--- /dev/null
+//===------------------------- __complex_cmath.h --------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// std::complex header copied from the libcxx source and simplified for use in
+// OpenMP target offload regions.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _OPENMP
+#error "This file is for OpenMP compilation only."
+#endif
+
+#ifndef __cplusplus
+#error "This file is for C++ compilation only."
+#endif
+
+#ifndef _LIBCPP_COMPLEX
+#define _LIBCPP_COMPLEX
+
+#include <cmath>
+#include <type_traits>
+
+#define __DEVICE__ static constexpr __attribute__((nothrow))
+
+namespace std {
+
+// abs
+
+template <class _Tp> __DEVICE__ _Tp abs(const std::complex<_Tp> &__c) {
+ return hypot(__c.real(), __c.imag());
+}
+
+// arg
+
+template <class _Tp> __DEVICE__ _Tp arg(const std::complex<_Tp> &__c) {
+ return atan2(__c.imag(), __c.real());
+}
+
+template <class _Tp>
+typename enable_if<is_integral<_Tp>::value || is_same<_Tp, double>::value,
+ double>::type
+arg(_Tp __re) {
+ return atan2(0., __re);
+}
+
+template <class _Tp>
+typename enable_if<is_same<_Tp, float>::value, float>::type arg(_Tp __re) {
+ return atan2f(0.F, __re);
+}
+
+// norm
+
+template <class _Tp> __DEVICE__ _Tp norm(const std::complex<_Tp> &__c) {
+ if (std::isinf(__c.real()))
+ return abs(__c.real());
+ if (std::isinf(__c.imag()))
+ return abs(__c.imag());
+ return __c.real() * __c.real() + __c.imag() * __c.imag();
+}
+
+// conj
+
+template <class _Tp> std::complex<_Tp> conj(const std::complex<_Tp> &__c) {
+ return std::complex<_Tp>(__c.real(), -__c.imag());
+}
+
+// proj
+
+template <class _Tp> std::complex<_Tp> proj(const std::complex<_Tp> &__c) {
+ std::complex<_Tp> __r = __c;
+ if (std::isinf(__c.real()) || std::isinf(__c.imag()))
+ __r = std::complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
+ return __r;
+}
+
+// polar
+
+template <class _Tp>
+complex<_Tp> polar(const _Tp &__rho, const _Tp &__theta = _Tp()) {
+ if (std::isnan(__rho) || signbit(__rho))
+ return std::complex<_Tp>(_Tp(NAN), _Tp(NAN));
+ if (std::isnan(__theta)) {
+ if (std::isinf(__rho))
+ return std::complex<_Tp>(__rho, __theta);
+ return std::complex<_Tp>(__theta, __theta);
+ }
+ if (std::isinf(__theta)) {
+ if (std::isinf(__rho))
+ return std::complex<_Tp>(__rho, _Tp(NAN));
+ return std::complex<_Tp>(_Tp(NAN), _Tp(NAN));
+ }
+ _Tp __x = __rho * cos(__theta);
+ if (std::isnan(__x))
+ __x = 0;
+ _Tp __y = __rho * sin(__theta);
+ if (std::isnan(__y))
+ __y = 0;
+ return std::complex<_Tp>(__x, __y);
+}
+
+// log
+
+template <class _Tp> std::complex<_Tp> log(const std::complex<_Tp> &__x) {
+ return std::complex<_Tp>(log(abs(__x)), arg(__x));
+}
+
+// log10
+
+template <class _Tp> std::complex<_Tp> log10(const std::complex<_Tp> &__x) {
+ return log(__x) / log(_Tp(10));
+}
+
+// sqrt
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> sqrt(const std::complex<_Tp> &__x) {
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(_Tp(INFINITY), __x.imag());
+ if (std::isinf(__x.real())) {
+ if (__x.real() > _Tp(0))
+ return std::complex<_Tp>(__x.real(), std::isnan(__x.imag())
+ ? __x.imag()
+ : copysign(_Tp(0), __x.imag()));
+ return std::complex<_Tp>(std::isnan(__x.imag()) ? __x.imag() : _Tp(0),
+ copysign(__x.real(), __x.imag()));
+ }
+ return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
+}
+
+// exp
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> exp(const std::complex<_Tp> &__x) {
+ _Tp __i = __x.imag();
+ if (std::isinf(__x.real())) {
+ if (__x.real() < _Tp(0)) {
+ if (!std::isfinite(__i))
+ __i = _Tp(1);
+ } else if (__i == 0 || !std::isfinite(__i)) {
+ if (std::isinf(__i))
+ __i = _Tp(NAN);
+ return std::complex<_Tp>(__x.real(), __i);
+ }
+ } else if (std::isnan(__x.real()) && __x.imag() == 0)
+ return __x;
+ _Tp __e = exp(__x.real());
+ return std::complex<_Tp>(__e * cos(__i), __e * sin(__i));
+}
+
+// pow
+
+template <class _Tp>
+std::complex<_Tp> pow(const std::complex<_Tp> &__x,
+ const std::complex<_Tp> &__y) {
+ return exp(__y * log(__x));
+}
+
+// __sqr, computes pow(x, 2)
+
+template <class _Tp> std::complex<_Tp> __sqr(const std::complex<_Tp> &__x) {
+ return std::complex<_Tp>((__x.real() - __x.imag()) *
+ (__x.real() + __x.imag()),
+ _Tp(2) * __x.real() * __x.imag());
+}
+
+// asinh
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> asinh(const std::complex<_Tp> &__x) {
+ const _Tp __pi(atan2(+0., -0.));
+ if (std::isinf(__x.real())) {
+ if (std::isnan(__x.imag()))
+ return __x;
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(__x.real(),
+ copysign(__pi * _Tp(0.25), __x.imag()));
+ return std::complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
+ }
+ if (std::isnan(__x.real())) {
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(__x.imag(), __x.real());
+ if (__x.imag() == 0)
+ return __x;
+ return std::complex<_Tp>(__x.real(), __x.real());
+ }
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(copysign(__x.imag(), __x.real()),
+ copysign(__pi / _Tp(2), __x.imag()));
+ std::complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1)));
+ return std::complex<_Tp>(copysign(__z.real(), __x.real()),
+ copysign(__z.imag(), __x.imag()));
+}
+
+// acosh
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> acosh(const std::complex<_Tp> &__x) {
+ const _Tp __pi(atan2(+0., -0.));
+ if (std::isinf(__x.real())) {
+ if (std::isnan(__x.imag()))
+ return std::complex<_Tp>(abs(__x.real()), __x.imag());
+ if (std::isinf(__x.imag())) {
+ if (__x.real() > 0)
+ return std::complex<_Tp>(__x.real(),
+ copysign(__pi * _Tp(0.25), __x.imag()));
+ else
+ return std::complex<_Tp>(-__x.real(),
+ copysign(__pi * _Tp(0.75), __x.imag()));
+ }
+ if (__x.real() < 0)
+ return std::complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
+ return std::complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
+ }
+ if (std::isnan(__x.real())) {
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(abs(__x.imag()), __x.real());
+ return std::complex<_Tp>(__x.real(), __x.real());
+ }
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(abs(__x.imag()),
+ copysign(__pi / _Tp(2), __x.imag()));
+ std::complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
+ return std::complex<_Tp>(copysign(__z.real(), _Tp(0)),
+ copysign(__z.imag(), __x.imag()));
+}
+
+// atanh
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> atanh(const std::complex<_Tp> &__x) {
+ const _Tp __pi(atan2(+0., -0.));
+ if (std::isinf(__x.imag())) {
+ return std::complex<_Tp>(copysign(_Tp(0), __x.real()),
+ copysign(__pi / _Tp(2), __x.imag()));
+ }
+ if (std::isnan(__x.imag())) {
+ if (std::isinf(__x.real()) || __x.real() == 0)
+ return std::complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
+ return std::complex<_Tp>(__x.imag(), __x.imag());
+ }
+ if (std::isnan(__x.real())) {
+ return std::complex<_Tp>(__x.real(), __x.real());
+ }
+ if (std::isinf(__x.real())) {
+ return std::complex<_Tp>(copysign(_Tp(0), __x.real()),
+ copysign(__pi / _Tp(2), __x.imag()));
+ }
+ if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) {
+ return std::complex<_Tp>(copysign(_Tp(INFINITY), __x.real()),
+ copysign(_Tp(0), __x.imag()));
+ }
+ std::complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
+ return std::complex<_Tp>(copysign(__z.real(), __x.real()),
+ copysign(__z.imag(), __x.imag()));
+}
+
+// sinh
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> sinh(const std::complex<_Tp> &__x) {
+ if (std::isinf(__x.real()) && !std::isfinite(__x.imag()))
+ return std::complex<_Tp>(__x.real(), _Tp(NAN));
+ if (__x.real() == 0 && !std::isfinite(__x.imag()))
+ return std::complex<_Tp>(__x.real(), _Tp(NAN));
+ if (__x.imag() == 0 && !std::isfinite(__x.real()))
+ return __x;
+ return std::complex<_Tp>(sinh(__x.real()) * cos(__x.imag()),
+ cosh(__x.real()) * sin(__x.imag()));
+}
+
+// cosh
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> cosh(const std::complex<_Tp> &__x) {
+ if (std::isinf(__x.real()) && !std::isfinite(__x.imag()))
+ return std::complex<_Tp>(abs(__x.real()), _Tp(NAN));
+ if (__x.real() == 0 && !std::isfinite(__x.imag()))
+ return std::complex<_Tp>(_Tp(NAN), __x.real());
+ if (__x.real() == 0 && __x.imag() == 0)
+ return std::complex<_Tp>(_Tp(1), __x.imag());
+ if (__x.imag() == 0 && !std::isfinite(__x.real()))
+ return std::complex<_Tp>(abs(__x.real()), __x.imag());
+ return std::complex<_Tp>(cosh(__x.real()) * cos(__x.imag()),
+ sinh(__x.real()) * sin(__x.imag()));
+}
+
+// tanh
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> tanh(const std::complex<_Tp> &__x) {
+ if (std::isinf(__x.real())) {
+ if (!std::isfinite(__x.imag()))
+ return std::complex<_Tp>(_Tp(1), _Tp(0));
+ return std::complex<_Tp>(_Tp(1),
+ copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
+ }
+ if (std::isnan(__x.real()) && __x.imag() == 0)
+ return __x;
+ _Tp __2r(_Tp(2) * __x.real());
+ _Tp __2i(_Tp(2) * __x.imag());
+ _Tp __d(cosh(__2r) + cos(__2i));
+ _Tp __2rsh(sinh(__2r));
+ if (std::isinf(__2rsh) && std::isinf(__d))
+ return std::complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
+ __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
+ return std::complex<_Tp>(__2rsh / __d, sin(__2i) / __d);
+}
+
+// asin
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> asin(const std::complex<_Tp> &__x) {
+ std::complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
+ return std::complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// acos
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> acos(const std::complex<_Tp> &__x) {
+ const _Tp __pi(atan2(+0., -0.));
+ if (std::isinf(__x.real())) {
+ if (std::isnan(__x.imag()))
+ return std::complex<_Tp>(__x.imag(), __x.real());
+ if (std::isinf(__x.imag())) {
+ if (__x.real() < _Tp(0))
+ return std::complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
+ return std::complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
+ }
+ if (__x.real() < _Tp(0))
+ return std::complex<_Tp>(__pi,
+ signbit(__x.imag()) ? -__x.real() : __x.real());
+ return std::complex<_Tp>(_Tp(0),
+ signbit(__x.imag()) ? __x.real() : -__x.real());
+ }
+ if (std::isnan(__x.real())) {
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(__x.real(), -__x.imag());
+ return std::complex<_Tp>(__x.real(), __x.real());
+ }
+ if (std::isinf(__x.imag()))
+ return std::complex<_Tp>(__pi / _Tp(2), -__x.imag());
+ if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
+ return std::complex<_Tp>(__pi / _Tp(2), -__x.imag());
+ std::complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
+ if (signbit(__x.imag()))
+ return std::complex<_Tp>(abs(__z.imag()), abs(__z.real()));
+ return std::complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
+}
+
+// atan
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> atan(const std::complex<_Tp> &__x) {
+ std::complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
+ return std::complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// sin
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> sin(const std::complex<_Tp> &__x) {
+ std::complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
+ return std::complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// cos
+
+template <class _Tp> std::complex<_Tp> cos(const std::complex<_Tp> &__x) {
+ return cosh(complex<_Tp>(-__x.imag(), __x.real()));
+}
+
+// tan
+
+template <class _Tp>
+__DEVICE__ std::complex<_Tp> tan(const std::complex<_Tp> &__x) {
+ std::complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
+ return std::complex<_Tp>(__z.imag(), -__z.real());
+}
+
+} // namespace std
+
+#endif