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