Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 1 | /* Complex math module */ |
| 2 | |
| 3 | /* much code borrowed from mathmodule.c */ |
| 4 | |
Roger E. Masse | 24070ca | 1996-12-09 22:59:53 +0000 | [diff] [blame] | 5 | #include "Python.h" |
Mark Dickinson | f371859 | 2009-12-21 15:27:41 +0000 | [diff] [blame] | 6 | #include "_math.h" |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 7 | /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from |
| 8 | float.h. We assume that FLT_RADIX is either 2 or 16. */ |
| 9 | #include <float.h> |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 10 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 11 | #include "clinic/cmathmodule.c.h" |
| 12 | /*[clinic input] |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 13 | module cmath |
| 14 | [clinic start generated code]*/ |
Serhiy Storchaka | 1009bf1 | 2015-04-03 23:53:51 +0300 | [diff] [blame] | 15 | /*[clinic end generated code: output=da39a3ee5e6b4b0d input=308d6839f4a46333]*/ |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 16 | |
| 17 | /*[python input] |
| 18 | class Py_complex_protected_converter(Py_complex_converter): |
| 19 | def modify(self): |
| 20 | return 'errno = 0; PyFPE_START_PROTECT("complex function", goto exit);' |
| 21 | |
| 22 | |
| 23 | class Py_complex_protected_return_converter(CReturnConverter): |
| 24 | type = "Py_complex" |
| 25 | |
| 26 | def render(self, function, data): |
| 27 | self.declare(data) |
| 28 | data.return_conversion.append(""" |
| 29 | PyFPE_END_PROTECT(_return_value); |
Serhiy Storchaka | ebe95fd | 2016-06-09 16:02:15 +0300 | [diff] [blame] | 30 | if (errno == EDOM) { |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 31 | PyErr_SetString(PyExc_ValueError, "math domain error"); |
| 32 | goto exit; |
Serhiy Storchaka | ebe95fd | 2016-06-09 16:02:15 +0300 | [diff] [blame] | 33 | } |
| 34 | else if (errno == ERANGE) { |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 35 | PyErr_SetString(PyExc_OverflowError, "math range error"); |
| 36 | goto exit; |
Serhiy Storchaka | ebe95fd | 2016-06-09 16:02:15 +0300 | [diff] [blame] | 37 | } |
| 38 | else { |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 39 | return_value = PyComplex_FromCComplex(_return_value); |
Serhiy Storchaka | ebe95fd | 2016-06-09 16:02:15 +0300 | [diff] [blame] | 40 | } |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 41 | """.strip()) |
| 42 | [python start generated code]*/ |
Serhiy Storchaka | ebe95fd | 2016-06-09 16:02:15 +0300 | [diff] [blame] | 43 | /*[python end generated code: output=da39a3ee5e6b4b0d input=345daa075b1028e7]*/ |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 44 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 45 | #if (FLT_RADIX != 2 && FLT_RADIX != 16) |
| 46 | #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16" |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 47 | #endif |
| 48 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 49 | #ifndef M_LN2 |
| 50 | #define M_LN2 (0.6931471805599453094) /* natural log of 2 */ |
| 51 | #endif |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 52 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 53 | #ifndef M_LN10 |
| 54 | #define M_LN10 (2.302585092994045684) /* natural log of 10 */ |
| 55 | #endif |
| 56 | |
| 57 | /* |
| 58 | CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log, |
| 59 | inverse trig and inverse hyperbolic trig functions. Its log is used in the |
Ezio Melotti | 1392500 | 2011-03-16 11:05:33 +0200 | [diff] [blame] | 60 | evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unnecessary |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 61 | overflow. |
| 62 | */ |
| 63 | |
| 64 | #define CM_LARGE_DOUBLE (DBL_MAX/4.) |
| 65 | #define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE)) |
| 66 | #define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE)) |
| 67 | #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN)) |
| 68 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 69 | /* |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 70 | CM_SCALE_UP is an odd integer chosen such that multiplication by |
| 71 | 2**CM_SCALE_UP is sufficient to turn a subnormal into a normal. |
| 72 | CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute |
| 73 | square roots accurately when the real and imaginary parts of the argument |
| 74 | are subnormal. |
| 75 | */ |
| 76 | |
| 77 | #if FLT_RADIX==2 |
| 78 | #define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1) |
| 79 | #elif FLT_RADIX==16 |
| 80 | #define CM_SCALE_UP (4*DBL_MANT_DIG+1) |
| 81 | #endif |
| 82 | #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2) |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 83 | |
Mark Dickinson | 84e6311 | 2016-08-29 13:56:58 +0100 | [diff] [blame] | 84 | /* Constants cmath.inf, cmath.infj, cmath.nan, cmath.nanj. |
| 85 | cmath.nan and cmath.nanj are defined only when either |
| 86 | PY_NO_SHORT_FLOAT_REPR is *not* defined (which should be |
| 87 | the most common situation on machines using an IEEE 754 |
| 88 | representation), or Py_NAN is defined. */ |
| 89 | |
| 90 | static double |
| 91 | m_inf(void) |
| 92 | { |
| 93 | #ifndef PY_NO_SHORT_FLOAT_REPR |
| 94 | return _Py_dg_infinity(0); |
| 95 | #else |
| 96 | return Py_HUGE_VAL; |
| 97 | #endif |
| 98 | } |
| 99 | |
| 100 | static Py_complex |
| 101 | c_infj(void) |
| 102 | { |
| 103 | Py_complex r; |
| 104 | r.real = 0.0; |
| 105 | r.imag = m_inf(); |
| 106 | return r; |
| 107 | } |
| 108 | |
| 109 | #if !defined(PY_NO_SHORT_FLOAT_REPR) || defined(Py_NAN) |
| 110 | |
| 111 | static double |
| 112 | m_nan(void) |
| 113 | { |
| 114 | #ifndef PY_NO_SHORT_FLOAT_REPR |
| 115 | return _Py_dg_stdnan(0); |
| 116 | #else |
| 117 | return Py_NAN; |
| 118 | #endif |
| 119 | } |
| 120 | |
| 121 | static Py_complex |
| 122 | c_nanj(void) |
| 123 | { |
| 124 | Py_complex r; |
| 125 | r.real = 0.0; |
| 126 | r.imag = m_nan(); |
| 127 | return r; |
| 128 | } |
| 129 | |
| 130 | #endif |
| 131 | |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 132 | /* forward declarations */ |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 133 | static Py_complex cmath_asinh_impl(PyObject *, Py_complex); |
| 134 | static Py_complex cmath_atanh_impl(PyObject *, Py_complex); |
| 135 | static Py_complex cmath_cosh_impl(PyObject *, Py_complex); |
| 136 | static Py_complex cmath_sinh_impl(PyObject *, Py_complex); |
| 137 | static Py_complex cmath_sqrt_impl(PyObject *, Py_complex); |
| 138 | static Py_complex cmath_tanh_impl(PyObject *, Py_complex); |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 139 | static PyObject * math_error(void); |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 140 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 141 | /* Code to deal with special values (infinities, NaNs, etc.). */ |
| 142 | |
| 143 | /* special_type takes a double and returns an integer code indicating |
| 144 | the type of the double as follows: |
| 145 | */ |
| 146 | |
| 147 | enum special_types { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 148 | ST_NINF, /* 0, negative infinity */ |
| 149 | ST_NEG, /* 1, negative finite number (nonzero) */ |
| 150 | ST_NZERO, /* 2, -0. */ |
| 151 | ST_PZERO, /* 3, +0. */ |
| 152 | ST_POS, /* 4, positive finite number (nonzero) */ |
| 153 | ST_PINF, /* 5, positive infinity */ |
| 154 | ST_NAN /* 6, Not a Number */ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 155 | }; |
| 156 | |
| 157 | static enum special_types |
| 158 | special_type(double d) |
| 159 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 160 | if (Py_IS_FINITE(d)) { |
| 161 | if (d != 0) { |
| 162 | if (copysign(1., d) == 1.) |
| 163 | return ST_POS; |
| 164 | else |
| 165 | return ST_NEG; |
| 166 | } |
| 167 | else { |
| 168 | if (copysign(1., d) == 1.) |
| 169 | return ST_PZERO; |
| 170 | else |
| 171 | return ST_NZERO; |
| 172 | } |
| 173 | } |
| 174 | if (Py_IS_NAN(d)) |
| 175 | return ST_NAN; |
| 176 | if (copysign(1., d) == 1.) |
| 177 | return ST_PINF; |
| 178 | else |
| 179 | return ST_NINF; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 180 | } |
| 181 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 182 | #define SPECIAL_VALUE(z, table) \ |
| 183 | if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) { \ |
| 184 | errno = 0; \ |
| 185 | return table[special_type((z).real)] \ |
| 186 | [special_type((z).imag)]; \ |
| 187 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 188 | |
| 189 | #define P Py_MATH_PI |
| 190 | #define P14 0.25*Py_MATH_PI |
| 191 | #define P12 0.5*Py_MATH_PI |
| 192 | #define P34 0.75*Py_MATH_PI |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 193 | #define INF Py_HUGE_VAL |
| 194 | #define N Py_NAN |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 195 | #define U -9.5426319407711027e33 /* unlikely value, used as placeholder */ |
| 196 | |
| 197 | /* First, the C functions that do the real work. Each of the c_* |
| 198 | functions computes and returns the C99 Annex G recommended result |
| 199 | and also sets errno as follows: errno = 0 if no floating-point |
| 200 | exception is associated with the result; errno = EDOM if C99 Annex |
| 201 | G recommends raising divide-by-zero or invalid for this result; and |
| 202 | errno = ERANGE where the overflow floating-point signal should be |
| 203 | raised. |
| 204 | */ |
| 205 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 206 | static Py_complex acos_special_values[7][7]; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 207 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 208 | /*[clinic input] |
| 209 | cmath.acos -> Py_complex_protected |
| 210 | |
| 211 | z: Py_complex_protected |
| 212 | / |
| 213 | |
| 214 | Return the arc cosine of z. |
| 215 | [clinic start generated code]*/ |
| 216 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 217 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 218 | cmath_acos_impl(PyObject *module, Py_complex z) |
| 219 | /*[clinic end generated code: output=40bd42853fd460ae input=bd6cbd78ae851927]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 220 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 221 | Py_complex s1, s2, r; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 222 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 223 | SPECIAL_VALUE(z, acos_special_values); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 224 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 225 | if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) { |
| 226 | /* avoid unnecessary overflow for large arguments */ |
| 227 | r.real = atan2(fabs(z.imag), z.real); |
| 228 | /* split into cases to make sure that the branch cut has the |
| 229 | correct continuity on systems with unsigned zeros */ |
| 230 | if (z.real < 0.) { |
| 231 | r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) + |
| 232 | M_LN2*2., z.imag); |
| 233 | } else { |
| 234 | r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) + |
| 235 | M_LN2*2., -z.imag); |
| 236 | } |
| 237 | } else { |
| 238 | s1.real = 1.-z.real; |
| 239 | s1.imag = -z.imag; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 240 | s1 = cmath_sqrt_impl(module, s1); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 241 | s2.real = 1.+z.real; |
| 242 | s2.imag = z.imag; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 243 | s2 = cmath_sqrt_impl(module, s2); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 244 | r.real = 2.*atan2(s1.real, s2.real); |
| 245 | r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real); |
| 246 | } |
| 247 | errno = 0; |
| 248 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 249 | } |
| 250 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 251 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 252 | static Py_complex acosh_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 253 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 254 | /*[clinic input] |
| 255 | cmath.acosh = cmath.acos |
| 256 | |
Mark Dickinson | cc8617b | 2015-01-11 13:22:44 +0000 | [diff] [blame] | 257 | Return the inverse hyperbolic cosine of z. |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 258 | [clinic start generated code]*/ |
| 259 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 260 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 261 | cmath_acosh_impl(PyObject *module, Py_complex z) |
| 262 | /*[clinic end generated code: output=3e2454d4fcf404ca input=3f61bee7d703e53c]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 263 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 264 | Py_complex s1, s2, r; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 265 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 266 | SPECIAL_VALUE(z, acosh_special_values); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 267 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 268 | if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) { |
| 269 | /* avoid unnecessary overflow for large arguments */ |
| 270 | r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.; |
| 271 | r.imag = atan2(z.imag, z.real); |
| 272 | } else { |
| 273 | s1.real = z.real - 1.; |
| 274 | s1.imag = z.imag; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 275 | s1 = cmath_sqrt_impl(module, s1); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 276 | s2.real = z.real + 1.; |
| 277 | s2.imag = z.imag; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 278 | s2 = cmath_sqrt_impl(module, s2); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 279 | r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag); |
| 280 | r.imag = 2.*atan2(s1.imag, s2.real); |
| 281 | } |
| 282 | errno = 0; |
| 283 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 284 | } |
| 285 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 286 | /*[clinic input] |
| 287 | cmath.asin = cmath.acos |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 288 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 289 | Return the arc sine of z. |
| 290 | [clinic start generated code]*/ |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 291 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 292 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 293 | cmath_asin_impl(PyObject *module, Py_complex z) |
| 294 | /*[clinic end generated code: output=3b264cd1b16bf4e1 input=be0bf0cfdd5239c5]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 295 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 296 | /* asin(z) = -i asinh(iz) */ |
| 297 | Py_complex s, r; |
| 298 | s.real = -z.imag; |
| 299 | s.imag = z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 300 | s = cmath_asinh_impl(module, s); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 301 | r.real = s.imag; |
| 302 | r.imag = -s.real; |
| 303 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 304 | } |
| 305 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 306 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 307 | static Py_complex asinh_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 308 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 309 | /*[clinic input] |
| 310 | cmath.asinh = cmath.acos |
| 311 | |
Mark Dickinson | cc8617b | 2015-01-11 13:22:44 +0000 | [diff] [blame] | 312 | Return the inverse hyperbolic sine of z. |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 313 | [clinic start generated code]*/ |
| 314 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 315 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 316 | cmath_asinh_impl(PyObject *module, Py_complex z) |
| 317 | /*[clinic end generated code: output=733d8107841a7599 input=5c09448fcfc89a79]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 318 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 319 | Py_complex s1, s2, r; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 320 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 321 | SPECIAL_VALUE(z, asinh_special_values); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 322 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 323 | if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) { |
| 324 | if (z.imag >= 0.) { |
| 325 | r.real = copysign(log(hypot(z.real/2., z.imag/2.)) + |
| 326 | M_LN2*2., z.real); |
| 327 | } else { |
| 328 | r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) + |
| 329 | M_LN2*2., -z.real); |
| 330 | } |
| 331 | r.imag = atan2(z.imag, fabs(z.real)); |
| 332 | } else { |
| 333 | s1.real = 1.+z.imag; |
| 334 | s1.imag = -z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 335 | s1 = cmath_sqrt_impl(module, s1); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 336 | s2.real = 1.-z.imag; |
| 337 | s2.imag = z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 338 | s2 = cmath_sqrt_impl(module, s2); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 339 | r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag); |
| 340 | r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag); |
| 341 | } |
| 342 | errno = 0; |
| 343 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 344 | } |
| 345 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 346 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 347 | /*[clinic input] |
| 348 | cmath.atan = cmath.acos |
| 349 | |
| 350 | Return the arc tangent of z. |
| 351 | [clinic start generated code]*/ |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 352 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 353 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 354 | cmath_atan_impl(PyObject *module, Py_complex z) |
| 355 | /*[clinic end generated code: output=b6bfc497058acba4 input=3b21ff7d5eac632a]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 356 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 357 | /* atan(z) = -i atanh(iz) */ |
| 358 | Py_complex s, r; |
| 359 | s.real = -z.imag; |
| 360 | s.imag = z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 361 | s = cmath_atanh_impl(module, s); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 362 | r.real = s.imag; |
| 363 | r.imag = -s.real; |
| 364 | return r; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 365 | } |
| 366 | |
Christian Heimes | e57950f | 2008-04-21 13:08:03 +0000 | [diff] [blame] | 367 | /* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow |
| 368 | C99 for atan2(0., 0.). */ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 369 | static double |
| 370 | c_atan2(Py_complex z) |
| 371 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 372 | if (Py_IS_NAN(z.real) || Py_IS_NAN(z.imag)) |
| 373 | return Py_NAN; |
| 374 | if (Py_IS_INFINITY(z.imag)) { |
| 375 | if (Py_IS_INFINITY(z.real)) { |
| 376 | if (copysign(1., z.real) == 1.) |
| 377 | /* atan2(+-inf, +inf) == +-pi/4 */ |
| 378 | return copysign(0.25*Py_MATH_PI, z.imag); |
| 379 | else |
| 380 | /* atan2(+-inf, -inf) == +-pi*3/4 */ |
| 381 | return copysign(0.75*Py_MATH_PI, z.imag); |
| 382 | } |
| 383 | /* atan2(+-inf, x) == +-pi/2 for finite x */ |
| 384 | return copysign(0.5*Py_MATH_PI, z.imag); |
| 385 | } |
| 386 | if (Py_IS_INFINITY(z.real) || z.imag == 0.) { |
| 387 | if (copysign(1., z.real) == 1.) |
| 388 | /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */ |
| 389 | return copysign(0., z.imag); |
| 390 | else |
| 391 | /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */ |
| 392 | return copysign(Py_MATH_PI, z.imag); |
| 393 | } |
| 394 | return atan2(z.imag, z.real); |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 395 | } |
| 396 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 397 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 398 | static Py_complex atanh_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 399 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 400 | /*[clinic input] |
| 401 | cmath.atanh = cmath.acos |
| 402 | |
Mark Dickinson | cc8617b | 2015-01-11 13:22:44 +0000 | [diff] [blame] | 403 | Return the inverse hyperbolic tangent of z. |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 404 | [clinic start generated code]*/ |
| 405 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 406 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 407 | cmath_atanh_impl(PyObject *module, Py_complex z) |
| 408 | /*[clinic end generated code: output=e83355f93a989c9e input=2b3fdb82fb34487b]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 409 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 410 | Py_complex r; |
| 411 | double ay, h; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 412 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 413 | SPECIAL_VALUE(z, atanh_special_values); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 414 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 415 | /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */ |
| 416 | if (z.real < 0.) { |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 417 | return _Py_c_neg(cmath_atanh_impl(module, _Py_c_neg(z))); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 418 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 419 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 420 | ay = fabs(z.imag); |
| 421 | if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) { |
| 422 | /* |
| 423 | if abs(z) is large then we use the approximation |
| 424 | atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign |
| 425 | of z.imag) |
| 426 | */ |
| 427 | h = hypot(z.real/2., z.imag/2.); /* safe from overflow */ |
| 428 | r.real = z.real/4./h/h; |
| 429 | /* the two negations in the next line cancel each other out |
| 430 | except when working with unsigned zeros: they're there to |
| 431 | ensure that the branch cut has the correct continuity on |
| 432 | systems that don't support signed zeros */ |
| 433 | r.imag = -copysign(Py_MATH_PI/2., -z.imag); |
| 434 | errno = 0; |
| 435 | } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) { |
| 436 | /* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */ |
| 437 | if (ay == 0.) { |
| 438 | r.real = INF; |
| 439 | r.imag = z.imag; |
| 440 | errno = EDOM; |
| 441 | } else { |
| 442 | r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.))); |
| 443 | r.imag = copysign(atan2(2., -ay)/2, z.imag); |
| 444 | errno = 0; |
| 445 | } |
| 446 | } else { |
| 447 | r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.; |
| 448 | r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.; |
| 449 | errno = 0; |
| 450 | } |
| 451 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 452 | } |
| 453 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 454 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 455 | /*[clinic input] |
| 456 | cmath.cos = cmath.acos |
| 457 | |
| 458 | Return the cosine of z. |
| 459 | [clinic start generated code]*/ |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 460 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 461 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 462 | cmath_cos_impl(PyObject *module, Py_complex z) |
| 463 | /*[clinic end generated code: output=fd64918d5b3186db input=6022e39b77127ac7]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 464 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 465 | /* cos(z) = cosh(iz) */ |
| 466 | Py_complex r; |
| 467 | r.real = -z.imag; |
| 468 | r.imag = z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 469 | r = cmath_cosh_impl(module, r); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 470 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 471 | } |
| 472 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 473 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 474 | /* cosh(infinity + i*y) needs to be dealt with specially */ |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 475 | static Py_complex cosh_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 476 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 477 | /*[clinic input] |
| 478 | cmath.cosh = cmath.acos |
| 479 | |
| 480 | Return the hyperbolic cosine of z. |
| 481 | [clinic start generated code]*/ |
| 482 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 483 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 484 | cmath_cosh_impl(PyObject *module, Py_complex z) |
| 485 | /*[clinic end generated code: output=2e969047da601bdb input=d6b66339e9cc332b]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 486 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 487 | Py_complex r; |
| 488 | double x_minus_one; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 489 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 490 | /* special treatment for cosh(+/-inf + iy) if y is not a NaN */ |
| 491 | if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) { |
| 492 | if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) && |
| 493 | (z.imag != 0.)) { |
| 494 | if (z.real > 0) { |
| 495 | r.real = copysign(INF, cos(z.imag)); |
| 496 | r.imag = copysign(INF, sin(z.imag)); |
| 497 | } |
| 498 | else { |
| 499 | r.real = copysign(INF, cos(z.imag)); |
| 500 | r.imag = -copysign(INF, sin(z.imag)); |
| 501 | } |
| 502 | } |
| 503 | else { |
| 504 | r = cosh_special_values[special_type(z.real)] |
| 505 | [special_type(z.imag)]; |
| 506 | } |
| 507 | /* need to set errno = EDOM if y is +/- infinity and x is not |
| 508 | a NaN */ |
| 509 | if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real)) |
| 510 | errno = EDOM; |
| 511 | else |
| 512 | errno = 0; |
| 513 | return r; |
| 514 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 515 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 516 | if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) { |
| 517 | /* deal correctly with cases where cosh(z.real) overflows but |
| 518 | cosh(z) does not. */ |
| 519 | x_minus_one = z.real - copysign(1., z.real); |
| 520 | r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E; |
| 521 | r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E; |
| 522 | } else { |
| 523 | r.real = cos(z.imag) * cosh(z.real); |
| 524 | r.imag = sin(z.imag) * sinh(z.real); |
| 525 | } |
| 526 | /* detect overflow, and set errno accordingly */ |
| 527 | if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag)) |
| 528 | errno = ERANGE; |
| 529 | else |
| 530 | errno = 0; |
| 531 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 532 | } |
| 533 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 534 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 535 | /* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for |
| 536 | finite y */ |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 537 | static Py_complex exp_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 538 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 539 | /*[clinic input] |
| 540 | cmath.exp = cmath.acos |
| 541 | |
| 542 | Return the exponential value e**z. |
| 543 | [clinic start generated code]*/ |
| 544 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 545 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 546 | cmath_exp_impl(PyObject *module, Py_complex z) |
| 547 | /*[clinic end generated code: output=edcec61fb9dfda6c input=8b9e6cf8a92174c3]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 548 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 549 | Py_complex r; |
| 550 | double l; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 551 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 552 | if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) { |
| 553 | if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) |
| 554 | && (z.imag != 0.)) { |
| 555 | if (z.real > 0) { |
| 556 | r.real = copysign(INF, cos(z.imag)); |
| 557 | r.imag = copysign(INF, sin(z.imag)); |
| 558 | } |
| 559 | else { |
| 560 | r.real = copysign(0., cos(z.imag)); |
| 561 | r.imag = copysign(0., sin(z.imag)); |
| 562 | } |
| 563 | } |
| 564 | else { |
| 565 | r = exp_special_values[special_type(z.real)] |
| 566 | [special_type(z.imag)]; |
| 567 | } |
| 568 | /* need to set errno = EDOM if y is +/- infinity and x is not |
| 569 | a NaN and not -infinity */ |
| 570 | if (Py_IS_INFINITY(z.imag) && |
| 571 | (Py_IS_FINITE(z.real) || |
| 572 | (Py_IS_INFINITY(z.real) && z.real > 0))) |
| 573 | errno = EDOM; |
| 574 | else |
| 575 | errno = 0; |
| 576 | return r; |
| 577 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 578 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 579 | if (z.real > CM_LOG_LARGE_DOUBLE) { |
| 580 | l = exp(z.real-1.); |
| 581 | r.real = l*cos(z.imag)*Py_MATH_E; |
| 582 | r.imag = l*sin(z.imag)*Py_MATH_E; |
| 583 | } else { |
| 584 | l = exp(z.real); |
| 585 | r.real = l*cos(z.imag); |
| 586 | r.imag = l*sin(z.imag); |
| 587 | } |
| 588 | /* detect overflow, and set errno accordingly */ |
| 589 | if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag)) |
| 590 | errno = ERANGE; |
| 591 | else |
| 592 | errno = 0; |
| 593 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 594 | } |
| 595 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 596 | static Py_complex log_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 597 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 598 | static Py_complex |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 599 | c_log(Py_complex z) |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 600 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 601 | /* |
| 602 | The usual formula for the real part is log(hypot(z.real, z.imag)). |
| 603 | There are four situations where this formula is potentially |
| 604 | problematic: |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 605 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 606 | (1) the absolute value of z is subnormal. Then hypot is subnormal, |
| 607 | so has fewer than the usual number of bits of accuracy, hence may |
| 608 | have large relative error. This then gives a large absolute error |
| 609 | in the log. This can be solved by rescaling z by a suitable power |
| 610 | of 2. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 611 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 612 | (2) the absolute value of z is greater than DBL_MAX (e.g. when both |
| 613 | z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX) |
| 614 | Again, rescaling solves this. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 615 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 616 | (3) the absolute value of z is close to 1. In this case it's |
| 617 | difficult to achieve good accuracy, at least in part because a |
| 618 | change of 1ulp in the real or imaginary part of z can result in a |
| 619 | change of billions of ulps in the correctly rounded answer. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 620 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 621 | (4) z = 0. The simplest thing to do here is to call the |
| 622 | floating-point log with an argument of 0, and let its behaviour |
| 623 | (returning -infinity, signaling a floating-point exception, setting |
| 624 | errno, or whatever) determine that of c_log. So the usual formula |
| 625 | is fine here. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 626 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 627 | */ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 628 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 629 | Py_complex r; |
| 630 | double ax, ay, am, an, h; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 631 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 632 | SPECIAL_VALUE(z, log_special_values); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 633 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 634 | ax = fabs(z.real); |
| 635 | ay = fabs(z.imag); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 636 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 637 | if (ax > CM_LARGE_DOUBLE || ay > CM_LARGE_DOUBLE) { |
| 638 | r.real = log(hypot(ax/2., ay/2.)) + M_LN2; |
| 639 | } else if (ax < DBL_MIN && ay < DBL_MIN) { |
| 640 | if (ax > 0. || ay > 0.) { |
| 641 | /* catch cases where hypot(ax, ay) is subnormal */ |
| 642 | r.real = log(hypot(ldexp(ax, DBL_MANT_DIG), |
| 643 | ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2; |
| 644 | } |
| 645 | else { |
| 646 | /* log(+/-0. +/- 0i) */ |
| 647 | r.real = -INF; |
| 648 | r.imag = atan2(z.imag, z.real); |
| 649 | errno = EDOM; |
| 650 | return r; |
| 651 | } |
| 652 | } else { |
| 653 | h = hypot(ax, ay); |
| 654 | if (0.71 <= h && h <= 1.73) { |
| 655 | am = ax > ay ? ax : ay; /* max(ax, ay) */ |
| 656 | an = ax > ay ? ay : ax; /* min(ax, ay) */ |
| 657 | r.real = m_log1p((am-1)*(am+1)+an*an)/2.; |
| 658 | } else { |
| 659 | r.real = log(h); |
| 660 | } |
| 661 | } |
| 662 | r.imag = atan2(z.imag, z.real); |
| 663 | errno = 0; |
| 664 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 665 | } |
| 666 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 667 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 668 | /*[clinic input] |
| 669 | cmath.log10 = cmath.acos |
| 670 | |
| 671 | Return the base-10 logarithm of z. |
| 672 | [clinic start generated code]*/ |
| 673 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 674 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 675 | cmath_log10_impl(PyObject *module, Py_complex z) |
| 676 | /*[clinic end generated code: output=2922779a7c38cbe1 input=cff5644f73c1519c]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 677 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 678 | Py_complex r; |
| 679 | int errno_save; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 680 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 681 | r = c_log(z); |
| 682 | errno_save = errno; /* just in case the divisions affect errno */ |
| 683 | r.real = r.real / M_LN10; |
| 684 | r.imag = r.imag / M_LN10; |
| 685 | errno = errno_save; |
| 686 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 687 | } |
| 688 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 689 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 690 | /*[clinic input] |
| 691 | cmath.sin = cmath.acos |
| 692 | |
| 693 | Return the sine of z. |
| 694 | [clinic start generated code]*/ |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 695 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 696 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 697 | cmath_sin_impl(PyObject *module, Py_complex z) |
| 698 | /*[clinic end generated code: output=980370d2ff0bb5aa input=2d3519842a8b4b85]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 699 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 700 | /* sin(z) = -i sin(iz) */ |
| 701 | Py_complex s, r; |
| 702 | s.real = -z.imag; |
| 703 | s.imag = z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 704 | s = cmath_sinh_impl(module, s); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 705 | r.real = s.imag; |
| 706 | r.imag = -s.real; |
| 707 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 708 | } |
| 709 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 710 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 711 | /* sinh(infinity + i*y) needs to be dealt with specially */ |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 712 | static Py_complex sinh_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 713 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 714 | /*[clinic input] |
| 715 | cmath.sinh = cmath.acos |
| 716 | |
| 717 | Return the hyperbolic sine of z. |
| 718 | [clinic start generated code]*/ |
| 719 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 720 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 721 | cmath_sinh_impl(PyObject *module, Py_complex z) |
| 722 | /*[clinic end generated code: output=38b0a6cce26f3536 input=d2d3fc8c1ddfd2dd]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 723 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 724 | Py_complex r; |
| 725 | double x_minus_one; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 726 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 727 | /* special treatment for sinh(+/-inf + iy) if y is finite and |
| 728 | nonzero */ |
| 729 | if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) { |
| 730 | if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) |
| 731 | && (z.imag != 0.)) { |
| 732 | if (z.real > 0) { |
| 733 | r.real = copysign(INF, cos(z.imag)); |
| 734 | r.imag = copysign(INF, sin(z.imag)); |
| 735 | } |
| 736 | else { |
| 737 | r.real = -copysign(INF, cos(z.imag)); |
| 738 | r.imag = copysign(INF, sin(z.imag)); |
| 739 | } |
| 740 | } |
| 741 | else { |
| 742 | r = sinh_special_values[special_type(z.real)] |
| 743 | [special_type(z.imag)]; |
| 744 | } |
| 745 | /* need to set errno = EDOM if y is +/- infinity and x is not |
| 746 | a NaN */ |
| 747 | if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real)) |
| 748 | errno = EDOM; |
| 749 | else |
| 750 | errno = 0; |
| 751 | return r; |
| 752 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 753 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 754 | if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) { |
| 755 | x_minus_one = z.real - copysign(1., z.real); |
| 756 | r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E; |
| 757 | r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E; |
| 758 | } else { |
| 759 | r.real = cos(z.imag) * sinh(z.real); |
| 760 | r.imag = sin(z.imag) * cosh(z.real); |
| 761 | } |
| 762 | /* detect overflow, and set errno accordingly */ |
| 763 | if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag)) |
| 764 | errno = ERANGE; |
| 765 | else |
| 766 | errno = 0; |
| 767 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 768 | } |
| 769 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 770 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 771 | static Py_complex sqrt_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 772 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 773 | /*[clinic input] |
| 774 | cmath.sqrt = cmath.acos |
| 775 | |
| 776 | Return the square root of z. |
| 777 | [clinic start generated code]*/ |
| 778 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 779 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 780 | cmath_sqrt_impl(PyObject *module, Py_complex z) |
| 781 | /*[clinic end generated code: output=b6507b3029c339fc input=7088b166fc9a58c7]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 782 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 783 | /* |
| 784 | Method: use symmetries to reduce to the case when x = z.real and y |
| 785 | = z.imag are nonnegative. Then the real part of the result is |
| 786 | given by |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 787 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 788 | s = sqrt((x + hypot(x, y))/2) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 789 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 790 | and the imaginary part is |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 791 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 792 | d = (y/2)/s |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 793 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 794 | If either x or y is very large then there's a risk of overflow in |
| 795 | computation of the expression x + hypot(x, y). We can avoid this |
| 796 | by rewriting the formula for s as: |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 797 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 798 | s = 2*sqrt(x/8 + hypot(x/8, y/8)) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 799 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 800 | This costs us two extra multiplications/divisions, but avoids the |
| 801 | overhead of checking for x and y large. |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 802 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 803 | If both x and y are subnormal then hypot(x, y) may also be |
| 804 | subnormal, so will lack full precision. We solve this by rescaling |
| 805 | x and y by a sufficiently large power of 2 to ensure that x and y |
| 806 | are normal. |
| 807 | */ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 808 | |
| 809 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 810 | Py_complex r; |
| 811 | double s,d; |
| 812 | double ax, ay; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 813 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 814 | SPECIAL_VALUE(z, sqrt_special_values); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 815 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 816 | if (z.real == 0. && z.imag == 0.) { |
| 817 | r.real = 0.; |
| 818 | r.imag = z.imag; |
| 819 | return r; |
| 820 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 821 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 822 | ax = fabs(z.real); |
| 823 | ay = fabs(z.imag); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 824 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 825 | if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) { |
| 826 | /* here we catch cases where hypot(ax, ay) is subnormal */ |
| 827 | ax = ldexp(ax, CM_SCALE_UP); |
| 828 | s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))), |
| 829 | CM_SCALE_DOWN); |
| 830 | } else { |
| 831 | ax /= 8.; |
| 832 | s = 2.*sqrt(ax + hypot(ax, ay/8.)); |
| 833 | } |
| 834 | d = ay/(2.*s); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 835 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 836 | if (z.real >= 0.) { |
| 837 | r.real = s; |
| 838 | r.imag = copysign(d, z.imag); |
| 839 | } else { |
| 840 | r.real = d; |
| 841 | r.imag = copysign(s, z.imag); |
| 842 | } |
| 843 | errno = 0; |
| 844 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 845 | } |
| 846 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 847 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 848 | /*[clinic input] |
| 849 | cmath.tan = cmath.acos |
| 850 | |
| 851 | Return the tangent of z. |
| 852 | [clinic start generated code]*/ |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 853 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 854 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 855 | cmath_tan_impl(PyObject *module, Py_complex z) |
| 856 | /*[clinic end generated code: output=7c5f13158a72eb13 input=fc167e528767888e]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 857 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 858 | /* tan(z) = -i tanh(iz) */ |
| 859 | Py_complex s, r; |
| 860 | s.real = -z.imag; |
| 861 | s.imag = z.real; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 862 | s = cmath_tanh_impl(module, s); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 863 | r.real = s.imag; |
| 864 | r.imag = -s.real; |
| 865 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 866 | } |
| 867 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 868 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 869 | /* tanh(infinity + i*y) needs to be dealt with specially */ |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 870 | static Py_complex tanh_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 871 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 872 | /*[clinic input] |
| 873 | cmath.tanh = cmath.acos |
| 874 | |
| 875 | Return the hyperbolic tangent of z. |
| 876 | [clinic start generated code]*/ |
| 877 | |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 878 | static Py_complex |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 879 | cmath_tanh_impl(PyObject *module, Py_complex z) |
| 880 | /*[clinic end generated code: output=36d547ef7aca116c input=22f67f9dc6d29685]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 881 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 882 | /* Formula: |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 883 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 884 | tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) / |
| 885 | (1+tan(y)^2 tanh(x)^2) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 886 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 887 | To avoid excessive roundoff error, 1-tanh(x)^2 is better computed |
| 888 | as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2 |
| 889 | by 4 exp(-2*x) instead, to avoid possible overflow in the |
| 890 | computation of cosh(x). |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 891 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 892 | */ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 893 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 894 | Py_complex r; |
| 895 | double tx, ty, cx, txty, denom; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 896 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 897 | /* special treatment for tanh(+/-inf + iy) if y is finite and |
| 898 | nonzero */ |
| 899 | if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) { |
| 900 | if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) |
| 901 | && (z.imag != 0.)) { |
| 902 | if (z.real > 0) { |
| 903 | r.real = 1.0; |
| 904 | r.imag = copysign(0., |
| 905 | 2.*sin(z.imag)*cos(z.imag)); |
| 906 | } |
| 907 | else { |
| 908 | r.real = -1.0; |
| 909 | r.imag = copysign(0., |
| 910 | 2.*sin(z.imag)*cos(z.imag)); |
| 911 | } |
| 912 | } |
| 913 | else { |
| 914 | r = tanh_special_values[special_type(z.real)] |
| 915 | [special_type(z.imag)]; |
| 916 | } |
| 917 | /* need to set errno = EDOM if z.imag is +/-infinity and |
| 918 | z.real is finite */ |
| 919 | if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real)) |
| 920 | errno = EDOM; |
| 921 | else |
| 922 | errno = 0; |
| 923 | return r; |
| 924 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 925 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 926 | /* danger of overflow in 2.*z.imag !*/ |
| 927 | if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) { |
| 928 | r.real = copysign(1., z.real); |
| 929 | r.imag = 4.*sin(z.imag)*cos(z.imag)*exp(-2.*fabs(z.real)); |
| 930 | } else { |
| 931 | tx = tanh(z.real); |
| 932 | ty = tan(z.imag); |
| 933 | cx = 1./cosh(z.real); |
| 934 | txty = tx*ty; |
| 935 | denom = 1. + txty*txty; |
| 936 | r.real = tx*(1.+ty*ty)/denom; |
| 937 | r.imag = ((ty/denom)*cx)*cx; |
| 938 | } |
| 939 | errno = 0; |
| 940 | return r; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 941 | } |
| 942 | |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 943 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 944 | /*[clinic input] |
| 945 | cmath.log |
| 946 | |
| 947 | x: Py_complex |
| 948 | y_obj: object = NULL |
| 949 | / |
| 950 | |
| 951 | The logarithm of z to the given base. |
| 952 | |
| 953 | If the base not specified, returns the natural logarithm (base e) of z. |
| 954 | [clinic start generated code]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 955 | |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 956 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 957 | cmath_log_impl(PyObject *module, Py_complex x, PyObject *y_obj) |
| 958 | /*[clinic end generated code: output=4effdb7d258e0d94 input=ee0e823a7c6e68ea]*/ |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 959 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 960 | Py_complex y; |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 961 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 962 | errno = 0; |
| 963 | PyFPE_START_PROTECT("complex function", return 0) |
| 964 | x = c_log(x); |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 965 | if (y_obj != NULL) { |
| 966 | y = PyComplex_AsCComplex(y_obj); |
| 967 | if (PyErr_Occurred()) { |
| 968 | return NULL; |
| 969 | } |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 970 | y = c_log(y); |
Antoine Pitrou | de08cb6 | 2014-07-07 19:08:47 -0400 | [diff] [blame] | 971 | x = _Py_c_quot(x, y); |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 972 | } |
| 973 | PyFPE_END_PROTECT(x) |
| 974 | if (errno != 0) |
| 975 | return math_error(); |
| 976 | return PyComplex_FromCComplex(x); |
Raymond Hettinger | b67ad7e | 2004-06-14 07:40:10 +0000 | [diff] [blame] | 977 | } |
| 978 | |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 979 | |
| 980 | /* And now the glue to make them available from Python: */ |
| 981 | |
Roger E. Masse | 24070ca | 1996-12-09 22:59:53 +0000 | [diff] [blame] | 982 | static PyObject * |
Thomas Wouters | f3f33dc | 2000-07-21 06:00:07 +0000 | [diff] [blame] | 983 | math_error(void) |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 984 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 985 | if (errno == EDOM) |
| 986 | PyErr_SetString(PyExc_ValueError, "math domain error"); |
| 987 | else if (errno == ERANGE) |
| 988 | PyErr_SetString(PyExc_OverflowError, "math range error"); |
| 989 | else /* Unexpected math error */ |
| 990 | PyErr_SetFromErrno(PyExc_ValueError); |
| 991 | return NULL; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 992 | } |
| 993 | |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 994 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 995 | /*[clinic input] |
| 996 | cmath.phase |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 997 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 998 | z: Py_complex |
| 999 | / |
| 1000 | |
| 1001 | Return argument, also known as the phase angle, of a complex. |
| 1002 | [clinic start generated code]*/ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 1003 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1004 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1005 | cmath_phase_impl(PyObject *module, Py_complex z) |
| 1006 | /*[clinic end generated code: output=50725086a7bfd253 input=5cf75228ba94b69d]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1007 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1008 | double phi; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1009 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1010 | errno = 0; |
| 1011 | PyFPE_START_PROTECT("arg function", return 0) |
| 1012 | phi = c_atan2(z); |
| 1013 | PyFPE_END_PROTECT(phi) |
| 1014 | if (errno != 0) |
| 1015 | return math_error(); |
| 1016 | else |
| 1017 | return PyFloat_FromDouble(phi); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1018 | } |
| 1019 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1020 | /*[clinic input] |
| 1021 | cmath.polar |
| 1022 | |
| 1023 | z: Py_complex |
| 1024 | / |
| 1025 | |
| 1026 | Convert a complex from rectangular coordinates to polar coordinates. |
| 1027 | |
| 1028 | r is the distance from 0 and phi the phase angle. |
| 1029 | [clinic start generated code]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1030 | |
| 1031 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1032 | cmath_polar_impl(PyObject *module, Py_complex z) |
| 1033 | /*[clinic end generated code: output=d0a8147c41dbb654 input=26c353574fd1a861]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1034 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1035 | double r, phi; |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1036 | |
Antoine Pitrou | 6bc217d | 2015-06-23 14:31:11 +0200 | [diff] [blame] | 1037 | errno = 0; |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1038 | PyFPE_START_PROTECT("polar function", return 0) |
| 1039 | phi = c_atan2(z); /* should not cause any exception */ |
Antoine Pitrou | a72f0cd | 2015-06-23 14:38:13 +0200 | [diff] [blame] | 1040 | r = _Py_c_abs(z); /* sets errno to ERANGE on overflow */ |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1041 | PyFPE_END_PROTECT(r) |
| 1042 | if (errno != 0) |
| 1043 | return math_error(); |
| 1044 | else |
| 1045 | return Py_BuildValue("dd", r, phi); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1046 | } |
| 1047 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1048 | /* |
| 1049 | rect() isn't covered by the C99 standard, but it's not too hard to |
| 1050 | figure out 'spirit of C99' rules for special value handing: |
| 1051 | |
| 1052 | rect(x, t) should behave like exp(log(x) + it) for positive-signed x |
| 1053 | rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x |
| 1054 | rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0) |
| 1055 | gives nan +- i0 with the sign of the imaginary part unspecified. |
| 1056 | |
| 1057 | */ |
| 1058 | |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1059 | static Py_complex rect_special_values[7][7]; |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1060 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1061 | /*[clinic input] |
| 1062 | cmath.rect |
| 1063 | |
| 1064 | r: double |
| 1065 | phi: double |
| 1066 | / |
| 1067 | |
| 1068 | Convert from polar coordinates to rectangular coordinates. |
| 1069 | [clinic start generated code]*/ |
| 1070 | |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1071 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1072 | cmath_rect_impl(PyObject *module, double r, double phi) |
| 1073 | /*[clinic end generated code: output=385a0690925df2d5 input=24c5646d147efd69]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1074 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1075 | Py_complex z; |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1076 | errno = 0; |
| 1077 | PyFPE_START_PROTECT("rect function", return 0) |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1078 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1079 | /* deal with special values */ |
| 1080 | if (!Py_IS_FINITE(r) || !Py_IS_FINITE(phi)) { |
| 1081 | /* if r is +/-infinity and phi is finite but nonzero then |
| 1082 | result is (+-INF +-INF i), but we need to compute cos(phi) |
| 1083 | and sin(phi) to figure out the signs. */ |
| 1084 | if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi) |
| 1085 | && (phi != 0.))) { |
| 1086 | if (r > 0) { |
| 1087 | z.real = copysign(INF, cos(phi)); |
| 1088 | z.imag = copysign(INF, sin(phi)); |
| 1089 | } |
| 1090 | else { |
| 1091 | z.real = -copysign(INF, cos(phi)); |
| 1092 | z.imag = -copysign(INF, sin(phi)); |
| 1093 | } |
| 1094 | } |
| 1095 | else { |
| 1096 | z = rect_special_values[special_type(r)] |
| 1097 | [special_type(phi)]; |
| 1098 | } |
| 1099 | /* need to set errno = EDOM if r is a nonzero number and phi |
| 1100 | is infinite */ |
| 1101 | if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi)) |
| 1102 | errno = EDOM; |
| 1103 | else |
| 1104 | errno = 0; |
| 1105 | } |
Mark Dickinson | 58ceecf | 2013-07-20 17:59:13 +0100 | [diff] [blame] | 1106 | else if (phi == 0.0) { |
| 1107 | /* Workaround for buggy results with phi=-0.0 on OS X 10.8. See |
| 1108 | bugs.python.org/issue18513. */ |
| 1109 | z.real = r; |
| 1110 | z.imag = r * phi; |
| 1111 | errno = 0; |
| 1112 | } |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1113 | else { |
| 1114 | z.real = r * cos(phi); |
| 1115 | z.imag = r * sin(phi); |
| 1116 | errno = 0; |
| 1117 | } |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1118 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1119 | PyFPE_END_PROTECT(z) |
| 1120 | if (errno != 0) |
| 1121 | return math_error(); |
| 1122 | else |
| 1123 | return PyComplex_FromCComplex(z); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1124 | } |
| 1125 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1126 | /*[clinic input] |
| 1127 | cmath.isfinite = cmath.polar |
| 1128 | |
| 1129 | Return True if both the real and imaginary parts of z are finite, else False. |
| 1130 | [clinic start generated code]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1131 | |
| 1132 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1133 | cmath_isfinite_impl(PyObject *module, Py_complex z) |
| 1134 | /*[clinic end generated code: output=ac76611e2c774a36 input=848e7ee701895815]*/ |
Mark Dickinson | 8e0c996 | 2010-07-11 17:38:24 +0000 | [diff] [blame] | 1135 | { |
Mark Dickinson | 8e0c996 | 2010-07-11 17:38:24 +0000 | [diff] [blame] | 1136 | return PyBool_FromLong(Py_IS_FINITE(z.real) && Py_IS_FINITE(z.imag)); |
| 1137 | } |
| 1138 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1139 | /*[clinic input] |
| 1140 | cmath.isnan = cmath.polar |
| 1141 | |
| 1142 | Checks if the real or imaginary part of z not a number (NaN). |
| 1143 | [clinic start generated code]*/ |
Mark Dickinson | 8e0c996 | 2010-07-11 17:38:24 +0000 | [diff] [blame] | 1144 | |
| 1145 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1146 | cmath_isnan_impl(PyObject *module, Py_complex z) |
| 1147 | /*[clinic end generated code: output=e7abf6e0b28beab7 input=71799f5d284c9baf]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1148 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1149 | return PyBool_FromLong(Py_IS_NAN(z.real) || Py_IS_NAN(z.imag)); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1150 | } |
| 1151 | |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1152 | /*[clinic input] |
| 1153 | cmath.isinf = cmath.polar |
| 1154 | |
| 1155 | Checks if the real or imaginary part of z is infinite. |
| 1156 | [clinic start generated code]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1157 | |
| 1158 | static PyObject * |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1159 | cmath_isinf_impl(PyObject *module, Py_complex z) |
| 1160 | /*[clinic end generated code: output=502a75a79c773469 input=363df155c7181329]*/ |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1161 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1162 | return PyBool_FromLong(Py_IS_INFINITY(z.real) || |
| 1163 | Py_IS_INFINITY(z.imag)); |
Christian Heimes | 53876d9 | 2008-04-19 00:31:39 +0000 | [diff] [blame] | 1164 | } |
| 1165 | |
Tal Einat | d5519ed | 2015-05-31 22:05:00 +0300 | [diff] [blame] | 1166 | /*[clinic input] |
| 1167 | cmath.isclose -> bool |
| 1168 | |
| 1169 | a: Py_complex |
| 1170 | b: Py_complex |
| 1171 | * |
| 1172 | rel_tol: double = 1e-09 |
| 1173 | maximum difference for being considered "close", relative to the |
| 1174 | magnitude of the input values |
| 1175 | abs_tol: double = 0.0 |
| 1176 | maximum difference for being considered "close", regardless of the |
| 1177 | magnitude of the input values |
| 1178 | |
| 1179 | Determine whether two complex numbers are close in value. |
| 1180 | |
| 1181 | Return True if a is close in value to b, and False otherwise. |
| 1182 | |
| 1183 | For the values to be considered close, the difference between them must be |
| 1184 | smaller than at least one of the tolerances. |
| 1185 | |
| 1186 | -inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is |
| 1187 | not close to anything, even itself. inf and -inf are only close to themselves. |
| 1188 | [clinic start generated code]*/ |
| 1189 | |
| 1190 | static int |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1191 | cmath_isclose_impl(PyObject *module, Py_complex a, Py_complex b, |
Tal Einat | d5519ed | 2015-05-31 22:05:00 +0300 | [diff] [blame] | 1192 | double rel_tol, double abs_tol) |
Serhiy Storchaka | 1a2b24f | 2016-07-07 17:35:15 +0300 | [diff] [blame] | 1193 | /*[clinic end generated code: output=8a2486cc6e0014d1 input=df9636d7de1d4ac3]*/ |
Tal Einat | d5519ed | 2015-05-31 22:05:00 +0300 | [diff] [blame] | 1194 | { |
| 1195 | double diff; |
| 1196 | |
| 1197 | /* sanity check on the inputs */ |
| 1198 | if (rel_tol < 0.0 || abs_tol < 0.0 ) { |
| 1199 | PyErr_SetString(PyExc_ValueError, |
| 1200 | "tolerances must be non-negative"); |
| 1201 | return -1; |
| 1202 | } |
| 1203 | |
| 1204 | if ( (a.real == b.real) && (a.imag == b.imag) ) { |
| 1205 | /* short circuit exact equality -- needed to catch two infinities of |
| 1206 | the same sign. And perhaps speeds things up a bit sometimes. |
| 1207 | */ |
| 1208 | return 1; |
| 1209 | } |
| 1210 | |
| 1211 | /* This catches the case of two infinities of opposite sign, or |
| 1212 | one infinity and one finite number. Two infinities of opposite |
| 1213 | sign would otherwise have an infinite relative tolerance. |
| 1214 | Two infinities of the same sign are caught by the equality check |
| 1215 | above. |
| 1216 | */ |
| 1217 | |
| 1218 | if (Py_IS_INFINITY(a.real) || Py_IS_INFINITY(a.imag) || |
| 1219 | Py_IS_INFINITY(b.real) || Py_IS_INFINITY(b.imag)) { |
| 1220 | return 0; |
| 1221 | } |
| 1222 | |
| 1223 | /* now do the regular computation |
| 1224 | this is essentially the "weak" test from the Boost library |
| 1225 | */ |
| 1226 | |
| 1227 | diff = _Py_c_abs(_Py_c_diff(a, b)); |
| 1228 | |
| 1229 | return (((diff <= rel_tol * _Py_c_abs(b)) || |
| 1230 | (diff <= rel_tol * _Py_c_abs(a))) || |
| 1231 | (diff <= abs_tol)); |
| 1232 | } |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 1233 | |
Martin v. Löwis | 14f8b4c | 2002-06-13 20:33:02 +0000 | [diff] [blame] | 1234 | PyDoc_STRVAR(module_doc, |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 1235 | "This module is always available. It provides access to mathematical\n" |
Martin v. Löwis | 14f8b4c | 2002-06-13 20:33:02 +0000 | [diff] [blame] | 1236 | "functions for complex numbers."); |
Guido van Rossum | c6e2290 | 1998-12-04 19:26:43 +0000 | [diff] [blame] | 1237 | |
Roger E. Masse | 24070ca | 1996-12-09 22:59:53 +0000 | [diff] [blame] | 1238 | static PyMethodDef cmath_methods[] = { |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1239 | CMATH_ACOS_METHODDEF |
| 1240 | CMATH_ACOSH_METHODDEF |
| 1241 | CMATH_ASIN_METHODDEF |
| 1242 | CMATH_ASINH_METHODDEF |
| 1243 | CMATH_ATAN_METHODDEF |
| 1244 | CMATH_ATANH_METHODDEF |
| 1245 | CMATH_COS_METHODDEF |
| 1246 | CMATH_COSH_METHODDEF |
| 1247 | CMATH_EXP_METHODDEF |
Tal Einat | d5519ed | 2015-05-31 22:05:00 +0300 | [diff] [blame] | 1248 | CMATH_ISCLOSE_METHODDEF |
Brett Cannon | b0fc490 | 2014-10-14 17:37:02 -0400 | [diff] [blame] | 1249 | CMATH_ISFINITE_METHODDEF |
| 1250 | CMATH_ISINF_METHODDEF |
| 1251 | CMATH_ISNAN_METHODDEF |
| 1252 | CMATH_LOG_METHODDEF |
| 1253 | CMATH_LOG10_METHODDEF |
| 1254 | CMATH_PHASE_METHODDEF |
| 1255 | CMATH_POLAR_METHODDEF |
| 1256 | CMATH_RECT_METHODDEF |
| 1257 | CMATH_SIN_METHODDEF |
| 1258 | CMATH_SINH_METHODDEF |
| 1259 | CMATH_SQRT_METHODDEF |
| 1260 | CMATH_TAN_METHODDEF |
| 1261 | CMATH_TANH_METHODDEF |
| 1262 | {NULL, NULL} /* sentinel */ |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 1263 | }; |
| 1264 | |
Martin v. Löwis | 1a21451 | 2008-06-11 05:26:20 +0000 | [diff] [blame] | 1265 | |
| 1266 | static struct PyModuleDef cmathmodule = { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1267 | PyModuleDef_HEAD_INIT, |
| 1268 | "cmath", |
| 1269 | module_doc, |
| 1270 | -1, |
| 1271 | cmath_methods, |
| 1272 | NULL, |
| 1273 | NULL, |
| 1274 | NULL, |
| 1275 | NULL |
Martin v. Löwis | 1a21451 | 2008-06-11 05:26:20 +0000 | [diff] [blame] | 1276 | }; |
| 1277 | |
Mark Hammond | fe51c6d | 2002-08-02 02:27:13 +0000 | [diff] [blame] | 1278 | PyMODINIT_FUNC |
Martin v. Löwis | 1a21451 | 2008-06-11 05:26:20 +0000 | [diff] [blame] | 1279 | PyInit_cmath(void) |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 1280 | { |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1281 | PyObject *m; |
Tim Peters | 14e2640 | 2001-02-20 20:15:19 +0000 | [diff] [blame] | 1282 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1283 | m = PyModule_Create(&cmathmodule); |
| 1284 | if (m == NULL) |
| 1285 | return NULL; |
Fred Drake | f4e3484 | 2002-04-01 03:45:06 +0000 | [diff] [blame] | 1286 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1287 | PyModule_AddObject(m, "pi", |
| 1288 | PyFloat_FromDouble(Py_MATH_PI)); |
| 1289 | PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E)); |
Guido van Rossum | 0a891d7 | 2016-08-15 09:12:52 -0700 | [diff] [blame] | 1290 | PyModule_AddObject(m, "tau", PyFloat_FromDouble(Py_MATH_TAU)); /* 2pi */ |
Mark Dickinson | 84e6311 | 2016-08-29 13:56:58 +0100 | [diff] [blame] | 1291 | PyModule_AddObject(m, "inf", PyFloat_FromDouble(m_inf())); |
| 1292 | PyModule_AddObject(m, "infj", PyComplex_FromCComplex(c_infj())); |
| 1293 | #if !defined(PY_NO_SHORT_FLOAT_REPR) || defined(Py_NAN) |
| 1294 | PyModule_AddObject(m, "nan", PyFloat_FromDouble(m_nan())); |
| 1295 | PyModule_AddObject(m, "nanj", PyComplex_FromCComplex(c_nanj())); |
| 1296 | #endif |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1297 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1298 | /* initialize special value tables */ |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1299 | |
| 1300 | #define INIT_SPECIAL_VALUES(NAME, BODY) { Py_complex* p = (Py_complex*)NAME; BODY } |
| 1301 | #define C(REAL, IMAG) p->real = REAL; p->imag = IMAG; ++p; |
| 1302 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1303 | INIT_SPECIAL_VALUES(acos_special_values, { |
| 1304 | C(P34,INF) C(P,INF) C(P,INF) C(P,-INF) C(P,-INF) C(P34,-INF) C(N,INF) |
| 1305 | C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N) |
| 1306 | C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N) |
| 1307 | C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N) |
| 1308 | C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N) |
| 1309 | C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF) |
| 1310 | C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N) |
| 1311 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1312 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1313 | INIT_SPECIAL_VALUES(acosh_special_values, { |
| 1314 | C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N) |
| 1315 | C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N) |
| 1316 | C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N) |
| 1317 | C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N) |
| 1318 | C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N) |
| 1319 | C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N) |
| 1320 | C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N) |
| 1321 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1322 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1323 | INIT_SPECIAL_VALUES(asinh_special_values, { |
| 1324 | C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N) |
| 1325 | C(-INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-INF,P12) C(N,N) |
| 1326 | C(-INF,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-INF,P12) C(N,N) |
| 1327 | C(INF,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,P12) C(N,N) |
| 1328 | C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N) |
| 1329 | C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N) |
| 1330 | C(INF,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(INF,N) C(N,N) |
| 1331 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1332 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1333 | INIT_SPECIAL_VALUES(atanh_special_values, { |
| 1334 | C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,N) |
| 1335 | C(-0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-0.,P12) C(N,N) |
| 1336 | C(-0.,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-0.,P12) C(-0.,N) |
| 1337 | C(0.,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,P12) C(0.,N) |
| 1338 | C(0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(0.,P12) C(N,N) |
| 1339 | C(0.,-P12) C(0.,-P12) C(0.,-P12) C(0.,P12) C(0.,P12) C(0.,P12) C(0.,N) |
| 1340 | C(0.,-P12) C(N,N) C(N,N) C(N,N) C(N,N) C(0.,P12) C(N,N) |
| 1341 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1342 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1343 | INIT_SPECIAL_VALUES(cosh_special_values, { |
| 1344 | C(INF,N) C(U,U) C(INF,0.) C(INF,-0.) C(U,U) C(INF,N) C(INF,N) |
| 1345 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1346 | C(N,0.) C(U,U) C(1.,0.) C(1.,-0.) C(U,U) C(N,0.) C(N,0.) |
| 1347 | C(N,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,0.) C(N,0.) |
| 1348 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1349 | C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N) |
| 1350 | C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N) |
| 1351 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1352 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1353 | INIT_SPECIAL_VALUES(exp_special_values, { |
| 1354 | C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.) |
| 1355 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1356 | C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N) |
| 1357 | C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N) |
| 1358 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1359 | C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N) |
| 1360 | C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N) |
| 1361 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1362 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1363 | INIT_SPECIAL_VALUES(log_special_values, { |
| 1364 | C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N) |
| 1365 | C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N) |
| 1366 | C(INF,-P12) C(U,U) C(-INF,-P) C(-INF,P) C(U,U) C(INF,P12) C(N,N) |
| 1367 | C(INF,-P12) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,P12) C(N,N) |
| 1368 | C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N) |
| 1369 | C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N) |
| 1370 | C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N) |
| 1371 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1372 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1373 | INIT_SPECIAL_VALUES(sinh_special_values, { |
| 1374 | C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N) |
| 1375 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1376 | C(0.,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(0.,N) C(0.,N) |
| 1377 | C(0.,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,N) C(0.,N) |
| 1378 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1379 | C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N) |
| 1380 | C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N) |
| 1381 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1382 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1383 | INIT_SPECIAL_VALUES(sqrt_special_values, { |
| 1384 | C(INF,-INF) C(0.,-INF) C(0.,-INF) C(0.,INF) C(0.,INF) C(INF,INF) C(N,INF) |
| 1385 | C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N) |
| 1386 | C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N) |
| 1387 | C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N) |
| 1388 | C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N) |
| 1389 | C(INF,-INF) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,INF) C(INF,N) |
| 1390 | C(INF,-INF) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,INF) C(N,N) |
| 1391 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1392 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1393 | INIT_SPECIAL_VALUES(tanh_special_values, { |
| 1394 | C(-1.,0.) C(U,U) C(-1.,-0.) C(-1.,0.) C(U,U) C(-1.,0.) C(-1.,0.) |
| 1395 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1396 | C(N,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(N,N) C(N,N) |
| 1397 | C(N,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(N,N) C(N,N) |
| 1398 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1399 | C(1.,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(1.,0.) C(1.,0.) |
| 1400 | C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N) |
| 1401 | }) |
Christian Heimes | a342c01 | 2008-04-20 21:01:16 +0000 | [diff] [blame] | 1402 | |
Antoine Pitrou | f95a1b3 | 2010-05-09 15:52:27 +0000 | [diff] [blame] | 1403 | INIT_SPECIAL_VALUES(rect_special_values, { |
| 1404 | C(INF,N) C(U,U) C(-INF,0.) C(-INF,-0.) C(U,U) C(INF,N) C(INF,N) |
| 1405 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1406 | C(0.,0.) C(U,U) C(-0.,0.) C(-0.,-0.) C(U,U) C(0.,0.) C(0.,0.) |
| 1407 | C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.) |
| 1408 | C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N) |
| 1409 | C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N) |
| 1410 | C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N) |
| 1411 | }) |
| 1412 | return m; |
Guido van Rossum | 71aa32f | 1996-01-12 01:34:57 +0000 | [diff] [blame] | 1413 | } |