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

annotate Modules/mathmodule.c @ 74006:88198b93ff2f

Issue #13560: Add PyUnicode_EncodeLocale() * Use PyUnicode_EncodeLocale() in time.strftime() if wcsftime() is not available * Document my last changes in Misc/NEWS

author	Victor Stinner <victor.stinner@haypocalc.com>
date	Sat, 17 Dec 2011 04:13:41 +0100
parents	b534b56379cb
children	7d96679c5d46

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)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	748 if (can_overflow)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	749 PyErr_SetString(PyExc_OverflowError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	750 "math range error"); /* overflow */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	751 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	752 PyErr_SetString(PyExc_ValueError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	753 "math domain error"); /* singularity */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	754 return NULL;
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) {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	890 static PyObject *ceil_str = NULL;
62684 3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same. Mark Dickinson <dickinsm@gmail.com> parents: 62680 diff changeset	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
62680 35370d7236c9 fix lookup of __ceil__ Benjamin Peterson <benjamin@python.org> parents: 62679 diff changeset	893 method = _PyObject_LookupSpecial(number, "__ceil__", &ceil_str);
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) {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	928 static PyObject *floor_str = NULL;
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	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
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	931 method = _PyObject_LookupSpecial(number, "__floor__", &floor_str);
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 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1384
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1385 goto done;
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 done:
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1390 Py_DECREF(inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1391 return outer;
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
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1394 /* Lookup table for small factorial values */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1395
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1396 static const unsigned long SmallFactorials[] = {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1397 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	1398 362880, 3628800, 39916800, 479001600,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1399 #if SIZEOF_LONG >= 8
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1400 6227020800, 87178291200, 1307674368000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1401 20922789888000, 355687428096000, 6402373705728000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1402 121645100408832000, 2432902008176640000
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1403 #endif
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1404 };
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1405
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1406 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	1407 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	1408 {
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1409 long x;
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1410 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	1411
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1412 if (PyFloat_Check(arg)) {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1413 PyObject *lx;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1414 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	1415 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	1416 PyErr_SetString(PyExc_ValueError,
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1417 "factorial() only accepts integral values");
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1418 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1419 }
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1420 lx = PyLong_FromDouble(dx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1421 if (lx == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1422 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1423 x = PyLong_AsLong(lx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1424 Py_DECREF(lx);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1425 }
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1426 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1427 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	1428
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1429 if (x == -1 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1430 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1431 if (x < 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1432 PyErr_SetString(PyExc_ValueError,
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1433 "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	1434 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1435 }
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	1436
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1437 /* 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	1438 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	1439 return PyLong_FromUnsignedLong(SmallFactorials[x]);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1440
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1441 /* 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	1442 odd_part << two_valuation. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1443 odd_part = factorial_odd_part(x);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1444 if (odd_part == NULL)
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1445 return NULL;
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1446 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	1447 if (two_valuation == NULL) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1448 Py_DECREF(odd_part);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1449 return NULL;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1450 }
61599 1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1451 result = PyNumber_Lshift(odd_part, two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1452 Py_DECREF(two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial: Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1453 Py_DECREF(odd_part);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1454 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	1455 }
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	1456
50250 1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1457 PyDoc_STRVAR(math_factorial_doc,
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1458 "factorial(x) -> Integral\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1459 "\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50123 diff changeset	1460 "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	1461
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	1462 static PyObject *
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1463 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	1464 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1465 static PyObject *trunc_str = NULL;
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1466 PyObject trunc, result;
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1467
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1468 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	1469 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	1470 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1471 }
45082 d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1472
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1473 trunc = _PyObject_LookupSpecial(number, "__trunc__", &trunc_str);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1474 if (trunc == NULL) {
62668 a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1475 if (!PyErr_Occurred())
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1476 PyErr_Format(PyExc_TypeError,
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1477 "type %.100s doesn't define __trunc__ method",
a89a3d92f8ae correctly lookup __trunc__ and __floor__ Benjamin Peterson <benjamin@python.org> parents: 62495 diff changeset	1478 Py_TYPE(number)->tp_name);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1479 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1480 }
62679 4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1481 result = PyObject_CallFunctionObjArgs(trunc, NULL);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1482 Py_DECREF(trunc);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial Benjamin Peterson <benjamin@python.org> parents: 62668 diff changeset	1483 return result;
45082 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
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1486 PyDoc_STRVAR(math_trunc_doc,
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1487 "trunc(x:Real) -> Integral\n"
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1488 "\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	1489 "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	1490
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45029 diff changeset	1491 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1492 math_frexp(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1493 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1494 int i;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1495 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1496 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1497 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1498 /* 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	1499 differences */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1500 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	1501 i = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1502 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1503 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1504 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	1505 x = frexp(x, &i);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1506 PyFPE_END_PROTECT(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1507 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1508 return Py_BuildValue("(di)", x, i);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1509 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1510
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1511 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	1512 "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	1513 "\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 "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	1515 "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	1516 "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	1517
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1518 static PyObject *
13326 24717405dd89 ANSI-fication, remove Py_PROTO, etc. Fred Drake <fdrake@acm.org> parents: 13309 diff changeset	1519 math_ldexp(PyObject self, PyObject args)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1520 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1521 double x, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1522 PyObject *oexp;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1523 long exp;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1524 int overflow;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1525 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	1526 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	1527
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1528 if (PyLong_Check(oexp)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1529 /* 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	1530 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	1531 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1532 if (exp == -1 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1533 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1534 if (overflow)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1535 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	1536 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1537 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1538 PyErr_SetString(PyExc_TypeError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1539 "Expected an int or long as second argument "
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1540 "to ldexp.");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1541 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1542 }
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	1543
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1544 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	1545 /* 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	1546 r = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1547 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1548 } else if (exp > INT_MAX) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1549 /* overflow */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1550 r = copysign(Py_HUGE_VAL, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1551 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1552 } else if (exp < INT_MIN) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1553 /* underflow to +-0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1554 r = copysign(0., x);
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 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1557 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1558 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	1559 r = ldexp(x, (int)exp);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1560 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1561 if (Py_IS_INFINITY(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1562 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1563 }
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	1564
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1565 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1566 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1567 return PyFloat_FromDouble(r);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1568 }
9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1569
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1570 PyDoc_STRVAR(math_ldexp_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1571 "ldexp(x, i)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1572 Return x * (2**i).");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1573
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1574 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1575 math_modf(PyObject self, PyObject arg)
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1576 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1577 double y, x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1578 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1579 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1580 /* 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	1581 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	1582 if (!Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1583 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1584 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	1585 else if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1586 return Py_BuildValue("(dd)", x, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1587 }
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	1588
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1589 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1590 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	1591 x = modf(x, &y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1592 PyFPE_END_PROTECT(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1593 return Py_BuildValue("(dd)", x, y);
407 9b3d557665a9 Added frexp, ldexp, modf, fmod. Guido van Rossum <guido@python.org> parents: 320 diff changeset	1594 }
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1595
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1596 PyDoc_STRVAR(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	1597 "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	1598 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor. Tim Peters <tim.peters@gmail.com> parents: 19048 diff changeset	1599 "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	1600 "of x and are floats.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1601
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	1602 /* A decent logarithm is easy to compute even for huge longs, but libm can't
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1603 do that by itself -- loghelper can. func is log or log10, and name is
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1604 "log" or "log10". Note that overflow of the result isn't possible: a long
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1605 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	1606 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	1607 small enough to fit in an IEEE single. log and log10 are even smaller.
58088 46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1608 However, intermediate overflow is possible for a long if the number of bits
46d60e5ff103 Merged revisions 77234 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 57866 diff changeset	1609 in that long is larger than PY_SSIZE_T_MAX. */
19713 9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1610
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 static PyObject*
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1612 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	1613 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1614 /* If it is long, do it ourselves. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1615 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	1616 double x, result;
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 58125 diff changeset	1617 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	1618
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	1619 /* 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	1620 if (Py_SIZE(arg) <= 0) {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1621 PyErr_SetString(PyExc_ValueError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1622 "math domain error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1623 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1624 }
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	1625
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	1626 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	1627 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	1628 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	1629 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	1630 /* 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	1631 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	1632 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	1633 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	1634 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	1635 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	1636 /* 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	1637 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	1638 }
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 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	1640 /* 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	1641 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	1642 return PyFloat_FromDouble(result);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1643 }
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	1644
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1645 /* 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	1646 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	1647 }
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
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 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	1650 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	1651 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1652 PyObject *arg;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1653 PyObject *base = NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1654 PyObject num, den;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1655 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	1656
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1657 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	1658 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	1659
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1660 num = loghelper(arg, m_log, "log");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1661 if (num == NULL \|\| base == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1662 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	1663
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1664 den = loghelper(base, m_log, "log");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1665 if (den == NULL) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1666 Py_DECREF(num);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1667 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1668 }
26661 b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]). Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1669
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1670 ans = PyNumber_TrueDivide(num, den);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1671 Py_DECREF(num);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1672 Py_DECREF(den);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1673 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	1674 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1675
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1676 PyDoc_STRVAR(math_log_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1677 "log(x[, base])\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1678 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	1679 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	1680
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1681 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	1682 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	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 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	1685 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1686
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1687 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	1688 "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	1689
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark Victor Stinner <victor.stinner@haypocalc.com> parents: 68457 diff changeset	1690 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1691 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	1692 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1693 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	1694 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were Tim Peters <tim.peters@gmail.com> parents: 19712 diff changeset	1695
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1696 PyDoc_STRVAR(math_log10_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1697 "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	1698
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1699 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1700 math_fmod(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1701 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1702 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1703 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1704 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	1705 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1706 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1707 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1708 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	1709 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1710 /* 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	1711 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	1712 return PyFloat_FromDouble(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1713 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1714 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	1715 r = fmod(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1716 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1717 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1718 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	1719 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1720 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1721 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1722 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1723 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1724 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1725 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1726 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1727 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1728
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1729 PyDoc_STRVAR(math_fmod_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1730 "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	1731 " x % y may differ.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1732
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1733 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1734 math_hypot(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1735 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1736 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1737 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1738 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	1739 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1740 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1741 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1742 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	1743 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1744 /* 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	1745 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1746 return PyFloat_FromDouble(fabs(x));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1747 if (Py_IS_INFINITY(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1748 return PyFloat_FromDouble(fabs(y));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1749 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1750 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	1751 r = hypot(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1752 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1753 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1754 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	1755 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1756 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1757 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1758 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1759 else if (Py_IS_INFINITY(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1760 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	1761 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1762 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1763 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1764 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1765 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1766 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1767 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1768 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1769 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1770
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1771 PyDoc_STRVAR(math_hypot_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1772 "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	1773
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1774 /* 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	1775 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	1776 (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	1777 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	1778 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1779
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1780 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1781 math_pow(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1782 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1783 PyObject ox, oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1784 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1785 int odd_y;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1786
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1787 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	1788 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1789 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1790 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1791 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	1792 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	1793
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1794 /* 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	1795 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	1796 r = 0.; /* silence compiler warning */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1797 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	1798 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1799 if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1800 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	1801 else if (Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1802 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	1803 else if (Py_IS_INFINITY(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1804 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	1805 if (y > 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1806 r = odd_y ? x : fabs(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1807 else if (y == 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1808 r = 1.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1809 else /* y < 0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1810 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	1811 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1812 else if (Py_IS_INFINITY(y)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1813 if (fabs(x) == 1.0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1814 r = 1.;
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;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1817 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	1818 r = -y; /* result is +inf */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1819 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	1820 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1821 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1822 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1823 r = 0.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1824 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1825 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1826 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1827 /* let libm handle finite*finite /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1828 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1829 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	1830 r = pow(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1831 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1832 /* 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	1833 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	1834 if (!Py_IS_FINITE(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1835 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1836 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1837 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1838 /*
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1839 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	1840 (A) (+/-0.)**negative (-> divide-by-zero)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1841 (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	1842 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1843 else if (Py_IS_INFINITY(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1844 if (x == 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1845 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1846 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1847 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1848 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1849 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1850 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1851
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1852 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1853 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1854 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1855 return PyFloat_FromDouble(r);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1856 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1857
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	1858 PyDoc_STRVAR(math_pow_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1859 "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	1860
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1861 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	1862 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	1863
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1864 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1865 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	1866 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1867 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1868 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1869 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1870 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	1871 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1872
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1873 PyDoc_STRVAR(math_degrees_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1874 "degrees(x)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1875 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	1876
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1877 static PyObject *
40450 cc992d75d5b3 Four months of trunk changes (including a few releases...) Thomas Wouters <thomas@python.org> parents: 37191 diff changeset	1878 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	1879 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1880 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1881 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1882 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1883 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	1884 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and Raymond Hettinger <python@rcn.com> parents: 19758 diff changeset	1885
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1886 PyDoc_STRVAR(math_radians_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1887 "radians(x)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1888 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	1889
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1890 static PyObject *
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1891 math_isfinite(PyObject self, PyObject arg)
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1892 {
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1893 double x = PyFloat_AsDouble(arg);
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1894 if (x == -1.0 && PyErr_Occurred())
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1895 return NULL;
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1896 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	1897 }
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1898
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1899 PyDoc_STRVAR(math_isfinite_doc,
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1900 "isfinite(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1901 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	1902
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62859 diff changeset	1903 static PyObject *
44441 b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1904 math_isnan(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1905 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1906 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1907 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1908 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1909 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	1910 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1911
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1912 PyDoc_STRVAR(math_isnan_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1913 "isnan(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1914 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	1915
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1916 static PyObject *
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1917 math_isinf(PyObject self, PyObject arg)
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1918 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1919 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1920 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1921 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1922 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	1923 }
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1924
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 44351 diff changeset	1925 PyDoc_STRVAR(math_isinf_doc,
57210 a0951f11be3d Merged revisions 76235 via svnmerge from Benjamin Peterson <benjamin@python.org> parents: 50250 diff changeset	1926 "isinf(x) -> bool\n\n\
62970 4c11e4140ced Improve docstrings for isnan, isinf and isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 62968 diff changeset	1927 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	1928
4635 49745ddb4f69 Renamed Barry Warsaw <barry@python.org> parents: 4503 diff changeset	1929 static PyMethodDef math_methods[] = {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1930 {"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	1931 {"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	1932 {"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	1933 {"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	1934 {"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	1935 {"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	1936 {"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	1937 {"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	1938 {"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	1939 {"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	1940 {"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	1941 {"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	1942 {"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	1943 {"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	1944 {"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	1945 {"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	1946 {"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	1947 {"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	1948 {"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	1949 {"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	1950 {"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	1951 {"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	1952 {"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	1953 {"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	1954 {"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	1955 {"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	1956 {"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	1957 {"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	1958 {"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	1959 {"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	1960 {"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	1961 {"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	1962 {"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	1963 {"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	1964 {"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	1965 {"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	1966 {"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	1967 {"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	1968 {"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	1969 {"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	1970 {"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	1971 {"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	1972 {NULL, NULL} /* sentinel */
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1973 };
fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1974
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1975
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 23427 diff changeset	1976 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	1977 "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	1978 "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	1979
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1980
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1981 static struct PyModuleDef mathmodule = {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1982 PyModuleDef_HEAD_INIT,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1983 "math",
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1984 module_doc,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1985 -1,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1986 math_methods,
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,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1989 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1990 NULL
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1991 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1992
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 23832 diff changeset	1993 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47562 diff changeset	1994 PyInit_math(void)
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	1995 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1996 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	1997
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1998 m = PyModule_Create(&mathmodule);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	1999 if (m == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	2000 goto finally;
4752 7367fb107108 Better error checking in initmath(). Barry Warsaw <barry@python.org> parents: 4635 diff changeset	2001
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	2002 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	2003 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	2004
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 45134 diff changeset	2005 finally:
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57210 diff changeset	2006 return m;
6 fc6fcd7df4f7 Initial revision Guido van Rossum <guido@python.org> parents: diff changeset	2007 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 74006:88198b93ff2f