
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	166 #define LANCZOS_N 13
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	167 static const double lanczos_g = 6.024680040776729583740234375;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	168 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	169 static const double lanczos_num_coeffs[LANCZOS_N] = {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	170 23531376880.410759688572007674451636754734846804940,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	171 42919803642.649098768957899047001988850926355848959,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	172 35711959237.355668049440185451547166705960488635843,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	173 17921034426.037209699919755754458931112671403265390,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	174 6039542586.3520280050642916443072979210699388420708,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	175 1439720407.3117216736632230727949123939715485786772,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	176 248874557.86205415651146038641322942321632125127801,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	177 31426415.585400194380614231628318205362874684987640,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	178 2876370.6289353724412254090516208496135991145378768,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	179 186056.26539522349504029498971604569928220784236328,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	180 8071.6720023658162106380029022722506138218516325024,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	181 210.82427775157934587250973392071336271166969580291,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	182 2.5066282746310002701649081771338373386264310793408
56270 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
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	185 /* 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	186 static const double lanczos_den_coeffs[LANCZOS_N] = {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	187 0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	188 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	189
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	190 /* 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	191 #define NGAMMA_INTEGRAL 23
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	192 static const double gamma_integral[NGAMMA_INTEGRAL] = {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	193 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	194 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	195 1307674368000.0, 20922789888000.0, 355687428096000.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	196 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	197 51090942171709440000.0, 1124000727777607680000.0,
56270 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
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	200 /* Lanczos' sum L_g(x), for positive x */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	201
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	202 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	203 lanczos_sum(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	204 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	205 double num = 0.0, den = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	206 int i;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	207 assert(x > 0.0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	208 /* evaluate the rational function lanczos_sum(x). For large
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	209 x, the obvious algorithm risks overflow, so we instead
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	210 rescale the denominator and numerator of the rational
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	211 function by x**(1-LANCZOS_N) and treat this as a
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	212 rational function in 1/x. This also reduces the error for
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	213 larger x values. The choice of cutoff point (5.0 below) is
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	214 somewhat arbitrary; in tests, smaller cutoff values than
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	215 this resulted in lower accuracy. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	216 if (x < 5.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	217 for (i = LANCZOS_N; --i >= 0; ) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	218 num = num * x + lanczos_num_coeffs[i];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	219 den = den * x + lanczos_den_coeffs[i];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	220 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	221 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	222 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	223 for (i = 0; i < LANCZOS_N; i++) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	224 num = num / x + lanczos_num_coeffs[i];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	225 den = den / x + lanczos_den_coeffs[i];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	226 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	227 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	228 return num/den;
56270 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
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	231 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	232 m_tgamma(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	233 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	234 double absx, r, y, z, sqrtpow;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	235
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	236 /* special cases */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	237 if (!Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	238 if (Py_IS_NAN(x) \|\| x > 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	239 return x; /* tgamma(nan) = nan, tgamma(inf) = inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	240 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	241 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	242 return Py_NAN; /* tgamma(-inf) = nan, invalid */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	243 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	244 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	245 if (x == 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	246 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	247 return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	248 }
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	249
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	250 /* integer arguments */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	251 if (x == floor(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	252 if (x < 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	253 errno = EDOM; /* tgamma(n) = nan, invalid for */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	254 return Py_NAN; /* negative integers n */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	255 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	256 if (x <= NGAMMA_INTEGRAL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	257 return gamma_integral[(int)x - 1];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	258 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	259 absx = fabs(x);
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	260
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	261 /* tiny arguments: tgamma(x) ~ 1/x for x near 0 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	262 if (absx < 1e-20) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	263 r = 1.0/x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	264 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	265 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	266 return r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	267 }
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	268
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	269 /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	270 x > 200, and underflows to +-0.0 for x < -200, not a negative
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	271 integer. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	272 if (absx > 200.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	273 if (x < 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	274 return 0.0/sinpi(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	275 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	276 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	277 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	278 return Py_HUGE_VAL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	279 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	280 }
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	281
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	282 y = absx + lanczos_g_minus_half;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	283 /* compute error in sum */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	284 if (absx > lanczos_g_minus_half) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	285 /* note: the correction can be foiled by an optimizing
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	286 compiler that (incorrectly) thinks that an expression like
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	287 a + b - a - b can be optimized to 0.0. This shouldn't
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	288 happen in a standards-conforming compiler. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	289 double q = y - absx;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	290 z = q - lanczos_g_minus_half;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	291 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	292 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	293 double q = y - lanczos_g_minus_half;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	294 z = q - absx;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	295 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	296 z = z * lanczos_g / y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	297 if (x < 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	298 r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	299 r -= z * r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	300 if (absx < 140.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	301 r /= pow(y, absx - 0.5);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	302 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	303 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	304 sqrtpow = pow(y, absx / 2.0 - 0.25);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	305 r /= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	306 r /= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	307 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	308 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	309 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	310 r = lanczos_sum(absx) / exp(y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	311 r += z * r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	312 if (absx < 140.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	313 r *= pow(y, absx - 0.5);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	314 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	315 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	316 sqrtpow = pow(y, absx / 2.0 - 0.25);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	317 r *= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	318 r *= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	319 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	320 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	321 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	322 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	323 return r;
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	324 }
56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	325
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	326 /*
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	327 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	328 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	329 */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	330
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	331 static double
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	332 m_lgamma(double x)
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	333 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	334 double r, absx;
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	335
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	336 /* special cases */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	337 if (!Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	338 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	339 return x; /* lgamma(nan) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	340 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	341 return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	342 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	343
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	344 /* integer arguments */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	345 if (x == floor(x) && x <= 2.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	346 if (x <= 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	347 errno = EDOM; /* lgamma(n) = inf, divide-by-zero for */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	348 return Py_HUGE_VAL; /* integers n <= 0 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	349 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	350 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	351 return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	352 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	353 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	354
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	355 absx = fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	356 /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	357 if (absx < 1e-20)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	358 return -log(absx);
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	359
62843 e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	360 /* Lanczos' formula. We could save a fraction of a ulp in accuracy by
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	361 having a second set of numerator coefficients for lanczos_sum that
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	362 absorbed the exp(-lanczos_g) term, and throwing out the lanczos_g
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	363 subtraction below; it's probably not worth it. */
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	364 r = log(lanczos_sum(absx)) - lanczos_g;
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	365 r += (absx - 0.5) * (log(absx + lanczos_g - 0.5) - 1);
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	366 if (x < 0.0)
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	367 /* Use reflection formula to get value for negative x. */
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	368 r = logpi - log(fabs(sinpi(absx))) - log(absx) - r;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	369 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	370 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	371 return r;
57660 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
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	374 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	375 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	376 function erfc(x).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	377
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	378 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	379 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	380 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	381 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	382 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	383
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	384 The series expansion used is:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	385
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	386 erf(x) = xexp(-xx)/sqrt(pi) * [
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	387 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	388
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	389 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	390 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	391
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	392 The continued fraction expansion used is:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	393
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	394 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	395 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	396
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	397 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	398
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	399 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	400
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	401 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	402 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	403 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	404 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	405 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	406
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	407 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	408 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	409 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	410 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	411
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	412 #define ERF_SERIES_CUTOFF 1.5
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	413 #define ERF_SERIES_TERMS 25
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	414 #define ERFC_CONTFRAC_CUTOFF 30.0
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	415 #define ERFC_CONTFRAC_TERMS 50
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	416
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	417 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	418 Error function, via power series.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	419
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	420 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	421 Converges reasonably fast for small x.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	422 */
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 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	425 m_erf_series(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	426 {
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	427 double x2, acc, fk, result;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	428 int i, saved_errno;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	429
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	430 x2 = x * x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	431 acc = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	432 fk = (double)ERF_SERIES_TERMS + 0.5;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	433 for (i = 0; i < ERF_SERIES_TERMS; i++) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	434 acc = 2.0 + x2 * acc / fk;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	435 fk -= 1.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	436 }
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	437 /* Make sure the exp call doesn't affect errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	438 see m_erfc_contfrac for more. */
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	439 saved_errno = errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	440 result = acc * x * exp(-x2) / sqrtpi;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	441 errno = saved_errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	442 return result;
57770 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 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	446 Complementary error function, via continued fraction expansion.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	447
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	448 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	449 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	450 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	451 <= 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	452 than the smallest representable nonzero float. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	453
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	454 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	455 m_erfc_contfrac(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	456 {
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	457 double x2, a, da, p, p_last, q, q_last, b, result;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	458 int i, saved_errno;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	459
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	460 if (x >= ERFC_CONTFRAC_CUTOFF)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	461 return 0.0;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	462
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	463 x2 = x*x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	464 a = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	465 da = 0.5;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	466 p = 1.0; p_last = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	467 q = da + x2; q_last = 1.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	468 for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	469 double temp;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	470 a += da;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	471 da += 2.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	472 b = da + x2;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	473 temp = p; p = bp - ap_last; p_last = temp;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	474 temp = q; q = bq - aq_last; q_last = temp;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	475 }
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	476 /* Issue #8986: On some platforms, exp sets errno on underflow to zero;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	477 save the current errno value so that we can restore it later. */
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	478 saved_errno = errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	479 result = p / q * x * exp(-x2) / sqrtpi;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	480 errno = saved_errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	481 return result;
57770 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
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	484 /* Error function erf(x), for general x */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	485
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	486 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	487 m_erf(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	488 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	489 double absx, cf;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	490
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	491 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	492 return x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	493 absx = fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	494 if (absx < ERF_SERIES_CUTOFF)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	495 return m_erf_series(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	496 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	497 cf = m_erfc_contfrac(absx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	498 return x > 0.0 ? 1.0 - cf : cf - 1.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	499 }
57770 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
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	502 /* Complementary error function erfc(x), for general x. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	503
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	504 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	505 m_erfc(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	506 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	507 double absx, cf;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	508
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	509 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	510 return x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	511 absx = fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	512 if (absx < ERF_SERIES_CUTOFF)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	513 return 1.0 - m_erf_series(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	514 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	515 cf = m_erfc_contfrac(absx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	516 return x > 0.0 ? cf : 2.0 - cf;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	517 }
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	518 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	519
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	520 /*
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	521 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	522 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	523 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	524 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	525 always follow C99.
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	526 */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	527
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	528 static double
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	529 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	530 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	531 if (Py_IS_NAN(x) \|\| Py_IS_NAN(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	532 return Py_NAN;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	533 if (Py_IS_INFINITY(y)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	534 if (Py_IS_INFINITY(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	535 if (copysign(1., x) == 1.)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	536 /* atan2(+-inf, +inf) == +-pi/4 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	537 return copysign(0.25*Py_MATH_PI, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	538 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	539 /* atan2(+-inf, -inf) == +-pi3/4 /
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	540 return copysign(0.75*Py_MATH_PI, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	541 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	542 /* atan2(+-inf, x) == +-pi/2 for finite x */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	543 return copysign(0.5*Py_MATH_PI, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	544 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	545 if (Py_IS_INFINITY(x) \|\| y == 0.) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	546 if (copysign(1., x) == 1.)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	547 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	548 return copysign(0., y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	549 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	550 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	551 return copysign(Py_MATH_PI, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	552 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	553 return atan2(y, x);
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	554 }
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	555
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	556 /*
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	557 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	558 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	559 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	560 the system log/log10.
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	561 */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	562
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	563 static double
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	564 m_log(double x)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	565 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	566 if (Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	567 if (x > 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	568 return log(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	569 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	570 if (x == 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	571 return -Py_HUGE_VAL; /* log(0) = -inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	572 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	573 return Py_NAN; /* log(-ve) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	574 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	575 else if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	576 return x; /* log(nan) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	577 else if (x > 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	578 return x; /* log(inf) = inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	579 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	580 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	581 return Py_NAN; /* log(-inf) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	582 }
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	583 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	584
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	585 static double
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	586 m_log10(double x)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	587 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	588 if (Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	589 if (x > 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	590 return log10(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	591 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	592 if (x == 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	593 return -Py_HUGE_VAL; /* log10(0) = -inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	594 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	595 return Py_NAN; /* log10(-ve) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	596 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	597 else if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	598 return x; /* log10(nan) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	599 else if (x > 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	600 return x; /* log10(inf) = inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	601 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	602 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	603 return Py_NAN; /* log10(-inf) = nan */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	604 }
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	605 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	606
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	607
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	608 /* 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	609 * 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	610 * 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	611 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	612 static int
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	613 is_error(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	614 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	615 int result = 1; /* presumption of guilt */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	616 assert(errno); /* non-zero errno is a precondition for calling */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	617 if (errno == EDOM)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	618 PyErr_SetString(PyExc_ValueError, "math domain error");
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	619
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	620 else if (errno == ERANGE) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	621 /* ANSI C generally requires libm functions to set ERANGE
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	622 * on overflow, but also generally allows them to set
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	623 * ERANGE on underflow too. There's no consistency about
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	624 * the latter across platforms.
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	625 * Alas, C99 never requires that errno be set.
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	626 * Here we suppress the underflow errors (libm functions
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	627 * should return a zero on underflow, and +- HUGE_VAL on
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	628 * overflow, so testing the result for zero suffices to
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	629 * distinguish the cases).
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	630 *
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	631 * On some platforms (Ubuntu/ia64) it seems that errno can be
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	632 * set to ERANGE for subnormal results that do not underflow
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	633 * to zero. So to be safe, we'll ignore ERANGE whenever the
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	634 * function result is less than one in absolute value.
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	635 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	636 if (fabs(x) < 1.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	637 result = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	638 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	639 PyErr_SetString(PyExc_OverflowError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	640 "math range error");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	641 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	642 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	643 /* Unexpected math error */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	644 PyErr_SetFromErrno(PyExc_ValueError);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	645 return result;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	646 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	647
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	648 /*
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	649 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	650 arguments and returns a double.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	651
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	652 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	653 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	654 platforms.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	655
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	656 - 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	657 - 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	658 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	659 is 0.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	660 - 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	661 raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	662 - 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	663 OverflowError is raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	664
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	665 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	666 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	667
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	668 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	669 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	670 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	671 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	672 '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	673 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	674 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	675 care about right now.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	676 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	677
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	678 static PyObject *
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	679 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	680 PyObject (from_double_func) (double),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	681 int can_overflow)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	682 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	683 double x, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	684 x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	685 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	686 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	687 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	688 PyFPE_START_PROTECT("in math_1", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	689 r = (*func)(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	690 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	691 if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	692 PyErr_SetString(PyExc_ValueError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	693 "math domain error"); /* invalid arg */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	694 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	695 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	696 if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	697 if (can_overflow)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	698 PyErr_SetString(PyExc_OverflowError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	699 "math range error"); /* overflow */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	700 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	701 PyErr_SetString(PyExc_ValueError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	702 "math domain error"); /* singularity */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	703 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	704 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	705 if (Py_IS_FINITE(r) && errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	706 /* this branch unnecessary on most platforms */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	707 return NULL;
46617 e42fe19ba6fd Whoops. errno should only be tested when the result is finite. Mark Dickinson <dickinsm@gmail.com> parents: 46616 diff changeset	708
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	709 return (*from_double_func)(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	710 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	711
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	712 /* 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	713 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	714 errno = ERANGE for overflow). */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	715
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	716 static PyObject *
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	717 math_1a(PyObject arg, double (func) (double))
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	718 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	719 double x, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	720 x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	721 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	722 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	723 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	724 PyFPE_START_PROTECT("in math_1a", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	725 r = (*func)(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	726 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	727 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	728 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	729 return PyFloat_FromDouble(r);
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	730 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	731
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	732 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	733 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	734 arguments and returns a double.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	735
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	736 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	737 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	738 platforms.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	739
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	740 - 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	741 - 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	742 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	743 - 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	744 raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	745 - 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	746 OverflowError is raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	747
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	748 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	749 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	750
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	751 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	752 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	753 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	754 '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	755 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	756 OverflowError.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	757 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	758
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	759 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	760 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	761 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	762 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	763 }
31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	764
31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	765 static PyObject *
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	766 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	767 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	768 return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	769 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	770
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	771 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	772 math_2(PyObject args, double (func) (double, double), char *funcname)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	773 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	774 PyObject ox, oy;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	775 double x, y, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	776 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	777 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	778 x = PyFloat_AsDouble(ox);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	779 y = PyFloat_AsDouble(oy);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	780 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	781 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	782 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	783 PyFPE_START_PROTECT("in math_2", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	784 r = (*func)(x, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	785 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	786 if (Py_IS_NAN(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	787 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	788 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	789 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	790 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	791 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	792 else if (Py_IS_INFINITY(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	793 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	794 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	795 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	796 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	797 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	798 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	799 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	800 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	801 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	802 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	803
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	804 #define FUNC1(funcname, func, can_overflow, docstring) \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	805 static PyObject * math_##funcname(PyObject self, PyObject args) { \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	806 return math_1(args, func, can_overflow); \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	807 }\
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	808 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	809
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	810 #define FUNC1A(funcname, func, docstring) \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	811 static PyObject * math_##funcname(PyObject self, PyObject args) { \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	812 return math_1a(args, func); \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	813 }\
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	814 PyDoc_STRVAR(math_##funcname##_doc, docstring);
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	815
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	816 #define FUNC2(funcname, func, docstring) \
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	817 static PyObject * math_##funcname(PyObject self, PyObject args) { \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	818 return math_2(args, func, #funcname); \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	819 }\
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	820 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	821
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	822 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	823 "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	824 FUNC1(acosh, m_acosh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	825 "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	826 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	827 "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	828 FUNC1(asinh, m_asinh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	829 "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	830 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	831 "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	832 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	833 "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	834 "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	835 FUNC1(atanh, m_atanh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	836 "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	837
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 static PyObject * math_ceil(PyObject self, PyObject number) {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	839 static PyObject *ceil_str = NULL;
62684 3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	840 PyObject method, result;
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	841
62680 35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	842 method = _PyObject_LookupSpecial(number, "__ceil__", &ceil_str);
35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	843 if (method == NULL) {
35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	844 if (PyErr_Occurred())
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	845 return NULL;
62680 35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	846 return math_1_to_int(number, ceil, 0);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	847 }
62684 3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	848 result = PyObject_CallFunctionObjArgs(method, NULL);
3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	849 Py_DECREF(method);
3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	850 return result;
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 }
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
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	853 PyDoc_STRVAR(math_ceil_doc,
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	854 "ceil(x)\n\nReturn the ceiling of x as an int.\n"
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	855 "This is the smallest integral value >= 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	856
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	857 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	858 "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	859 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	860 "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	861 FUNC1(cosh, cosh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	862 "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	863 FUNC1A(erf, m_erf,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	864 "erf(x)\n\nError function at x.")
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	865 FUNC1A(erfc, m_erfc,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	866 "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	867 FUNC1(exp, exp, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	868 "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	869 FUNC1(expm1, m_expm1, 1,
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	870 "expm1(x)\n\nReturn exp(x)-1.\n"
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	871 "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	872 "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	873 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	874 "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	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 static PyObject * math_floor(PyObject self, PyObject number) {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	877 static PyObject *floor_str = NULL;
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	878 PyObject method, result;
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	879
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	880 method = _PyObject_LookupSpecial(number, "__floor__", &floor_str);
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	881 if (method == NULL) {
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	882 if (PyErr_Occurred())
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	883 return NULL;
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	884 return math_1_to_int(number, floor, 0);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	885 }
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	886 result = PyObject_CallFunctionObjArgs(method, NULL);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	887 Py_DECREF(method);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	888 return result;
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	889 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	890
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 PyDoc_STRVAR(math_floor_doc,
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	892 "floor(x)\n\nReturn the floor of x as an int.\n"
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	893 "This is the largest integral value <= 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	894
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	895 FUNC1A(gamma, m_tgamma,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	896 "gamma(x)\n\nGamma function at x.")
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	897 FUNC1A(lgamma, m_lgamma,
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	898 "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
62844 87555f45cd6b Issue #9186: log1p(-1.0) should raise ValueError, not OverflowError. Mark Dickinson <dickinsm@gmail.com> parents: 62843 diff changeset	899 FUNC1(log1p, m_log1p, 0,
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	900 "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	901 "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	902 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	903 "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	904 FUNC1(sinh, sinh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	905 "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	906 FUNC1(sqrt, sqrt, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	907 "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	908 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	909 "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	910 FUNC1(tanh, tanh, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	911 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	912
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	913 /* 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	914 <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	915 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	916 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	917 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	918
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 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	920 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	921 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	922
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 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	924 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	925 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	926 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	927
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	928 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	929 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	930 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	931 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	932 prevents double rounding because any addition or subtraction of two doubles
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	933 can be resolved exactly into double-sized hi and lo values. As long as the
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	934 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	935 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	936 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	937 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	938
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 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	940 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	941
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	942 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	943 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	944 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	945 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	946 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	947 */
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 #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	950
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	951 /* 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	952 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	953 _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	954 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	955 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	956 void *v = NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	957 Py_ssize_t m = *m_ptr;
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	958
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	959 m += m; /* double */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	960 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	961 double p = p_ptr;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	962 if (p == ps) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	963 v = PyMem_Malloc(sizeof(double) * m);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	964 if (v != NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	965 memcpy(v, ps, sizeof(double) * n);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	966 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	967 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	968 v = PyMem_Realloc(p, sizeof(double) * m);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	969 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	970 if (v == NULL) { /* size overflow or no memory */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	971 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	972 return 1;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	973 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	974 p_ptr = (double) v;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	975 *m_ptr = m;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	976 return 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	977 }
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 /* 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	980
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 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	982 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	983 for x in iterable:
62495 1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	984 i = 0
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	985 for y in partials:
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	986 if abs(x) < abs(y):
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	987 x, y = y, x
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	988 hi = x + y
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	989 lo = y - (hi - x)
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	990 if lo:
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	991 partials[i] = lo
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	992 i += 1
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	993 x = hi
1c5c146de642 Merged revisions 82221 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 62317 diff changeset	994 partials[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	995 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	996
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 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	998 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	999 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	1000
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 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	1002 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	1003 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	1004 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	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 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	1007 */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1008
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 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	1010 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	1011 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1012 PyObject item, iter, *sum = NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1013 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1014 double x, y, t, ps[NUM_PARTIALS], *p = ps;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1015 double xsave, special_sum = 0.0, inf_sum = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1016 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	1017
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1018 iter = PyObject_GetIter(seq);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1019 if (iter == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1020 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
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1022 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	1023
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1024 for(;;) { /* for x in iterable */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1025 assert(0 <= n && n <= m);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1026 assert((m == NUM_PARTIALS && p == ps) \|\|
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1027 (m > NUM_PARTIALS && p != 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	1028
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1029 item = PyIter_Next(iter);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1030 if (item == NULL) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1031 if (PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1032 goto _fsum_error;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1033 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1034 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1035 x = PyFloat_AsDouble(item);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1036 Py_DECREF(item);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1037 if (PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1038 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	1039
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1040 xsave = x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1041 for (i = j = 0; j < n; j++) { /* for y in partials */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1042 y = p[j];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1043 if (fabs(x) < fabs(y)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1044 t = x; x = y; y = t;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1045 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1046 hi = x + y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1047 yr = hi - x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1048 lo = y - yr;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1049 if (lo != 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1050 p[i++] = lo;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1051 x = hi;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1052 }
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1053
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1054 n = i; /* ps[i:] = [x] */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1055 if (x != 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1056 if (! Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1057 /* a nonfinite x could arise either as
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1058 a result of intermediate overflow, or
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1059 as a result of a nan or inf in the
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1060 summands */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1061 if (Py_IS_FINITE(xsave)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1062 PyErr_SetString(PyExc_OverflowError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1063 "intermediate overflow in fsum");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1064 goto _fsum_error;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1065 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1066 if (Py_IS_INFINITY(xsave))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1067 inf_sum += xsave;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1068 special_sum += xsave;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1069 /* reset partials */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1070 n = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1071 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1072 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1073 goto _fsum_error;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1074 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1075 p[n++] = x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1076 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1077 }
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	1078
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1079 if (special_sum != 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1080 if (Py_IS_NAN(inf_sum))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1081 PyErr_SetString(PyExc_ValueError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1082 "-inf + inf in fsum");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1083 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1084 sum = PyFloat_FromDouble(special_sum);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1085 goto _fsum_error;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1086 }
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1087
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1088 hi = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1089 if (n > 0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1090 hi = p[--n];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1091 /* sum_exact(ps, hi) from the top, stop when the sum becomes
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1092 inexact. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1093 while (n > 0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1094 x = hi;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1095 y = p[--n];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1096 assert(fabs(y) < fabs(x));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1097 hi = x + y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1098 yr = hi - x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1099 lo = y - yr;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1100 if (lo != 0.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1101 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1102 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1103 /* Make half-even rounding work across multiple partials.
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1104 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1105 digit to two instead of down to zero (the 1e-16 makes the 1
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1106 slightly closer to two). With a potential 1 ULP rounding
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1107 error fixed-up, math.fsum() can guarantee commutativity. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1108 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) \|\|
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1109 (lo > 0.0 && p[n-1] > 0.0))) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1110 y = lo * 2.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1111 x = hi + y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1112 yr = x - hi;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1113 if (y == yr)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1114 hi = x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1115 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1116 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1117 sum = PyFloat_FromDouble(hi);
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
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1119 _fsum_error:
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1120 PyFPE_END_PROTECT(hi)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1121 Py_DECREF(iter);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1122 if (p != ps)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1123 PyMem_Free(p);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1124 return 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	1125 }
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
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1127 #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	1128
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1129 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	1130 "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	1131 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	1132 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	1133
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1134 /* Return the smallest integer k such that n < 2**k, or 0 if n == 0.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1135 * Equivalent to floor(lg(x))+1. Also equivalent to: bitwidth_of_type -
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1136 * count_leading_zero_bits(x)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1137 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1138
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1139 /* XXX: This routine does more or less the same thing as
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1140 * bits_in_digit() in Objects/longobject.c. Someday it would be nice to
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1141 * consolidate them. On BSD, there's a library function called fls()
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1142 * that we could use, and GCC provides __builtin_clz().
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1143 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1144
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1145 static unsigned long
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1146 bit_length(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1147 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1148 unsigned long len = 0;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1149 while (n != 0) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1150 ++len;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1151 n >>= 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1152 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1153 return len;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1154 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1155
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1156 static unsigned long
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1157 count_set_bits(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1158 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1159 unsigned long count = 0;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1160 while (n != 0) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1161 ++count;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1162 n &= n - 1; /* clear least significant bit */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1163 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1164 return count;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1165 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1166
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1167 /* Divide-and-conquer factorial algorithm
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1168 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1169 * Based on the formula and psuedo-code provided at:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1170 * http://www.luschny.de/math/factorial/binarysplitfact.html
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1171 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1172 * Faster algorithms exist, but they're more complicated and depend on
62859 ca05371cff10 Fix typo in a comment in mathmodule.c. Ezio Melotti <ezio.melotti@gmail.com> parents: 62844 diff changeset	1173 * a fast prime factorization algorithm.
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1174 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1175 * Notes on the algorithm
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1176 * ----------------------
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1177 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1178 * factorial(n) is written in the form 2*k m, with m odd. k and m are
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1179 * computed separately, and then combined using a left shift.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1180 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1181 * The function factorial_odd_part computes the odd part m (i.e., the greatest
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1182 * odd divisor) of factorial(n), using the formula:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1183 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1184 * factorial_odd_part(n) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1185 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1186 * product_{i >= 0} product_{0 < j <= n / 2**i, j odd} j
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1187 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1188 * Example: factorial_odd_part(20) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1189 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1190 * (1) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1191 * (1) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1192 * (1 * 3 * 5) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1193 * (1 * 3 * 5 * 7 * 9)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1194 * (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1195 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1196 * Here i goes from large to small: the first term corresponds to i=4 (any
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1197 * larger i gives an empty product), and the last term corresponds to i=0.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1198 * Each term can be computed from the last by multiplying by the extra odd
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1199 * numbers required: e.g., to get from the penultimate term to the last one,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1200 * we multiply by (11 * 13 * 15 * 17 * 19).
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1201 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1202 * To see a hint of why this formula works, here are the same numbers as above
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1203 * but with the even parts (i.e., the appropriate powers of 2) included. For
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1204 * each subterm in the product for i, we multiply that subterm by 2**i:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1205 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1206 * factorial(20) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1207 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1208 * (16) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1209 * (8) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1210 * (4 * 12 * 20) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1211 * (2 * 6 * 10 * 14 * 18) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1212 * (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1213 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1214 * The factorial_partial_product function computes the product of all odd j in
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1215 * range(start, stop) for given start and stop. It's used to compute the
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1216 * partial products like (11 * 13 * 15 * 17 * 19) in the example above. It
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1217 * operates recursively, repeatedly splitting the range into two roughly equal
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1218 * pieces until the subranges are small enough to be computed using only C
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1219 * integer arithmetic.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1220 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1221 * The two-valuation k (i.e., the exponent of the largest power of 2 dividing
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1222 * the factorial) is computed independently in the main math_factorial
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1223 * function. By standard results, its value is:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1224 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1225 * two_valuation = n//2 + n//4 + n//8 + ....
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1226 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1227 * It can be shown (e.g., by complete induction on n) that two_valuation is
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1228 * equal to n - count_set_bits(n), where count_set_bits(n) gives the number of
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1229 * '1'-bits in the binary expansion of n.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1230 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1231
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1232 /* factorial_partial_product: Compute product(range(start, stop, 2)) using
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1233 * divide and conquer. Assumes start and stop are odd and stop > start.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1234 * max_bits must be >= bit_length(stop - 2). */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1235
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1236 static PyObject *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1237 factorial_partial_product(unsigned long start, unsigned long stop,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1238 unsigned long max_bits)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1239 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1240 unsigned long midpoint, num_operands;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1241 PyObject left = NULL, right = NULL, *result = NULL;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1242
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1243 /* If the return value will fit an unsigned long, then we can
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1244 * multiply in a tight, fast loop where each multiply is O(1).
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1245 * Compute an upper bound on the number of bits required to store
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1246 * the answer.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1247 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1248 * Storing some integer z requires floor(lg(z))+1 bits, which is
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1249 * conveniently the value returned by bit_length(z). The
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1250 * product x*y will require at most
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1251 * bit_length(x) + bit_length(y) bits to store, based
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1252 * on the idea that lg product = lg x + lg y.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1253 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1254 * We know that stop - 2 is the largest number to be multiplied. From
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1255 * there, we have: bit_length(answer) <= num_operands *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1256 * bit_length(stop - 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1257 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1258
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1259 num_operands = (stop - start) / 2;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1260 /* The "num_operands <= 8 * SIZEOF_LONG" check guards against the
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1261 * unlikely case of an overflow in num_operands * max_bits. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1262 if (num_operands <= 8 * SIZEOF_LONG &&
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1263 num_operands * max_bits <= 8 * SIZEOF_LONG) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1264 unsigned long j, total;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1265 for (total = start, j = start + 2; j < stop; j += 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1266 total *= j;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1267 return PyLong_FromUnsignedLong(total);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1268 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1269
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1270 /* find midpoint of range(start, stop), rounded up to next odd number. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1271 midpoint = (start + num_operands) \| 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1272 left = factorial_partial_product(start, midpoint,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1273 bit_length(midpoint - 2));
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1274 if (left == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1275 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1276 right = factorial_partial_product(midpoint, stop, max_bits);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1277 if (right == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1278 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1279 result = PyNumber_Multiply(left, right);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1280
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1281 error:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1282 Py_XDECREF(left);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1283 Py_XDECREF(right);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1284 return result;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1285 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1286
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1287 /* factorial_odd_part: compute the odd part of factorial(n). */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1288
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1289 static PyObject *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1290 factorial_odd_part(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1291 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1292 long i;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1293 unsigned long v, lower, upper;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1294 PyObject partial, tmp, inner, outer;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1295
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1296 inner = PyLong_FromLong(1);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1297 if (inner == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1298 return NULL;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1299 outer = inner;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1300 Py_INCREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1301
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1302 upper = 3;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1303 for (i = bit_length(n) - 2; i >= 0; i--) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1304 v = n >> i;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1305 if (v <= 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1306 continue;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1307 lower = upper;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1308 /* (v + 1) \| 1 = least odd integer strictly larger than n / 2*i /
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1309 upper = (v + 1) \| 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1310 /* Here inner is the product of all odd integers j in the range (0,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1311 n/2**(i+1)]. The factorial_partial_product call below gives the
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1312 product of all odd integers j in the range (n/2(i+1), n/2i]. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1313 partial = factorial_partial_product(lower, upper, bit_length(upper-2));
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1314 /* inner = partial /
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1315 if (partial == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1316 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1317 tmp = PyNumber_Multiply(inner, partial);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1318 Py_DECREF(partial);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1319 if (tmp == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1320 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1321 Py_DECREF(inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1322 inner = tmp;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1323 /* Now inner is the product of all odd integers j in the range (0,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1324 n/2*i], giving the inner product in the formula above. /
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1325
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1326 /* outer = inner; /
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1327 tmp = PyNumber_Multiply(outer, inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1328 if (tmp == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1329 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1330 Py_DECREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1331 outer = tmp;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1332 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1333
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1334 goto done;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1335
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1336 error:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1337 Py_DECREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1338 done:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1339 Py_DECREF(inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1340 return outer;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1341 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1342
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1343 /* Lookup table for small factorial values */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1344
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1345 static const unsigned long SmallFactorials[] = {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1346 1, 1, 2, 6, 24, 120, 720, 5040, 40320,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1347 362880, 3628800, 39916800, 479001600,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1348 #if SIZEOF_LONG >= 8
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1349 6227020800, 87178291200, 1307674368000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1350 20922789888000, 355687428096000, 6402373705728000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1351 121645100408832000, 2432902008176640000
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1352 #endif
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1353 };
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1354
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1355 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	1356 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	1357 {
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1358 long x;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1359 PyObject result, odd_part, *two_valuation;
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	1360
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1361 if (PyFloat_Check(arg)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1362 PyObject *lx;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1363 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1364 if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1365 PyErr_SetString(PyExc_ValueError,
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1366 "factorial() only accepts integral values");
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1367 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1368 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1369 lx = PyLong_FromDouble(dx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1370 if (lx == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1371 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1372 x = PyLong_AsLong(lx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1373 Py_DECREF(lx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1374 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1375 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1376 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	1377
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1378 if (x == -1 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1379 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1380 if (x < 0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1381 PyErr_SetString(PyExc_ValueError,
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1382 "factorial() not defined for negative values");
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1383 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1384 }
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	1385
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1386 /* use lookup table if x is small */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1387 if (x < (long)(sizeof(SmallFactorials)/sizeof(SmallFactorials[0])))
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1388 return PyLong_FromUnsignedLong(SmallFactorials[x]);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1389
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1390 /* else express in the form odd_part * 2**two_valuation, and compute as
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1391 odd_part << two_valuation. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1392 odd_part = factorial_odd_part(x);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1393 if (odd_part == NULL)
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1394 return NULL;
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1395 two_valuation = PyLong_FromLong(x - count_set_bits(x));
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1396 if (two_valuation == NULL) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1397 Py_DECREF(odd_part);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1398 return NULL;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1399 }
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1400 result = PyNumber_Lshift(odd_part, two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1401 Py_DECREF(two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1402 Py_DECREF(odd_part);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1403 return result;
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	1404 }
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	1405
50250 1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1406 PyDoc_STRVAR(math_factorial_doc,
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1407 "factorial(x) -> Integral\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1408 "\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1409 "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	1410
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	1411 static PyObject *
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1412 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	1413 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1414 static PyObject *trunc_str = NULL;
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1415 PyObject trunc, result;
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1416
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1417 if (Py_TYPE(number)->tp_dict == NULL) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1418 if (PyType_Ready(Py_TYPE(number)) < 0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1419 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1420 }
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1421
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1422 trunc = _PyObject_LookupSpecial(number, "__trunc__", &trunc_str);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1423 if (trunc == NULL) {
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1424 if (!PyErr_Occurred())
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1425 PyErr_Format(PyExc_TypeError,
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1426 "type %.100s doesn't define __trunc__ method",
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1427 Py_TYPE(number)->tp_name);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1428 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1429 }
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1430 result = PyObject_CallFunctionObjArgs(trunc, NULL);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1431 Py_DECREF(trunc);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1432 return result;
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1433 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1434
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1435 PyDoc_STRVAR(math_trunc_doc,
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1436 "trunc(x:Real) -> Integral\n"
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1437 "\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	1438 "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	1439
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1440 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1441 math_frexp(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1442 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1443 int i;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1444 double x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1445 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1446 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1447 /* deal with special cases directly, to sidestep platform
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1448 differences */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1449 if (Py_IS_NAN(x) \|\| Py_IS_INFINITY(x) \|\| !x) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1450 i = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1451 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1452 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1453 PyFPE_START_PROTECT("in math_frexp", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1454 x = frexp(x, &i);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1455 PyFPE_END_PROTECT(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1456 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1457 return Py_BuildValue("(di)", x, i);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1458 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1459
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1460 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	1461 "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	1462 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1463 "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	1464 "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	1465 "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	1466
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1467 static PyObject *
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1468 math_ldexp(PyObject self, PyObject args)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1469 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1470 double x, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1471 PyObject *oexp;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1472 long exp;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1473 int overflow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1474 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1475 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	1476
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1477 if (PyLong_Check(oexp)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1478 /* on overflow, replace exponent with either LONG_MAX
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1479 or LONG_MIN, depending on the sign. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1480 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1481 if (exp == -1 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1482 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1483 if (overflow)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1484 exp = overflow < 0 ? LONG_MIN : LONG_MAX;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1485 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1486 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1487 PyErr_SetString(PyExc_TypeError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1488 "Expected an int or long as second argument "
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1489 "to ldexp.");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1490 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1491 }
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	1492
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1493 if (x == 0. \|\| !Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1494 /* NaNs, zeros and infinities are returned unchanged */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1495 r = x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1496 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1497 } else if (exp > INT_MAX) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1498 /* overflow */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1499 r = copysign(Py_HUGE_VAL, x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1500 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1501 } else if (exp < INT_MIN) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1502 /* underflow to +-0 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1503 r = copysign(0., x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1504 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1505 } else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1506 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1507 PyFPE_START_PROTECT("in math_ldexp", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1508 r = ldexp(x, (int)exp);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1509 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1510 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1511 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1512 }
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	1513
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1514 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1515 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1516 return PyFloat_FromDouble(r);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1517 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1518
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1519 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	1520 "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	1521 Return x * (2**i).");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1522
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1523 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1524 math_modf(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1525 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1526 double y, x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1527 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1528 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1529 /* some platforms don't do the right thing for NaNs and
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1530 infinities, so we take care of special cases directly. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1531 if (!Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1532 if (Py_IS_INFINITY(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1533 return Py_BuildValue("(dd)", copysign(0., x), x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1534 else if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1535 return Py_BuildValue("(dd)", x, x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 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
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1538 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1539 PyFPE_START_PROTECT("in math_modf", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1540 x = modf(x, &y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1541 PyFPE_END_PROTECT(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1542 return Py_BuildValue("(dd)", x, y);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1543 }
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1544
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1545 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	1546 "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	1547 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1548 "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	1549 "of x and are floats.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1550
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	1551 /* 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	1552 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	1553 "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	1554 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	1555 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	1556 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	1557 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	1558 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	1559
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1560 static PyObject*
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1561 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	1562 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1563 /* If it is long, do it ourselves. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1564 if (PyLong_Check(arg)) {
65026 a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1565 double x, result;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1566 Py_ssize_t e;
65026 a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1567
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1568 /* Negative or zero inputs give a ValueError. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1569 if (Py_SIZE(arg) <= 0) {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1570 PyErr_SetString(PyExc_ValueError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1571 "math domain error");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1572 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1573 }
64969 c8dc4b5e54fb Issue #9599: Tweak loghelper algorithm to return slightly improved results for powers of 2. Mark Dickinson <dickinsm@gmail.com> parents: 62970 diff changeset	1574
65026 a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1575 x = PyLong_AsDouble(arg);
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1576 if (x == -1.0 && PyErr_Occurred()) {
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1577 if (!PyErr_ExceptionMatches(PyExc_OverflowError))
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1578 return NULL;
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1579 /* Here the conversion to double overflowed, but it's possible
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1580 to compute the log anyway. Clear the exception and continue. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1581 PyErr_Clear();
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1582 x = _PyLong_Frexp((PyLongObject *)arg, &e);
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1583 if (x == -1.0 && PyErr_Occurred())
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1584 return NULL;
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1585 /* Value is ~= x * 2*e, so the log ~= log(x) + log(2) e. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1586 result = func(x) + func(2.0) * e;
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1587 }
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1588 else
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1589 /* Successfully converted x to a double. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1590 result = func(x);
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10. Mark Dickinson <dickinsm@gmail.com> parents: 64969 diff changeset	1591 return PyFloat_FromDouble(result);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1592 }
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	1593
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1594 /* Else let libm handle it by itself. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1595 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	1596 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1597
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1598 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	1599 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	1600 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1601 PyObject *arg;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1602 PyObject *base = NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1603 PyObject num, den;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1604 PyObject *ans;
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1605
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1606 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1607 return NULL;
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1608
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1609 num = loghelper(arg, m_log, "log");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1610 if (num == NULL \|\| base == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1611 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	1612
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1613 den = loghelper(base, m_log, "log");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1614 if (den == NULL) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1615 Py_DECREF(num);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1616 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1617 }
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1618
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1619 ans = PyNumber_TrueDivide(num, den);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1620 Py_DECREF(num);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1621 Py_DECREF(den);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1622 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	1623 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1624
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1625 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	1626 "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	1627 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	1628 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	1629
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1630 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1631 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	1632 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1633 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	1634 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1635
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1636 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	1637 "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	1638
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1639 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1640 math_fmod(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1641 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1642 PyObject ox, oy;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1643 double r, x, y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1644 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1645 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1646 x = PyFloat_AsDouble(ox);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1647 y = PyFloat_AsDouble(oy);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1648 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1649 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1650 /* fmod(x, +/-Inf) returns x for finite x. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1651 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1652 return PyFloat_FromDouble(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1653 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1654 PyFPE_START_PROTECT("in math_fmod", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1655 r = fmod(x, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1656 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1657 if (Py_IS_NAN(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1658 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1659 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1660 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1661 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1662 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1663 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1664 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1665 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1666 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1667 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1668
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1669 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	1670 "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	1671 " x % y may differ.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1672
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1673 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1674 math_hypot(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1675 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1676 PyObject ox, oy;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1677 double r, x, y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1678 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1679 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1680 x = PyFloat_AsDouble(ox);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1681 y = PyFloat_AsDouble(oy);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1682 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1683 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1684 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1685 if (Py_IS_INFINITY(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1686 return PyFloat_FromDouble(fabs(x));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1687 if (Py_IS_INFINITY(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1688 return PyFloat_FromDouble(fabs(y));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1689 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1690 PyFPE_START_PROTECT("in math_hypot", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1691 r = hypot(x, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1692 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1693 if (Py_IS_NAN(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1694 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1695 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1696 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1697 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1698 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1699 else if (Py_IS_INFINITY(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1700 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1701 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1702 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1703 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1704 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1705 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1706 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1707 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1708 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1709 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1710
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1711 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	1712 "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	1713
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1714 /* 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	1715 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	1716 (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	1717 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	1718 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1719
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1720 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1721 math_pow(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1722 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1723 PyObject ox, oy;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1724 double r, x, y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1725 int odd_y;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1726
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1727 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1728 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1729 x = PyFloat_AsDouble(ox);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1730 y = PyFloat_AsDouble(oy);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1731 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1732 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	1733
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1734 /* deal directly with IEEE specials, to cope with problems on various
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1735 platforms whose semantics don't exactly match C99 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1736 r = 0.; /* silence compiler warning */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1737 if (!Py_IS_FINITE(x) \|\| !Py_IS_FINITE(y)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1738 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1739 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1740 r = y == 0. ? 1. : x; /* NaN*0 = 1 /
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1741 else if (Py_IS_NAN(y))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1742 r = x == 1. ? 1. : y; /* 1*NaN = 1 /
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1743 else if (Py_IS_INFINITY(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1744 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1745 if (y > 0.)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1746 r = odd_y ? x : fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1747 else if (y == 0.)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1748 r = 1.;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1749 else /* y < 0. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1750 r = odd_y ? copysign(0., x) : 0.;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1751 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1752 else if (Py_IS_INFINITY(y)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1753 if (fabs(x) == 1.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1754 r = 1.;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1755 else if (y > 0. && fabs(x) > 1.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1756 r = y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1757 else if (y < 0. && fabs(x) < 1.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1758 r = -y; /* result is +inf */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1759 if (x == 0.) /* 0*-inf: divide-by-zero /
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1760 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1761 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1762 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1763 r = 0.;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1764 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1765 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1766 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1767 /* let libm handle finite*finite /
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1768 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1769 PyFPE_START_PROTECT("in math_pow", return 0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1770 r = pow(x, y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1771 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1772 /* a NaN result should arise only from (-ve)**(finite
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1773 non-integer); in this case we want to raise ValueError. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1774 if (!Py_IS_FINITE(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1775 if (Py_IS_NAN(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1776 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1777 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1778 /*
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1779 an infinite result here arises either from:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1780 (A) (+/-0.)**negative (-> divide-by-zero)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1781 (B) overflow of x**y with x and y finite
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1782 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1783 else if (Py_IS_INFINITY(r)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1784 if (x == 0.)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1785 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1786 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1787 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1788 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1789 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1790 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1791
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1792 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1793 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1794 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1795 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1796 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1797
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1798 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	1799 "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	1800
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1801 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	1802 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	1803
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1804 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1805 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	1806 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1807 double x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1808 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1809 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1810 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	1811 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1812
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1813 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	1814 "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	1815 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	1816
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1817 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1818 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	1819 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1820 double x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1821 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1822 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1823 return PyFloat_FromDouble(x * degToRad);
23427 a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1824 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1825
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1826 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	1827 "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	1828 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	1829
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1830 static PyObject *
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1831 math_isfinite(PyObject self, PyObject arg)
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1832 {
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1833 double x = PyFloat_AsDouble(arg);
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1834 if (x == -1.0 && PyErr_Occurred())
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1835 return NULL;
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1836 return PyBool_FromLong((long)Py_IS_FINITE(x));
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1837 }
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1838
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1839 PyDoc_STRVAR(math_isfinite_doc,
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1840 "isfinite(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1841 Return True if x is neither an infinity nor a NaN, and False otherwise.");
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1842
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1843 static PyObject *
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1844 math_isnan(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1845 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1846 double x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1847 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1848 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1849 return PyBool_FromLong((long)Py_IS_NAN(x));
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1850 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1851
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1852 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	1853 "isnan(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1854 Return True if x is a NaN (not a number), and False otherwise.");
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1855
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1856 static PyObject *
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1857 math_isinf(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1858 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1859 double x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1860 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1861 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1862 return PyBool_FromLong((long)Py_IS_INFINITY(x));
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1863 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1864
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1865 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	1866 "isinf(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1867 Return True if x is a positive or negative infinity, and False otherwise.");
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1868
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1869 static PyMethodDef math_methods[] = {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1870 {"acos", math_acos, METH_O, math_acos_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1871 {"acosh", math_acosh, METH_O, math_acosh_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1872 {"asin", math_asin, METH_O, math_asin_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1873 {"asinh", math_asinh, METH_O, math_asinh_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1874 {"atan", math_atan, METH_O, math_atan_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1875 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1876 {"atanh", math_atanh, METH_O, math_atanh_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1877 {"ceil", math_ceil, METH_O, math_ceil_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1878 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1879 {"cos", math_cos, METH_O, math_cos_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1880 {"cosh", math_cosh, METH_O, math_cosh_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1881 {"degrees", math_degrees, METH_O, math_degrees_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1882 {"erf", math_erf, METH_O, math_erf_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1883 {"erfc", math_erfc, METH_O, math_erfc_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1884 {"exp", math_exp, METH_O, math_exp_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1885 {"expm1", math_expm1, METH_O, math_expm1_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1886 {"fabs", math_fabs, METH_O, math_fabs_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1887 {"factorial", math_factorial, METH_O, math_factorial_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1888 {"floor", math_floor, METH_O, math_floor_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1889 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1890 {"frexp", math_frexp, METH_O, math_frexp_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1891 {"fsum", math_fsum, METH_O, math_fsum_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1892 {"gamma", math_gamma, METH_O, math_gamma_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1893 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1894 {"isfinite", math_isfinite, METH_O, math_isfinite_doc},
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1895 {"isinf", math_isinf, METH_O, math_isinf_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1896 {"isnan", math_isnan, METH_O, math_isnan_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1897 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1898 {"lgamma", math_lgamma, METH_O, math_lgamma_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1899 {"log", math_log, METH_VARARGS, math_log_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1900 {"log1p", math_log1p, METH_O, math_log1p_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1901 {"log10", math_log10, METH_O, math_log10_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1902 {"modf", math_modf, METH_O, math_modf_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1903 {"pow", math_pow, METH_VARARGS, math_pow_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1904 {"radians", math_radians, METH_O, math_radians_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1905 {"sin", math_sin, METH_O, math_sin_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1906 {"sinh", math_sinh, METH_O, math_sinh_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1907 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1908 {"tan", math_tan, METH_O, math_tan_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1909 {"tanh", math_tanh, METH_O, math_tanh_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1910 {"trunc", math_trunc, METH_O, math_trunc_doc},
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1911 {NULL, NULL} /* sentinel */
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1912 };
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1913
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1914
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1915 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	1916 "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	1917 "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	1918
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1919
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1920 static struct PyModuleDef mathmodule = {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1921 PyModuleDef_HEAD_INIT,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1922 "math",
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1923 module_doc,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1924 -1,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1925 math_methods,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1926 NULL,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1927 NULL,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1928 NULL,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1929 NULL
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1930 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1931
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 23832 diff changeset	1932 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1933 PyInit_math(void)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1934 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1935 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	1936
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1937 m = PyModule_Create(&mathmodule);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1938 if (m == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1939 goto finally;
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	1940
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1941 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1942 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	1943
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1944 finally:
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1945 return m;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1946 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 66410:dcb60bf26dce