cpython-lru_cache-weakref: Python/pymath.c annotate

annotate Python/pymath.c @ 66978:aed2bbafa550 3.1

Blocked revisions 87324 via svnmerge ........ r87324 | r.david.murray | 2010-12-16 14:08:51 -0500 (Thu, 16 Dec 2010) | 9 lines #10719: restore messages generated on invalid compileall args Before the introduction of filename arguments to compileall it gave semi useful messages about not being able to 'list' names that weren't valid directories. This fix restores that behavior. In addition to the test for this case, the patch also adds a test for the default behavior of compileall when no arguments are provided, and fixes a bug in one of the previously added tests. ........

author	R. David Murray <rdmurray@bitdance.com>
date	Thu, 16 Dec 2010 19:10:16 +0000
parents	f197407bdba2
children	3c9232a684ae

rev	line source
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	1 #include "Python.h"
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	2
51485 f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	3 #ifdef X87_DOUBLE_ROUNDING
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	4 /* On x86 platforms using an x87 FPU, this function is called from the
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	5 Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	6 number out of an 80-bit x87 FPU register and into a 64-bit memory location,
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	7 thus rounding from extended precision to double precision. */
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	8 double _Py_force_double(double x)
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	9 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	10 volatile double y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	11 y = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	12 return y;
51485 f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	13 }
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	14 #endif
f9f2ed79b00f Merged revisions 69459 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 49270 diff changeset	15
53240 28645a961004 The SSE2 detection and enabling could potentially cause Mark Dickinson <dickinsm@gmail.com> parents: 53223 diff changeset	16 #ifdef HAVE_GCC_ASM_FOR_X87
53185 97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	17
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	18 /* inline assembly for getting and setting the 387 FPU control word on
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	19 gcc/x86 */
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	20
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	21 unsigned short _Py_get_387controlword(void) {
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	22 unsigned short cw;
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	23 __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	24 return cw;
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	25 }
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	26
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	27 void _Py_set_387controlword(unsigned short cw) {
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	28 __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	29 }
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	30
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	31 #endif
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	32
97ae7a709c1d Issue #1580: use short float repr where possible. Mark Dickinson <dickinsm@gmail.com> parents: 51485 diff changeset	33
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	34 #ifndef HAVE_HYPOT
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	35 double hypot(double x, double y)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	36 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	37 double yx;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	38
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	39 x = fabs(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	40 y = fabs(y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	41 if (x < y) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	42 double temp = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	43 x = y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	44 y = temp;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	45 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	46 if (x == 0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	47 return 0.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	48 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	49 yx = y/x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	50 return xsqrt(1.+yxyx);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	51 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	52 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	53 #endif /* HAVE_HYPOT */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	54
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	55 #ifndef HAVE_COPYSIGN
53223 8209b6c32e61 Merged revisions 71705 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 53221 diff changeset	56 double
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	57 copysign(double x, double y)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	58 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	59 /* use atan2 to distinguish -0. from 0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	60 if (y > 0. \|\| (y == 0. && atan2(y, -1.) > 0.)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	61 return fabs(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	62 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	63 return -fabs(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	64 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	65 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	66 #endif /* HAVE_COPYSIGN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	67
53221 c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	68 #ifndef HAVE_ROUND
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	69 double
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	70 round(double x)
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	71 {
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	72 double absx, y;
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	73 absx = fabs(x);
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	74 y = floor(absx);
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	75 if (absx - y >= 0.5)
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	76 y += 1.0;
53221 c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	77 return copysign(y, x);
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	78 }
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	79 #endif /* HAVE_ROUND */
c5c8680ee0b1 Add check for C99 round function to configure, and define Mark Dickinson <dickinsm@gmail.com> parents: 53185 diff changeset	80
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	81 #ifndef HAVE_LOG1P
49270 e86ed113535c Merged revisions 66552-66553 via svnmerge from Andrew MacIntyre <andymac@bullseye.apana.org.au> parents: 46477 diff changeset	82 #include <float.h>
e86ed113535c Merged revisions 66552-66553 via svnmerge from Andrew MacIntyre <andymac@bullseye.apana.org.au> parents: 46477 diff changeset	83
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	84 double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	85 log1p(double x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	86 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	87 /* For x small, we use the following approach. Let y be the nearest
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	88 float to 1+x, then
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	89
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	90 1+x = y * (1 - (y-1-x)/y)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	91
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	92 so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	93 the second term is well approximated by (y-1-x)/y. If abs(x) >=
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	94 DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	95 then y-1-x will be exactly representable, and is computed exactly
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	96 by (y-1)-x.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	97
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	98 If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	99 round-to-nearest then this method is slightly dangerous: 1+x could
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	100 be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	101 case y-1-x will not be exactly representable any more and the
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	102 result can be off by many ulps. But this is easily fixed: for a
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	103 floating-point number \|x\| < DBL_EPSILON/2., the closest
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	104 floating-point number to log(1+x) is exactly x.
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	105 */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	106
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	107 double y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	108 if (fabs(x) < DBL_EPSILON/2.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	109 return x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	110 } else if (-0.5 <= x && x <= 1.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	111 /* WARNING: it's possible than an overeager compiler
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	112 will incorrectly optimize the following two lines
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	113 to the equivalent of "return log(1.+x)". If this
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	114 happens, then results from log1p will be inaccurate
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	115 for small x. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	116 y = 1.+x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	117 return log(y)-((y-1.)-x)/y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	118 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	119 /* NaNs and infinities should end up here */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	120 return log(1.+x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	121 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	122 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	123 #endif /* HAVE_LOG1P */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	124
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	125 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	126 * ====================================================
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	127 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	128 *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	129 * Developed at SunPro, a Sun Microsystems, Inc. business.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	130 * Permission to use, copy, modify, and distribute this
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	131 * software is freely granted, provided that this notice
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	132 * is preserved.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	133 * ====================================================
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	134 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	135
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	136 static const double ln2 = 6.93147180559945286227E-01;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	137 static const double two_pow_m28 = 3.7252902984619141E-09; /* 2*-28 /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	138 static const double two_pow_p28 = 268435456.0; /* 2*28 /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	139 static const double zero = 0.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	140
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	141 /* asinh(x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	142 * Method :
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	143 * Based on
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	144 * asinh(x) = sign(x) * log [ \|x\| + sqrt(x*x+1) ]
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	145 * we have
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	146 * asinh(x) := x if 1+x*x=1,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	147 * := sign(x)*(log(x)+ln2)) for large \|x\|, else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	148 * := sign(x)log(2\|x\|+1/(\|x\|+sqrt(xx+1))) if\|x\|>2, else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	149 * := sign(x)*log1p(\|x\| + x^2/(1 + sqrt(1+x^2)))
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	150 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	151
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	152 #ifndef HAVE_ASINH
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	153 double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	154 asinh(double x)
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	155 {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	156 double w;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	157 double absx = fabs(x);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	158
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	159 if (Py_IS_NAN(x) \|\| Py_IS_INFINITY(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	160 return x+x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	161 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	162 if (absx < two_pow_m28) { /* \|x\| < 2*-28 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	163 return x; /* return x inexact except 0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	164 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	165 if (absx > two_pow_p28) { /* \|x\| > 2*28 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	166 w = log(absx)+ln2;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	167 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	168 else if (absx > 2.0) { /* 2 < \|x\| < 2*28 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	169 w = log(2.0absx + 1.0 / (sqrt(xx + 1.0) + absx));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	170 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	171 else { /* 2*-28 <= \|x\| < 2= /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	172 double t = x*x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	173 w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	174 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	175 return copysign(w, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	176
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	177 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	178 #endif /* HAVE_ASINH */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	179
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	180 /* acosh(x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	181 * Method :
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	182 * Based on
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	183 * acosh(x) = log [ x + sqrt(x*x-1) ]
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	184 * we have
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	185 * acosh(x) := log(x)+ln2, if x is large; else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	186 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	187 * acosh(x) := log1p(t+sqrt(2.0t+tt)); where t=x-1.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	188 *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	189 * Special cases:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	190 * acosh(x) is NaN with signal if x<1.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	191 * acosh(NaN) is NaN without signal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	192 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	193
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	194 #ifndef HAVE_ACOSH
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	195 double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	196 acosh(double x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	197 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	198 if (Py_IS_NAN(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	199 return x+x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	200 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	201 if (x < 1.) { /* x < 1; return a signaling NaN */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	202 errno = EDOM;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	203 #ifdef Py_NAN
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	204 return Py_NAN;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	205 #else
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	206 return (x-x)/(x-x);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	207 #endif
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	208 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	209 else if (x >= two_pow_p28) { /* x > 2*28 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	210 if (Py_IS_INFINITY(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	211 return x+x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	212 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	213 return log(x)+ln2; /* acosh(huge)=log(2x) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	214 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	215 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	216 else if (x == 1.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	217 return 0.0; /* acosh(1) = 0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	218 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	219 else if (x > 2.) { /* 2 < x < 2*28 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	220 double t = x*x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	221 return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	222 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	223 else { /* 1 < x <= 2 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	224 double t = x - 1.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	225 return log1p(t + sqrt(2.0t + tt));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	226 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	227 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	228 #endif /* HAVE_ACOSH */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	229
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	230 /* atanh(x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	231 * Method :
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	232 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	233 * 2.For x>=0.5
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	234 * 1 2x x
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	235 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	236 * 2 1 - x 1 - x
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	237 *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	238 * For x<0.5
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	239 * atanh(x) = 0.5log1p(2x+2xx/(1-x))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	240 *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	241 * Special cases:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	242 * atanh(x) is NaN if \|x\| >= 1 with signal;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	243 * atanh(NaN) is that NaN with no signal;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	244 *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	245 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	246
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	247 #ifndef HAVE_ATANH
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	248 double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	249 atanh(double x)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	250 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	251 double absx;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	252 double t;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	253
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	254 if (Py_IS_NAN(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	255 return x+x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	256 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	257 absx = fabs(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	258 if (absx >= 1.) { /* \|x\| >= 1 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	259 errno = EDOM;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	260 #ifdef Py_NAN
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	261 return Py_NAN;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	262 #else
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	263 return x/zero;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	264 #endif
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	265 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	266 if (absx < two_pow_m28) { /* \|x\| < 2*-28 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	267 return x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	268 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	269 if (absx < 0.5) { /* \|x\| < 0.5 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	270 t = absx+absx;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	271 t = 0.5 * log1p(t + t*absx / (1.0 - absx));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	272 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	273 else { /* 0.5 <= \|x\| <= 1.0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	274 t = 0.5 * log1p((absx + absx) / (1.0 - absx));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	275 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 53240 diff changeset	276 return copysign(t, x);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	277 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: diff changeset	278 #endif /* HAVE_ATANH */

Mercurial > cpython-lru_cache-weakref

annotate Python/pymath.c @ 66978:aed2bbafa550 3.1