Sasha Smundak | 4b1f33a | 2021-01-11 15:05:07 -0800 | [diff] [blame] | 1 | //===------------------------- __complex_cmath.h --------------------------===// |
| 2 | // |
| 3 | // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| 4 | // See https://llvm.org/LICENSE.txt for license information. |
| 5 | // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| 6 | // |
| 7 | //===----------------------------------------------------------------------===// |
| 8 | // |
| 9 | // std::complex header copied from the libcxx source and simplified for use in |
| 10 | // OpenMP target offload regions. |
| 11 | // |
| 12 | //===----------------------------------------------------------------------===// |
| 13 | |
| 14 | #ifndef _OPENMP |
| 15 | #error "This file is for OpenMP compilation only." |
| 16 | #endif |
| 17 | |
| 18 | #ifndef __cplusplus |
| 19 | #error "This file is for C++ compilation only." |
| 20 | #endif |
| 21 | |
| 22 | #ifndef _LIBCPP_COMPLEX |
| 23 | #define _LIBCPP_COMPLEX |
| 24 | |
| 25 | #include <cmath> |
| 26 | #include <type_traits> |
| 27 | |
| 28 | #define __DEVICE__ static constexpr __attribute__((nothrow)) |
| 29 | |
| 30 | namespace std { |
| 31 | |
| 32 | // abs |
| 33 | |
| 34 | template <class _Tp> __DEVICE__ _Tp abs(const std::complex<_Tp> &__c) { |
| 35 | return hypot(__c.real(), __c.imag()); |
| 36 | } |
| 37 | |
| 38 | // arg |
| 39 | |
| 40 | template <class _Tp> __DEVICE__ _Tp arg(const std::complex<_Tp> &__c) { |
| 41 | return atan2(__c.imag(), __c.real()); |
| 42 | } |
| 43 | |
| 44 | template <class _Tp> |
| 45 | typename enable_if<is_integral<_Tp>::value || is_same<_Tp, double>::value, |
| 46 | double>::type |
| 47 | arg(_Tp __re) { |
| 48 | return atan2(0., __re); |
| 49 | } |
| 50 | |
| 51 | template <class _Tp> |
| 52 | typename enable_if<is_same<_Tp, float>::value, float>::type arg(_Tp __re) { |
| 53 | return atan2f(0.F, __re); |
| 54 | } |
| 55 | |
| 56 | // norm |
| 57 | |
| 58 | template <class _Tp> __DEVICE__ _Tp norm(const std::complex<_Tp> &__c) { |
| 59 | if (std::isinf(__c.real())) |
| 60 | return abs(__c.real()); |
| 61 | if (std::isinf(__c.imag())) |
| 62 | return abs(__c.imag()); |
| 63 | return __c.real() * __c.real() + __c.imag() * __c.imag(); |
| 64 | } |
| 65 | |
| 66 | // conj |
| 67 | |
| 68 | template <class _Tp> std::complex<_Tp> conj(const std::complex<_Tp> &__c) { |
| 69 | return std::complex<_Tp>(__c.real(), -__c.imag()); |
| 70 | } |
| 71 | |
| 72 | // proj |
| 73 | |
| 74 | template <class _Tp> std::complex<_Tp> proj(const std::complex<_Tp> &__c) { |
| 75 | std::complex<_Tp> __r = __c; |
| 76 | if (std::isinf(__c.real()) || std::isinf(__c.imag())) |
| 77 | __r = std::complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag())); |
| 78 | return __r; |
| 79 | } |
| 80 | |
| 81 | // polar |
| 82 | |
| 83 | template <class _Tp> |
| 84 | complex<_Tp> polar(const _Tp &__rho, const _Tp &__theta = _Tp()) { |
| 85 | if (std::isnan(__rho) || signbit(__rho)) |
| 86 | return std::complex<_Tp>(_Tp(NAN), _Tp(NAN)); |
| 87 | if (std::isnan(__theta)) { |
| 88 | if (std::isinf(__rho)) |
| 89 | return std::complex<_Tp>(__rho, __theta); |
| 90 | return std::complex<_Tp>(__theta, __theta); |
| 91 | } |
| 92 | if (std::isinf(__theta)) { |
| 93 | if (std::isinf(__rho)) |
| 94 | return std::complex<_Tp>(__rho, _Tp(NAN)); |
| 95 | return std::complex<_Tp>(_Tp(NAN), _Tp(NAN)); |
| 96 | } |
| 97 | _Tp __x = __rho * cos(__theta); |
| 98 | if (std::isnan(__x)) |
| 99 | __x = 0; |
| 100 | _Tp __y = __rho * sin(__theta); |
| 101 | if (std::isnan(__y)) |
| 102 | __y = 0; |
| 103 | return std::complex<_Tp>(__x, __y); |
| 104 | } |
| 105 | |
| 106 | // log |
| 107 | |
| 108 | template <class _Tp> std::complex<_Tp> log(const std::complex<_Tp> &__x) { |
| 109 | return std::complex<_Tp>(log(abs(__x)), arg(__x)); |
| 110 | } |
| 111 | |
| 112 | // log10 |
| 113 | |
| 114 | template <class _Tp> std::complex<_Tp> log10(const std::complex<_Tp> &__x) { |
| 115 | return log(__x) / log(_Tp(10)); |
| 116 | } |
| 117 | |
| 118 | // sqrt |
| 119 | |
| 120 | template <class _Tp> |
| 121 | __DEVICE__ std::complex<_Tp> sqrt(const std::complex<_Tp> &__x) { |
| 122 | if (std::isinf(__x.imag())) |
| 123 | return std::complex<_Tp>(_Tp(INFINITY), __x.imag()); |
| 124 | if (std::isinf(__x.real())) { |
| 125 | if (__x.real() > _Tp(0)) |
| 126 | return std::complex<_Tp>(__x.real(), std::isnan(__x.imag()) |
| 127 | ? __x.imag() |
| 128 | : copysign(_Tp(0), __x.imag())); |
| 129 | return std::complex<_Tp>(std::isnan(__x.imag()) ? __x.imag() : _Tp(0), |
| 130 | copysign(__x.real(), __x.imag())); |
| 131 | } |
| 132 | return polar(sqrt(abs(__x)), arg(__x) / _Tp(2)); |
| 133 | } |
| 134 | |
| 135 | // exp |
| 136 | |
| 137 | template <class _Tp> |
| 138 | __DEVICE__ std::complex<_Tp> exp(const std::complex<_Tp> &__x) { |
| 139 | _Tp __i = __x.imag(); |
| 140 | if (std::isinf(__x.real())) { |
| 141 | if (__x.real() < _Tp(0)) { |
| 142 | if (!std::isfinite(__i)) |
| 143 | __i = _Tp(1); |
| 144 | } else if (__i == 0 || !std::isfinite(__i)) { |
| 145 | if (std::isinf(__i)) |
| 146 | __i = _Tp(NAN); |
| 147 | return std::complex<_Tp>(__x.real(), __i); |
| 148 | } |
| 149 | } else if (std::isnan(__x.real()) && __x.imag() == 0) |
| 150 | return __x; |
| 151 | _Tp __e = exp(__x.real()); |
| 152 | return std::complex<_Tp>(__e * cos(__i), __e * sin(__i)); |
| 153 | } |
| 154 | |
| 155 | // pow |
| 156 | |
| 157 | template <class _Tp> |
| 158 | std::complex<_Tp> pow(const std::complex<_Tp> &__x, |
| 159 | const std::complex<_Tp> &__y) { |
| 160 | return exp(__y * log(__x)); |
| 161 | } |
| 162 | |
| 163 | // __sqr, computes pow(x, 2) |
| 164 | |
| 165 | template <class _Tp> std::complex<_Tp> __sqr(const std::complex<_Tp> &__x) { |
| 166 | return std::complex<_Tp>((__x.real() - __x.imag()) * |
| 167 | (__x.real() + __x.imag()), |
| 168 | _Tp(2) * __x.real() * __x.imag()); |
| 169 | } |
| 170 | |
| 171 | // asinh |
| 172 | |
| 173 | template <class _Tp> |
| 174 | __DEVICE__ std::complex<_Tp> asinh(const std::complex<_Tp> &__x) { |
| 175 | const _Tp __pi(atan2(+0., -0.)); |
| 176 | if (std::isinf(__x.real())) { |
| 177 | if (std::isnan(__x.imag())) |
| 178 | return __x; |
| 179 | if (std::isinf(__x.imag())) |
| 180 | return std::complex<_Tp>(__x.real(), |
| 181 | copysign(__pi * _Tp(0.25), __x.imag())); |
| 182 | return std::complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag())); |
| 183 | } |
| 184 | if (std::isnan(__x.real())) { |
| 185 | if (std::isinf(__x.imag())) |
| 186 | return std::complex<_Tp>(__x.imag(), __x.real()); |
| 187 | if (__x.imag() == 0) |
| 188 | return __x; |
| 189 | return std::complex<_Tp>(__x.real(), __x.real()); |
| 190 | } |
| 191 | if (std::isinf(__x.imag())) |
| 192 | return std::complex<_Tp>(copysign(__x.imag(), __x.real()), |
| 193 | copysign(__pi / _Tp(2), __x.imag())); |
| 194 | std::complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1))); |
| 195 | return std::complex<_Tp>(copysign(__z.real(), __x.real()), |
| 196 | copysign(__z.imag(), __x.imag())); |
| 197 | } |
| 198 | |
| 199 | // acosh |
| 200 | |
| 201 | template <class _Tp> |
| 202 | __DEVICE__ std::complex<_Tp> acosh(const std::complex<_Tp> &__x) { |
| 203 | const _Tp __pi(atan2(+0., -0.)); |
| 204 | if (std::isinf(__x.real())) { |
| 205 | if (std::isnan(__x.imag())) |
| 206 | return std::complex<_Tp>(abs(__x.real()), __x.imag()); |
| 207 | if (std::isinf(__x.imag())) { |
| 208 | if (__x.real() > 0) |
| 209 | return std::complex<_Tp>(__x.real(), |
| 210 | copysign(__pi * _Tp(0.25), __x.imag())); |
| 211 | else |
| 212 | return std::complex<_Tp>(-__x.real(), |
| 213 | copysign(__pi * _Tp(0.75), __x.imag())); |
| 214 | } |
| 215 | if (__x.real() < 0) |
| 216 | return std::complex<_Tp>(-__x.real(), copysign(__pi, __x.imag())); |
| 217 | return std::complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag())); |
| 218 | } |
| 219 | if (std::isnan(__x.real())) { |
| 220 | if (std::isinf(__x.imag())) |
| 221 | return std::complex<_Tp>(abs(__x.imag()), __x.real()); |
| 222 | return std::complex<_Tp>(__x.real(), __x.real()); |
| 223 | } |
| 224 | if (std::isinf(__x.imag())) |
| 225 | return std::complex<_Tp>(abs(__x.imag()), |
| 226 | copysign(__pi / _Tp(2), __x.imag())); |
| 227 | std::complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1))); |
| 228 | return std::complex<_Tp>(copysign(__z.real(), _Tp(0)), |
| 229 | copysign(__z.imag(), __x.imag())); |
| 230 | } |
| 231 | |
| 232 | // atanh |
| 233 | |
| 234 | template <class _Tp> |
| 235 | __DEVICE__ std::complex<_Tp> atanh(const std::complex<_Tp> &__x) { |
| 236 | const _Tp __pi(atan2(+0., -0.)); |
| 237 | if (std::isinf(__x.imag())) { |
| 238 | return std::complex<_Tp>(copysign(_Tp(0), __x.real()), |
| 239 | copysign(__pi / _Tp(2), __x.imag())); |
| 240 | } |
| 241 | if (std::isnan(__x.imag())) { |
| 242 | if (std::isinf(__x.real()) || __x.real() == 0) |
| 243 | return std::complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag()); |
| 244 | return std::complex<_Tp>(__x.imag(), __x.imag()); |
| 245 | } |
| 246 | if (std::isnan(__x.real())) { |
| 247 | return std::complex<_Tp>(__x.real(), __x.real()); |
| 248 | } |
| 249 | if (std::isinf(__x.real())) { |
| 250 | return std::complex<_Tp>(copysign(_Tp(0), __x.real()), |
| 251 | copysign(__pi / _Tp(2), __x.imag())); |
| 252 | } |
| 253 | if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) { |
| 254 | return std::complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), |
| 255 | copysign(_Tp(0), __x.imag())); |
| 256 | } |
| 257 | std::complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2); |
| 258 | return std::complex<_Tp>(copysign(__z.real(), __x.real()), |
| 259 | copysign(__z.imag(), __x.imag())); |
| 260 | } |
| 261 | |
| 262 | // sinh |
| 263 | |
| 264 | template <class _Tp> |
| 265 | __DEVICE__ std::complex<_Tp> sinh(const std::complex<_Tp> &__x) { |
| 266 | if (std::isinf(__x.real()) && !std::isfinite(__x.imag())) |
| 267 | return std::complex<_Tp>(__x.real(), _Tp(NAN)); |
| 268 | if (__x.real() == 0 && !std::isfinite(__x.imag())) |
| 269 | return std::complex<_Tp>(__x.real(), _Tp(NAN)); |
| 270 | if (__x.imag() == 0 && !std::isfinite(__x.real())) |
| 271 | return __x; |
| 272 | return std::complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), |
| 273 | cosh(__x.real()) * sin(__x.imag())); |
| 274 | } |
| 275 | |
| 276 | // cosh |
| 277 | |
| 278 | template <class _Tp> |
| 279 | __DEVICE__ std::complex<_Tp> cosh(const std::complex<_Tp> &__x) { |
| 280 | if (std::isinf(__x.real()) && !std::isfinite(__x.imag())) |
| 281 | return std::complex<_Tp>(abs(__x.real()), _Tp(NAN)); |
| 282 | if (__x.real() == 0 && !std::isfinite(__x.imag())) |
| 283 | return std::complex<_Tp>(_Tp(NAN), __x.real()); |
| 284 | if (__x.real() == 0 && __x.imag() == 0) |
| 285 | return std::complex<_Tp>(_Tp(1), __x.imag()); |
| 286 | if (__x.imag() == 0 && !std::isfinite(__x.real())) |
| 287 | return std::complex<_Tp>(abs(__x.real()), __x.imag()); |
| 288 | return std::complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), |
| 289 | sinh(__x.real()) * sin(__x.imag())); |
| 290 | } |
| 291 | |
| 292 | // tanh |
| 293 | |
| 294 | template <class _Tp> |
| 295 | __DEVICE__ std::complex<_Tp> tanh(const std::complex<_Tp> &__x) { |
| 296 | if (std::isinf(__x.real())) { |
| 297 | if (!std::isfinite(__x.imag())) |
| 298 | return std::complex<_Tp>(_Tp(1), _Tp(0)); |
| 299 | return std::complex<_Tp>(_Tp(1), |
| 300 | copysign(_Tp(0), sin(_Tp(2) * __x.imag()))); |
| 301 | } |
| 302 | if (std::isnan(__x.real()) && __x.imag() == 0) |
| 303 | return __x; |
| 304 | _Tp __2r(_Tp(2) * __x.real()); |
| 305 | _Tp __2i(_Tp(2) * __x.imag()); |
| 306 | _Tp __d(cosh(__2r) + cos(__2i)); |
| 307 | _Tp __2rsh(sinh(__2r)); |
| 308 | if (std::isinf(__2rsh) && std::isinf(__d)) |
| 309 | return std::complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), |
| 310 | __2i > _Tp(0) ? _Tp(0) : _Tp(-0.)); |
| 311 | return std::complex<_Tp>(__2rsh / __d, sin(__2i) / __d); |
| 312 | } |
| 313 | |
| 314 | // asin |
| 315 | |
| 316 | template <class _Tp> |
| 317 | __DEVICE__ std::complex<_Tp> asin(const std::complex<_Tp> &__x) { |
| 318 | std::complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real())); |
| 319 | return std::complex<_Tp>(__z.imag(), -__z.real()); |
| 320 | } |
| 321 | |
| 322 | // acos |
| 323 | |
| 324 | template <class _Tp> |
| 325 | __DEVICE__ std::complex<_Tp> acos(const std::complex<_Tp> &__x) { |
| 326 | const _Tp __pi(atan2(+0., -0.)); |
| 327 | if (std::isinf(__x.real())) { |
| 328 | if (std::isnan(__x.imag())) |
| 329 | return std::complex<_Tp>(__x.imag(), __x.real()); |
| 330 | if (std::isinf(__x.imag())) { |
| 331 | if (__x.real() < _Tp(0)) |
| 332 | return std::complex<_Tp>(_Tp(0.75) * __pi, -__x.imag()); |
| 333 | return std::complex<_Tp>(_Tp(0.25) * __pi, -__x.imag()); |
| 334 | } |
| 335 | if (__x.real() < _Tp(0)) |
| 336 | return std::complex<_Tp>(__pi, |
| 337 | signbit(__x.imag()) ? -__x.real() : __x.real()); |
| 338 | return std::complex<_Tp>(_Tp(0), |
| 339 | signbit(__x.imag()) ? __x.real() : -__x.real()); |
| 340 | } |
| 341 | if (std::isnan(__x.real())) { |
| 342 | if (std::isinf(__x.imag())) |
| 343 | return std::complex<_Tp>(__x.real(), -__x.imag()); |
| 344 | return std::complex<_Tp>(__x.real(), __x.real()); |
| 345 | } |
| 346 | if (std::isinf(__x.imag())) |
| 347 | return std::complex<_Tp>(__pi / _Tp(2), -__x.imag()); |
| 348 | if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag()))) |
| 349 | return std::complex<_Tp>(__pi / _Tp(2), -__x.imag()); |
| 350 | std::complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1))); |
| 351 | if (signbit(__x.imag())) |
| 352 | return std::complex<_Tp>(abs(__z.imag()), abs(__z.real())); |
| 353 | return std::complex<_Tp>(abs(__z.imag()), -abs(__z.real())); |
| 354 | } |
| 355 | |
| 356 | // atan |
| 357 | |
| 358 | template <class _Tp> |
| 359 | __DEVICE__ std::complex<_Tp> atan(const std::complex<_Tp> &__x) { |
| 360 | std::complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real())); |
| 361 | return std::complex<_Tp>(__z.imag(), -__z.real()); |
| 362 | } |
| 363 | |
| 364 | // sin |
| 365 | |
| 366 | template <class _Tp> |
| 367 | __DEVICE__ std::complex<_Tp> sin(const std::complex<_Tp> &__x) { |
| 368 | std::complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real())); |
| 369 | return std::complex<_Tp>(__z.imag(), -__z.real()); |
| 370 | } |
| 371 | |
| 372 | // cos |
| 373 | |
| 374 | template <class _Tp> std::complex<_Tp> cos(const std::complex<_Tp> &__x) { |
| 375 | return cosh(complex<_Tp>(-__x.imag(), __x.real())); |
| 376 | } |
| 377 | |
| 378 | // tan |
| 379 | |
| 380 | template <class _Tp> |
| 381 | __DEVICE__ std::complex<_Tp> tan(const std::complex<_Tp> &__x) { |
| 382 | std::complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real())); |
| 383 | return std::complex<_Tp>(__z.imag(), -__z.real()); |
| 384 | } |
| 385 | |
| 386 | } // namespace std |
| 387 | |
| 388 | #endif |