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

annotate Modules/mathmodule.c @ 87690:66c1c9f32567 default tip

Add use_weakref option to functools.lru_cache The use_weakref option makes lru_cache create weak references to the function arguments when creating the cache key, which prevents them from staying in the memory forever even after all other references to them are gone. This is a proof of concept for http://bugs.python.org/issue19859

author	Radomir Dopieralski <devel@sheep.art.pl>
date	Tue, 03 Dec 2013 16:02:48 +0100
parents	4d62a62ba44d
children

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
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	58 /*
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	59 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	60 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	61 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	62 754-2008 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	63 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	64
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	65 static const double pi = 3.141592653589793238462643383279502884197;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	66 static const double sqrtpi = 1.772453850905516027298167483341145182798;
62843 e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	67 static const double logpi = 1.144729885849400174143427351353058711647;
56270 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 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	70 sinpi(double x)
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	71 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	72 double y, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	73 int n;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	74 /* 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	75 assert(Py_IS_FINITE(x));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	76 y = fmod(fabs(x), 2.0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	77 n = (int)round(2.0*y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	78 assert(0 <= n && n <= 4);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	79 switch (n) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	80 case 0:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	81 r = sin(pi*y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	82 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	83 case 1:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	84 r = cos(pi*(y-0.5));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	85 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	86 case 2:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	87 /* 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	88 -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	89 r = sin(pi*(1.0-y));
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 3:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	92 r = -cos(pi*(y-1.5));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	93 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	94 case 4:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	95 r = sin(pi*(y-2.0));
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	96 break;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	97 default:
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	98 assert(0); /* should never get here */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	99 r = -1.23e200; /* silence gcc warning */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	100 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	101 return copysign(1.0, x)*r;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	102 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	103
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	104 /* 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	105 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	106 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	107 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	108 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	109 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	110
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	111 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	112 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	113 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	114 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	115 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	116 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	117
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	118 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	119
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	120 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	121 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	122 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	123 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	124 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	125 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	126 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	127 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	128
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	129 Correction factor
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	130 -----------------
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	131 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	132 double, and e is tiny. Then:
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 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	135 = pow(y, x-0.5)/exp(y) * C,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	136
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	137 where the correction_factor C is given by
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 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	140
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	141 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	142
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	143 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	144
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	145 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	146
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	147 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	148
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	149 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	150
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	151 r + eg/yr;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	152
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	153 than
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	154
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	155 r * (1 + e*g/y);
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	156
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	157 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	158 information in e*g/y.
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
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	161 #define LANCZOS_N 13
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	162 static const double lanczos_g = 6.024680040776729583740234375;
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	163 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	164 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	165 23531376880.410759688572007674451636754734846804940,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	166 42919803642.649098768957899047001988850926355848959,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	167 35711959237.355668049440185451547166705960488635843,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	168 17921034426.037209699919755754458931112671403265390,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	169 6039542586.3520280050642916443072979210699388420708,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	170 1439720407.3117216736632230727949123939715485786772,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	171 248874557.86205415651146038641322942321632125127801,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	172 31426415.585400194380614231628318205362874684987640,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	173 2876370.6289353724412254090516208496135991145378768,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	174 186056.26539522349504029498971604569928220784236328,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	175 8071.6720023658162106380029022722506138218516325024,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	176 210.82427775157934587250973392071336271166969580291,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	177 2.5066282746310002701649081771338373386264310793408
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	178 };
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	179
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	180 /* 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	181 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	182 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	183 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	184
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	185 /* 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	186 #define NGAMMA_INTEGRAL 23
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	187 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	188 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	189 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	190 1307674368000.0, 20922789888000.0, 355687428096000.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	191 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	192 51090942171709440000.0, 1124000727777607680000.0,
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	193 };
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	194
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	195 /* Lanczos' sum L_g(x), for positive x */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	196
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	197 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	198 lanczos_sum(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	199 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	200 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	201 int i;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	202 assert(x > 0.0);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	203 /* 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	204 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	205 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	206 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	207 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	208 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	209 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	210 this resulted in lower accuracy. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	211 if (x < 5.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	212 for (i = LANCZOS_N; --i >= 0; ) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	213 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	214 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	215 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	216 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	217 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	218 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	219 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	220 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	221 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	222 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	223 return num/den;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	224 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	225
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	226 static double
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	227 m_tgamma(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	228 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	229 double absx, r, y, z, sqrtpow;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	230
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	231 /* special cases */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	232 if (!Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	233 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	234 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	235 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	236 errno = EDOM;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	237 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	238 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	239 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	240 if (x == 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	241 errno = EDOM;
72467 7482d0e3476a Return +-Py_HUGE_VAL for tgamma(+-0) instead of risking FP exceptions by computing 1.0 / 0.0. Mark Dickinson <mdickinson@enthought.com> parents: 69975 diff changeset	242 /* tgamma(+-0.0) = +-inf, divide-by-zero */
7482d0e3476a Return +-Py_HUGE_VAL for tgamma(+-0) instead of risking FP exceptions by computing 1.0 / 0.0. Mark Dickinson <mdickinson@enthought.com> parents: 69975 diff changeset	243 return copysign(Py_HUGE_VAL, x);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	244 }
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	245
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	246 /* integer arguments */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	247 if (x == floor(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	248 if (x < 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	249 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	250 return Py_NAN; /* negative integers n */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	251 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	252 if (x <= NGAMMA_INTEGRAL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	253 return gamma_integral[(int)x - 1];
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	254 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	255 absx = fabs(x);
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	256
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	257 /* 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	258 if (absx < 1e-20) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	259 r = 1.0/x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	260 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	261 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	262 return r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	263 }
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	264
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	265 /* 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	266 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	267 integer. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	268 if (absx > 200.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	269 if (x < 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	270 return 0.0/sinpi(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	271 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	272 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	273 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	274 return Py_HUGE_VAL;
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 }
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	277
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	278 y = absx + lanczos_g_minus_half;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	279 /* compute error in sum */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	280 if (absx > lanczos_g_minus_half) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	281 /* 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	282 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	283 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	284 happen in a standards-conforming compiler. */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	285 double q = y - absx;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	286 z = q - lanczos_g_minus_half;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	287 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	288 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	289 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	290 z = q - absx;
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 z = z * lanczos_g / y;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	293 if (x < 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	294 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	295 r -= z * r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	296 if (absx < 140.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	297 r /= pow(y, absx - 0.5);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	298 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	299 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	300 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	301 r /= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	302 r /= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	303 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	304 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	305 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	306 r = lanczos_sum(absx) / exp(y);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	307 r += z * r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	308 if (absx < 140.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	309 r *= pow(y, absx - 0.5);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	310 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	311 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	312 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	313 r *= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	314 r *= sqrtpow;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	315 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	316 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	317 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	318 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	319 return r;
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	320 }
56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	321
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	322 /*
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	323 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	324 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	325 */
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	326
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	327 static double
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	328 m_lgamma(double x)
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	329 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	330 double r, absx;
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	331
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	332 /* special cases */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	333 if (!Py_IS_FINITE(x)) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	334 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	335 return x; /* lgamma(nan) = nan */
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	336 else
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	337 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	338 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	339
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	340 /* integer arguments */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	341 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	342 if (x <= 0.0) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	343 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	344 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	345 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	346 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	347 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	348 }
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	349 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	350
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	351 absx = fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	352 /* 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	353 if (absx < 1e-20)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	354 return -log(absx);
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	355
62843 e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	356 /* 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	357 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	358 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	359 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	360 r = log(lanczos_sum(absx)) - lanczos_g;
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	361 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	362 if (x < 0.0)
e655849e79c6 Minor refactoring in lgamma code, for clarity. Mark Dickinson <dickinsm@gmail.com> parents: 62684 diff changeset	363 /* 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	364 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	365 if (Py_IS_INFINITY(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	366 errno = ERANGE;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	367 return r;
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	368 }
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	369
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	370 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	371 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	372 function erfc(x).
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	373
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	374 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	375 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	376 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	377 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	378 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	379
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	380 The series expansion used is:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	381
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	382 erf(x) = xexp(-xx)/sqrt(pi) * [
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	383 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	384
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	385 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	386 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	387
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	388 The continued fraction expansion used is:
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	389
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	390 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	391 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	392
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	393 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	394
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	395 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	396
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	397 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	398 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	399 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	400 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	401 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	402
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	403 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	404 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	405 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	406 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	407
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	408 #define ERF_SERIES_CUTOFF 1.5
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	409 #define ERF_SERIES_TERMS 25
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	410 #define ERFC_CONTFRAC_CUTOFF 30.0
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	411 #define ERFC_CONTFRAC_TERMS 50
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	412
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	413 /*
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	414 Error function, via power series.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	415
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	416 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	417 Converges reasonably fast for small x.
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	418 */
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 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	421 m_erf_series(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	422 {
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	423 double x2, acc, fk, result;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	424 int i, saved_errno;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	425
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	426 x2 = x * x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	427 acc = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	428 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	429 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	430 acc = 2.0 + x2 * acc / fk;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	431 fk -= 1.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	432 }
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	433 /* 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	434 see m_erfc_contfrac for more. */
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	435 saved_errno = errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	436 result = acc * x * exp(-x2) / sqrtpi;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	437 errno = saved_errno;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	438 return result;
498 56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	439 }
56bb1067a880 Improve error handling. Guido van Rossum <guido@python.org> parents: 438 diff changeset	440
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	441 /*
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	442 Complementary error function, via continued fraction expansion.
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 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	445 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	446 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	447 <= 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	448 than the smallest representable nonzero float. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	449
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	450 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	451 m_erfc_contfrac(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	452 {
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	453 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	454 int i, saved_errno;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	455
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	456 if (x >= ERFC_CONTFRAC_CUTOFF)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	457 return 0.0;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	458
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	459 x2 = x*x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	460 a = 0.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	461 da = 0.5;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	462 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	463 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	464 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	465 double temp;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	466 a += da;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	467 da += 2.0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	468 b = da + x2;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	469 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	470 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	471 }
62317 d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	472 /* 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	473 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	474 saved_errno = errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	475 result = p / q * x * exp(-x2) / sqrtpi;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	476 errno = saved_errno;
d064e8934f4d Merged revisions 81967 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61599 diff changeset	477 return result;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	478 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	479
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	480 /* Error function erf(x), for general x */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	481
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	482 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	483 m_erf(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	484 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	485 double absx, cf;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	486
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	487 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	488 return x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	489 absx = fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	490 if (absx < ERF_SERIES_CUTOFF)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	491 return m_erf_series(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	492 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	493 cf = m_erfc_contfrac(absx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	494 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	495 }
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	496 }
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	497
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	498 /* Complementary error function erfc(x), for general x. */
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	499
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	500 static double
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	501 m_erfc(double x)
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	502 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	503 double absx, cf;
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	504
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	505 if (Py_IS_NAN(x))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	506 return x;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	507 absx = fabs(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	508 if (absx < ERF_SERIES_CUTOFF)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	509 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	510 else {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	511 cf = m_erfc_contfrac(absx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	512 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	513 }
57770 1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	514 }
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	515
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	516 /*
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	517 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	518 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	519 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	520 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	521 always follow C99.
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	522 */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	523
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	524 static double
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	525 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	526 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	527 if (Py_IS_NAN(x) \|\| Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	528 return Py_NAN;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	529 if (Py_IS_INFINITY(y)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	530 if (Py_IS_INFINITY(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	531 if (copysign(1., x) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	532 /* atan2(+-inf, +inf) == +-pi/4 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	533 return copysign(0.25*Py_MATH_PI, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	534 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	535 /* atan2(+-inf, -inf) == +-pi3/4 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	536 return copysign(0.75*Py_MATH_PI, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	537 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	538 /* atan2(+-inf, x) == +-pi/2 for finite x */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	539 return copysign(0.5*Py_MATH_PI, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	540 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	541 if (Py_IS_INFINITY(x) \|\| y == 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	542 if (copysign(1., x) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	543 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	544 return copysign(0., y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	545 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	546 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	547 return copysign(Py_MATH_PI, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	548 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	549 return atan2(y, x);
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	550 }
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	551
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	552 /*
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	553 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	554 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	555 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	556 the system log/log10.
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	557 */
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	558
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	559 static double
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	560 m_log(double x)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	561 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	562 if (Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	563 if (x > 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	564 return log(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	565 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	566 if (x == 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	567 return -Py_HUGE_VAL; /* log(0) = -inf */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	568 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	569 return Py_NAN; /* log(-ve) = nan */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	570 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	571 else if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	572 return x; /* log(nan) = nan */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	573 else if (x > 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	574 return x; /* log(inf) = inf */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	575 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	576 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	577 return Py_NAN; /* log(-inf) = nan */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	578 }
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	579 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	580
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	581 /*
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	582 log2: log to base 2.
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	583
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	584 Uses an algorithm that should:
69973 627780933948 Grammatical fix for a comment for log2, to avoid referring to an algorithm as monotonic. Mark Dickinson <mdickinson@enthought.com> parents: 69971 diff changeset	585
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	586 (a) produce exact results for powers of 2, and
69973 627780933948 Grammatical fix for a comment for log2, to avoid referring to an algorithm as monotonic. Mark Dickinson <mdickinson@enthought.com> parents: 69971 diff changeset	587 (b) give a monotonic log2 (for positive finite floats),
627780933948 Grammatical fix for a comment for log2, to avoid referring to an algorithm as monotonic. Mark Dickinson <mdickinson@enthought.com> parents: 69971 diff changeset	588 assuming that the system log is monotonic.
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	589 */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	590
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	591 static double
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	592 m_log2(double x)
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	593 {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	594 if (!Py_IS_FINITE(x)) {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	595 if (Py_IS_NAN(x))
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	596 return x; /* log2(nan) = nan */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	597 else if (x > 0.0)
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	598 return x; /* log2(+inf) = +inf */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	599 else {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	600 errno = EDOM;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	601 return Py_NAN; /* log2(-inf) = nan, invalid-operation */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	602 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	603 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	604
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	605 if (x > 0.0) {
69975 565f43f6bed4 Issue #11888: Use system log2() when available Victor Stinner <victor.stinner@haypocalc.com> parents: 69973 diff changeset	606 #ifdef HAVE_LOG2
565f43f6bed4 Issue #11888: Use system log2() when available Victor Stinner <victor.stinner@haypocalc.com> parents: 69973 diff changeset	607 return log2(x);
565f43f6bed4 Issue #11888: Use system log2() when available Victor Stinner <victor.stinner@haypocalc.com> parents: 69973 diff changeset	608 #else
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	609 double m;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	610 int e;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	611 m = frexp(x, &e);
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	612 /* We want log2(m * 2**e) == log(m) / log(2) + e. Care is needed when
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	613 * x is just greater than 1.0: in that case e is 1, log(m) is negative,
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	614 * and we get significant cancellation error from the addition of
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	615 * log(m) / log(2) to e. The slight rewrite of the expression below
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	616 * avoids this problem.
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	617 */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	618 if (x >= 1.0) {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	619 return log(2.0 * m) / log(2.0) + (e - 1);
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	620 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	621 else {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	622 return log(m) / log(2.0) + e;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	623 }
69975 565f43f6bed4 Issue #11888: Use system log2() when available Victor Stinner <victor.stinner@haypocalc.com> parents: 69973 diff changeset	624 #endif
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	625 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	626 else if (x == 0.0) {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	627 errno = EDOM;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	628 return -Py_HUGE_VAL; /* log2(0) = -inf, divide-by-zero */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	629 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	630 else {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	631 errno = EDOM;
69971 12c65eb7d6de Fix cut-and-paste typo in comment: log10 -> log2. Mark Dickinson <mdickinson@enthought.com> parents: 69946 diff changeset	632 return Py_NAN; /* log2(-inf) = nan, invalid-operation */
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	633 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	634 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	635
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	636 static double
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	637 m_log10(double x)
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	638 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	639 if (Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	640 if (x > 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	641 return log10(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	642 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	643 if (x == 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	644 return -Py_HUGE_VAL; /* log10(0) = -inf */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	645 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	646 return Py_NAN; /* log10(-ve) = nan */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	647 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	648 else if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	649 return x; /* log10(nan) = nan */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	650 else if (x > 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	651 return x; /* log10(inf) = inf */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	652 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	653 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	654 return Py_NAN; /* log10(-inf) = nan */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	655 }
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	656 }
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	657
20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	658
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	659 /* 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	660 * 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	661 * 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	662 */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	663 static int
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	664 is_error(double x)
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	665 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	666 int result = 1; /* presumption of guilt */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	667 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	668 if (errno == EDOM)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	669 PyErr_SetString(PyExc_ValueError, "math domain error");
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	670
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	671 else if (errno == ERANGE) {
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	672 /* 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	673 * 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	674 * 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	675 * the latter across platforms.
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	676 * 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	677 * 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	678 * 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	679 * 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	680 * distinguish the cases).
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	681 *
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	682 * 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	683 * 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	684 * 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	685 * 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	686 */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	687 if (fabs(x) < 1.0)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	688 result = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	689 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	690 PyErr_SetString(PyExc_OverflowError,
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	691 "math range error");
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	692 }
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	693 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	694 /* Unexpected math error */
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	695 PyErr_SetFromErrno(PyExc_ValueError);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	696 return result;
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	697 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	698
50123 20a84e063052 Merged revisions 67708 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48606 diff changeset	699 /*
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	700 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	701 arguments and returns a double.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	702
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	703 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	704 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	705 platforms.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	706
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	707 - 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	708 - 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	709 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	710 is 0.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	711 - 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	712 raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	713 - 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	714 OverflowError is raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	715
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	716 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	717 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	718
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	719 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	720 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	721 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	722 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	723 '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	724 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	725 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	726 care about right now.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	727 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	728
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	729 static PyObject *
44499 31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	730 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	731 PyObject (from_double_func) (double),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	732 int can_overflow)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	733 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	734 double x, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	735 x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	736 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	737 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	738 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	739 PyFPE_START_PROTECT("in math_1", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	740 r = (*func)(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	741 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	742 if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	743 PyErr_SetString(PyExc_ValueError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	744 "math domain error"); /* invalid arg */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	745 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	746 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	747 if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
75604 692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	748 if (can_overflow)
692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	749 PyErr_SetString(PyExc_OverflowError,
692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	750 "math range error"); /* overflow */
692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	751 else
692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	752 PyErr_SetString(PyExc_ValueError,
692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	753 "math domain error"); /* singularity */
692efd6ac771 fix indentation Benjamin Peterson <benjamin@python.org> parents: 68257 diff changeset	754 return NULL;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	755 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	756 if (Py_IS_FINITE(r) && errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	757 /* this branch unnecessary on most platforms */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	758 return NULL;
46617 e42fe19ba6fd Whoops. errno should only be tested when the result is finite. Mark Dickinson <dickinsm@gmail.com> parents: 46616 diff changeset	759
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	760 return (*from_double_func)(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	761 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	762
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	763 /* 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	764 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	765 errno = ERANGE for overflow). */
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	766
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	767 static PyObject *
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	768 math_1a(PyObject arg, double (func) (double))
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	769 {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	770 double x, r;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	771 x = PyFloat_AsDouble(arg);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	772 if (x == -1.0 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	773 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	774 errno = 0;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	775 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	776 r = (*func)(x);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	777 PyFPE_END_PROTECT(r);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	778 if (errno && is_error(r))
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	779 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	780 return PyFloat_FromDouble(r);
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	781 }
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	782
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	783 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	784 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	785 arguments and returns a double.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	786
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	787 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	788 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	789 platforms.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	790
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	791 - 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	792 - 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	793 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	794 - 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	795 raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	796 - 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	797 OverflowError is raised
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	798
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	799 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	800 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	801
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	802 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	803 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	804 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	805 '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	806 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	807 OverflowError.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	808 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	809
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	810 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	811 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	812 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	813 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	814 }
31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	815
31e294d08ce1 Make math.floor and math.ceil return ints instead of floats. Jeffrey Yasskin <jyasskin@gmail.com> parents: 44460 diff changeset	816 static PyObject *
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	817 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	818 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	819 return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	820 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	821
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	822 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	823 math_2(PyObject args, double (func) (double, double), char *funcname)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	824 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	825 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	826 double x, y, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	827 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	828 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	829 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	830 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	831 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	832 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	833 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	834 PyFPE_START_PROTECT("in math_2", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	835 r = (*func)(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	836 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	837 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	838 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	839 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	840 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	841 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	842 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	843 else if (Py_IS_INFINITY(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	844 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	845 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	846 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	847 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	848 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	849 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	850 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	851 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	852 return PyFloat_FromDouble(r);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	853 }
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	854
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	855 #define FUNC1(funcname, func, can_overflow, docstring) \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	856 static PyObject * math_##funcname(PyObject self, PyObject args) { \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	857 return math_1(args, func, can_overflow); \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	858 }\
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	859 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	860
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	861 #define FUNC1A(funcname, func, docstring) \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	862 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	863 return math_1a(args, func); \
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	864 }\
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	865 PyDoc_STRVAR(math_##funcname##_doc, docstring);
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	866
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	867 #define FUNC2(funcname, func, docstring) \
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	868 static PyObject * math_##funcname(PyObject self, PyObject args) { \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	869 return math_2(args, func, #funcname); \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	870 }\
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	871 PyDoc_STRVAR(math_##funcname##_doc, docstring);
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	872
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	873 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	874 "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	875 FUNC1(acosh, m_acosh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	876 "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	877 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	878 "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	879 FUNC1(asinh, m_asinh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	880 "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	881 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	882 "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	883 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	884 "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	885 "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	886 FUNC1(atanh, m_atanh, 0,
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	887 "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	888
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	889 static PyObject * math_ceil(PyObject self, PyObject number) {
74578 7d96679c5d46 use the static identifier api for looking up special methods Benjamin Peterson <benjamin@python.org> parents: 72510 diff changeset	890 _Py_IDENTIFIER(__ceil__);
62684 3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	891 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	892
74578 7d96679c5d46 use the static identifier api for looking up special methods Benjamin Peterson <benjamin@python.org> parents: 72510 diff changeset	893 method = _PyObject_LookupSpecial(number, &PyId___ceil__);
62680 35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	894 if (method == NULL) {
35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	895 if (PyErr_Occurred())
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	896 return NULL;
62680 35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	897 return math_1_to_int(number, ceil, 0);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	898 }
62684 3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	899 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	900 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	901 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	902 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	903
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	904 PyDoc_STRVAR(math_ceil_doc,
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	905 "ceil(x)\n\nReturn the ceiling of x as an int.\n"
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	906 "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	907
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	908 FUNC2(copysign, copysign,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	909 "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	910 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	911 "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	912 FUNC1(cosh, cosh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	913 "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	914 FUNC1A(erf, m_erf,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	915 "erf(x)\n\nError function at x.")
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	916 FUNC1A(erfc, m_erfc,
1e8164b5f36d Merged revisions 76878 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57758 diff changeset	917 "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	918 FUNC1(exp, exp, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	919 "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	920 FUNC1(expm1, m_expm1, 1,
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	921 "expm1(x)\n\nReturn exp(x)-1.\n"
b45ca11b9a3e Merged revisions 76861 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57660 diff changeset	922 "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	923 "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	924 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	925 "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	926
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	927 static PyObject * math_floor(PyObject self, PyObject number) {
74578 7d96679c5d46 use the static identifier api for looking up special methods Benjamin Peterson <benjamin@python.org> parents: 72510 diff changeset	928 _Py_IDENTIFIER(__floor__);
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	929 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	930
74578 7d96679c5d46 use the static identifier api for looking up special methods Benjamin Peterson <benjamin@python.org> parents: 72510 diff changeset	931 method = _PyObject_LookupSpecial(number, &PyId___floor__);
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	932 if (method == NULL) {
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	933 if (PyErr_Occurred())
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	934 return NULL;
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	935 return math_1_to_int(number, floor, 0);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	936 }
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	937 result = PyObject_CallFunctionObjArgs(method, NULL);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	938 Py_DECREF(method);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	939 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	940 }
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	941
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__ Guido van Rossum <guido@python.org> parents: 42334 diff changeset	942 PyDoc_STRVAR(math_floor_doc,
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	943 "floor(x)\n\nReturn the floor of x as an int.\n"
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	944 "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	945
56270 47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	946 FUNC1A(gamma, m_tgamma,
47b82fbdc2bb Merged revisions 75117 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 50250 diff changeset	947 "gamma(x)\n\nGamma function at x.")
57660 7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	948 FUNC1A(lgamma, m_lgamma,
7cb73e7c176d Merged revisions 76755 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57209 diff changeset	949 "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	950 FUNC1(log1p, m_log1p, 0,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	951 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	952 "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	953 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	954 "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	955 FUNC1(sinh, sinh, 1,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	956 "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	957 FUNC1(sqrt, sqrt, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	958 "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	959 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	960 "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	961 FUNC1(tanh, tanh, 0,
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	962 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	963
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	964 /* 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	965 <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	966 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	967 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	968 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	969
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	970 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	971 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	972 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	973
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	974 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	975 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	976 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	977 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	978
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	979 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	980 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	981 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	982 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	983 prevents double rounding because any addition or subtraction of two doubles
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	984 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	985 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	986 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	987 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	988 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	989
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	990 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	991 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	992
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	993 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	994 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	995 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	996 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	997 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	998 */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	999
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 #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	1001
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 /* 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	1003 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	1004 _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	1005 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	1006 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1007 void *v = NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1008 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	1009
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1010 m += m; /* double */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1011 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1012 double p = p_ptr;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1013 if (p == ps) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1014 v = PyMem_Malloc(sizeof(double) * m);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1015 if (v != NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1016 memcpy(v, ps, sizeof(double) * n);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1017 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1018 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1019 v = PyMem_Realloc(p, sizeof(double) * m);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1020 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1021 if (v == NULL) { /* size overflow or no memory */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1022 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1023 return 1;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1024 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1025 p_ptr = (double) v;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1026 *m_ptr = m;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1027 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	1028 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1029
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1030 /* 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	1031
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1032 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	1033 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	1034 for x in iterable:
62496 0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1035 i = 0
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1036 for y in partials:
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1037 if abs(x) < abs(y):
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1038 x, y = y, x
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1039 hi = x + y
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1040 lo = y - (hi - x)
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1041 if lo:
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1042 partials[i] = lo
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1043 i += 1
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1044 x = hi
0c87490767bf Merged revisions 82223 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 61467 diff changeset	1045 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	1046 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	1047
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1048 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	1049 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	1050 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	1051
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1052 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	1053 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	1054 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	1055 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	1056
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1057 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	1058 */
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1059
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1060 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	1061 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	1062 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1063 PyObject item, iter, *sum = NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1064 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1065 double x, y, t, ps[NUM_PARTIALS], *p = ps;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1066 double xsave, special_sum = 0.0, inf_sum = 0.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1067 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	1068
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1069 iter = PyObject_GetIter(seq);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1070 if (iter == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1071 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	1072
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1073 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	1074
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1075 for(;;) { /* for x in iterable */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1076 assert(0 <= n && n <= m);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1077 assert((m == NUM_PARTIALS && p == ps) \|\|
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1078 (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	1079
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1080 item = PyIter_Next(iter);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1081 if (item == NULL) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1082 if (PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1083 goto _fsum_error;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1084 break;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1085 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1086 x = PyFloat_AsDouble(item);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1087 Py_DECREF(item);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1088 if (PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1089 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	1090
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1091 xsave = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1092 for (i = j = 0; j < n; j++) { /* for y in partials */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1093 y = p[j];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1094 if (fabs(x) < fabs(y)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1095 t = x; x = y; y = t;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1096 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1097 hi = x + y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1098 yr = hi - x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1099 lo = y - yr;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1100 if (lo != 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1101 p[i++] = lo;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1102 x = hi;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1103 }
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1104
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1105 n = i; /* ps[i:] = [x] */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1106 if (x != 0.0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1107 if (! Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1108 /* a nonfinite x could arise either as
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1109 a result of intermediate overflow, or
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1110 as a result of a nan or inf in the
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1111 summands */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1112 if (Py_IS_FINITE(xsave)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1113 PyErr_SetString(PyExc_OverflowError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1114 "intermediate overflow in fsum");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1115 goto _fsum_error;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1116 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1117 if (Py_IS_INFINITY(xsave))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1118 inf_sum += xsave;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1119 special_sum += xsave;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1120 /* reset partials */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1121 n = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1122 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1123 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1124 goto _fsum_error;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1125 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1126 p[n++] = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1127 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1128 }
47320 3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1129
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1130 if (special_sum != 0.0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1131 if (Py_IS_NAN(inf_sum))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1132 PyErr_SetString(PyExc_ValueError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1133 "-inf + inf in fsum");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1134 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1135 sum = PyFloat_FromDouble(special_sum);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1136 goto _fsum_error;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1137 }
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1138
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1139 hi = 0.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1140 if (n > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1141 hi = p[--n];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1142 /* sum_exact(ps, hi) from the top, stop when the sum becomes
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1143 inexact. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1144 while (n > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1145 x = hi;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1146 y = p[--n];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1147 assert(fabs(y) < fabs(x));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1148 hi = x + y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1149 yr = hi - x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1150 lo = y - yr;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1151 if (lo != 0.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1152 break;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1153 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1154 /* Make half-even rounding work across multiple partials.
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1155 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1156 digit to two instead of down to zero (the 1e-16 makes the 1
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1157 slightly closer to two). With a potential 1 ULP rounding
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1158 error fixed-up, math.fsum() can guarantee commutativity. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1159 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) \|\|
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1160 (lo > 0.0 && p[n-1] > 0.0))) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1161 y = lo * 2.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1162 x = hi + y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1163 yr = x - hi;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1164 if (y == yr)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1165 hi = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1166 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1167 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1168 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	1169
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1170 _fsum_error:
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1171 PyFPE_END_PROTECT(hi)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1172 Py_DECREF(iter);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1173 if (p != ps)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1174 PyMem_Free(p);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1175 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	1176 }
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1177
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 47175 diff changeset	1178 #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	1179
48606 f121a963ab69 Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48407 diff changeset	1180 PyDoc_STRVAR(math_fsum_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1181 "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	1182 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	1183 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	1184
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1185 /* 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	1186 * 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	1187 * count_leading_zero_bits(x)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1188 */
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 /* 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	1191 * 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	1192 * 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	1193 * 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	1194 */
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 static unsigned long
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1197 bit_length(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1198 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1199 unsigned long len = 0;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1200 while (n != 0) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1201 ++len;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1202 n >>= 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1203 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1204 return len;
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
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1207 static unsigned long
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1208 count_set_bits(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1209 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1210 unsigned long count = 0;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1211 while (n != 0) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1212 ++count;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1213 n &= n - 1; /* clear least significant bit */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1214 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1215 return count;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1216 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1217
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1218 /* Divide-and-conquer factorial algorithm
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1219 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1220 * 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	1221 * 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	1222 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1223 * 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	1224 * a fast prime factorization algorithm.
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1225 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1226 * Notes on the algorithm
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1227 * ----------------------
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1228 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1229 * 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	1230 * 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	1231 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1232 * 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	1233 * 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	1234 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1235 * factorial_odd_part(n) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1236 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1237 * 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	1238 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1239 * Example: factorial_odd_part(20) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1240 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1241 * (1) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1242 * (1) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1243 * (1 * 3 * 5) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1244 * (1 * 3 * 5 * 7 * 9)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1245 * (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	1246 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1247 * 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	1248 * 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	1249 * 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	1250 * 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	1251 * 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	1252 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1253 * 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	1254 * 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	1255 * 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	1256 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1257 * factorial(20) =
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 * (16) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1260 * (8) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1261 * (4 * 12 * 20) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1262 * (2 * 6 * 10 * 14 * 18) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1263 * (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	1264 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1265 * 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	1266 * 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	1267 * 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	1268 * 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	1269 * 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	1270 * integer arithmetic.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1271 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1272 * 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	1273 * 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	1274 * function. By standard results, its value is:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1275 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1276 * 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	1277 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1278 * 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	1279 * 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	1280 * '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	1281 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1282
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1283 /* 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	1284 * 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	1285 * 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	1286
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1287 static PyObject *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1288 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	1289 unsigned long max_bits)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1290 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1291 unsigned long midpoint, num_operands;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1292 PyObject left = NULL, right = NULL, *result = NULL;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1293
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1294 /* 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	1295 * 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	1296 * 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	1297 * the answer.
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1298 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1299 * 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	1300 * 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	1301 * product x*y will require at most
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1302 * 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	1303 * 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	1304 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1305 * 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	1306 * 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	1307 * bit_length(stop - 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1308 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1309
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1310 num_operands = (stop - start) / 2;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1311 /* 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	1312 * 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	1313 if (num_operands <= 8 * SIZEOF_LONG &&
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1314 num_operands * max_bits <= 8 * SIZEOF_LONG) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1315 unsigned long j, total;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1316 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	1317 total *= j;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1318 return PyLong_FromUnsignedLong(total);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1319 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1320
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1321 /* 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	1322 midpoint = (start + num_operands) \| 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1323 left = factorial_partial_product(start, midpoint,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1324 bit_length(midpoint - 2));
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1325 if (left == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1326 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1327 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	1328 if (right == 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 result = PyNumber_Multiply(left, right);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1331
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1332 error:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1333 Py_XDECREF(left);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1334 Py_XDECREF(right);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1335 return result;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1336 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1337
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1338 /* 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	1339
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1340 static PyObject *
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1341 factorial_odd_part(unsigned long n)
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 long i;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1344 unsigned long v, lower, upper;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1345 PyObject partial, tmp, inner, outer;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1346
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1347 inner = PyLong_FromLong(1);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1348 if (inner == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1349 return NULL;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1350 outer = inner;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1351 Py_INCREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1352
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1353 upper = 3;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1354 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	1355 v = n >> i;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1356 if (v <= 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1357 continue;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1358 lower = upper;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1359 /* (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	1360 upper = (v + 1) \| 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1361 /* 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	1362 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	1363 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	1364 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	1365 /* inner = partial /
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1366 if (partial == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1367 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1368 tmp = PyNumber_Multiply(inner, partial);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1369 Py_DECREF(partial);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1370 if (tmp == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1371 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1372 Py_DECREF(inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1373 inner = tmp;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1374 /* 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	1375 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	1376
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1377 /* outer = inner; /
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1378 tmp = PyNumber_Multiply(outer, inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1379 if (tmp == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1380 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1381 Py_DECREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1382 outer = tmp;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1383 }
79933 b4bfcf7a4773 Fix math.factorial KeyboardInterrupt segfault. Thanks Amaury for report and diagnosis. Mark Dickinson <mdickinson@enthought.com> parents: 75604 diff changeset	1384 Py_DECREF(inner);
b4bfcf7a4773 Fix math.factorial KeyboardInterrupt segfault. Thanks Amaury for report and diagnosis. Mark Dickinson <mdickinson@enthought.com> parents: 75604 diff changeset	1385 return outer;
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1386
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1387 error:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1388 Py_DECREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1389 Py_DECREF(inner);
79933 b4bfcf7a4773 Fix math.factorial KeyboardInterrupt segfault. Thanks Amaury for report and diagnosis. Mark Dickinson <mdickinson@enthought.com> parents: 75604 diff changeset	1390 return NULL;
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1391 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1392
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1393 /* Lookup table for small factorial values */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1394
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1395 static const unsigned long SmallFactorials[] = {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1396 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	1397 362880, 3628800, 39916800, 479001600,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1398 #if SIZEOF_LONG >= 8
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1399 6227020800, 87178291200, 1307674368000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1400 20922789888000, 355687428096000, 6402373705728000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1401 121645100408832000, 2432902008176640000
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1402 #endif
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1403 };
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1404
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1405 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	1406 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	1407 {
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1408 long x;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1409 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	1410
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1411 if (PyFloat_Check(arg)) {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1412 PyObject *lx;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1413 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1414 if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1415 PyErr_SetString(PyExc_ValueError,
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1416 "factorial() only accepts integral values");
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1417 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1418 }
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1419 lx = PyLong_FromDouble(dx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1420 if (lx == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1421 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1422 x = PyLong_AsLong(lx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1423 Py_DECREF(lx);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1424 }
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1425 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1426 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	1427
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1428 if (x == -1 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1429 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1430 if (x < 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1431 PyErr_SetString(PyExc_ValueError,
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1432 "factorial() not defined for negative values");
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1433 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1434 }
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	1435
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1436 /* use lookup table if x is small */
72510 b534b56379cb Use the new Py_ARRAY_LENGTH macro Victor Stinner <victor.stinner@haypocalc.com> parents: 72467 diff changeset	1437 if (x < (long)Py_ARRAY_LENGTH(SmallFactorials))
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1438 return PyLong_FromUnsignedLong(SmallFactorials[x]);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1439
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1440 /* 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	1441 odd_part << two_valuation. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1442 odd_part = factorial_odd_part(x);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1443 if (odd_part == NULL)
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1444 return NULL;
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1445 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	1446 if (two_valuation == NULL) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1447 Py_DECREF(odd_part);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1448 return NULL;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1449 }
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1450 result = PyNumber_Lshift(odd_part, two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1451 Py_DECREF(two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1452 Py_DECREF(odd_part);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1453 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	1454 }
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	1455
50250 1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1456 PyDoc_STRVAR(math_factorial_doc,
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1457 "factorial(x) -> Integral\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1458 "\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1459 "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	1460
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	1461 static PyObject *
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1462 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	1463 {
74578 7d96679c5d46 use the static identifier api for looking up special methods Benjamin Peterson <benjamin@python.org> parents: 72510 diff changeset	1464 _Py_IDENTIFIER(__trunc__);
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1465 PyObject trunc, result;
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1466
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1467 if (Py_TYPE(number)->tp_dict == NULL) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1468 if (PyType_Ready(Py_TYPE(number)) < 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1469 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1470 }
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1471
74578 7d96679c5d46 use the static identifier api for looking up special methods Benjamin Peterson <benjamin@python.org> parents: 72510 diff changeset	1472 trunc = _PyObject_LookupSpecial(number, &PyId___trunc__);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1473 if (trunc == NULL) {
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1474 if (!PyErr_Occurred())
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1475 PyErr_Format(PyExc_TypeError,
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1476 "type %.100s doesn't define __trunc__ method",
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1477 Py_TYPE(number)->tp_name);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1478 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1479 }
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1480 result = PyObject_CallFunctionObjArgs(trunc, NULL);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1481 Py_DECREF(trunc);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1482 return result;
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1483 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1484
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1485 PyDoc_STRVAR(math_trunc_doc,
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1486 "trunc(x:Real) -> Integral\n"
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1487 "\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	1488 "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	1489
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1490 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1491 math_frexp(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1492 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1493 int i;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1494 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1495 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1496 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1497 /* deal with special cases directly, to sidestep platform
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1498 differences */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1499 if (Py_IS_NAN(x) \|\| Py_IS_INFINITY(x) \|\| !x) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1500 i = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1501 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1502 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1503 PyFPE_START_PROTECT("in math_frexp", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1504 x = frexp(x, &i);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1505 PyFPE_END_PROTECT(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1506 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1507 return Py_BuildValue("(di)", x, i);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1508 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1509
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1510 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	1511 "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	1512 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1513 "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	1514 "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	1515 "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	1516
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1517 static PyObject *
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1518 math_ldexp(PyObject self, PyObject args)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1519 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1520 double x, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1521 PyObject *oexp;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1522 long exp;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1523 int overflow;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1524 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1525 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	1526
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1527 if (PyLong_Check(oexp)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1528 /* on overflow, replace exponent with either LONG_MAX
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1529 or LONG_MIN, depending on the sign. */
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1530 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1531 if (exp == -1 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1532 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1533 if (overflow)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1534 exp = overflow < 0 ? LONG_MIN : LONG_MAX;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1535 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1536 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1537 PyErr_SetString(PyExc_TypeError,
85418 4d62a62ba44d Issue #18783: Removed existing mentions of Python long type in docstrings, Serhiy Storchaka <storchaka@gmail.com> parents: 79934 diff changeset	1538 "Expected an int as second argument to ldexp.");
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1539 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1540 }
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	1541
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1542 if (x == 0. \|\| !Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1543 /* NaNs, zeros and infinities are returned unchanged */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1544 r = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1545 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1546 } else if (exp > INT_MAX) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1547 /* overflow */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1548 r = copysign(Py_HUGE_VAL, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1549 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1550 } else if (exp < INT_MIN) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1551 /* underflow to +-0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1552 r = copysign(0., x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1553 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1554 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1555 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1556 PyFPE_START_PROTECT("in math_ldexp", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1557 r = ldexp(x, (int)exp);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1558 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1559 if (Py_IS_INFINITY(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1560 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1561 }
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	1562
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1563 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1564 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1565 return PyFloat_FromDouble(r);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1566 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1567
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1568 PyDoc_STRVAR(math_ldexp_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1569 "ldexp(x, i)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1570 Return x * (2**i).");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1571
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1572 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1573 math_modf(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1574 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1575 double y, x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1576 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1577 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1578 /* some platforms don't do the right thing for NaNs and
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1579 infinities, so we take care of special cases directly. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1580 if (!Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1581 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1582 return Py_BuildValue("(dd)", copysign(0., x), x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1583 else if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1584 return Py_BuildValue("(dd)", x, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1585 }
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	1586
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1587 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1588 PyFPE_START_PROTECT("in math_modf", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1589 x = modf(x, &y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1590 PyFPE_END_PROTECT(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1591 return Py_BuildValue("(dd)", x, y);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1592 }
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1593
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1594 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	1595 "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	1596 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1597 "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	1598 "of x and are floats.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1599
85418 4d62a62ba44d Issue #18783: Removed existing mentions of Python long type in docstrings, Serhiy Storchaka <storchaka@gmail.com> parents: 79934 diff changeset	1600 /* A decent logarithm is easy to compute even for huge ints, but libm can't
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	1601 do that by itself -- loghelper can. func is log or log10, and name is
85418 4d62a62ba44d Issue #18783: Removed existing mentions of Python long type in docstrings, Serhiy Storchaka <storchaka@gmail.com> parents: 79934 diff changeset	1602 "log" or "log10". Note that overflow of the result isn't possible: an int
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1603 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	1604 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	1605 small enough to fit in an IEEE single. log and log10 are even smaller.
85418 4d62a62ba44d Issue #18783: Removed existing mentions of Python long type in docstrings, Serhiy Storchaka <storchaka@gmail.com> parents: 79934 diff changeset	1606 However, intermediate overflow is possible for an int if the number of bits
4d62a62ba44d Issue #18783: Removed existing mentions of Python long type in docstrings, Serhiy Storchaka <storchaka@gmail.com> parents: 79934 diff changeset	1607 in that int 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	1608
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1609 static PyObject*
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1610 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	1611 {
85418 4d62a62ba44d Issue #18783: Removed existing mentions of Python long type in docstrings, Serhiy Storchaka <storchaka@gmail.com> parents: 79934 diff changeset	1612 /* If it is int, do it ourselves. */
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1613 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	1614 double x, result;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1615 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	1616
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	1617 /* 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	1618 if (Py_SIZE(arg) <= 0) {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1619 PyErr_SetString(PyExc_ValueError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1620 "math domain error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1621 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1622 }
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	1623
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	1624 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	1625 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	1626 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	1627 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	1628 /* 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	1629 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	1630 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	1631 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	1632 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	1633 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	1634 /* 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	1635 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	1636 }
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	1637 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	1638 /* 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	1639 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	1640 return PyFloat_FromDouble(result);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1641 }
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	1642
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1643 /* Else let libm handle it by itself. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1644 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	1645 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1646
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1647 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	1648 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	1649 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1650 PyObject *arg;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1651 PyObject *base = NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1652 PyObject num, den;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1653 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	1654
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1655 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1656 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	1657
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1658 num = loghelper(arg, m_log, "log");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1659 if (num == NULL \|\| base == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1660 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	1661
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1662 den = loghelper(base, m_log, "log");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1663 if (den == NULL) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1664 Py_DECREF(num);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1665 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1666 }
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1667
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1668 ans = PyNumber_TrueDivide(num, den);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1669 Py_DECREF(num);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1670 Py_DECREF(den);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1671 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	1672 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1673
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1674 PyDoc_STRVAR(math_log_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1675 "log(x[, base])\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1676 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	1677 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	1678
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1679 static PyObject *
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1680 math_log2(PyObject self, PyObject arg)
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1681 {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1682 return loghelper(arg, m_log2, "log2");
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1683 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1684
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1685 PyDoc_STRVAR(math_log2_doc,
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1686 "log2(x)\n\nReturn the base 2 logarithm of x.");
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1687
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1688 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1689 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	1690 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1691 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	1692 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1693
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1694 PyDoc_STRVAR(math_log10_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1695 "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	1696
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1697 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1698 math_fmod(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1699 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1700 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1701 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1702 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1703 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1704 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1705 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1706 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1707 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1708 /* fmod(x, +/-Inf) returns x for finite x. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1709 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1710 return PyFloat_FromDouble(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1711 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1712 PyFPE_START_PROTECT("in math_fmod", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1713 r = fmod(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1714 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1715 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1716 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1717 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1718 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1719 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1720 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1721 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1722 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1723 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1724 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1725 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1726
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1727 PyDoc_STRVAR(math_fmod_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1728 "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	1729 " x % y may differ.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1730
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1731 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1732 math_hypot(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1733 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1734 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1735 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1736 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1737 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1738 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1739 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1740 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1741 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1742 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1743 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1744 return PyFloat_FromDouble(fabs(x));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1745 if (Py_IS_INFINITY(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1746 return PyFloat_FromDouble(fabs(y));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1747 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1748 PyFPE_START_PROTECT("in math_hypot", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1749 r = hypot(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1750 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1751 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1752 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1753 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1754 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1755 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1756 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1757 else if (Py_IS_INFINITY(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1758 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1759 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1760 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1761 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1762 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1763 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1764 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1765 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1766 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1767 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1768
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1769 PyDoc_STRVAR(math_hypot_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1770 "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	1771
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1772 /* 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	1773 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	1774 (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	1775 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	1776 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1777
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1778 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1779 math_pow(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1780 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1781 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1782 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1783 int odd_y;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1784
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1785 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1786 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1787 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1788 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1789 if ((x == -1.0 \|\| y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1790 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	1791
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1792 /* deal directly with IEEE specials, to cope with problems on various
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1793 platforms whose semantics don't exactly match C99 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1794 r = 0.; /* silence compiler warning */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1795 if (!Py_IS_FINITE(x) \|\| !Py_IS_FINITE(y)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1796 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1797 if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1798 r = y == 0. ? 1. : x; /* NaN*0 = 1 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1799 else if (Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1800 r = x == 1. ? 1. : y; /* 1*NaN = 1 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1801 else if (Py_IS_INFINITY(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1802 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1803 if (y > 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1804 r = odd_y ? x : fabs(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1805 else if (y == 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1806 r = 1.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1807 else /* y < 0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1808 r = odd_y ? copysign(0., x) : 0.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1809 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1810 else if (Py_IS_INFINITY(y)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1811 if (fabs(x) == 1.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1812 r = 1.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1813 else if (y > 0. && fabs(x) > 1.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1814 r = y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1815 else if (y < 0. && fabs(x) < 1.0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1816 r = -y; /* result is +inf */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1817 if (x == 0.) /* 0*-inf: divide-by-zero /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1818 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1819 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1820 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1821 r = 0.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1822 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1823 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1824 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1825 /* let libm handle finite*finite /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1826 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1827 PyFPE_START_PROTECT("in math_pow", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1828 r = pow(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1829 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1830 /* a NaN result should arise only from (-ve)**(finite
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1831 non-integer); in this case we want to raise ValueError. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1832 if (!Py_IS_FINITE(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1833 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1834 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1835 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1836 /*
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1837 an infinite result here arises either from:
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1838 (A) (+/-0.)**negative (-> divide-by-zero)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1839 (B) overflow of x**y with x and y finite
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1840 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1841 else if (Py_IS_INFINITY(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1842 if (x == 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1843 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1844 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1845 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1846 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1847 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1848 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1849
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1850 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1851 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1852 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1853 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1854 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1855
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1856 PyDoc_STRVAR(math_pow_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1857 "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	1858
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1859 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	1860 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	1861
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1862 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1863 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	1864 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1865 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1866 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1867 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1868 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	1869 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1870
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1871 PyDoc_STRVAR(math_degrees_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1872 "degrees(x)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1873 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	1874
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1875 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1876 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	1877 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1878 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1879 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1880 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1881 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	1882 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1883
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1884 PyDoc_STRVAR(math_radians_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1885 "radians(x)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1886 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	1887
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1888 static PyObject *
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1889 math_isfinite(PyObject self, PyObject arg)
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1890 {
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1891 double x = PyFloat_AsDouble(arg);
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1892 if (x == -1.0 && PyErr_Occurred())
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1893 return NULL;
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1894 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	1895 }
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1896
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1897 PyDoc_STRVAR(math_isfinite_doc,
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1898 "isfinite(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1899 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	1900
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1901 static PyObject *
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1902 math_isnan(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1903 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1904 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1905 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1906 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1907 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	1908 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1909
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1910 PyDoc_STRVAR(math_isnan_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1911 "isnan(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1912 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	1913
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1914 static PyObject *
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1915 math_isinf(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1916 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1917 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1918 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1919 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1920 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	1921 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1922
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1923 PyDoc_STRVAR(math_isinf_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1924 "isinf(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1925 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	1926
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1927 static PyMethodDef math_methods[] = {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1928 {"acos", math_acos, METH_O, math_acos_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1929 {"acosh", math_acosh, METH_O, math_acosh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1930 {"asin", math_asin, METH_O, math_asin_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1931 {"asinh", math_asinh, METH_O, math_asinh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1932 {"atan", math_atan, METH_O, math_atan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1933 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1934 {"atanh", math_atanh, METH_O, math_atanh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1935 {"ceil", math_ceil, METH_O, math_ceil_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1936 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1937 {"cos", math_cos, METH_O, math_cos_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1938 {"cosh", math_cosh, METH_O, math_cosh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1939 {"degrees", math_degrees, METH_O, math_degrees_doc},
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1940 {"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	1941 {"erfc", math_erfc, METH_O, math_erfc_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1942 {"exp", math_exp, METH_O, math_exp_doc},
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1943 {"expm1", math_expm1, METH_O, math_expm1_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1944 {"fabs", math_fabs, METH_O, math_fabs_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1945 {"factorial", math_factorial, METH_O, math_factorial_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1946 {"floor", math_floor, METH_O, math_floor_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1947 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1948 {"frexp", math_frexp, METH_O, math_frexp_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1949 {"fsum", math_fsum, METH_O, math_fsum_doc},
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1950 {"gamma", math_gamma, METH_O, math_gamma_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1951 {"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	1952 {"isfinite", math_isfinite, METH_O, math_isfinite_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1953 {"isinf", math_isinf, METH_O, math_isinf_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1954 {"isnan", math_isnan, METH_O, math_isnan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1955 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1956 {"lgamma", math_lgamma, METH_O, math_lgamma_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1957 {"log", math_log, METH_VARARGS, math_log_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1958 {"log1p", math_log1p, METH_O, math_log1p_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1959 {"log10", math_log10, METH_O, math_log10_doc},
69946 6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1960 {"log2", math_log2, METH_O, math_log2_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1961 {"modf", math_modf, METH_O, math_modf_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1962 {"pow", math_pow, METH_VARARGS, math_pow_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1963 {"radians", math_radians, METH_O, math_radians_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1964 {"sin", math_sin, METH_O, math_sin_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1965 {"sinh", math_sinh, METH_O, math_sinh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1966 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1967 {"tan", math_tan, METH_O, math_tan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1968 {"tanh", math_tanh, METH_O, math_tanh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1969 {"trunc", math_trunc, METH_O, math_trunc_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1970 {NULL, NULL} /* sentinel */
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1971 };
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1972
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1973
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1974 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	1975 "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	1976 "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	1977
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1978
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1979 static struct PyModuleDef mathmodule = {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1980 PyModuleDef_HEAD_INIT,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1981 "math",
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1982 module_doc,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1983 -1,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1984 math_methods,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1985 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1986 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1987 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1988 NULL
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1989 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1990
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 23832 diff changeset	1991 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1992 PyInit_math(void)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1993 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1994 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	1995
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1996 m = PyModule_Create(&mathmodule);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1997 if (m == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1998 goto finally;
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	1999
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	2000 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	2001 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	2002
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	2003 finally:
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	2004 return m;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	2005 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 87690:66c1c9f32567 default tip