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

annotate Modules/cmathmodule.c @ 49955:878d40468c4e legacy-trunk

Issue #4384: Added logging integration with warnings module using captureWarnings(). This change includes a NullHandler which does nothing; it will be of use to library developers who want to avoid the "No handlers could be found for logger XXX" message which can appear if the library user doesn't configure logging.

author	Vinay Sajip <vinay_sajip@yahoo.co.uk>
date	Wed, 03 Dec 2008 23:22:58 +0000
parents	f772476ad90d
children	676567e2a711

rev	line source
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1 /* Complex math module */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	2
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	3 /* much code borrowed from mathmodule.c */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	4
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	5 #include "Python.h"
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	6 /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	7 float.h. We assume that FLT_RADIX is either 2 or 16. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	8 #include <float.h>
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	9
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	10 #if (FLT_RADIX != 2 && FLT_RADIX != 16)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	11 #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	12 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	13
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	14 #ifndef M_LN2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	15 #define M_LN2 (0.6931471805599453094) /* natural log of 2 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	16 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	17
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	18 #ifndef M_LN10
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	19 #define M_LN10 (2.302585092994045684) /* natural log of 10 */
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	20 #endif
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	21
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	22 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	23 CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	24 inverse trig and inverse hyperbolic trig functions. Its log is used in the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	25 evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unecessary
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	26 overflow.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	27 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	28
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	29 #define CM_LARGE_DOUBLE (DBL_MAX/4.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	30 #define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	31 #define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	32 #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	33
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	34 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	35 CM_SCALE_UP is an odd integer chosen such that multiplication by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	36 2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	37 CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	38 square roots accurately when the real and imaginary parts of the argument
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	39 are subnormal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	40 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	41
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	42 #if FLT_RADIX==2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	43 #define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	44 #elif FLT_RADIX==16
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	45 #define CM_SCALE_UP (4*DBL_MANT_DIG+1)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	46 #endif
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	47 #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	48
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	49 /* forward declarations */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	50 static Py_complex c_asinh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	51 static Py_complex c_atanh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	52 static Py_complex c_cosh(Py_complex);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	53 static Py_complex c_sinh(Py_complex);
24280 1598a1e473e2 staticforward bites the dust. Jeremy Hylton <jeremy@alum.mit.edu> parents: 23832 diff changeset	54 static Py_complex c_sqrt(Py_complex);
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	55 static Py_complex c_tanh(Py_complex);
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	56 static PyObject * math_error(void);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	57
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	58 /* Code to deal with special values (infinities, NaNs, etc.). */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	59
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	60 /* special_type takes a double and returns an integer code indicating
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	61 the type of the double as follows:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	62 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	63
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	64 enum special_types {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	65 ST_NINF, /* 0, negative infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	66 ST_NEG, /* 1, negative finite number (nonzero) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	67 ST_NZERO, /* 2, -0. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	68 ST_PZERO, /* 3, +0. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	69 ST_POS, /* 4, positive finite number (nonzero) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	70 ST_PINF, /* 5, positive infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	71 ST_NAN, /* 6, Not a Number */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	72 };
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	73
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	74 static enum special_types
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	75 special_type(double d)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	76 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	77 if (Py_IS_FINITE(d)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	78 if (d != 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	79 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	80 return ST_POS;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	81 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	82 return ST_NEG;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	83 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	84 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	85 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	86 return ST_PZERO;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	87 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	88 return ST_NZERO;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	89 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	90 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	91 if (Py_IS_NAN(d))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	92 return ST_NAN;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	93 if (copysign(1., d) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	94 return ST_PINF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	95 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	96 return ST_NINF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	97 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	98
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	99 #define SPECIAL_VALUE(z, table) \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	100 if (!Py_IS_FINITE((z).real) \|\| !Py_IS_FINITE((z).imag)) { \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	101 errno = 0; \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	102 return table[special_type((z).real)] \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	103 [special_type((z).imag)]; \
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	104 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	105
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	106 #define P Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	107 #define P14 0.25*Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	108 #define P12 0.5*Py_MATH_PI
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	109 #define P34 0.75*Py_MATH_PI
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	110 #define INF Py_HUGE_VAL
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	111 #define N Py_NAN
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	112 #define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	113
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	114 /* First, the C functions that do the real work. Each of the c_*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	115 functions computes and returns the C99 Annex G recommended result
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	116 and also sets errno as follows: errno = 0 if no floating-point
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	117 exception is associated with the result; errno = EDOM if C99 Annex
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	118 G recommends raising divide-by-zero or invalid for this result; and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	119 errno = ERANGE where the overflow floating-point signal should be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	120 raised.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	121 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	122
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	123 static Py_complex acos_special_values[7][7];
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	124
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	125 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	126 c_acos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	127 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	128 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	129
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	130 SPECIAL_VALUE(z, acos_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	131
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	132 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	133 /* avoid unnecessary overflow for large arguments */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	134 r.real = atan2(fabs(z.imag), z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	135 /* split into cases to make sure that the branch cut has the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	136 correct continuity on systems with unsigned zeros */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	137 if (z.real < 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	138 r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	139 M_LN2*2., z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	140 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	141 r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	142 M_LN2*2., -z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	143 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	144 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	145 s1.real = 1.-z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	146 s1.imag = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	147 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	148 s2.real = 1.+z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	149 s2.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	150 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	151 r.real = 2.*atan2(s1.real, s2.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	152 r.imag = asinh(s2.reals1.imag - s2.imags1.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	153 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	154 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	155 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	156 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	157
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	158 PyDoc_STRVAR(c_acos_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	159 "acos(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	160 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	161 "Return the arc cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	162
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	163
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	164 static Py_complex acosh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	165
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	166 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	167 c_acosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	168 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	169 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	170
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	171 SPECIAL_VALUE(z, acosh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	172
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	173 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	174 /* avoid unnecessary overflow for large arguments */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	175 r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	176 r.imag = atan2(z.imag, z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	177 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	178 s1.real = z.real - 1.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	179 s1.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	180 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	181 s2.real = z.real + 1.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	182 s2.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	183 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	184 r.real = asinh(s1.reals2.real + s1.imags2.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	185 r.imag = 2.*atan2(s1.imag, s2.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	186 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	187 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	188 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	189 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	190
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	191 PyDoc_STRVAR(c_acosh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	192 "acosh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	193 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	194 "Return the hyperbolic arccosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	195
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	196
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	197 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	198 c_asin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	199 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	200 /* asin(z) = -i asinh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	201 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	202 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	203 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	204 s = c_asinh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	205 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	206 r.imag = -s.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	207 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	208 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	209
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	210 PyDoc_STRVAR(c_asin_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	211 "asin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	212 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	213 "Return the arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	214
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	215
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	216 static Py_complex asinh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	217
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	218 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	219 c_asinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	220 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	221 Py_complex s1, s2, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	222
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	223 SPECIAL_VALUE(z, asinh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	224
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	225 if (fabs(z.real) > CM_LARGE_DOUBLE \|\| fabs(z.imag) > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	226 if (z.imag >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	227 r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	228 M_LN2*2., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	229 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	230 r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	231 M_LN2*2., -z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	232 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	233 r.imag = atan2(z.imag, fabs(z.real));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	234 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	235 s1.real = 1.+z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	236 s1.imag = -z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	237 s1 = c_sqrt(s1);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	238 s2.real = 1.-z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	239 s2.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	240 s2 = c_sqrt(s2);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	241 r.real = asinh(s1.reals2.imag-s2.reals1.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	242 r.imag = atan2(z.imag, s1.reals2.real-s1.imags2.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	243 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	244 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	245 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	246 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	247
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	248 PyDoc_STRVAR(c_asinh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	249 "asinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	250 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	251 "Return the hyperbolic arc sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	252
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	253
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	254 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	255 c_atan(Py_complex z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	256 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	257 /* atan(z) = -i atanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	258 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	259 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	260 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	261 s = c_atanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	262 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	263 r.imag = -s.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	264 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	265 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	266
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	267 /* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	268 C99 for atan2(0., 0.). */
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	269 static double
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	270 c_atan2(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	271 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	272 if (Py_IS_NAN(z.real) \|\| Py_IS_NAN(z.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	273 return Py_NAN;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	274 if (Py_IS_INFINITY(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	275 if (Py_IS_INFINITY(z.real)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	276 if (copysign(1., z.real) == 1.)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	277 /* atan2(+-inf, +inf) == +-pi/4 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	278 return copysign(0.25*Py_MATH_PI, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	279 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	280 /* atan2(+-inf, -inf) == +-pi3/4 /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	281 return copysign(0.75*Py_MATH_PI, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	282 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	283 /* atan2(+-inf, x) == +-pi/2 for finite x */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	284 return copysign(0.5*Py_MATH_PI, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	285 }
46516 ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	286 if (Py_IS_INFINITY(z.real) \|\| z.imag == 0.) {
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	287 if (copysign(1., z.real) == 1.)
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	288 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	289 return copysign(0., z.imag);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	290 else
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	291 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	292 return copysign(Py_MATH_PI, z.imag);
ec48490b969a Merged revisions 62420-62421,62423-62424 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46505 diff changeset	293 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	294 return atan2(z.imag, z.real);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	295 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	296
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	297 PyDoc_STRVAR(c_atan_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	298 "atan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	299 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	300 "Return the arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	301
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	302
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	303 static Py_complex atanh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	304
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	305 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	306 c_atanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	307 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	308 Py_complex r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	309 double ay, h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	310
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	311 SPECIAL_VALUE(z, atanh_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	312
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	313 /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	314 if (z.real < 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	315 return c_neg(c_atanh(c_neg(z)));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	316 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	317
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	318 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	319 if (z.real > CM_SQRT_LARGE_DOUBLE \|\| ay > CM_SQRT_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	320 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	321 if abs(z) is large then we use the approximation
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	322 atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	323 of z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	324 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	325 h = hypot(z.real/2., z.imag/2.); /* safe from overflow */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	326 r.real = z.real/4./h/h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	327 /* the two negations in the next line cancel each other out
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	328 except when working with unsigned zeros: they're there to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	329 ensure that the branch cut has the correct continuity on
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	330 systems that don't support signed zeros */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	331 r.imag = -copysign(Py_MATH_PI/2., -z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	332 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	333 } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	334 /* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	335 if (ay == 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	336 r.real = INF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	337 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	338 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	339 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	340 r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	341 r.imag = copysign(atan2(2., -ay)/2, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	342 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	343 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	344 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	345 r.real = log1p(4.z.real/((1-z.real)(1-z.real) + ay*ay))/4.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	346 r.imag = -atan2(-2.z.imag, (1-z.real)(1+z.real) - ay*ay)/2.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	347 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	348 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	349 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	350 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	351
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	352 PyDoc_STRVAR(c_atanh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	353 "atanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	354 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	355 "Return the hyperbolic arc tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	356
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	357
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	358 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	359 c_cos(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	360 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	361 /* cos(z) = cosh(iz) */
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	362 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	363 r.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	364 r.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	365 r = c_cosh(r);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	366 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	367 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	368
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	369 PyDoc_STRVAR(c_cos_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	370 "cos(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	371 "n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	372 "Return the cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	373
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	374
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	375 /* cosh(infinity + iy) needs to be dealt with specially /
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	376 static Py_complex cosh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	377
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	378 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	379 c_cosh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	380 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	381 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	382 double x_minus_one;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	383
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	384 /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	385 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	386 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	387 (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	388 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	389 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	390 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	391 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	392 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	393 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	394 r.imag = -copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	395 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	396 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	397 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	398 r = cosh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	399 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	400 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	401 /* need to set errno = EDOM if y is +/- infinity and x is not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	402 a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	403 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	404 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	405 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	406 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	407 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	408 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	409
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	410 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	411 /* deal correctly with cases where cosh(z.real) overflows but
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	412 cosh(z) does not. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	413 x_minus_one = z.real - copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	414 r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	415 r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	416 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	417 r.real = cos(z.imag) * cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	418 r.imag = sin(z.imag) * sinh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	419 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	420 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	421 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	422 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	423 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	424 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	425 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	426 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	427
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	428 PyDoc_STRVAR(c_cosh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	429 "cosh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	430 "n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	431 "Return the hyperbolic cosine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	432
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	433
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	434 /* exp(infinity + iy) and exp(-infinity + iy) need special treatment for
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	435 finite y */
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	436 static Py_complex exp_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	437
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	438 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	439 c_exp(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	440 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	441 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	442 double l;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	443
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	444 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	445 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	446 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	447 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	448 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	449 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	450 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	451 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	452 r.real = copysign(0., cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	453 r.imag = copysign(0., sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	454 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	455 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	456 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	457 r = exp_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	458 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	459 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	460 /* need to set errno = EDOM if y is +/- infinity and x is not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	461 a NaN and not -infinity */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	462 if (Py_IS_INFINITY(z.imag) &&
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	463 (Py_IS_FINITE(z.real) \|\|
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	464 (Py_IS_INFINITY(z.real) && z.real > 0)))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	465 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	466 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	467 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	468 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	469 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	470
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	471 if (z.real > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	472 l = exp(z.real-1.);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	473 r.real = lcos(z.imag)Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	474 r.imag = lsin(z.imag)Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	475 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	476 l = exp(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	477 r.real = l*cos(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	478 r.imag = l*sin(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	479 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	480 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	481 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	482 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	483 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	484 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	485 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	486 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	487
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	488 PyDoc_STRVAR(c_exp_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	489 "exp(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	490 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	491 "Return the exponential value e**x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	492
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	493
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	494 static Py_complex log_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	495
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	496 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	497 c_log(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	498 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	499 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	500 The usual formula for the real part is log(hypot(z.real, z.imag)).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	501 There are four situations where this formula is potentially
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	502 problematic:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	503
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	504 (1) the absolute value of z is subnormal. Then hypot is subnormal,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	505 so has fewer than the usual number of bits of accuracy, hence may
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	506 have large relative error. This then gives a large absolute error
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	507 in the log. This can be solved by rescaling z by a suitable power
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	508 of 2.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	509
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	510 (2) the absolute value of z is greater than DBL_MAX (e.g. when both
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	511 z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	512 Again, rescaling solves this.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	513
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	514 (3) the absolute value of z is close to 1. In this case it's
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	515 difficult to achieve good accuracy, at least in part because a
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	516 change of 1ulp in the real or imaginary part of z can result in a
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	517 change of billions of ulps in the correctly rounded answer.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	518
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	519 (4) z = 0. The simplest thing to do here is to call the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	520 floating-point log with an argument of 0, and let its behaviour
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	521 (returning -infinity, signaling a floating-point exception, setting
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	522 errno, or whatever) determine that of c_log. So the usual formula
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	523 is fine here.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	524
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	525 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	526
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	527 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	528 double ax, ay, am, an, h;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	529
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	530 SPECIAL_VALUE(z, log_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	531
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	532 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	533 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	534
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	535 if (ax > CM_LARGE_DOUBLE \|\| ay > CM_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	536 r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	537 } else if (ax < DBL_MIN && ay < DBL_MIN) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	538 if (ax > 0. \|\| ay > 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	539 /* catch cases where hypot(ax, ay) is subnormal */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	540 r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	541 ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	542 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	543 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	544 /* log(+/-0. +/- 0i) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	545 r.real = -INF;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	546 r.imag = atan2(z.imag, z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	547 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	548 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	549 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	550 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	551 h = hypot(ax, ay);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	552 if (0.71 <= h && h <= 1.73) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	553 am = ax > ay ? ax : ay; /* max(ax, ay) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	554 an = ax > ay ? ay : ax; /* min(ax, ay) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	555 r.real = log1p((am-1)(am+1)+anan)/2.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	556 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	557 r.real = log(h);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	558 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	559 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	560 r.imag = atan2(z.imag, z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	561 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	562 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	563 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	564
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	565
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	566 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	567 c_log10(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	568 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	569 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	570 int errno_save;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	571
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	572 r = c_log(z);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	573 errno_save = errno; /* just in case the divisions affect errno */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	574 r.real = r.real / M_LN10;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	575 r.imag = r.imag / M_LN10;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	576 errno = errno_save;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	577 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	578 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	579
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	580 PyDoc_STRVAR(c_log10_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	581 "log10(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	582 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	583 "Return the base-10 logarithm of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	584
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	585
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	586 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	587 c_sin(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	588 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	589 /* sin(z) = -i sin(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	590 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	591 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	592 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	593 s = c_sinh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	594 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	595 r.imag = -s.real;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	596 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	597 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	598
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	599 PyDoc_STRVAR(c_sin_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	600 "sin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	601 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	602 "Return the sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	603
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	604
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	605 /* sinh(infinity + iy) needs to be dealt with specially /
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	606 static Py_complex sinh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	607
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	608 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	609 c_sinh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	610 {
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	611 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	612 double x_minus_one;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	613
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	614 /* special treatment for sinh(+/-inf + iy) if y is finite and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	615 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	616 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	617 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	618 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	619 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	620 r.real = copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	621 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	622 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	623 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	624 r.real = -copysign(INF, cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	625 r.imag = copysign(INF, sin(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	626 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	627 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	628 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	629 r = sinh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	630 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	631 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	632 /* need to set errno = EDOM if y is +/- infinity and x is not
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	633 a NaN */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	634 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	635 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	636 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	637 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	638 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	639 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	640
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	641 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	642 x_minus_one = z.real - copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	643 r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	644 r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	645 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	646 r.real = cos(z.imag) * sinh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	647 r.imag = sin(z.imag) * cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	648 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	649 /* detect overflow, and set errno accordingly */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	650 if (Py_IS_INFINITY(r.real) \|\| Py_IS_INFINITY(r.imag))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	651 errno = ERANGE;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	652 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	653 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	654 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	655 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	656
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	657 PyDoc_STRVAR(c_sinh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	658 "sinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	659 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	660 "Return the hyperbolic sine of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	661
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	662
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	663 static Py_complex sqrt_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	664
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	665 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	666 c_sqrt(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	667 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	668 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	669 Method: use symmetries to reduce to the case when x = z.real and y
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	670 = z.imag are nonnegative. Then the real part of the result is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	671 given by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	672
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	673 s = sqrt((x + hypot(x, y))/2)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	674
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	675 and the imaginary part is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	676
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	677 d = (y/2)/s
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	678
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	679 If either x or y is very large then there's a risk of overflow in
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	680 computation of the expression x + hypot(x, y). We can avoid this
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	681 by rewriting the formula for s as:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	682
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	683 s = 2*sqrt(x/8 + hypot(x/8, y/8))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	684
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	685 This costs us two extra multiplications/divisions, but avoids the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	686 overhead of checking for x and y large.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	687
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	688 If both x and y are subnormal then hypot(x, y) may also be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	689 subnormal, so will lack full precision. We solve this by rescaling
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	690 x and y by a sufficiently large power of 2 to ensure that x and y
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	691 are normal.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	692 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	693
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	694
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	695 Py_complex r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	696 double s,d;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	697 double ax, ay;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	698
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	699 SPECIAL_VALUE(z, sqrt_special_values);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	700
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	701 if (z.real == 0. && z.imag == 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	702 r.real = 0.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	703 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	704 return r;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	705 }
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	706
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	707 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	708 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	709
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	710 if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. \|\| ay > 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	711 /* here we catch cases where hypot(ax, ay) is subnormal */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	712 ax = ldexp(ax, CM_SCALE_UP);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	713 s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	714 CM_SCALE_DOWN);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	715 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	716 ax /= 8.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	717 s = 2.*sqrt(ax + hypot(ax, ay/8.));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	718 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	719 d = ay/(2.*s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	720
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	721 if (z.real >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	722 r.real = s;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	723 r.imag = copysign(d, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	724 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	725 r.real = d;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	726 r.imag = copysign(s, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	727 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	728 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	729 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	730 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	731
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	732 PyDoc_STRVAR(c_sqrt_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	733 "sqrt(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	734 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	735 "Return the square root of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	736
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	737
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	738 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	739 c_tan(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	740 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	741 /* tan(z) = -i tanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	742 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	743 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	744 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	745 s = c_tanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	746 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	747 r.imag = -s.real;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	748 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	749 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	750
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	751 PyDoc_STRVAR(c_tan_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	752 "tan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	753 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	754 "Return the tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	755
f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	756
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	757 /* tanh(infinity + iy) needs to be dealt with specially /
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	758 static Py_complex tanh_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	759
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	760 static Py_complex
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	761 c_tanh(Py_complex z)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	762 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	763 /* Formula:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	764
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	765 tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	766 (1+tan(y)^2 tanh(x)^2)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	767
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	768 To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	769 as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	770 by 4 exp(-2*x) instead, to avoid possible overflow in the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	771 computation of cosh(x).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	772
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	773 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	774
3771 d0988318b756 complex -> Py_complex Guido van Rossum <guido@python.org> parents: 3615 diff changeset	775 Py_complex r;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	776 double tx, ty, cx, txty, denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	777
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	778 /* special treatment for tanh(+/-inf + iy) if y is finite and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	779 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	780 if (!Py_IS_FINITE(z.real) \|\| !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	781 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	782 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	783 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	784 r.real = 1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	785 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	786 2.sin(z.imag)cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	787 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	788 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	789 r.real = -1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	790 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	791 2.sin(z.imag)cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	792 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	793 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	794 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	795 r = tanh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	796 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	797 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	798 /* need to set errno = EDOM if z.imag is +/-infinity and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	799 z.real is finite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	800 if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	801 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	802 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	803 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	804 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	805 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	806
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	807 /* danger of overflow in 2.z.imag !/
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	808 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	809 r.real = copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	810 r.imag = 4.sin(z.imag)cos(z.imag)exp(-2.fabs(z.real));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	811 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	812 tx = tanh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	813 ty = tan(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	814 cx = 1./cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	815 txty = tx*ty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	816 denom = 1. + txty*txty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	817 r.real = tx(1.+tyty)/denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	818 r.imag = ((ty/denom)cx)cx;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	819 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	820 errno = 0;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	821 return r;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	822 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	823
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	824 PyDoc_STRVAR(c_tanh_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	825 "tanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	826 "\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	827 "Return the hyperbolic tangent of x.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	828
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	829
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	830 static PyObject *
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	831 cmath_log(PyObject self, PyObject args)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	832 {
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	833 Py_complex x;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	834 Py_complex y;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	835
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	836 if (!PyArg_ParseTuple(args, "D\|D", &x, &y))
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	837 return NULL;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	838
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	839 errno = 0;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	840 PyFPE_START_PROTECT("complex function", return 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	841 x = c_log(x);
47890 f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue Mark Dickinson <dickinsm@gmail.com> parents: 47093 diff changeset	842 if (PyTuple_GET_SIZE(args) == 2) {
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue Mark Dickinson <dickinsm@gmail.com> parents: 47093 diff changeset	843 y = c_log(y);
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue Mark Dickinson <dickinsm@gmail.com> parents: 47093 diff changeset	844 x = c_quot(x, y);
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue Mark Dickinson <dickinsm@gmail.com> parents: 47093 diff changeset	845 }
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	846 PyFPE_END_PROTECT(x)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	847 if (errno != 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	848 return math_error();
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	849 return PyComplex_FromCComplex(x);
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	850 }
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	851
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	852 PyDoc_STRVAR(cmath_log_doc,
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	853 "log(x[, base]) -> the logarithm of x to the given base.\n\
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	854 If the base not specified, returns the natural logarithm (base e) of x.");
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	855
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	856
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	857 /* And now the glue to make them available from Python: */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	858
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	859 static PyObject *
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13493 diff changeset	860 math_error(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	861 {
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	862 if (errno == EDOM)
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	863 PyErr_SetString(PyExc_ValueError, "math domain error");
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	864 else if (errno == ERANGE)
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	865 PyErr_SetString(PyExc_OverflowError, "math range error");
97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	866 else /* Unexpected math error */
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	867 PyErr_SetFromErrno(PyExc_ValueError);
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	868 return NULL;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	869 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	870
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	871 static PyObject *
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	872 math_1(PyObject args, Py_complex (func)(Py_complex))
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	873 {
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	874 Py_complex x,r ;
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	875 if (!PyArg_ParseTuple(args, "D", &x))
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	876 return NULL;
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	877 errno = 0;
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	878 PyFPE_START_PROTECT("complex function", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	879 r = (*func)(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	880 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	881 if (errno == EDOM) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	882 PyErr_SetString(PyExc_ValueError, "math domain error");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	883 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	884 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	885 else if (errno == ERANGE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	886 PyErr_SetString(PyExc_OverflowError, "math range error");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	887 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	888 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	889 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	890 return PyComplex_FromCComplex(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	891 }
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	892 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	893
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	894 #define FUNC1(stubname, func) \
13493 8bacf8631a11 ANSI-fication Peter Schneider-Kamp <nowonder@nowonder.de> parents: 13447 diff changeset	895 static PyObject * stubname(PyObject self, PyObject args) { \
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	896 return math_1(args, func); \
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	897 }
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	898
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	899 FUNC1(cmath_acos, c_acos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	900 FUNC1(cmath_acosh, c_acosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	901 FUNC1(cmath_asin, c_asin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	902 FUNC1(cmath_asinh, c_asinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	903 FUNC1(cmath_atan, c_atan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	904 FUNC1(cmath_atanh, c_atanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	905 FUNC1(cmath_cos, c_cos)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	906 FUNC1(cmath_cosh, c_cosh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	907 FUNC1(cmath_exp, c_exp)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	908 FUNC1(cmath_log10, c_log10)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	909 FUNC1(cmath_sin, c_sin)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	910 FUNC1(cmath_sinh, c_sinh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	911 FUNC1(cmath_sqrt, c_sqrt)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	912 FUNC1(cmath_tan, c_tan)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	913 FUNC1(cmath_tanh, c_tanh)
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	914
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	915 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	916 cmath_phase(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	917 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	918 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	919 double phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	920 if (!PyArg_ParseTuple(args, "D:phase", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	921 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	922 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	923 PyFPE_START_PROTECT("arg function", return 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	924 phi = c_atan2(z);
47093 54fd0458550c Following Amaury's advice Christian Heimes <christian@cheimes.de> parents: 47092 diff changeset	925 PyFPE_END_PROTECT(phi)
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	926 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	927 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	928 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	929 return PyFloat_FromDouble(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	930 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	931
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	932 PyDoc_STRVAR(cmath_phase_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	933 "phase(z) -> float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	934 Return argument, also known as the phase angle, of a complex.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	935
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	936 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	937 cmath_polar(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	938 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	939 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	940 double r, phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	941 if (!PyArg_ParseTuple(args, "D:polar", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	942 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	943 PyFPE_START_PROTECT("polar function", return 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	944 phi = c_atan2(z); /* should not cause any exception */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	945 r = c_abs(z); /* sets errno to ERANGE on overflow; otherwise 0 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	946 PyFPE_END_PROTECT(r)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	947 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	948 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	949 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	950 return Py_BuildValue("dd", r, phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	951 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	952
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	953 PyDoc_STRVAR(cmath_polar_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	954 "polar(z) -> r: float, phi: float\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	955 Convert a complex from rectangular coordinates to polar coordinates. r is\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	956 the distance from 0 and phi the phase angle.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	957
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	958 /*
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	959 rect() isn't covered by the C99 standard, but it's not too hard to
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	960 figure out 'spirit of C99' rules for special value handing:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	961
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	962 rect(x, t) should behave like exp(log(x) + it) for positive-signed x
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	963 rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	964 rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	965 gives nan +- i0 with the sign of the imaginary part unspecified.
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	966
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	967 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	968
46505 63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	969 static Py_complex rect_special_values[7][7];
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	970
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	971 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	972 cmath_rect(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	973 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	974 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	975 double r, phi;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	976 if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	977 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	978 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	979 PyFPE_START_PROTECT("rect function", return 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	980
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	981 /* deal with special values */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	982 if (!Py_IS_FINITE(r) \|\| !Py_IS_FINITE(phi)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	983 /* if r is +/-infinity and phi is finite but nonzero then
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	984 result is (+-INF +-INF i), but we need to compute cos(phi)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	985 and sin(phi) to figure out the signs. */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	986 if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	987 && (phi != 0.))) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	988 if (r > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	989 z.real = copysign(INF, cos(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	990 z.imag = copysign(INF, sin(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	991 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	992 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	993 z.real = -copysign(INF, cos(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	994 z.imag = -copysign(INF, sin(phi));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	995 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	996 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	997 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	998 z = rect_special_values[special_type(r)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	999 [special_type(phi)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1000 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1001 /* need to set errno = EDOM if r is a nonzero number and phi
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1002 is infinite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1003 if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1004 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1005 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1006 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1007 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1008 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1009 z.real = r * cos(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1010 z.imag = r * sin(phi);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1011 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1012 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1013
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1014 PyFPE_END_PROTECT(z)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1015 if (errno != 0)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1016 return math_error();
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1017 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1018 return PyComplex_FromCComplex(z);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1019 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1020
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1021 PyDoc_STRVAR(cmath_rect_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1022 "rect(r, phi) -> z: complex\n\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1023 Convert from polar coordinates to rectangular coordinates.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1024
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1025 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1026 cmath_isnan(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1027 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1028 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1029 if (!PyArg_ParseTuple(args, "D:isnan", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1030 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1031 return PyBool_FromLong(Py_IS_NAN(z.real) \|\| Py_IS_NAN(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1032 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1033
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1034 PyDoc_STRVAR(cmath_isnan_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1035 "isnan(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1036 Checks if the real or imaginary part of z not a number (NaN)");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1037
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1038 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1039 cmath_isinf(PyObject self, PyObject args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1040 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1041 Py_complex z;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1042 if (!PyArg_ParseTuple(args, "D:isnan", &z))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1043 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1044 return PyBool_FromLong(Py_IS_INFINITY(z.real) \|\|
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1045 Py_IS_INFINITY(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1046 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1047
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1048 PyDoc_STRVAR(cmath_isinf_doc,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1049 "isinf(z) -> bool\n\
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1050 Checks if the real or imaginary part of z is infinite.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1051
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1052
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	1053 PyDoc_STRVAR(module_doc,
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1054 "This module is always available. It provides access to mathematical\n"
23832 ed1ba37a46b7 Patch #568124: Add doc string macros. Martin v. Löwis <martin@v.loewis.de> parents: 22722 diff changeset	1055 "functions for complex numbers.");
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1056
4639 97ec9dfbb2b6 Renamed Grandly Roger E. Masse <rmasse@newcnri.cnri.reston.va.us> parents: 4600 diff changeset	1057 static PyMethodDef cmath_methods[] = {
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1058 {"acos", cmath_acos, METH_VARARGS, c_acos_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1059 {"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1060 {"asin", cmath_asin, METH_VARARGS, c_asin_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1061 {"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1062 {"atan", cmath_atan, METH_VARARGS, c_atan_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1063 {"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1064 {"cos", cmath_cos, METH_VARARGS, c_cos_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1065 {"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1066 {"exp", cmath_exp, METH_VARARGS, c_exp_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1067 {"isinf", cmath_isinf, METH_VARARGS, cmath_isinf_doc},
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1068 {"isnan", cmath_isnan, METH_VARARGS, cmath_isnan_doc},
32350 11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209 Raymond Hettinger <python@rcn.com> parents: 24471 diff changeset	1069 {"log", cmath_log, METH_VARARGS, cmath_log_doc},
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1070 {"log10", cmath_log10, METH_VARARGS, c_log10_doc},
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1071 {"phase", cmath_phase, METH_VARARGS, cmath_phase_doc},
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1072 {"polar", cmath_polar, METH_VARARGS, cmath_polar_doc},
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1073 {"rect", cmath_rect, METH_VARARGS, cmath_rect_doc},
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1074 {"sin", cmath_sin, METH_VARARGS, c_sin_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1075 {"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1076 {"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1077 {"tan", cmath_tan, METH_VARARGS, c_tan_doc},
9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1078 {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1079 {NULL, NULL} /* sentinel */
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1080 };
969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1081
24471 f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/. Required adding a prototype Mark Hammond <mhammond@skippinet.com.au>* parents: 24280 diff changeset	1082 PyMODINIT_FUNC
13651 8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)', Thomas Wouters <thomas@python.org> parents: 13493 diff changeset	1083 initcmath(void)
3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1084 {
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1085 PyObject *m;
16707 9696c95d09b7 Mechanical edits just so I can read it. Tim Peters <tim.peters@gmail.com> parents: 13817 diff changeset	1086
9593 f22f769bf3d9 Added Doc strings -- by Chris Petrilli. Guido van Rossum <guido@python.org> parents: 9588 diff changeset	1087 m = Py_InitModule3("cmath", cmath_methods, module_doc);
36324 1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 32350 diff changeset	1088 if (m == NULL)
1af7f719ed28 Check return result from Py_InitModule(). This API can fail. Neal Norwitz <nnorwitz@gmail.com>* parents: 32350 diff changeset	1089 return;
22722 ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1090
ba68dda15df0 Use the PyModule_() API instead of manipulating the module dictionary Fred Drake <fdrake@acm.org>* parents: 22227 diff changeset	1091 PyModule_AddObject(m, "pi",
46477 b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1092 PyFloat_FromDouble(Py_MATH_PI));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 36324 diff changeset	1093 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	1094
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	1095 /* 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	1096
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	1097 #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	1098 #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	1099
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	1100 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	1101 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	1102 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	1103 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1104 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1105 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	1106 C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1107 C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N)
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	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
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 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	1111 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	1112 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	1113 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) 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	1114 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) 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	1115 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	1116 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	1117 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	1118 })
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
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 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	1121 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	1126 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	1127 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	1129
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 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	1131 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	1136 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	1139
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 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	1141 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	1145 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) 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	1149
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 INIT_SPECIAL_VALUES(exp_special_values, {
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63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1154 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	1155 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) 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	1159
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 INIT_SPECIAL_VALUES(log_special_values, {
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63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1163 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	1164 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	1165 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	1166 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	1167 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	1169
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 INIT_SPECIAL_VALUES(sinh_special_values, {
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1171 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	1175 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) 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	1179
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 INIT_SPECIAL_VALUES(sqrt_special_values, {
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63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from Christian Heimes <christian@cheimes.de> parents: 46477 diff changeset	1194 C(N,N) C(U,U) C(0.,-0.) C(0.,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	1195 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) 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	1197 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) 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	1198 })
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	1199
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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	1201 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	1206 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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3334 969bd911e114 complex math Guido van Rossum <guido@python.org> parents: diff changeset	1209 }

Mercurial > cpython-lru_cache-weakref

annotate Modules/cmathmodule.c @ 49955:878d40468c4e legacy-trunk