1/* 2 * Copyright (c) 1999 3 * Silicon Graphics Computer Systems, Inc. 4 * 5 * Copyright (c) 1999 6 * Boris Fomitchev 7 * 8 * This material is provided "as is", with absolutely no warranty expressed 9 * or implied. Any use is at your own risk. 10 * 11 * Permission to use or copy this software for any purpose is hereby granted 12 * without fee, provided the above notices are retained on all copies. 13 * Permission to modify the code and to distribute modified code is granted, 14 * provided the above notices are retained, and a notice that the code was 15 * modified is included with the above copyright notice. 16 * 17 */ 18 19#include "stlport_prefix.h" 20 21#include <numeric> 22#include <cmath> 23#include <complex> 24 25#if defined (_STLP_MSVC_LIB) && (_STLP_MSVC_LIB >= 1400) 26// hypot is deprecated. 27# if defined (_STLP_MSVC) 28# pragma warning (disable : 4996) 29# elif defined (__ICL) 30# pragma warning (disable : 1478) 31# endif 32#endif 33 34_STLP_BEGIN_NAMESPACE 35 36// Complex division and square roots. 37 38// Absolute value 39_STLP_TEMPLATE_NULL 40_STLP_DECLSPEC float _STLP_CALL abs(const complex<float>& __z) 41{ return ::hypot(__z._M_re, __z._M_im); } 42_STLP_TEMPLATE_NULL 43_STLP_DECLSPEC double _STLP_CALL abs(const complex<double>& __z) 44{ return ::hypot(__z._M_re, __z._M_im); } 45 46#if !defined (_STLP_NO_LONG_DOUBLE) 47_STLP_TEMPLATE_NULL 48_STLP_DECLSPEC long double _STLP_CALL abs(const complex<long double>& __z) 49{ return ::hypot(__z._M_re, __z._M_im); } 50#endif 51 52// Phase 53 54_STLP_TEMPLATE_NULL 55_STLP_DECLSPEC float _STLP_CALL arg(const complex<float>& __z) 56{ return ::atan2(__z._M_im, __z._M_re); } 57 58_STLP_TEMPLATE_NULL 59_STLP_DECLSPEC double _STLP_CALL arg(const complex<double>& __z) 60{ return ::atan2(__z._M_im, __z._M_re); } 61 62#if !defined (_STLP_NO_LONG_DOUBLE) 63_STLP_TEMPLATE_NULL 64_STLP_DECLSPEC long double _STLP_CALL arg(const complex<long double>& __z) 65{ return ::atan2(__z._M_im, __z._M_re); } 66#endif 67 68// Construct a complex number from polar representation 69_STLP_TEMPLATE_NULL 70_STLP_DECLSPEC complex<float> _STLP_CALL polar(const float& __rho, const float& __phi) 71{ return complex<float>(__rho * ::cos(__phi), __rho * ::sin(__phi)); } 72_STLP_TEMPLATE_NULL 73_STLP_DECLSPEC complex<double> _STLP_CALL polar(const double& __rho, const double& __phi) 74{ return complex<double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); } 75 76#if !defined (_STLP_NO_LONG_DOUBLE) 77_STLP_TEMPLATE_NULL 78_STLP_DECLSPEC complex<long double> _STLP_CALL polar(const long double& __rho, const long double& __phi) 79{ return complex<long double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); } 80#endif 81 82// Division 83template <class _Tp> 84static void _divT(const _Tp& __z1_r, const _Tp& __z1_i, 85 const _Tp& __z2_r, const _Tp& __z2_i, 86 _Tp& __res_r, _Tp& __res_i) { 87 _Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r; 88 _Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i; 89 90 if (__ar <= __ai) { 91 _Tp __ratio = __z2_r / __z2_i; 92 _Tp __denom = __z2_i * (1 + __ratio * __ratio); 93 __res_r = (__z1_r * __ratio + __z1_i) / __denom; 94 __res_i = (__z1_i * __ratio - __z1_r) / __denom; 95 } 96 else { 97 _Tp __ratio = __z2_i / __z2_r; 98 _Tp __denom = __z2_r * (1 + __ratio * __ratio); 99 __res_r = (__z1_r + __z1_i * __ratio) / __denom; 100 __res_i = (__z1_i - __z1_r * __ratio) / __denom; 101 } 102} 103 104template <class _Tp> 105static void _divT(const _Tp& __z1_r, 106 const _Tp& __z2_r, const _Tp& __z2_i, 107 _Tp& __res_r, _Tp& __res_i) { 108 _Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r; 109 _Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i; 110 111 if (__ar <= __ai) { 112 _Tp __ratio = __z2_r / __z2_i; 113 _Tp __denom = __z2_i * (1 + __ratio * __ratio); 114 __res_r = (__z1_r * __ratio) / __denom; 115 __res_i = - __z1_r / __denom; 116 } 117 else { 118 _Tp __ratio = __z2_i / __z2_r; 119 _Tp __denom = __z2_r * (1 + __ratio * __ratio); 120 __res_r = __z1_r / __denom; 121 __res_i = - (__z1_r * __ratio) / __denom; 122 } 123} 124 125void _STLP_CALL 126complex<float>::_div(const float& __z1_r, const float& __z1_i, 127 const float& __z2_r, const float& __z2_i, 128 float& __res_r, float& __res_i) 129{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); } 130 131void _STLP_CALL 132complex<float>::_div(const float& __z1_r, 133 const float& __z2_r, const float& __z2_i, 134 float& __res_r, float& __res_i) 135{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); } 136 137 138void _STLP_CALL 139complex<double>::_div(const double& __z1_r, const double& __z1_i, 140 const double& __z2_r, const double& __z2_i, 141 double& __res_r, double& __res_i) 142{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); } 143 144void _STLP_CALL 145complex<double>::_div(const double& __z1_r, 146 const double& __z2_r, const double& __z2_i, 147 double& __res_r, double& __res_i) 148{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); } 149 150#if !defined (_STLP_NO_LONG_DOUBLE) 151void _STLP_CALL 152complex<long double>::_div(const long double& __z1_r, const long double& __z1_i, 153 const long double& __z2_r, const long double& __z2_i, 154 long double& __res_r, long double& __res_i) 155{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); } 156 157void _STLP_CALL 158complex<long double>::_div(const long double& __z1_r, 159 const long double& __z2_r, const long double& __z2_i, 160 long double& __res_r, long double& __res_i) 161{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); } 162#endif 163 164//---------------------------------------------------------------------- 165// Square root 166template <class _Tp> 167static complex<_Tp> sqrtT(const complex<_Tp>& z) { 168 _Tp re = z._M_re; 169 _Tp im = z._M_im; 170 _Tp mag = ::hypot(re, im); 171 complex<_Tp> result; 172 173 if (mag == 0.f) { 174 result._M_re = result._M_im = 0.f; 175 } else if (re > 0.f) { 176 result._M_re = ::sqrt(0.5f * (mag + re)); 177 result._M_im = im/result._M_re/2.f; 178 } else { 179 result._M_im = ::sqrt(0.5f * (mag - re)); 180 if (im < 0.f) 181 result._M_im = - result._M_im; 182 result._M_re = im/result._M_im/2.f; 183 } 184 return result; 185} 186 187complex<float> _STLP_CALL 188sqrt(const complex<float>& z) { return sqrtT(z); } 189 190complex<double> _STLP_CALL 191sqrt(const complex<double>& z) { return sqrtT(z); } 192 193#if !defined (_STLP_NO_LONG_DOUBLE) 194complex<long double> _STLP_CALL 195sqrt(const complex<long double>& z) { return sqrtT(z); } 196#endif 197 198// exp, log, pow for complex<float>, complex<double>, and complex<long double> 199//---------------------------------------------------------------------- 200// exp 201template <class _Tp> 202static complex<_Tp> expT(const complex<_Tp>& z) { 203 _Tp expx = ::exp(z._M_re); 204 return complex<_Tp>(expx * ::cos(z._M_im), 205 expx * ::sin(z._M_im)); 206} 207_STLP_DECLSPEC complex<float> _STLP_CALL exp(const complex<float>& z) 208{ return expT(z); } 209 210_STLP_DECLSPEC complex<double> _STLP_CALL exp(const complex<double>& z) 211{ return expT(z); } 212 213#if !defined (_STLP_NO_LONG_DOUBLE) 214_STLP_DECLSPEC complex<long double> _STLP_CALL exp(const complex<long double>& z) 215{ return expT(z); } 216#endif 217 218//---------------------------------------------------------------------- 219// log10 220template <class _Tp> 221static complex<_Tp> log10T(const complex<_Tp>& z, const _Tp& ln10_inv) { 222 complex<_Tp> r; 223 224 r._M_im = ::atan2(z._M_im, z._M_re) * ln10_inv; 225 r._M_re = ::log10(::hypot(z._M_re, z._M_im)); 226 return r; 227} 228 229_STLP_DECLSPEC complex<float> _STLP_CALL log10(const complex<float>& z) 230{ 231 const float LN10_INVF = 1.f / ::log(10.f); 232 return log10T(z, LN10_INVF); 233} 234 235_STLP_DECLSPEC complex<double> _STLP_CALL log10(const complex<double>& z) 236{ 237 const double LN10_INV = 1. / ::log10(10.); 238 return log10T(z, LN10_INV); 239} 240 241#if !defined (_STLP_NO_LONG_DOUBLE) 242_STLP_DECLSPEC complex<long double> _STLP_CALL log10(const complex<long double>& z) 243{ 244 const long double LN10_INVL = 1.l / ::log(10.l); 245 return log10T(z, LN10_INVL); 246} 247#endif 248 249//---------------------------------------------------------------------- 250// log 251template <class _Tp> 252static complex<_Tp> logT(const complex<_Tp>& z) { 253 complex<_Tp> r; 254 255 r._M_im = ::atan2(z._M_im, z._M_re); 256 r._M_re = ::log(::hypot(z._M_re, z._M_im)); 257 return r; 258} 259_STLP_DECLSPEC complex<float> _STLP_CALL log(const complex<float>& z) 260{ return logT(z); } 261 262_STLP_DECLSPEC complex<double> _STLP_CALL log(const complex<double>& z) 263{ return logT(z); } 264 265#ifndef _STLP_NO_LONG_DOUBLE 266_STLP_DECLSPEC complex<long double> _STLP_CALL log(const complex<long double>& z) 267{ return logT(z); } 268# endif 269 270//---------------------------------------------------------------------- 271// pow 272template <class _Tp> 273static complex<_Tp> powT(const _Tp& a, const complex<_Tp>& b) { 274 _Tp logr = ::log(a); 275 _Tp x = ::exp(logr * b._M_re); 276 _Tp y = logr * b._M_im; 277 278 return complex<_Tp>(x * ::cos(y), x * ::sin(y)); 279} 280 281template <class _Tp> 282static complex<_Tp> powT(const complex<_Tp>& z_in, int n) { 283 complex<_Tp> z = z_in; 284 z = _STLP_PRIV __power(z, (n < 0 ? -n : n), multiplies< complex<_Tp> >()); 285 if (n < 0) 286 return _Tp(1.0) / z; 287 else 288 return z; 289} 290 291template <class _Tp> 292static complex<_Tp> powT(const complex<_Tp>& a, const _Tp& b) { 293 _Tp logr = ::log(::hypot(a._M_re,a._M_im)); 294 _Tp logi = ::atan2(a._M_im, a._M_re); 295 _Tp x = ::exp(logr * b); 296 _Tp y = logi * b; 297 298 return complex<_Tp>(x * ::cos(y), x * ::sin(y)); 299} 300 301template <class _Tp> 302static complex<_Tp> powT(const complex<_Tp>& a, const complex<_Tp>& b) { 303 _Tp logr = ::log(::hypot(a._M_re,a._M_im)); 304 _Tp logi = ::atan2(a._M_im, a._M_re); 305 _Tp x = ::exp(logr * b._M_re - logi * b._M_im); 306 _Tp y = logr * b._M_im + logi * b._M_re; 307 308 return complex<_Tp>(x * ::cos(y), x * ::sin(y)); 309} 310 311_STLP_DECLSPEC complex<float> _STLP_CALL pow(const float& a, const complex<float>& b) 312{ return powT(a, b); } 313 314_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& z_in, int n) 315{ return powT(z_in, n); } 316 317_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const float& b) 318{ return powT(a, b); } 319 320_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const complex<float>& b) 321{ return powT(a, b); } 322 323_STLP_DECLSPEC complex<double> _STLP_CALL pow(const double& a, const complex<double>& b) 324{ return powT(a, b); } 325 326_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& z_in, int n) 327{ return powT(z_in, n); } 328 329_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const double& b) 330{ return powT(a, b); } 331 332_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const complex<double>& b) 333{ return powT(a, b); } 334 335#if !defined (_STLP_NO_LONG_DOUBLE) 336_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const long double& a, 337 const complex<long double>& b) 338{ return powT(a, b); } 339 340 341_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& z_in, int n) 342{ return powT(z_in, n); } 343 344_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a, 345 const long double& b) 346{ return powT(a, b); } 347 348_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a, 349 const complex<long double>& b) 350{ return powT(a, b); } 351#endif 352 353_STLP_END_NAMESPACE 354