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

annotate Modules/cmathmodule.c @ 58689:514b56efd89a 3.1

Merged revisions 77962 via svnmerge from svn+ssh://pythondev@svn.python.org/python/branches/py3k ................ r77962 | r.david.murray | 2010-02-04 11:41:57 -0500 (Thu, 04 Feb 2010) | 17 lines Merged revisions 77943,77959-77960 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r77943 | r.david.murray | 2010-02-03 08:36:23 -0500 (Wed, 03 Feb 2010) | 2 lines Explicitly mention the default value for formatdate's usegmt parameter. ........ r77959 | nick.coghlan | 2010-02-04 07:43:58 -0500 (Thu, 04 Feb 2010) | 1 line Issue 6760: Clarify args handling for subprocess.Popen. Patch by Chris Rebert ........ r77960 | r.david.murray | 2010-02-04 11:33:31 -0500 (Thu, 04 Feb 2010) | 2 lines Add Chris Rebert to ACKS for issue 6760 Popen doc improvements. ........ ................

author	R. David Murray <rdmurray@bitdance.com>
date	Thu, 04 Feb 2010 16:44:31 +0000
parents	8848c49ed5f5
children	f197407bdba2 9751ddcc1882

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"
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	6 /* 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	7 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	8 #include <float.h>
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	9
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	10 #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	11 #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	12 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	13
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	14 #ifndef M_LN2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	15 #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	16 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	17
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	18 #ifndef M_LN10
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	19 #define M_LN10 (2.302585092994045684) /* natural log of 10 */
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	20 #endif
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	21
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	22 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	23 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	24 inverse trig and inverse hyperbolic trig functions. Its log is used in the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	25 evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unecessary
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	26 overflow.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	27 */
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 #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	30 #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	31 #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	32 #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	33
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	34 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	35 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	36 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	37 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	38 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	39 are subnormal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	40 */
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 #if FLT_RADIX==2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	43 #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	44 #elif FLT_RADIX==16
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	45 #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	46 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	47 #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	48
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	49 /* forward declarations */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	50 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	51 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	52 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	53 static Py_complex c_sinh(Py_complex);
24280 1598a1e473e2 staticforward bites the dust. Jeremy Hylton <jeremy@alum.mit.edu> parents: 23832 diff changeset	54 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	55 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	56 static PyObject * math_error(void);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	57
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	58 /* 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	59
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	60 /* 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	61 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	62 */
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 enum special_types {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	65 ST_NINF, /* 0, negative infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	66 ST_NEG, /* 1, negative finite number (nonzero) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	67 ST_NZERO, /* 2, -0. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	68 ST_PZERO, /* 3, +0. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	69 ST_POS, /* 4, positive finite number (nonzero) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	70 ST_PINF, /* 5, positive infinity */
55541 8848c49ed5f5 Merged revisions 74305 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 51918 diff changeset	71 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	72 };
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 static enum special_types
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	75 special_type(double d)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	76 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	77 if (Py_IS_FINITE(d)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	78 if (d != 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	79 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	80 return ST_POS;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	81 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	82 return ST_NEG;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	83 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	84 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	85 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	86 return ST_PZERO;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	87 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	88 return ST_NZERO;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	89 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	90 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	91 if (Py_IS_NAN(d))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	92 return ST_NAN;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	93 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	94 return ST_PINF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	95 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	96 return ST_NINF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	97 }
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 #define SPECIAL_VALUE(z, table) \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	100 if (!Py_IS_FINITE((z).real) \|\| !Py_IS_FINITE((z).imag)) { \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	101 errno = 0; \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	102 return table[special_type((z).real)] \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	103 [special_type((z).imag)]; \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	104 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	105
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	106 #define P Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	107 #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	108 #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	109 #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	110 #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	111 #define N Py_NAN
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	112 #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	113
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	114 /* 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	115 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	116 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	117 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	118 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	119 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	120 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	121 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	122
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	123 static Py_complex acos_special_values[7][7];
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	124
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	125 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	126 c_acos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	127 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	128 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	129
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	130 SPECIAL_VALUE(z, acos_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	131
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	132 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	133 /* avoid unnecessary overflow for large arguments */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	134 r.real = atan2(fabs(z.imag), z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	135 /* split into cases to make sure that the branch cut has the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	136 correct continuity on systems with unsigned zeros */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	137 if (z.real < 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	138 r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	139 M_LN2*2., z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	140 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	141 r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	142 M_LN2*2., -z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	143 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	144 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	145 s1.real = 1.-z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	146 s1.imag = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	147 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	148 s2.real = 1.+z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	149 s2.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	150 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	151 r.real = 2.*atan2(s1.real, s2.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	152 r.imag = asinh(s2.reals1.imag - s2.imags1.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	153 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	154 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	155 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	156 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	157
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	158 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	159 "acos(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	160 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	161 "Return the arc cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	162
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	163
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	164 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	165
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	166 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	167 c_acosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	168 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	169 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	170
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	171 SPECIAL_VALUE(z, acosh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	172
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	173 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	174 /* avoid unnecessary overflow for large arguments */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	175 r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	176 r.imag = atan2(z.imag, z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	177 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	178 s1.real = z.real - 1.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	179 s1.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	180 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	181 s2.real = z.real + 1.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	182 s2.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	183 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	184 r.real = asinh(s1.reals2.real + s1.imags2.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	185 r.imag = 2.*atan2(s1.imag, s2.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	186 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	187 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	188 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	189 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	190
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	191 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	192 "acosh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	193 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	194 "Return the hyperbolic arccosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	195
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	196
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	197 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	198 c_asin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	199 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	200 /* asin(z) = -i asinh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	201 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	202 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	203 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	204 s = c_asinh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	205 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	206 r.imag = -s.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	207 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	208 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	209
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	210 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	211 "asin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	212 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	213 "Return the arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	214
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	215
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	216 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	217
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	218 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	219 c_asinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	220 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	221 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	222
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	223 SPECIAL_VALUE(z, asinh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	224
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	225 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	226 if (z.imag >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	227 r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	228 M_LN2*2., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	229 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	230 r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	231 M_LN2*2., -z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	232 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	233 r.imag = atan2(z.imag, fabs(z.real));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	234 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	235 s1.real = 1.+z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	236 s1.imag = -z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	237 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	238 s2.real = 1.-z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	239 s2.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	240 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	241 r.real = asinh(s1.reals2.imag-s2.reals1.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	242 r.imag = atan2(z.imag, s1.reals2.real-s1.imags2.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	243 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	244 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	245 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	246 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	247
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	248 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	249 "asinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	250 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	251 "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	252
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	253
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	254 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	255 c_atan(Py_complex z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	256 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	257 /* atan(z) = -i atanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	258 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	259 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	260 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	261 s = c_atanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	262 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	263 r.imag = -s.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	264 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	265 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	266
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	267 /* 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	268 C99 for atan2(0., 0.). */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	269 static double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	270 c_atan2(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	271 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	272 if (Py_IS_NAN(z.real) \|\| Py_IS_NAN(z.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	273 return Py_NAN;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	274 if (Py_IS_INFINITY(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	275 if (Py_IS_INFINITY(z.real)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	276 if (copysign(1., z.real) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	277 /* atan2(+-inf, +inf) == +-pi/4 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	278 return copysign(0.25*Py_MATH_PI, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	279 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	280 /* atan2(+-inf, -inf) == +-pi3/4 /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	281 return copysign(0.75*Py_MATH_PI, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	282 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	283 /* atan2(+-inf, x) == +-pi/2 for finite x */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	284 return copysign(0.5*Py_MATH_PI, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	285 }
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	286 if (Py_IS_INFINITY(z.real) \|\| z.imag == 0.) {
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	287 if (copysign(1., z.real) == 1.)
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	288 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	289 return copysign(0., z.imag);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	290 else
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	291 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	292 return copysign(Py_MATH_PI, z.imag);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	293 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	294 return atan2(z.imag, z.real);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	295 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	296
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	297 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	298 "atan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	299 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	300 "Return the arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	301
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	302
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	303 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	304
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	305 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	306 c_atanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	307 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	308 Py_complex r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	309 double ay, h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	310
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	311 SPECIAL_VALUE(z, atanh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	312
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	313 /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	314 if (z.real < 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	315 return c_neg(c_atanh(c_neg(z)));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	316 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	317
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	318 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	319 if (z.real > CM_SQRT_LARGE_DOUBLE \|\| ay > CM_SQRT_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	320 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	321 if abs(z) is large then we use the approximation
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	322 atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	323 of z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	324 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	325 h = hypot(z.real/2., z.imag/2.); /* safe from overflow */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	326 r.real = z.real/4./h/h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	327 /* the two negations in the next line cancel each other out
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	328 except when working with unsigned zeros: they're there to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	329 ensure that the branch cut has the correct continuity on
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	330 systems that don't support signed zeros */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	331 r.imag = -copysign(Py_MATH_PI/2., -z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	332 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	333 } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	334 /* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	335 if (ay == 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	336 r.real = INF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	337 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	338 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	339 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	340 r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	341 r.imag = copysign(atan2(2., -ay)/2, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	342 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	343 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	344 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	345 r.real = log1p(4.z.real/((1-z.real)(1-z.real) + ay*ay))/4.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	346 r.imag = -atan2(-2.z.imag, (1-z.real)(1+z.real) - ay*ay)/2.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	347 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	348 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	349 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	350 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	351
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	352 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	353 "atanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	354 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	355 "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	356
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	357
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	358 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	359 c_cos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	360 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	361 /* cos(z) = cosh(iz) */
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	362 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	363 r.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	364 r.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	365 r = c_cosh(r);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	366 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	367 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	368
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	369 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	370 "cos(x)\n"
51918 ae22631a787c Merged revisions 70063 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48494 diff changeset	371 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	372 "Return the cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	373
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	374
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	375 /* 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	376 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	377
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	378 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	379 c_cosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	380 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	381 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	382 double x_minus_one;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	383
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	384 /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	385 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	386 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	387 (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	388 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	389 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	390 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	391 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	392 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	393 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	394 r.imag = -copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	395 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	396 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	397 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	398 r = cosh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	399 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	400 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	401 /* need to set errno = EDOM if y is +/- infinity and x is not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	402 a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	403 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	404 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	405 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	406 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	407 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	408 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	409
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	410 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	411 /* deal correctly with cases where cosh(z.real) overflows but
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	412 cosh(z) does not. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	413 x_minus_one = z.real - copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	414 r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	415 r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	416 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	417 r.real = cos(z.imag) * cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	418 r.imag = sin(z.imag) * sinh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	419 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	420 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	421 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	422 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	423 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	424 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	425 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	426 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	427
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	428 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	429 "cosh(x)\n"
51918 ae22631a787c Merged revisions 70063 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48494 diff changeset	430 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	431 "Return the hyperbolic cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	432
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	433
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	434 /* 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	435 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	436 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	437
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	438 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	439 c_exp(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	440 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	441 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	442 double l;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	443
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	444 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	445 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	446 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	447 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	448 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	449 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	450 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	451 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	452 r.real = copysign(0., cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	453 r.imag = copysign(0., sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	454 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	455 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	456 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	457 r = exp_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	458 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	459 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	460 /* need to set errno = EDOM if y is +/- infinity and x is not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	461 a NaN and not -infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	462 if (Py_IS_INFINITY(z.imag) &&
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	463 (Py_IS_FINITE(z.real) \|\|
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	464 (Py_IS_INFINITY(z.real) && z.real > 0)))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	465 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	466 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	467 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	468 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	469 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	470
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	471 if (z.real > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	472 l = exp(z.real-1.);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	473 r.real = lcos(z.imag)Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	474 r.imag = lsin(z.imag)Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	475 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	476 l = exp(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	477 r.real = l*cos(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	478 r.imag = l*sin(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	479 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	480 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	481 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	482 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	483 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	484 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	485 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	486 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	487
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	488 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	489 "exp(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	490 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	491 "Return the exponential value e**x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	492
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	493
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	494 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	495
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	496 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	497 c_log(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	498 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	499 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	500 The usual formula for the real part is log(hypot(z.real, z.imag)).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	501 There are four situations where this formula is potentially
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	502 problematic:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	503
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	504 (1) the absolute value of z is subnormal. Then hypot is subnormal,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	505 so has fewer than the usual number of bits of accuracy, hence may
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	506 have large relative error. This then gives a large absolute error
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	507 in the log. This can be solved by rescaling z by a suitable power
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	508 of 2.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	509
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	510 (2) the absolute value of z is greater than DBL_MAX (e.g. when both
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	511 z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	512 Again, rescaling solves this.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	513
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	514 (3) the absolute value of z is close to 1. In this case it's
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	515 difficult to achieve good accuracy, at least in part because a
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	516 change of 1ulp in the real or imaginary part of z can result in a
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	517 change of billions of ulps in the correctly rounded answer.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	518
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	519 (4) z = 0. The simplest thing to do here is to call the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	520 floating-point log with an argument of 0, and let its behaviour
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	521 (returning -infinity, signaling a floating-point exception, setting
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	522 errno, or whatever) determine that of c_log. So the usual formula
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	523 is fine here.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	524
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	525 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	526
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	527 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	528 double ax, ay, am, an, h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	529
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	530 SPECIAL_VALUE(z, log_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	531
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	532 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	533 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	534
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	535 if (ax > CM_LARGE_DOUBLE \|\| ay > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	536 r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	537 } else if (ax < DBL_MIN && ay < DBL_MIN) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	538 if (ax > 0. \|\| ay > 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	539 /* catch cases where hypot(ax, ay) is subnormal */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	540 r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	541 ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	542 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	543 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	544 /* log(+/-0. +/- 0i) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	545 r.real = -INF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	546 r.imag = atan2(z.imag, z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	547 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	548 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	549 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	550 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	551 h = hypot(ax, ay);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	552 if (0.71 <= h && h <= 1.73) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	553 am = ax > ay ? ax : ay; /* max(ax, ay) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	554 an = ax > ay ? ay : ax; /* min(ax, ay) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	555 r.real = log1p((am-1)(am+1)+anan)/2.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	556 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	557 r.real = log(h);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	558 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	559 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	560 r.imag = atan2(z.imag, z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	561 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	562 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	563 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	564
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	565
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	566 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	567 c_log10(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	568 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	569 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	570 int errno_save;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	571
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	572 r = c_log(z);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	573 errno_save = errno; /* just in case the divisions affect errno */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	574 r.real = r.real / M_LN10;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	575 r.imag = r.imag / M_LN10;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	576 errno = errno_save;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	577 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	578 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	579
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	580 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	581 "log10(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	582 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	583 "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	584
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	585
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	586 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	587 c_sin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	588 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	589 /* sin(z) = -i sin(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	590 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	591 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	592 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	593 s = c_sinh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	594 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	595 r.imag = -s.real;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	596 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	597 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	598
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	599 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	600 "sin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	601 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	602 "Return the sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	603
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	604
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	605 /* 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	606 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	607
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	608 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	609 c_sinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	610 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	611 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	612 double x_minus_one;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	613
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	614 /* special treatment for sinh(+/-inf + iy) if y is finite and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	615 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	616 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	617 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	618 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	619 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	620 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	621 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	622 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	623 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	624 r.real = -copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	625 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	626 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	627 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	628 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	629 r = sinh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	630 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	631 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	632 /* need to set errno = EDOM if y is +/- infinity and x is not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	633 a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	634 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	635 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	636 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	637 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	638 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	639 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	640
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	641 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	642 x_minus_one = z.real - copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	643 r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	644 r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	645 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	646 r.real = cos(z.imag) * sinh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	647 r.imag = sin(z.imag) * cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	648 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	649 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	650 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	651 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	652 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	653 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	654 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	655 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	656
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	657 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	658 "sinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	659 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	660 "Return the hyperbolic sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	661
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	662
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	663 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	664
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	665 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	666 c_sqrt(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	667 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	668 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	669 Method: use symmetries to reduce to the case when x = z.real and y
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	670 = z.imag are nonnegative. Then the real part of the result is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	671 given by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	672
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	673 s = sqrt((x + hypot(x, y))/2)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	674
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	675 and the imaginary part is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	676
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	677 d = (y/2)/s
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	678
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	679 If either x or y is very large then there's a risk of overflow in
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	680 computation of the expression x + hypot(x, y). We can avoid this
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	681 by rewriting the formula for s as:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	682
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	683 s = 2*sqrt(x/8 + hypot(x/8, y/8))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	684
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	685 This costs us two extra multiplications/divisions, but avoids the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	686 overhead of checking for x and y large.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	687
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	688 If both x and y are subnormal then hypot(x, y) may also be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	689 subnormal, so will lack full precision. We solve this by rescaling
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	690 x and y by a sufficiently large power of 2 to ensure that x and y
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	691 are normal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	692 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	693
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	694
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	695 Py_complex r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	696 double s,d;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	697 double ax, ay;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	698
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	699 SPECIAL_VALUE(z, sqrt_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	700
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	701 if (z.real == 0. && z.imag == 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	702 r.real = 0.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	703 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	704 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	705 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	706
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	707 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	708 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	709
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	710 if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. \|\| ay > 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	711 /* here we catch cases where hypot(ax, ay) is subnormal */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	712 ax = ldexp(ax, CM_SCALE_UP);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	713 s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	714 CM_SCALE_DOWN);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	715 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	716 ax /= 8.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	717 s = 2.*sqrt(ax + hypot(ax, ay/8.));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	718 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	719 d = ay/(2.*s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	720
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	721 if (z.real >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	722 r.real = s;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	723 r.imag = copysign(d, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	724 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	725 r.real = d;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	726 r.imag = copysign(s, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	727 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	728 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	729 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	730 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	731
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	732 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	733 "sqrt(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	734 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	735 "Return the square root of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	736
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	737
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	738 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	739 c_tan(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	740 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	741 /* tan(z) = -i tanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	742 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	743 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	744 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	745 s = c_tanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	746 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	747 r.imag = -s.real;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	748 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	749 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	750
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	751 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	752 "tan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	753 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	754 "Return the tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	755
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	756
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	757 /* 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	758 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	759
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	760 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	761 c_tanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	762 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	763 /* Formula:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	764
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	765 tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	766 (1+tan(y)^2 tanh(x)^2)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	767
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	768 To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	769 as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	770 by 4 exp(-2*x) instead, to avoid possible overflow in the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	771 computation of cosh(x).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	772
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	773 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	774
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	775 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	776 double tx, ty, cx, txty, denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	777
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	778 /* special treatment for tanh(+/-inf + iy) if y is finite and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	779 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	780 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	781 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	782 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	783 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	784 r.real = 1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	785 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	786 2.sin(z.imag)cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	787 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	788 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	789 r.real = -1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	790 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	791 2.sin(z.imag)cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	792 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	793 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	794 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	795 r = tanh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	796 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	797 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	798 /* need to set errno = EDOM if z.imag is +/-infinity and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	799 z.real is finite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	800 if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	801 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	802 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	803 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	804 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	805 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	806
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	807 /* danger of overflow in 2.z.imag !/
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	808 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	809 r.real = copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	810 r.imag = 4.sin(z.imag)cos(z.imag)exp(-2.fabs(z.real));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	811 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	812 tx = tanh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	813 ty = tan(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	814 cx = 1./cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	815 txty = tx*ty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	816 denom = 1. + txty*txty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	817 r.real = tx(1.+tyty)/denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	818 r.imag = ((ty/denom)cx)cx;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	819 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	820 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	821 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	822 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	823
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	824 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	825 "tanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	826 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	827 "Return the hyperbolic tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	828
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	829
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	830 static PyObject *
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	831 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	832 {
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	833 Py_complex x;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	834 Py_complex y;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	835
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	836 if (!PyArg_ParseTuple(args, "D\|D", &x, &y))
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	837 return NULL;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	838
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	839 errno = 0;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	840 PyFPE_START_PROTECT("complex function", return 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	841 x = c_log(x);
48494 aca5b2e6a66f Merged revisions 64623,64640,64665,64687,64689-64690,64719,64721,64735,64742,64744-64746,64756-64761,64767-64769,64771-64772,64774-64775,64788,64793,64835-64836 via svnmerge from Georg Brandl <georg@python.org> parents: 47580 diff changeset	842 if (PyTuple_GET_SIZE(args) == 2) {
aca5b2e6a66f Merged revisions 64623,64640,64665,64687,64689-64690,64719,64721,64735,64742,64744-64746,64756-64761,64767-64769,64771-64772,64774-64775,64788,64793,64835-64836 via svnmerge from Georg Brandl <georg@python.org> parents: 47580 diff changeset	843 y = c_log(y);
aca5b2e6a66f Merged revisions 64623,64640,64665,64687,64689-64690,64719,64721,64735,64742,64744-64746,64756-64761,64767-64769,64771-64772,64774-64775,64788,64793,64835-64836 via svnmerge from Georg Brandl <georg@python.org> parents: 47580 diff changeset	844 x = c_quot(x, y);
aca5b2e6a66f Merged revisions 64623,64640,64665,64687,64689-64690,64719,64721,64735,64742,64744-64746,64756-64761,64767-64769,64771-64772,64774-64775,64788,64793,64835-64836 via svnmerge from Georg Brandl <georg@python.org> parents: 47580 diff changeset	845 }
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	846 PyFPE_END_PROTECT(x)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	847 if (errno != 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	848 return math_error();
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	849 return PyComplex_FromCComplex(x);
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	850 }
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 PyDoc_STRVAR(cmath_log_doc,
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	853 "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	854 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	855
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	856
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	857 /* And now the glue to make them available from Python: */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	858
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	859 static PyObject *
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13493 diff changeset	860 math_error(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	861 {
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	862 if (errno == EDOM)
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	863 PyErr_SetString(PyExc_ValueError, "math domain error");
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	864 else if (errno == ERANGE)
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	865 PyErr_SetString(PyExc_OverflowError, "math range error");
97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	866 else /* Unexpected math error */
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	867 PyErr_SetFromErrno(PyExc_ValueError);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	868 return NULL;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	869 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	870
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	871 static PyObject *
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	872 math_1(PyObject args, Py_complex (func)(Py_complex))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	873 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	874 Py_complex x,r ;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	875 if (!PyArg_ParseTuple(args, "D", &x))
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	876 return NULL;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	877 errno = 0;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	878 PyFPE_START_PROTECT("complex function", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	879 r = (*func)(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	880 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	881 if (errno == EDOM) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	882 PyErr_SetString(PyExc_ValueError, "math domain error");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	883 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	884 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	885 else if (errno == ERANGE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	886 PyErr_SetString(PyExc_OverflowError, "math range error");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	887 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	888 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	889 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	890 return PyComplex_FromCComplex(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	891 }
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	892 }
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 #define FUNC1(stubname, func) \
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	895 static PyObject * stubname(PyObject self, PyObject args) { \
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	896 return math_1(args, func); \
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	897 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	898
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	899 FUNC1(cmath_acos, c_acos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	900 FUNC1(cmath_acosh, c_acosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	901 FUNC1(cmath_asin, c_asin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	902 FUNC1(cmath_asinh, c_asinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	903 FUNC1(cmath_atan, c_atan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	904 FUNC1(cmath_atanh, c_atanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	905 FUNC1(cmath_cos, c_cos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	906 FUNC1(cmath_cosh, c_cosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	907 FUNC1(cmath_exp, c_exp)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	908 FUNC1(cmath_log10, c_log10)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	909 FUNC1(cmath_sin, c_sin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	910 FUNC1(cmath_sinh, c_sinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	911 FUNC1(cmath_sqrt, c_sqrt)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	912 FUNC1(cmath_tan, c_tan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	913 FUNC1(cmath_tanh, c_tanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	914
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	915 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	916 cmath_phase(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	917 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	918 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	919 double phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	920 if (!PyArg_ParseTuple(args, "D:phase", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	921 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	922 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	923 PyFPE_START_PROTECT("arg function", return 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	924 phi = c_atan2(z);
47109 a02bc2a84d19 Merged revisions 63361-63373,63375,63377-63380 via svnmerge from Alexandre Vassalotti <alexandre@peadrop.com> parents: 46516 diff changeset	925 PyFPE_END_PROTECT(phi)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	926 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	927 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	928 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	929 return PyFloat_FromDouble(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	930 }
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 PyDoc_STRVAR(cmath_phase_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	933 "phase(z) -> float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	934 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	935
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	936 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	937 cmath_polar(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	938 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	939 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	940 double r, phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	941 if (!PyArg_ParseTuple(args, "D:polar", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	942 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	943 PyFPE_START_PROTECT("polar function", return 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	944 phi = c_atan2(z); /* should not cause any exception */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	945 r = c_abs(z); /* sets errno to ERANGE on overflow; otherwise 0 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	946 PyFPE_END_PROTECT(r)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	947 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	948 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	949 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	950 return Py_BuildValue("dd", r, phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	951 }
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 PyDoc_STRVAR(cmath_polar_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	954 "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	955 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	956 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	957
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 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	960 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	961
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	962 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	963 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	964 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	965 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	966
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
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	969 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	970
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	971 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	972 cmath_rect(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	973 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	974 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	975 double r, phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	976 if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	977 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	978 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	979 PyFPE_START_PROTECT("rect function", return 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	980
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	981 /* deal with special values */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	982 if (!Py_IS_FINITE(r) \|\| !Py_IS_FINITE(phi)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	983 /* if r is +/-infinity and phi is finite but nonzero then
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	984 result is (+-INF +-INF i), but we need to compute cos(phi)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	985 and sin(phi) to figure out the signs. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	986 if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	987 && (phi != 0.))) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	988 if (r > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	989 z.real = copysign(INF, cos(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	990 z.imag = copysign(INF, sin(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	991 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	992 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	993 z.real = -copysign(INF, cos(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	994 z.imag = -copysign(INF, sin(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	995 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	996 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	997 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	998 z = rect_special_values[special_type(r)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	999 [special_type(phi)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1000 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1001 /* need to set errno = EDOM if r is a nonzero number and phi
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1002 is infinite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1003 if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1004 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1005 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1006 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1007 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1008 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1009 z.real = r * cos(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1010 z.imag = r * sin(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1011 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1012 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1013
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1014 PyFPE_END_PROTECT(z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1015 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1016 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1017 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1018 return PyComplex_FromCComplex(z);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1019 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1020
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1021 PyDoc_STRVAR(cmath_rect_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1022 "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	1023 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	1024
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1025 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1026 cmath_isnan(PyObject self, PyObject args)
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 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1029 if (!PyArg_ParseTuple(args, "D:isnan", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1030 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1031 return PyBool_FromLong(Py_IS_NAN(z.real) \|\| Py_IS_NAN(z.imag));
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1034 PyDoc_STRVAR(cmath_isnan_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1035 "isnan(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1036 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	1037
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1038 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1039 cmath_isinf(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1040 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1041 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1042 if (!PyArg_ParseTuple(args, "D:isnan", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1043 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1044 return PyBool_FromLong(Py_IS_INFINITY(z.real) \|\|
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1045 Py_IS_INFINITY(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1046 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1047
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1048 PyDoc_STRVAR(cmath_isinf_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1049 "isinf(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1050 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	1051
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1052
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	1053 PyDoc_STRVAR(module_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1054 "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	1055 "functions for complex numbers.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1056
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	1057 static PyMethodDef cmath_methods[] = {
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1058 {"acos", cmath_acos, METH_VARARGS, c_acos_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1059 {"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1060 {"asin", cmath_asin, METH_VARARGS, c_asin_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1061 {"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1062 {"atan", cmath_atan, METH_VARARGS, c_atan_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1063 {"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1064 {"cos", cmath_cos, METH_VARARGS, c_cos_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1065 {"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1066 {"exp", cmath_exp, METH_VARARGS, c_exp_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1067 {"isinf", cmath_isinf, METH_VARARGS, cmath_isinf_doc},
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1068 {"isnan", cmath_isnan, METH_VARARGS, cmath_isnan_doc},
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1069 {"log", cmath_log, METH_VARARGS, cmath_log_doc},
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1070 {"log10", cmath_log10, METH_VARARGS, c_log10_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1071 {"phase", cmath_phase, METH_VARARGS, cmath_phase_doc},
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1072 {"polar", cmath_polar, METH_VARARGS, cmath_polar_doc},
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1073 {"rect", cmath_rect, METH_VARARGS, cmath_rect_doc},
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1074 {"sin", cmath_sin, METH_VARARGS, c_sin_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1075 {"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1076 {"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1077 {"tan", cmath_tan, METH_VARARGS, c_tan_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1078 {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1079 {NULL, NULL} /* sentinel */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1080 };
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1081
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1082
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1083 static struct PyModuleDef cmathmodule = {
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1084 PyModuleDef_HEAD_INIT,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1085 "cmath",
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1086 module_doc,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1087 -1,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1088 cmath_methods,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1089 NULL,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1090 NULL,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1091 NULL,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1092 NULL
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1093 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1094
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 24280 diff changeset	1095 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1096 PyInit_cmath(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1097 {
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1098 PyObject *m;
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1099
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1100 m = PyModule_Create(&cmathmodule);
36324 1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 32350 diff changeset	1101 if (m == NULL)
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1102 return NULL;
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1103
ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1104 PyModule_AddObject(m, "pi",
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1105 PyFloat_FromDouble(Py_MATH_PI));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1106 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	1107
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	1108 /* initialize special value tables */
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	1109
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	1110 #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	1111 #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	1112
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	1113 INIT_SPECIAL_VALUES(acos_special_values, {
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	1114 C(P34,INF) C(P,INF) C(P,INF) C(P,-INF) C(P,-INF) C(P34,-INF) C(N,INF)
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	1115 C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
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	1116 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
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	1117 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
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	1118 C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
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	1119 C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
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	1120 C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N)
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	1121 })
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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	1123 INIT_SPECIAL_VALUES(acosh_special_values, {
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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
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 INIT_SPECIAL_VALUES(asinh_special_values, {
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 C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N)
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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	1138 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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	1139 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
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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	1142
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	1143 INIT_SPECIAL_VALUES(atanh_special_values, {
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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	1152
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	1153 INIT_SPECIAL_VALUES(cosh_special_values, {
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 C(INF,N) C(U,U) C(INF,0.) C(INF,-0.) C(U,U) C(INF,N) C(INF,N)
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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	1162
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	1163 INIT_SPECIAL_VALUES(exp_special_values, {
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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	1167 C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
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	1168 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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	1169 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
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	1170 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
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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	1172
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	1173 INIT_SPECIAL_VALUES(log_special_values, {
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 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
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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	1176 C(INF,-P12) C(U,U) C(-INF,-P) C(-INF,P) C(U,U) C(INF,P12) C(N,N)
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	1177 C(INF,-P12) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,P12) C(N,N)
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	1178 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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	1179 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
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	1180 C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
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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	1182
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	1183 INIT_SPECIAL_VALUES(sinh_special_values, {
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 C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N)
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47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1222 return m;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1223 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/cmathmodule.c @ 58689:514b56efd89a 3.1