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

annotate Modules/cmathmodule.c @ 58664:993f703a61ba

Merged revisions 77484,77487,77561,77570,77593,77603,77608,77667,77702-77703,77739,77858,77887,77889 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r77484 | skip.montanaro | 2010-01-13 19:12:34 -0600 (Wed, 13 Jan 2010) | 4 lines Update PyEval_EvalFrame to PyEval_EvalFrameEx. This looks to have been done partially before. Also add a comment describing how this might have to work with different versions of the interpreter. ........ r77487 | ezio.melotti | 2010-01-14 05:34:10 -0600 (Thu, 14 Jan 2010) | 1 line Fixed typo ........ r77561 | georg.brandl | 2010-01-17 02:42:30 -0600 (Sun, 17 Jan 2010) | 1 line #7699: improve datetime docs: straightforward linking to strftime/strptime section, mark classmethods as such. ........ r77570 | georg.brandl | 2010-01-17 06:14:42 -0600 (Sun, 17 Jan 2010) | 1 line Add note about usage of STRINGLIB_EMPTY. ........ r77593 | georg.brandl | 2010-01-17 17:33:53 -0600 (Sun, 17 Jan 2010) | 1 line Fix internal reference. ........ r77603 | benjamin.peterson | 2010-01-18 17:07:56 -0600 (Mon, 18 Jan 2010) | 8 lines data descriptors do not override the class dictionary if __get__ is not defined Adjust documentation and add a test to verify this behavior. See http://mail.python.org/pipermail/python-dev/2010-January/095637.html for discussion. ........ r77608 | gregory.p.smith | 2010-01-19 02:19:03 -0600 (Tue, 19 Jan 2010) | 6 lines Do not compile stubs for the sha2 series hashes in the openssl hashlib module when the openssl version is too old to support them. That leads both compiled code bloat and to unittests attempting to test implementations that don't exist for comparison purposes on such platforms. ........ r77667 | mark.dickinson | 2010-01-21 12:32:27 -0600 (Thu, 21 Jan 2010) | 1 line Add two more test_strtod test values. ........ r77702 | georg.brandl | 2010-01-23 02:43:31 -0600 (Sat, 23 Jan 2010) | 1 line #7762: fix refcount annotation of PyUnicode_Tailmatch(). ........ r77703 | georg.brandl | 2010-01-23 02:47:54 -0600 (Sat, 23 Jan 2010) | 1 line #7725: fix referencing issue. ........ r77739 | benjamin.peterson | 2010-01-24 21:52:52 -0600 (Sun, 24 Jan 2010) | 1 line mention from_float() in error message ........ r77858 | georg.brandl | 2010-01-30 11:57:48 -0600 (Sat, 30 Jan 2010) | 1 line #7802: fix invalid example (heh). ........ r77887 | georg.brandl | 2010-01-31 12:51:49 -0600 (Sun, 31 Jan 2010) | 5 lines Fix-up ftplib documentation: move exception descriptions to toplevel, not inside a class remove attribution in "versionadded" spell and grammar check docstring of FTP_TLS ........ r77889 | michael.foord | 2010-01-31 13:59:26 -0600 (Sun, 31 Jan 2010) | 1 line Minor modification to unittest documentation. ........

author	Benjamin Peterson <benjamin@python.org>
date	Wed, 03 Feb 2010 02:35:45 +0000
parents	9751ddcc1882
children	cab14be0ada1

rev	line source
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1 /* Complex math module */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	2
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	3 /* much code borrowed from mathmodule.c */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	4
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	5 #include "Python.h"
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	6 #include "_math.h"
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	7 /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	8 float.h. We assume that FLT_RADIX is either 2 or 16. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	9 #include <float.h>
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	10
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	11 #if (FLT_RADIX != 2 && FLT_RADIX != 16)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	12 #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	13 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	14
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	15 #ifndef M_LN2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	16 #define M_LN2 (0.6931471805599453094) /* natural log of 2 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	17 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	18
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	19 #ifndef M_LN10
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	20 #define M_LN10 (2.302585092994045684) /* natural log of 10 */
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	21 #endif
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	22
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	23 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	24 CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	25 inverse trig and inverse hyperbolic trig functions. Its log is used in the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	26 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	27 overflow.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	28 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	29
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	30 #define CM_LARGE_DOUBLE (DBL_MAX/4.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	31 #define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	32 #define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	33 #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	34
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	35 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	36 CM_SCALE_UP is an odd integer chosen such that multiplication by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	37 2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	38 CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	39 square roots accurately when the real and imaginary parts of the argument
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	40 are subnormal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	41 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	42
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	43 #if FLT_RADIX==2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	44 #define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	45 #elif FLT_RADIX==16
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	46 #define CM_SCALE_UP (4*DBL_MANT_DIG+1)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	47 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	48 #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	49
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	50 /* forward declarations */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	51 static Py_complex c_asinh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	52 static Py_complex c_atanh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	53 static Py_complex c_cosh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	54 static Py_complex c_sinh(Py_complex);
24280 1598a1e473e2 staticforward bites the dust. Jeremy Hylton <jeremy@alum.mit.edu> parents: 23832 diff changeset	55 static Py_complex c_sqrt(Py_complex);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	56 static Py_complex c_tanh(Py_complex);
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	57 static PyObject * math_error(void);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	58
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	59 /* Code to deal with special values (infinities, NaNs, etc.). */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	60
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	61 /* special_type takes a double and returns an integer code indicating
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	62 the type of the double as follows:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	63 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	64
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	65 enum special_types {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	66 ST_NINF, /* 0, negative infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	67 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	68 ST_NZERO, /* 2, -0. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	69 ST_PZERO, /* 3, +0. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	70 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	71 ST_PINF, /* 5, positive infinity */
55541 8848c49ed5f5 Merged revisions 74305 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 51918 diff changeset	72 ST_NAN /* 6, Not a Number */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	73 };
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	74
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	75 static enum special_types
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	76 special_type(double d)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	77 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	78 if (Py_IS_FINITE(d)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	79 if (d != 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	80 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	81 return ST_POS;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	82 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	83 return ST_NEG;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	84 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	85 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	86 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	87 return ST_PZERO;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	88 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	89 return ST_NZERO;
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 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	92 if (Py_IS_NAN(d))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	93 return ST_NAN;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	94 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	95 return ST_PINF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	96 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	97 return ST_NINF;
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	100 #define SPECIAL_VALUE(z, table) \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	101 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	102 errno = 0; \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	103 return table[special_type((z).real)] \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	104 [special_type((z).imag)]; \
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	107 #define P Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	108 #define P14 0.25*Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	109 #define P12 0.5*Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	110 #define P34 0.75*Py_MATH_PI
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	111 #define INF Py_HUGE_VAL
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	112 #define N Py_NAN
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	113 #define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	114
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	115 /* First, the C functions that do the real work. Each of the c_*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	116 functions computes and returns the C99 Annex G recommended result
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	117 and also sets errno as follows: errno = 0 if no floating-point
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	118 exception is associated with the result; errno = EDOM if C99 Annex
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	119 G recommends raising divide-by-zero or invalid for this result; and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	120 errno = ERANGE where the overflow floating-point signal should be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	121 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	122 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	123
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	124 static Py_complex acos_special_values[7][7];
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	125
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	126 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	127 c_acos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	128 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	129 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	130
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	131 SPECIAL_VALUE(z, acos_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	132
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	133 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	134 /* avoid unnecessary overflow for large arguments */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	135 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	136 /* 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	137 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	138 if (z.real < 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	139 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	140 M_LN2*2., z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	141 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	142 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	143 M_LN2*2., -z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	144 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	145 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	146 s1.real = 1.-z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	147 s1.imag = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	148 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	149 s2.real = 1.+z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	150 s2.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	151 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	152 r.real = 2.*atan2(s1.real, s2.real);
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	153 r.imag = m_asinh(s2.reals1.imag - s2.imags1.real);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	154 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	155 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	156 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	157 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	158
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	159 PyDoc_STRVAR(c_acos_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	160 "acos(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	161 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	162 "Return the arc cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	163
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	164
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	165 static Py_complex acosh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	166
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	167 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	168 c_acosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	169 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	170 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	171
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	172 SPECIAL_VALUE(z, acosh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	173
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	174 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	175 /* avoid unnecessary overflow for large arguments */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	176 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	177 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	178 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	179 s1.real = z.real - 1.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	180 s1.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	181 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	182 s2.real = z.real + 1.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	183 s2.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	184 s2 = c_sqrt(s2);
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	185 r.real = m_asinh(s1.reals2.real + s1.imags2.imag);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	186 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	187 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	188 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	189 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	190 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	191
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	192 PyDoc_STRVAR(c_acosh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	193 "acosh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	194 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	195 "Return the hyperbolic arccosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	196
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	197
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	198 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	199 c_asin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	200 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	201 /* asin(z) = -i asinh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	202 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	203 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	204 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	205 s = c_asinh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	206 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	207 r.imag = -s.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	208 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	209 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	210
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	211 PyDoc_STRVAR(c_asin_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	212 "asin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	213 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	214 "Return the arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	215
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	216
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	217 static Py_complex asinh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	218
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	219 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	220 c_asinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	221 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	222 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	223
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	224 SPECIAL_VALUE(z, asinh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	225
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	226 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	227 if (z.imag >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	228 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	229 M_LN2*2., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	230 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	231 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	232 M_LN2*2., -z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	233 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	234 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	235 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	236 s1.real = 1.+z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	237 s1.imag = -z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	238 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	239 s2.real = 1.-z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	240 s2.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	241 s2 = c_sqrt(s2);
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	242 r.real = m_asinh(s1.reals2.imag-s2.reals1.imag);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	243 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	244 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	245 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	246 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	247 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	248
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	249 PyDoc_STRVAR(c_asinh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	250 "asinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	251 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	252 "Return the hyperbolic arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	253
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	254
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	255 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	256 c_atan(Py_complex z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	257 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	258 /* atan(z) = -i atanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	259 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	260 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	261 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	262 s = c_atanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	263 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	264 r.imag = -s.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	265 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	266 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	267
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	268 /* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	269 C99 for atan2(0., 0.). */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	270 static double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	271 c_atan2(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	272 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	273 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	274 return Py_NAN;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	275 if (Py_IS_INFINITY(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	276 if (Py_IS_INFINITY(z.real)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	277 if (copysign(1., z.real) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	278 /* atan2(+-inf, +inf) == +-pi/4 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	279 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	280 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	281 /* atan2(+-inf, -inf) == +-pi3/4 /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	282 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	283 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	284 /* 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	285 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	286 }
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	287 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	288 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	289 /* 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	290 return copysign(0., z.imag);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	291 else
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	292 /* 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	293 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	294 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	295 return atan2(z.imag, z.real);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	296 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	297
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	298 PyDoc_STRVAR(c_atan_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	299 "atan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	300 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	301 "Return the arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	302
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	303
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	304 static Py_complex atanh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	305
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	306 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	307 c_atanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	308 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	309 Py_complex r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	310 double ay, h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	311
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	312 SPECIAL_VALUE(z, atanh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	313
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	314 /* 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	315 if (z.real < 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	316 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	317 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	318
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	319 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	320 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	321 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	322 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	323 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	324 of z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	325 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	326 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	327 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	328 /* 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	329 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	330 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	331 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	332 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	333 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	334 } 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	335 /* 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	336 if (ay == 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	337 r.real = INF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	338 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	339 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	340 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	341 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	342 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	343 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	344 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	345 } else {
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	346 r.real = m_log1p(4.z.real/((1-z.real)(1-z.real) + ay*ay))/4.;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	347 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	348 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	349 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	350 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	351 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	352
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	353 PyDoc_STRVAR(c_atanh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	354 "atanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	355 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	356 "Return the hyperbolic arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	357
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	358
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	359 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	360 c_cos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	361 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	362 /* cos(z) = cosh(iz) */
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	363 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	364 r.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	365 r.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	366 r = c_cosh(r);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	367 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	368 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	369
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	370 PyDoc_STRVAR(c_cos_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	371 "cos(x)\n"
51918 ae22631a787c Merged revisions 70063 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48494 diff changeset	372 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	373 "Return the cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	374
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	375
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	376 /* cosh(infinity + iy) needs to be dealt with specially /
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	377 static Py_complex cosh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	378
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	379 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	380 c_cosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	381 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	382 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	383 double x_minus_one;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	384
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	385 /* 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	386 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	387 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	388 (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	389 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	390 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	391 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	392 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	393 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	394 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	395 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	396 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	397 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	398 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	399 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	400 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	401 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	402 /* 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	403 a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	404 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	405 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	406 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	407 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	408 return r;
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	411 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	412 /* 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	413 cosh(z) does not. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	414 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	415 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	416 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	417 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	418 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	419 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	420 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	421 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	422 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	423 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	424 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	425 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	426 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	427 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	428
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	429 PyDoc_STRVAR(c_cosh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	430 "cosh(x)\n"
51918 ae22631a787c Merged revisions 70063 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 48494 diff changeset	431 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	432 "Return the hyperbolic cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	433
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	434
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	435 /* exp(infinity + iy) and exp(-infinity + iy) need special treatment for
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	436 finite y */
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	437 static Py_complex exp_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	438
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	439 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	440 c_exp(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	441 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	442 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	443 double l;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	444
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	445 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	446 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	447 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	448 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	449 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	450 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	451 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	452 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	453 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	454 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	455 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	456 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	457 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	458 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	459 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	460 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	461 /* 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	462 a NaN and not -infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	463 if (Py_IS_INFINITY(z.imag) &&
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	464 (Py_IS_FINITE(z.real) \|\|
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	465 (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	466 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	467 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	468 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	469 return r;
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	472 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	473 l = exp(z.real-1.);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	474 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	475 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	476 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	477 l = exp(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	478 r.real = l*cos(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	479 r.imag = l*sin(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	480 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	481 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	482 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	483 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	484 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	485 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	486 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	487 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	488
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	489 PyDoc_STRVAR(c_exp_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	490 "exp(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	491 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	492 "Return the exponential value e**x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	493
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	494
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	495 static Py_complex log_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	496
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	497 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	498 c_log(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	499 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	500 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	501 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	502 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	503 problematic:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	504
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	505 (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	506 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	507 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	508 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	509 of 2.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	510
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	511 (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	512 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	513 Again, rescaling solves this.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	514
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	515 (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	516 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	517 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	518 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	519
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	520 (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	521 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	522 (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	523 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	524 is fine here.
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 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	527
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	528 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	529 double ax, ay, am, an, h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	530
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	531 SPECIAL_VALUE(z, log_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	532
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	533 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	534 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	535
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	536 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	537 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	538 } 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	539 if (ax > 0. \|\| ay > 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	540 /* 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	541 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	542 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	543 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	544 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	545 /* log(+/-0. +/- 0i) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	546 r.real = -INF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	547 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	548 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	549 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	550 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	551 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	552 h = hypot(ax, ay);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	553 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	554 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	555 an = ax > ay ? ay : ax; /* min(ax, ay) */
57866 9751ddcc1882 Merged revisions 76978 via svnmerge from Mark Dickinson <dickinsm@gmail.com> parents: 55541 diff changeset	556 r.real = m_log1p((am-1)(am+1)+anan)/2.;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	557 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	558 r.real = log(h);
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 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	561 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	562 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	563 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	564 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	565
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	566
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	567 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	568 c_log10(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	569 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	570 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	571 int errno_save;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	572
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	573 r = c_log(z);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	574 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	575 r.real = r.real / M_LN10;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	576 r.imag = r.imag / M_LN10;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	577 errno = errno_save;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	578 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	579 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	580
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	581 PyDoc_STRVAR(c_log10_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	582 "log10(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	583 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	584 "Return the base-10 logarithm of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	585
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	586
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	587 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	588 c_sin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	589 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	590 /* sin(z) = -i sin(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	591 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	592 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	593 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	594 s = c_sinh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	595 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	596 r.imag = -s.real;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	597 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	598 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	599
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	600 PyDoc_STRVAR(c_sin_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	601 "sin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	602 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	603 "Return the sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	604
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	605
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	606 /* sinh(infinity + iy) needs to be dealt with specially /
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	607 static Py_complex sinh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	608
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	609 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	610 c_sinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	611 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	612 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	613 double x_minus_one;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	614
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	615 /* 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	616 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	617 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	618 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	619 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	620 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	621 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	622 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	623 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	624 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	625 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	626 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	627 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	628 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	629 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	630 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	631 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	632 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	633 /* 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	634 a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	635 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	636 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	637 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	638 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	639 return r;
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	642 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	643 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	644 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	645 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	646 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	647 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	648 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	649 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	650 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	651 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	652 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	653 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	654 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	655 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	656 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	657
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	658 PyDoc_STRVAR(c_sinh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	659 "sinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	660 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	661 "Return the hyperbolic sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	662
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	663
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	664 static Py_complex sqrt_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	665
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	666 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	667 c_sqrt(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	668 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	669 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	670 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	671 = 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	672 given by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	673
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	674 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	675
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	676 and the imaginary part is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	677
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	678 d = (y/2)/s
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	679
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	680 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	681 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	682 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	683
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	684 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	685
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	686 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	687 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	688
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	689 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	690 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	691 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	692 are normal.
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	695
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	696 Py_complex r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	697 double s,d;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	698 double ax, ay;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	699
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	700 SPECIAL_VALUE(z, sqrt_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	701
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	702 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	703 r.real = 0.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	704 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	705 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	706 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	707
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	708 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	709 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	710
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	711 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	712 /* 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	713 ax = ldexp(ax, CM_SCALE_UP);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	714 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	715 CM_SCALE_DOWN);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	716 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	717 ax /= 8.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	718 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	719 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	720 d = ay/(2.*s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	721
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	722 if (z.real >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	723 r.real = s;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	724 r.imag = copysign(d, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	725 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	726 r.real = d;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	727 r.imag = copysign(s, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	728 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	729 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	730 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	731 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	732
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	733 PyDoc_STRVAR(c_sqrt_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	734 "sqrt(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	735 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	736 "Return the square root of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	737
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	738
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	739 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	740 c_tan(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	741 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	742 /* tan(z) = -i tanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	743 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	744 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	745 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	746 s = c_tanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	747 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	748 r.imag = -s.real;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	749 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	750 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	751
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	752 PyDoc_STRVAR(c_tan_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	753 "tan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	754 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	755 "Return the tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	756
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	757
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	758 /* tanh(infinity + iy) needs to be dealt with specially /
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	759 static Py_complex tanh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	760
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	761 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	762 c_tanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	763 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	764 /* Formula:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	765
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	766 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	767 (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	768
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	769 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	770 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	771 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	772 computation of cosh(x).
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 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	775
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	776 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	777 double tx, ty, cx, txty, denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	778
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	779 /* 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	780 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	781 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	782 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	783 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	784 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	785 r.real = 1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	786 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	787 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	788 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	789 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	790 r.real = -1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	791 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	792 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	793 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	794 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	795 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	796 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	797 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	798 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	799 /* 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	800 z.real is finite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	801 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	802 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	803 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	804 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	805 return r;
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	808 /* 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	809 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	810 r.real = copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	811 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	812 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	813 tx = tanh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	814 ty = tan(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	815 cx = 1./cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	816 txty = tx*ty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	817 denom = 1. + txty*txty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	818 r.real = tx(1.+tyty)/denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	819 r.imag = ((ty/denom)cx)cx;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	820 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	821 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	822 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	823 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	824
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	825 PyDoc_STRVAR(c_tanh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	826 "tanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	827 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	828 "Return the hyperbolic tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	829
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	830
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	831 static PyObject *
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	832 cmath_log(PyObject self, PyObject args)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	833 {
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	834 Py_complex x;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	835 Py_complex y;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	836
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	837 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	838 return NULL;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	839
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	840 errno = 0;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	841 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	842 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	843 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	844 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	845 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	846 }
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	847 PyFPE_END_PROTECT(x)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	848 if (errno != 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	849 return math_error();
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	850 return PyComplex_FromCComplex(x);
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	851 }
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	852
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	853 PyDoc_STRVAR(cmath_log_doc,
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	854 "log(x[, base]) -> the logarithm of x to the given base.\n\
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	855 If the base not specified, returns the natural logarithm (base e) of x.");
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	856
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	857
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	858 /* And now the glue to make them available from Python: */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	859
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	860 static PyObject *
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13493 diff changeset	861 math_error(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	862 {
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	863 if (errno == EDOM)
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	864 PyErr_SetString(PyExc_ValueError, "math domain error");
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	865 else if (errno == ERANGE)
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	866 PyErr_SetString(PyExc_OverflowError, "math range error");
97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	867 else /* Unexpected math error */
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	868 PyErr_SetFromErrno(PyExc_ValueError);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	869 return NULL;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	870 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	871
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	872 static PyObject *
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	873 math_1(PyObject args, Py_complex (func)(Py_complex))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	874 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	875 Py_complex x,r ;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	876 if (!PyArg_ParseTuple(args, "D", &x))
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	877 return NULL;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	878 errno = 0;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	879 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	880 r = (*func)(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	881 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	882 if (errno == EDOM) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	883 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	884 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	885 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	886 else if (errno == ERANGE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	887 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	888 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	889 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	890 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	891 return PyComplex_FromCComplex(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	892 }
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	893 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	894
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	895 #define FUNC1(stubname, func) \
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	896 static PyObject * stubname(PyObject self, PyObject args) { \
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	897 return math_1(args, func); \
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
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	900 FUNC1(cmath_acos, c_acos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	901 FUNC1(cmath_acosh, c_acosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	902 FUNC1(cmath_asin, c_asin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	903 FUNC1(cmath_asinh, c_asinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	904 FUNC1(cmath_atan, c_atan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	905 FUNC1(cmath_atanh, c_atanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	906 FUNC1(cmath_cos, c_cos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	907 FUNC1(cmath_cosh, c_cosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	908 FUNC1(cmath_exp, c_exp)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	909 FUNC1(cmath_log10, c_log10)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	910 FUNC1(cmath_sin, c_sin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	911 FUNC1(cmath_sinh, c_sinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	912 FUNC1(cmath_sqrt, c_sqrt)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	913 FUNC1(cmath_tan, c_tan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	914 FUNC1(cmath_tanh, c_tanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	915
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	916 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	917 cmath_phase(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	918 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	919 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	920 double phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	921 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	922 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	923 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	924 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	925 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	926 PyFPE_END_PROTECT(phi)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	927 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	928 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	929 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	930 return PyFloat_FromDouble(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	931 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	932
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	933 PyDoc_STRVAR(cmath_phase_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	934 "phase(z) -> float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	935 Return argument, also known as the phase angle, of a complex.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	936
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	937 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	938 cmath_polar(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	939 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	940 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	941 double r, phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	942 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	943 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	944 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	945 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	946 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	947 PyFPE_END_PROTECT(r)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	948 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	949 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	950 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	951 return Py_BuildValue("dd", r, phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	952 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	953
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	954 PyDoc_STRVAR(cmath_polar_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	955 "polar(z) -> r: float, phi: float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	956 Convert a complex from rectangular coordinates to polar coordinates. r is\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	957 the distance from 0 and phi the phase angle.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	958
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	959 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	960 rect() isn't covered by the C99 standard, but it's not too hard to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	961 figure out 'spirit of C99' rules for special value handing:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	962
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	963 rect(x, t) should behave like exp(log(x) + it) for positive-signed x
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	964 rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	965 rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	966 gives nan +- i0 with the sign of the imaginary part unspecified.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	967
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	968 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	969
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	970 static Py_complex rect_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	971
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	972 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	973 cmath_rect(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	974 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	975 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	976 double r, phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	977 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	978 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	979 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	980 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	981
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	982 /* deal with special values */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	983 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	984 /* 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	985 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	986 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	987 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	988 && (phi != 0.))) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	989 if (r > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	990 z.real = copysign(INF, cos(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	991 z.imag = copysign(INF, sin(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	992 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	993 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	994 z.real = -copysign(INF, cos(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	995 z.imag = -copysign(INF, sin(phi));
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 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	998 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	999 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	1000 [special_type(phi)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1001 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1002 /* 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	1003 is infinite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1004 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	1005 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1006 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1007 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1008 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1009 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1010 z.real = r * cos(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1011 z.imag = r * sin(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1012 errno = 0;
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1015 PyFPE_END_PROTECT(z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1016 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1017 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1018 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1019 return PyComplex_FromCComplex(z);
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1022 PyDoc_STRVAR(cmath_rect_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1023 "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	1024 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	1025
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1026 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1027 cmath_isnan(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1028 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1029 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1030 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	1031 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1032 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	1033 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1034
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1035 PyDoc_STRVAR(cmath_isnan_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1036 "isnan(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1037 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	1038
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1039 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1040 cmath_isinf(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1041 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1042 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1043 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	1044 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1045 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	1046 Py_IS_INFINITY(z.imag));
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
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1049 PyDoc_STRVAR(cmath_isinf_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1050 "isinf(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1051 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	1052
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1053
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	1054 PyDoc_STRVAR(module_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1055 "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	1056 "functions for complex numbers.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1057
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	1058 static PyMethodDef cmath_methods[] = {
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1059 {"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	1060 {"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	1061 {"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	1062 {"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	1063 {"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	1064 {"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	1065 {"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	1066 {"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	1067 {"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	1068 {"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	1069 {"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	1070 {"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	1071 {"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	1072 {"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	1073 {"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	1074 {"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	1075 {"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	1076 {"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	1077 {"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	1078 {"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	1079 {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1080 {NULL, NULL} /* sentinel */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1081 };
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1082
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1083
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1084 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	1085 PyModuleDef_HEAD_INIT,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1086 "cmath",
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1087 module_doc,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1088 -1,
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1089 cmath_methods,
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 NULL
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1094 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1095
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 24280 diff changeset	1096 PyMODINIT_FUNC
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1097 PyInit_cmath(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1098 {
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1099 PyObject *m;
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1100
47580 94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API. Martin v. Löwis <martin@v.loewis.de> parents: 47109 diff changeset	1101 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	1102 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	1103 return NULL;
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1104
ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1105 PyModule_AddObject(m, "pi",
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1106 PyFloat_FromDouble(Py_MATH_PI));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1107 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	1108
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 /* 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	1110
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 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	1112 #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	1113
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 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	1115 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	1116 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	1117 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,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	1119 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	1120 C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
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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
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	1124 INIT_SPECIAL_VALUES(acosh_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	1125 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) 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	1126 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	1127 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) 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	1130 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	1131 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	1133
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 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	1135 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(0.,-0.) C(0.,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	1139 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	1140 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	1141 C(INF,N) C(N,N) C(N,-0.) C(N,0.) 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	1143
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1144 INIT_SPECIAL_VALUES(atanh_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	1145 C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,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	1147 C(-0.,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-0.,P12) C(-0.,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	1148 C(0.,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,P12) C(0.,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	1149 C(0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(0.,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	1150 C(0.,-P12) C(0.,-P12) C(0.,-P12) C(0.,P12) C(0.,P12) C(0.,P12) C(0.,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	1153
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 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	1155 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	1157 C(N,0.) C(U,U) C(1.,0.) C(1.,-0.) C(U,U) C(N,0.) C(N,0.)
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	1158 C(N,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,0.) C(N,0.)
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	1159 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	1160 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	1161 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	1163
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1164 INIT_SPECIAL_VALUES(exp_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	1165 C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
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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(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	1169 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	1170 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	1171 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	1173
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 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	1175 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) 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	1176 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	1177 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	1178 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	1179 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	1180 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	1181 C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,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	1182 })
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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	1184 INIT_SPECIAL_VALUES(sinh_special_values, {
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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	1223 return m;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1224 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/cmathmodule.c @ 58664:993f703a61ba