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

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

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

author	Radomir Dopieralski <devel@sheep.art.pl>
date	Tue, 03 Dec 2013 16:02:48 +0100
parents	ce771c2d0220
children

rev	line source
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1 /* Complex math module */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	2
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	3 /* much code borrowed from mathmodule.c */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	4
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	5 #include "Python.h"
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	6 #include "_math.h"
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	7 /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	8 float.h. We assume that FLT_RADIX is either 2 or 16. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	9 #include <float.h>
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	10
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	11 #if (FLT_RADIX != 2 && FLT_RADIX != 16)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	12 #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	13 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	14
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	15 #ifndef M_LN2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	16 #define M_LN2 (0.6931471805599453094) /* natural log of 2 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	17 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	18
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	19 #ifndef M_LN10
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	20 #define M_LN10 (2.302585092994045684) /* natural log of 10 */
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	21 #endif
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	22
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	23 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	24 CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	25 inverse trig and inverse hyperbolic trig functions. Its log is used in the
68585 bf94b6a73fc8 #11565: Fix several typos. Patch by Piotr Kasprzyk. Ezio Melotti <ezio.melotti@gmail.com> parents: 61467 diff changeset	26 evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unnecessary
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	27 overflow.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	28 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	29
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	30 #define CM_LARGE_DOUBLE (DBL_MAX/4.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	31 #define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	32 #define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	33 #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	34
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	35 /*
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	36 CM_SCALE_UP is an odd integer chosen such that multiplication by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	37 2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	38 CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	39 square roots accurately when the real and imaginary parts of the argument
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	40 are subnormal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	41 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	42
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	43 #if FLT_RADIX==2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	44 #define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	45 #elif FLT_RADIX==16
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	46 #define CM_SCALE_UP (4*DBL_MANT_DIG+1)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	47 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	48 #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	49
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	50 /* forward declarations */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	51 static Py_complex c_asinh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	52 static Py_complex c_atanh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	53 static Py_complex c_cosh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	54 static Py_complex c_sinh(Py_complex);
24280 1598a1e473e2 staticforward bites the dust. Jeremy Hylton <jeremy@alum.mit.edu> parents: 23832 diff changeset	55 static Py_complex c_sqrt(Py_complex);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	56 static Py_complex c_tanh(Py_complex);
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	57 static PyObject * math_error(void);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	58
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	59 /* Code to deal with special values (infinities, NaNs, etc.). */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	60
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	61 /* special_type takes a double and returns an integer code indicating
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	62 the type of the double as follows:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	63 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	64
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	65 enum special_types {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	66 ST_NINF, /* 0, negative infinity */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	67 ST_NEG, /* 1, negative finite number (nonzero) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	68 ST_NZERO, /* 2, -0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	69 ST_PZERO, /* 3, +0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	70 ST_POS, /* 4, positive finite number (nonzero) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	71 ST_PINF, /* 5, positive infinity */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	72 ST_NAN /* 6, Not a Number */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	73 };
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	74
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	75 static enum special_types
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	76 special_type(double d)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	77 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	78 if (Py_IS_FINITE(d)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	79 if (d != 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	80 if (copysign(1., d) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	81 return ST_POS;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	82 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	83 return ST_NEG;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	84 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	85 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	86 if (copysign(1., d) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	87 return ST_PZERO;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	88 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	89 return ST_NZERO;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	90 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	91 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	92 if (Py_IS_NAN(d))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	93 return ST_NAN;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	94 if (copysign(1., d) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	95 return ST_PINF;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	96 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	97 return ST_NINF;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	98 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	99
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	100 #define SPECIAL_VALUE(z, table) \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	101 if (!Py_IS_FINITE((z).real) \|\| !Py_IS_FINITE((z).imag)) { \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	102 errno = 0; \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	103 return table[special_type((z).real)] \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	104 [special_type((z).imag)]; \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	105 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	106
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	107 #define P Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	108 #define P14 0.25*Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	109 #define P12 0.5*Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	110 #define P34 0.75*Py_MATH_PI
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	111 #define INF Py_HUGE_VAL
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	112 #define N Py_NAN
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	113 #define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	114
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	115 /* First, the C functions that do the real work. Each of the c_*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	116 functions computes and returns the C99 Annex G recommended result
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	117 and also sets errno as follows: errno = 0 if no floating-point
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	118 exception is associated with the result; errno = EDOM if C99 Annex
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	119 G recommends raising divide-by-zero or invalid for this result; and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	120 errno = ERANGE where the overflow floating-point signal should be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	121 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	122 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	123
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	124 static Py_complex acos_special_values[7][7];
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	125
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	126 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	127 c_acos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	128 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	129 Py_complex s1, s2, r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	130
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	131 SPECIAL_VALUE(z, acos_special_values);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	132
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	133 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	134 /* avoid unnecessary overflow for large arguments */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	135 r.real = atan2(fabs(z.imag), z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	136 /* split into cases to make sure that the branch cut has the
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	137 correct continuity on systems with unsigned zeros */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	138 if (z.real < 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	139 r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	140 M_LN2*2., z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	141 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	142 r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	143 M_LN2*2., -z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	144 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	145 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	146 s1.real = 1.-z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	147 s1.imag = -z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	148 s1 = c_sqrt(s1);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	149 s2.real = 1.+z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	150 s2.imag = z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	151 s2 = c_sqrt(s2);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	152 r.real = 2.*atan2(s1.real, s2.real);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57866 diff changeset	153 r.imag = m_asinh(s2.reals1.imag - s2.imags1.real);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	154 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	155 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	156 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	157 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	158
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	159 PyDoc_STRVAR(c_acos_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	160 "acos(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	161 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	162 "Return the arc cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	163
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	164
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	165 static Py_complex acosh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	166
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	167 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	168 c_acosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	169 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	170 Py_complex s1, s2, r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	171
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	172 SPECIAL_VALUE(z, acosh_special_values);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	173
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	174 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	175 /* avoid unnecessary overflow for large arguments */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	176 r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	177 r.imag = atan2(z.imag, z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	178 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	179 s1.real = z.real - 1.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	180 s1.imag = z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	181 s1 = c_sqrt(s1);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	182 s2.real = z.real + 1.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	183 s2.imag = z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	184 s2 = c_sqrt(s2);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57866 diff changeset	185 r.real = m_asinh(s1.reals2.real + s1.imags2.imag);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	186 r.imag = 2.*atan2(s1.imag, s2.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	187 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	188 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	189 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	190 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	191
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	192 PyDoc_STRVAR(c_acosh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	193 "acosh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	194 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	195 "Return the hyperbolic arccosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	196
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	197
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	198 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	199 c_asin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	200 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	201 /* asin(z) = -i asinh(iz) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	202 Py_complex s, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	203 s.real = -z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	204 s.imag = z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	205 s = c_asinh(s);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	206 r.real = s.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	207 r.imag = -s.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	208 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	209 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	210
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	211 PyDoc_STRVAR(c_asin_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	212 "asin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	213 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	214 "Return the arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	215
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	216
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	217 static Py_complex asinh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	218
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	219 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	220 c_asinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	221 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	222 Py_complex s1, s2, r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	223
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	224 SPECIAL_VALUE(z, asinh_special_values);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	225
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	226 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	227 if (z.imag >= 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	228 r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	229 M_LN2*2., z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	230 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	231 r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	232 M_LN2*2., -z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	233 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	234 r.imag = atan2(z.imag, fabs(z.real));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	235 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	236 s1.real = 1.+z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	237 s1.imag = -z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	238 s1 = c_sqrt(s1);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	239 s2.real = 1.-z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	240 s2.imag = z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	241 s2 = c_sqrt(s2);
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57866 diff changeset	242 r.real = m_asinh(s1.reals2.imag-s2.reals1.imag);
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	243 r.imag = atan2(z.imag, s1.reals2.real-s1.imags2.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	244 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	245 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	246 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	247 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	248
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	249 PyDoc_STRVAR(c_asinh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	250 "asinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	251 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	252 "Return the hyperbolic arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	253
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	254
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	255 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	256 c_atan(Py_complex z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	257 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	258 /* atan(z) = -i atanh(iz) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	259 Py_complex s, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	260 s.real = -z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	261 s.imag = z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	262 s = c_atanh(s);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	263 r.real = s.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	264 r.imag = -s.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	265 return r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	266 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	267
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	268 /* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	269 C99 for atan2(0., 0.). */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	270 static double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	271 c_atan2(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	272 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	273 if (Py_IS_NAN(z.real) \|\| Py_IS_NAN(z.imag))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	274 return Py_NAN;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	275 if (Py_IS_INFINITY(z.imag)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	276 if (Py_IS_INFINITY(z.real)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	277 if (copysign(1., z.real) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	278 /* atan2(+-inf, +inf) == +-pi/4 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	279 return copysign(0.25*Py_MATH_PI, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	280 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	281 /* atan2(+-inf, -inf) == +-pi3/4 /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	282 return copysign(0.75*Py_MATH_PI, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	283 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	284 /* atan2(+-inf, x) == +-pi/2 for finite x */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	285 return copysign(0.5*Py_MATH_PI, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	286 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	287 if (Py_IS_INFINITY(z.real) \|\| z.imag == 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	288 if (copysign(1., z.real) == 1.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	289 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	290 return copysign(0., z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	291 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	292 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	293 return copysign(Py_MATH_PI, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	294 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	295 return atan2(z.imag, z.real);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	296 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	297
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	298 PyDoc_STRVAR(c_atan_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	299 "atan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	300 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	301 "Return the arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	302
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	303
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	304 static Py_complex atanh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	305
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	306 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	307 c_atanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	308 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	309 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	310 double ay, h;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	311
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	312 SPECIAL_VALUE(z, atanh_special_values);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	313
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	314 /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	315 if (z.real < 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	316 return c_neg(c_atanh(c_neg(z)));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	317 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	318
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	319 ay = fabs(z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	320 if (z.real > CM_SQRT_LARGE_DOUBLE \|\| ay > CM_SQRT_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	321 /*
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	322 if abs(z) is large then we use the approximation
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	323 atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	324 of z.imag)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	325 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	326 h = hypot(z.real/2., z.imag/2.); /* safe from overflow */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	327 r.real = z.real/4./h/h;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	328 /* the two negations in the next line cancel each other out
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	329 except when working with unsigned zeros: they're there to
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	330 ensure that the branch cut has the correct continuity on
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	331 systems that don't support signed zeros */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	332 r.imag = -copysign(Py_MATH_PI/2., -z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	333 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	334 } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	335 /* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	336 if (ay == 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	337 r.real = INF;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	338 r.imag = z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	339 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	340 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	341 r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	342 r.imag = copysign(atan2(2., -ay)/2, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	343 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	344 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	345 } else {
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57866 diff changeset	346 r.real = m_log1p(4.z.real/((1-z.real)(1-z.real) + ay*ay))/4.;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	347 r.imag = -atan2(-2.z.imag, (1-z.real)(1+z.real) - ay*ay)/2.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	348 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	349 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	350 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	351 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	352
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	353 PyDoc_STRVAR(c_atanh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	354 "atanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	355 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	356 "Return the hyperbolic arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	357
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	358
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	359 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	360 c_cos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	361 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	362 /* cos(z) = cosh(iz) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	363 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	364 r.real = -z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	365 r.imag = z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	366 r = c_cosh(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	367 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	368 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	369
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	370 PyDoc_STRVAR(c_cos_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	371 "cos(x)\n"
51918 ae22631a787c Merged revisions 70063 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48494 diff changeset	372 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	373 "Return the cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	374
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	375
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	376 /* cosh(infinity + iy) needs to be dealt with specially /
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	377 static Py_complex cosh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	378
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	379 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	380 c_cosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	381 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	382 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	383 double x_minus_one;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	384
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	385 /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	386 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	387 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	388 (z.imag != 0.)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	389 if (z.real > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	390 r.real = copysign(INF, cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	391 r.imag = copysign(INF, sin(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	392 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	393 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	394 r.real = copysign(INF, cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	395 r.imag = -copysign(INF, sin(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	396 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	397 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	398 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	399 r = cosh_special_values[special_type(z.real)]
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	400 [special_type(z.imag)];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	401 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	402 /* need to set errno = EDOM if y is +/- infinity and x is not
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	403 a NaN */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	404 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	405 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	406 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	407 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	408 return r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	409 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	410
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	411 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	412 /* deal correctly with cases where cosh(z.real) overflows but
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	413 cosh(z) does not. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	414 x_minus_one = z.real - copysign(1., z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	415 r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	416 r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	417 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	418 r.real = cos(z.imag) * cosh(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	419 r.imag = sin(z.imag) * sinh(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	420 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	421 /* detect overflow, and set errno accordingly */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	422 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	423 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	424 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	425 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	426 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	427 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	428
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	429 PyDoc_STRVAR(c_cosh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	430 "cosh(x)\n"
51918 ae22631a787c Merged revisions 70063 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48494 diff changeset	431 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	432 "Return the hyperbolic cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	433
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	434
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	435 /* exp(infinity + iy) and exp(-infinity + iy) need special treatment for
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	436 finite y */
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	437 static Py_complex exp_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	438
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	439 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	440 c_exp(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	441 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	442 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	443 double l;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	444
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	445 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	446 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	447 && (z.imag != 0.)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	448 if (z.real > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	449 r.real = copysign(INF, cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	450 r.imag = copysign(INF, sin(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	451 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	452 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	453 r.real = copysign(0., cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	454 r.imag = copysign(0., sin(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	455 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	456 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	457 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	458 r = exp_special_values[special_type(z.real)]
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	459 [special_type(z.imag)];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	460 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	461 /* need to set errno = EDOM if y is +/- infinity and x is not
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	462 a NaN and not -infinity */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	463 if (Py_IS_INFINITY(z.imag) &&
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	464 (Py_IS_FINITE(z.real) \|\|
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	465 (Py_IS_INFINITY(z.real) && z.real > 0)))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	466 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	467 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	468 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	469 return r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	470 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	471
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	472 if (z.real > CM_LOG_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	473 l = exp(z.real-1.);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	474 r.real = lcos(z.imag)Py_MATH_E;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	475 r.imag = lsin(z.imag)Py_MATH_E;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	476 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	477 l = exp(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	478 r.real = l*cos(z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	479 r.imag = l*sin(z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	480 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	481 /* detect overflow, and set errno accordingly */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	482 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	483 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	484 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	485 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	486 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	487 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	488
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	489 PyDoc_STRVAR(c_exp_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	490 "exp(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	491 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	492 "Return the exponential value e**x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	493
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	494
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	495 static Py_complex log_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	496
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	497 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	498 c_log(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	499 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	500 /*
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	501 The usual formula for the real part is log(hypot(z.real, z.imag)).
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	502 There are four situations where this formula is potentially
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	503 problematic:
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	504
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	505 (1) the absolute value of z is subnormal. Then hypot is subnormal,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	506 so has fewer than the usual number of bits of accuracy, hence may
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	507 have large relative error. This then gives a large absolute error
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	508 in the log. This can be solved by rescaling z by a suitable power
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	509 of 2.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	510
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	511 (2) the absolute value of z is greater than DBL_MAX (e.g. when both
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	512 z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	513 Again, rescaling solves this.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	514
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	515 (3) the absolute value of z is close to 1. In this case it's
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	516 difficult to achieve good accuracy, at least in part because a
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	517 change of 1ulp in the real or imaginary part of z can result in a
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	518 change of billions of ulps in the correctly rounded answer.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	519
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	520 (4) z = 0. The simplest thing to do here is to call the
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	521 floating-point log with an argument of 0, and let its behaviour
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	522 (returning -infinity, signaling a floating-point exception, setting
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	523 errno, or whatever) determine that of c_log. So the usual formula
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	524 is fine here.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	525
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	526 */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	527
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	528 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	529 double ax, ay, am, an, h;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	530
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	531 SPECIAL_VALUE(z, log_special_values);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	532
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	533 ax = fabs(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	534 ay = fabs(z.imag);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	535
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	536 if (ax > CM_LARGE_DOUBLE \|\| ay > CM_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	537 r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	538 } else if (ax < DBL_MIN && ay < DBL_MIN) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	539 if (ax > 0. \|\| ay > 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	540 /* catch cases where hypot(ax, ay) is subnormal */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	541 r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	542 ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	543 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	544 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	545 /* log(+/-0. +/- 0i) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	546 r.real = -INF;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	547 r.imag = atan2(z.imag, z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	548 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	549 return r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	550 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	551 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	552 h = hypot(ax, ay);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	553 if (0.71 <= h && h <= 1.73) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	554 am = ax > ay ? ax : ay; /* max(ax, ay) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	555 an = ax > ay ? ay : ax; /* min(ax, ay) */
61466 cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 57866 diff changeset	556 r.real = m_log1p((am-1)(am+1)+anan)/2.;
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	557 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	558 r.real = log(h);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	559 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	560 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	561 r.imag = atan2(z.imag, z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	562 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	563 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	564 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	565
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	566
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	567 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	568 c_log10(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	569 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	570 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	571 int errno_save;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	572
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	573 r = c_log(z);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	574 errno_save = errno; /* just in case the divisions affect errno */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	575 r.real = r.real / M_LN10;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	576 r.imag = r.imag / M_LN10;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	577 errno = errno_save;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	578 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	579 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	580
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	581 PyDoc_STRVAR(c_log10_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	582 "log10(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	583 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	584 "Return the base-10 logarithm of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	585
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	586
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	587 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	588 c_sin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	589 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	590 /* sin(z) = -i sin(iz) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	591 Py_complex s, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	592 s.real = -z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	593 s.imag = z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	594 s = c_sinh(s);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	595 r.real = s.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	596 r.imag = -s.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	597 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	598 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	599
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	600 PyDoc_STRVAR(c_sin_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	601 "sin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	602 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	603 "Return the sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	604
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	605
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	606 /* sinh(infinity + iy) needs to be dealt with specially /
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	607 static Py_complex sinh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	608
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	609 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	610 c_sinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	611 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	612 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	613 double x_minus_one;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	614
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	615 /* special treatment for sinh(+/-inf + iy) if y is finite and
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	616 nonzero */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	617 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	618 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	619 && (z.imag != 0.)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	620 if (z.real > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	621 r.real = copysign(INF, cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	622 r.imag = copysign(INF, sin(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	623 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	624 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	625 r.real = -copysign(INF, cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	626 r.imag = copysign(INF, sin(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	627 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	628 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	629 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	630 r = sinh_special_values[special_type(z.real)]
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	631 [special_type(z.imag)];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	632 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	633 /* need to set errno = EDOM if y is +/- infinity and x is not
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	634 a NaN */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	635 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	636 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	637 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	638 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	639 return r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	640 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	641
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	642 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	643 x_minus_one = z.real - copysign(1., z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	644 r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	645 r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	646 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	647 r.real = cos(z.imag) * sinh(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	648 r.imag = sin(z.imag) * cosh(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	649 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	650 /* detect overflow, and set errno accordingly */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	651 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	652 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	653 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	654 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	655 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	656 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	657
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	658 PyDoc_STRVAR(c_sinh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	659 "sinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	660 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	661 "Return the hyperbolic sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	662
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	663
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	664 static Py_complex sqrt_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	665
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	666 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	667 c_sqrt(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	668 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	669 /*
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	670 Method: use symmetries to reduce to the case when x = z.real and y
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	671 = z.imag are nonnegative. Then the real part of the result is
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	672 given by
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	673
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	674 s = sqrt((x + hypot(x, y))/2)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	675
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	676 and the imaginary part is
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	677
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	678 d = (y/2)/s
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	679
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	680 If either x or y is very large then there's a risk of overflow in
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	681 computation of the expression x + hypot(x, y). We can avoid this
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	682 by rewriting the formula for s as:
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	683
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	684 s = 2*sqrt(x/8 + hypot(x/8, y/8))
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	685
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	686 This costs us two extra multiplications/divisions, but avoids the
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	687 overhead of checking for x and y large.
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	688
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	689 If both x and y are subnormal then hypot(x, y) may also be
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	690 subnormal, so will lack full precision. We solve this by rescaling
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	691 x and y by a sufficiently large power of 2 to ensure that x and y
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	692 are normal.
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	693 */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	694
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	695
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	696 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	697 double s,d;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	698 double ax, ay;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	699
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	700 SPECIAL_VALUE(z, sqrt_special_values);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	701
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	702 if (z.real == 0. && z.imag == 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	703 r.real = 0.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	704 r.imag = z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	705 return r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	706 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	707
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	708 ax = fabs(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	709 ay = fabs(z.imag);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	710
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	711 if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. \|\| ay > 0.)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	712 /* here we catch cases where hypot(ax, ay) is subnormal */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	713 ax = ldexp(ax, CM_SCALE_UP);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	714 s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	715 CM_SCALE_DOWN);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	716 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	717 ax /= 8.;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	718 s = 2.*sqrt(ax + hypot(ax, ay/8.));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	719 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	720 d = ay/(2.*s);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	721
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	722 if (z.real >= 0.) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	723 r.real = s;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	724 r.imag = copysign(d, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	725 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	726 r.real = d;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	727 r.imag = copysign(s, z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	728 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	729 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	730 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	731 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	732
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	733 PyDoc_STRVAR(c_sqrt_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	734 "sqrt(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	735 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	736 "Return the square root of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	737
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	738
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	739 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	740 c_tan(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	741 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	742 /* tan(z) = -i tanh(iz) */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	743 Py_complex s, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	744 s.real = -z.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	745 s.imag = z.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	746 s = c_tanh(s);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	747 r.real = s.imag;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	748 r.imag = -s.real;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	749 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	750 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	751
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	752 PyDoc_STRVAR(c_tan_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	753 "tan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	754 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	755 "Return the tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	756
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	757
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	758 /* tanh(infinity + iy) needs to be dealt with specially /
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	759 static Py_complex tanh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	760
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	761 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	762 c_tanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	763 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	764 /* Formula:
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	765
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	766 tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	767 (1+tan(y)^2 tanh(x)^2)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	768
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	769 To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	770 as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	771 by 4 exp(-2*x) instead, to avoid possible overflow in the
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	772 computation of cosh(x).
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	773
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	774 */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	775
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	776 Py_complex r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	777 double tx, ty, cx, txty, denom;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	778
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	779 /* special treatment for tanh(+/-inf + iy) if y is finite and
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	780 nonzero */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	781 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	782 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	783 && (z.imag != 0.)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	784 if (z.real > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	785 r.real = 1.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	786 r.imag = copysign(0.,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	787 2.sin(z.imag)cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	788 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	789 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	790 r.real = -1.0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	791 r.imag = copysign(0.,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	792 2.sin(z.imag)cos(z.imag));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	793 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	794 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	795 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	796 r = tanh_special_values[special_type(z.real)]
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	797 [special_type(z.imag)];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	798 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	799 /* need to set errno = EDOM if z.imag is +/-infinity and
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	800 z.real is finite */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	801 if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	802 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	803 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	804 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	805 return r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	806 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	807
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	808 /* danger of overflow in 2.z.imag !/
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	809 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	810 r.real = copysign(1., z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	811 r.imag = 4.sin(z.imag)cos(z.imag)exp(-2.fabs(z.real));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	812 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	813 tx = tanh(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	814 ty = tan(z.imag);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	815 cx = 1./cosh(z.real);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	816 txty = tx*ty;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	817 denom = 1. + txty*txty;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	818 r.real = tx(1.+tyty)/denom;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	819 r.imag = ((ty/denom)cx)cx;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	820 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	821 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	822 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	823 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	824
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	825 PyDoc_STRVAR(c_tanh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	826 "tanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	827 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	828 "Return the hyperbolic tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	829
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	830
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	831 static PyObject *
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	832 cmath_log(PyObject self, PyObject args)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	833 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	834 Py_complex x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	835 Py_complex y;
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	836
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	837 if (!PyArg_ParseTuple(args, "D\|D", &x, &y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	838 return NULL;
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	839
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	840 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	841 PyFPE_START_PROTECT("complex function", return 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	842 x = c_log(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	843 if (PyTuple_GET_SIZE(args) == 2) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	844 y = c_log(y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	845 x = c_quot(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	846 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	847 PyFPE_END_PROTECT(x)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	848 if (errno != 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	849 return math_error();
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	850 return PyComplex_FromCComplex(x);
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	851 }
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	852
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	853 PyDoc_STRVAR(cmath_log_doc,
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	854 "log(x[, base]) -> the logarithm of x to the given base.\n\
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	855 If the base not specified, returns the natural logarithm (base e) of x.");
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	856
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	857
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	858 /* And now the glue to make them available from Python: */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	859
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	860 static PyObject *
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13493 diff changeset	861 math_error(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	862 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	863 if (errno == EDOM)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	864 PyErr_SetString(PyExc_ValueError, "math domain error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	865 else if (errno == ERANGE)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	866 PyErr_SetString(PyExc_OverflowError, "math range error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	867 else /* Unexpected math error */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	868 PyErr_SetFromErrno(PyExc_ValueError);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	869 return NULL;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	870 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	871
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	872 static PyObject *
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	873 math_1(PyObject args, Py_complex (func)(Py_complex))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	874 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	875 Py_complex x,r ;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	876 if (!PyArg_ParseTuple(args, "D", &x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	877 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	878 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	879 PyFPE_START_PROTECT("complex function", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	880 r = (*func)(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	881 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	882 if (errno == EDOM) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	883 PyErr_SetString(PyExc_ValueError, "math domain error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	884 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	885 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	886 else if (errno == ERANGE) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	887 PyErr_SetString(PyExc_OverflowError, "math range error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	888 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	889 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	890 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	891 return PyComplex_FromCComplex(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	892 }
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	893 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	894
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	895 #define FUNC1(stubname, func) \
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	896 static PyObject * stubname(PyObject self, PyObject args) { \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	897 return math_1(args, func); \
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	898 }
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	899
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	900 FUNC1(cmath_acos, c_acos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	901 FUNC1(cmath_acosh, c_acosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	902 FUNC1(cmath_asin, c_asin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	903 FUNC1(cmath_asinh, c_asinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	904 FUNC1(cmath_atan, c_atan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	905 FUNC1(cmath_atanh, c_atanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	906 FUNC1(cmath_cos, c_cos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	907 FUNC1(cmath_cosh, c_cosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	908 FUNC1(cmath_exp, c_exp)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	909 FUNC1(cmath_log10, c_log10)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	910 FUNC1(cmath_sin, c_sin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	911 FUNC1(cmath_sinh, c_sinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	912 FUNC1(cmath_sqrt, c_sqrt)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	913 FUNC1(cmath_tan, c_tan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	914 FUNC1(cmath_tanh, c_tanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	915
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	916 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	917 cmath_phase(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	918 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	919 Py_complex z;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	920 double phi;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	921 if (!PyArg_ParseTuple(args, "D:phase", &z))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	922 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	923 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	924 PyFPE_START_PROTECT("arg function", return 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	925 phi = c_atan2(z);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	926 PyFPE_END_PROTECT(phi)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	927 if (errno != 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	928 return math_error();
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	929 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	930 return PyFloat_FromDouble(phi);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	931 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	932
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	933 PyDoc_STRVAR(cmath_phase_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	934 "phase(z) -> float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	935 Return argument, also known as the phase angle, of a complex.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	936
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	937 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	938 cmath_polar(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	939 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	940 Py_complex z;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	941 double r, phi;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	942 if (!PyArg_ParseTuple(args, "D:polar", &z))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	943 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	944 PyFPE_START_PROTECT("polar function", return 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	945 phi = c_atan2(z); /* should not cause any exception */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	946 r = c_abs(z); /* sets errno to ERANGE on overflow; otherwise 0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	947 PyFPE_END_PROTECT(r)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	948 if (errno != 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	949 return math_error();
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	950 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	951 return Py_BuildValue("dd", r, phi);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	952 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	953
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	954 PyDoc_STRVAR(cmath_polar_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	955 "polar(z) -> r: float, phi: float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	956 Convert a complex from rectangular coordinates to polar coordinates. r is\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	957 the distance from 0 and phi the phase angle.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	958
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	959 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	960 rect() isn't covered by the C99 standard, but it's not too hard to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	961 figure out 'spirit of C99' rules for special value handing:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	962
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	963 rect(x, t) should behave like exp(log(x) + it) for positive-signed x
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	964 rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	965 rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	966 gives nan +- i0 with the sign of the imaginary part unspecified.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	967
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	968 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	969
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	970 static Py_complex rect_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	971
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	972 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	973 cmath_rect(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	974 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	975 Py_complex z;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	976 double r, phi;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	977 if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	978 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	979 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	980 PyFPE_START_PROTECT("rect function", return 0)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	981
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	982 /* deal with special values */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	983 if (!Py_IS_FINITE(r) \|\| !Py_IS_FINITE(phi)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	984 /* if r is +/-infinity and phi is finite but nonzero then
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	985 result is (+-INF +-INF i), but we need to compute cos(phi)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	986 and sin(phi) to figure out the signs. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	987 if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	988 && (phi != 0.))) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	989 if (r > 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	990 z.real = copysign(INF, cos(phi));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	991 z.imag = copysign(INF, sin(phi));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	992 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	993 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	994 z.real = -copysign(INF, cos(phi));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	995 z.imag = -copysign(INF, sin(phi));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	996 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	997 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	998 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	999 z = rect_special_values[special_type(r)]
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1000 [special_type(phi)];
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1001 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1002 /* need to set errno = EDOM if r is a nonzero number and phi
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1003 is infinite */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1004 if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1005 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1006 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1007 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1008 }
84736 ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1009 else if (phi == 0.0) {
ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1010 /* Workaround for buggy results with phi=-0.0 on OS X 10.8. See
ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1011 bugs.python.org/issue18513. */
ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1012 z.real = r;
ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1013 z.imag = r * phi;
ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1014 errno = 0;
ce771c2d0220 Issue #18513: Add workaround for OS X 10.8 cexp bug that leads to wrong cmath.rect(0.0,-0.0) results. Mark Dickinson <dickinsm@gmail.com> parents: 68586 diff changeset	1015 }
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1016 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1017 z.real = r * cos(phi);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1018 z.imag = r * sin(phi);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1019 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1020 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1021
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1022 PyFPE_END_PROTECT(z)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1023 if (errno != 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1024 return math_error();
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1025 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1026 return PyComplex_FromCComplex(z);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1027 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1028
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1029 PyDoc_STRVAR(cmath_rect_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1030 "rect(r, phi) -> z: complex\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1031 Convert from polar coordinates to rectangular coordinates.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1032
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1033 static PyObject *
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1034 cmath_isfinite(PyObject self, PyObject args)
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1035 {
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1036 Py_complex z;
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1037 if (!PyArg_ParseTuple(args, "D:isfinite", &z))
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1038 return NULL;
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1039 return PyBool_FromLong(Py_IS_FINITE(z.real) && Py_IS_FINITE(z.imag));
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1040 }
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1041
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1042 PyDoc_STRVAR(cmath_isfinite_doc,
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1043 "isfinite(z) -> bool\n\
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1044 Return True if both the real and imaginary parts of z are finite, else False.");
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1045
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1046 static PyObject *
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1047 cmath_isnan(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1048 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1049 Py_complex z;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1050 if (!PyArg_ParseTuple(args, "D:isnan", &z))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1051 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1052 return PyBool_FromLong(Py_IS_NAN(z.real) \|\| Py_IS_NAN(z.imag));
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1053 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1054
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1055 PyDoc_STRVAR(cmath_isnan_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1056 "isnan(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1057 Checks if the real or imaginary part of z not a number (NaN)");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1058
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1059 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1060 cmath_isinf(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1061 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1062 Py_complex z;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1063 if (!PyArg_ParseTuple(args, "D:isnan", &z))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1064 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1065 return PyBool_FromLong(Py_IS_INFINITY(z.real) \|\|
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1066 Py_IS_INFINITY(z.imag));
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1067 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1068
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1069 PyDoc_STRVAR(cmath_isinf_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1070 "isinf(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1071 Checks if the real or imaginary part of z is infinite.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1072
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1073
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	1074 PyDoc_STRVAR(module_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1075 "This module is always available. It provides access to mathematical\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	1076 "functions for complex numbers.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1077
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	1078 static PyMethodDef cmath_methods[] = {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1079 {"acos", cmath_acos, METH_VARARGS, c_acos_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1080 {"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1081 {"asin", cmath_asin, METH_VARARGS, c_asin_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1082 {"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1083 {"atan", cmath_atan, METH_VARARGS, c_atan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1084 {"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1085 {"cos", cmath_cos, METH_VARARGS, c_cos_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1086 {"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1087 {"exp", cmath_exp, METH_VARARGS, c_exp_doc},
62968 53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite. Mark Dickinson <dickinsm@gmail.com> parents: 61466 diff changeset	1088 {"isfinite", cmath_isfinite, METH_VARARGS, cmath_isfinite_doc},
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1089 {"isinf", cmath_isinf, METH_VARARGS, cmath_isinf_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1090 {"isnan", cmath_isnan, METH_VARARGS, cmath_isnan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1091 {"log", cmath_log, METH_VARARGS, cmath_log_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1092 {"log10", cmath_log10, METH_VARARGS, c_log10_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1093 {"phase", cmath_phase, METH_VARARGS, cmath_phase_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1094 {"polar", cmath_polar, METH_VARARGS, cmath_polar_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1095 {"rect", cmath_rect, METH_VARARGS, cmath_rect_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1096 {"sin", cmath_sin, METH_VARARGS, c_sin_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1097 {"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1098 {"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1099 {"tan", cmath_tan, METH_VARARGS, c_tan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1100 {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1101 {NULL, NULL} /* sentinel */
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1102 };
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1103
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1104
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1105 static struct PyModuleDef cmathmodule = {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1106 PyModuleDef_HEAD_INIT,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1107 "cmath",
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1108 module_doc,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1109 -1,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1110 cmath_methods,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1111 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1112 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1113 NULL,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1114 NULL
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1115 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1116
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 24280 diff changeset	1117 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1118 PyInit_cmath(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1119 {
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1120 PyObject *m;
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1121
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1122 m = PyModule_Create(&cmathmodule);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1123 if (m == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1124 return NULL;
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1125
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1126 PyModule_AddObject(m, "pi",
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1127 PyFloat_FromDouble(Py_MATH_PI));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1128 PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
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	1129
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1130 /* initialize special value tables */
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	1131
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	1132 #define INIT_SPECIAL_VALUES(NAME, BODY) { Py_complex* p = (Py_complex*)NAME; BODY }
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	1133 #define C(REAL, IMAG) p->real = REAL; p->imag = IMAG; ++p;
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	1134
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1135 INIT_SPECIAL_VALUES(acos_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1136 C(P34,INF) C(P,INF) C(P,INF) C(P,-INF) C(P,-INF) C(P34,-INF) C(N,INF)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1137 C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1138 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1139 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1140 C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1141 C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1142 C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1143 })
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	1144
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1145 INIT_SPECIAL_VALUES(acosh_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1146 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1147 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1148 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1149 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1150 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1151 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1152 C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1153 })
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	1154
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1155 INIT_SPECIAL_VALUES(asinh_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1156 C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1157 C(-INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1158 C(-INF,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1159 C(INF,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1160 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1161 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1162 C(INF,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(INF,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1163 })
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	1164
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1165 INIT_SPECIAL_VALUES(atanh_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1166 C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1167 C(-0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-0.,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1168 C(-0.,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-0.,P12) C(-0.,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1169 C(0.,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,P12) C(0.,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1170 C(0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(0.,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1171 C(0.,-P12) C(0.,-P12) C(0.,-P12) C(0.,P12) C(0.,P12) C(0.,P12) C(0.,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1172 C(0.,-P12) C(N,N) C(N,N) C(N,N) C(N,N) C(0.,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1173 })
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	1174
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1175 INIT_SPECIAL_VALUES(cosh_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1176 C(INF,N) C(U,U) C(INF,0.) C(INF,-0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1177 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1178 C(N,0.) C(U,U) C(1.,0.) C(1.,-0.) C(U,U) C(N,0.) C(N,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1179 C(N,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,0.) C(N,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1180 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1181 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1182 C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1183 })
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	1184
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1185 INIT_SPECIAL_VALUES(exp_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1186 C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1187 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1188 C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1189 C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1190 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1191 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1192 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1193 })
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	1194
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1195 INIT_SPECIAL_VALUES(log_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1196 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1197 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1198 C(INF,-P12) C(U,U) C(-INF,-P) C(-INF,P) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1199 C(INF,-P12) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1200 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1201 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1202 C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1203 })
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	1204
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1205 INIT_SPECIAL_VALUES(sinh_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1206 C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1207 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1208 C(0.,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(0.,N) C(0.,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1209 C(0.,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,N) C(0.,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1210 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1211 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1212 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1213 })
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	1214
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1215 INIT_SPECIAL_VALUES(sqrt_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1216 C(INF,-INF) C(0.,-INF) C(0.,-INF) C(0.,INF) C(0.,INF) C(INF,INF) C(N,INF)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1217 C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1218 C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1219 C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1220 C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1221 C(INF,-INF) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,INF) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1222 C(INF,-INF) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,INF) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1223 })
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	1224
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1225 INIT_SPECIAL_VALUES(tanh_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1226 C(-1.,0.) C(U,U) C(-1.,-0.) C(-1.,0.) C(U,U) C(-1.,0.) C(-1.,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1227 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1228 C(N,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1229 C(N,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1230 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1231 C(1.,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(1.,0.) C(1.,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1232 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1233 })
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	1234
61467 f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1235 INIT_SPECIAL_VALUES(rect_special_values, {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1236 C(INF,N) C(U,U) C(-INF,0.) C(-INF,-0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1237 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1238 C(0.,0.) C(U,U) C(-0.,0.) C(-0.,-0.) C(U,U) C(0.,0.) C(0.,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1239 C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1240 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1241 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1242 C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1243 })
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from Antoine Pitrou <solipsis@pitrou.net> parents: 55541 diff changeset	1244 return m;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1245 }

Mercurial > cpython-lru_cache-weakref

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