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+/*===-- __clang_cuda_complex_builtins - CUDA impls of runtime complex fns ---===
+ *
+ * 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
+ *
+ *===-----------------------------------------------------------------------===
+ */
+
+#ifndef __CLANG_CUDA_COMPLEX_BUILTINS
+#define __CLANG_CUDA_COMPLEX_BUILTINS
+
+// This header defines __muldc3, __mulsc3, __divdc3, and __divsc3. These are
+// libgcc functions that clang assumes are available when compiling c99 complex
+// operations. (These implementations come from libc++, and have been modified
+// to work with CUDA and OpenMP target offloading [in C and C++ mode].)
+
+#pragma push_macro("__DEVICE__")
+#if defined(__OPENMP_NVPTX__) || defined(__OPENMP_AMDGCN__)
+#pragma omp declare target
+#define __DEVICE__ __attribute__((noinline, nothrow, cold, weak))
+#else
+#define __DEVICE__ __device__ inline
+#endif
+
+// To make the algorithms available for C and C++ in CUDA and OpenMP we select
+// different but equivalent function versions. TODO: For OpenMP we currently
+// select the native builtins as the overload support for templates is lacking.
+#if !defined(__OPENMP_NVPTX__) && !defined(__OPENMP_AMDGCN__)
+#define _ISNANd std::isnan
+#define _ISNANf std::isnan
+#define _ISINFd std::isinf
+#define _ISINFf std::isinf
+#define _ISFINITEd std::isfinite
+#define _ISFINITEf std::isfinite
+#define _COPYSIGNd std::copysign
+#define _COPYSIGNf std::copysign
+#define _SCALBNd std::scalbn
+#define _SCALBNf std::scalbn
+#define _ABSd std::abs
+#define _ABSf std::abs
+#define _LOGBd std::logb
+#define _LOGBf std::logb
+// Rather than pulling in std::max from algorithm everytime, use available ::max.
+#define _fmaxd max
+#define _fmaxf max
+#else
+#ifdef __AMDGCN__
+#define _ISNANd __ocml_isnan_f64
+#define _ISNANf __ocml_isnan_f32
+#define _ISINFd __ocml_isinf_f64
+#define _ISINFf __ocml_isinf_f32
+#define _ISFINITEd __ocml_isfinite_f64
+#define _ISFINITEf __ocml_isfinite_f32
+#define _COPYSIGNd __ocml_copysign_f64
+#define _COPYSIGNf __ocml_copysign_f32
+#define _SCALBNd __ocml_scalbn_f64
+#define _SCALBNf __ocml_scalbn_f32
+#define _ABSd __ocml_fabs_f64
+#define _ABSf __ocml_fabs_f32
+#define _LOGBd __ocml_logb_f64
+#define _LOGBf __ocml_logb_f32
+#define _fmaxd __ocml_fmax_f64
+#define _fmaxf __ocml_fmax_f32
+#else
+#define _ISNANd __nv_isnand
+#define _ISNANf __nv_isnanf
+#define _ISINFd __nv_isinfd
+#define _ISINFf __nv_isinff
+#define _ISFINITEd __nv_isfinited
+#define _ISFINITEf __nv_finitef
+#define _COPYSIGNd __nv_copysign
+#define _COPYSIGNf __nv_copysignf
+#define _SCALBNd __nv_scalbn
+#define _SCALBNf __nv_scalbnf
+#define _ABSd __nv_fabs
+#define _ABSf __nv_fabsf
+#define _LOGBd __nv_logb
+#define _LOGBf __nv_logbf
+#define _fmaxd __nv_fmax
+#define _fmaxf __nv_fmaxf
+#endif
+#endif
+
+#if defined(__cplusplus)
+extern "C" {
+#endif
+
+__DEVICE__ double _Complex __muldc3(double __a, double __b, double __c,
+ double __d) {
+ double __ac = __a * __c;
+ double __bd = __b * __d;
+ double __ad = __a * __d;
+ double __bc = __b * __c;
+ double _Complex z;
+ __real__(z) = __ac - __bd;
+ __imag__(z) = __ad + __bc;
+ if (_ISNANd(__real__(z)) && _ISNANd(__imag__(z))) {
+ int __recalc = 0;
+ if (_ISINFd(__a) || _ISINFd(__b)) {
+ __a = _COPYSIGNd(_ISINFd(__a) ? 1 : 0, __a);
+ __b = _COPYSIGNd(_ISINFd(__b) ? 1 : 0, __b);
+ if (_ISNANd(__c))
+ __c = _COPYSIGNd(0, __c);
+ if (_ISNANd(__d))
+ __d = _COPYSIGNd(0, __d);
+ __recalc = 1;
+ }
+ if (_ISINFd(__c) || _ISINFd(__d)) {
+ __c = _COPYSIGNd(_ISINFd(__c) ? 1 : 0, __c);
+ __d = _COPYSIGNd(_ISINFd(__d) ? 1 : 0, __d);
+ if (_ISNANd(__a))
+ __a = _COPYSIGNd(0, __a);
+ if (_ISNANd(__b))
+ __b = _COPYSIGNd(0, __b);
+ __recalc = 1;
+ }
+ if (!__recalc &&
+ (_ISINFd(__ac) || _ISINFd(__bd) || _ISINFd(__ad) || _ISINFd(__bc))) {
+ if (_ISNANd(__a))
+ __a = _COPYSIGNd(0, __a);
+ if (_ISNANd(__b))
+ __b = _COPYSIGNd(0, __b);
+ if (_ISNANd(__c))
+ __c = _COPYSIGNd(0, __c);
+ if (_ISNANd(__d))
+ __d = _COPYSIGNd(0, __d);
+ __recalc = 1;
+ }
+ if (__recalc) {
+ // Can't use std::numeric_limits<double>::infinity() -- that doesn't have
+ // a device overload (and isn't constexpr before C++11, naturally).
+ __real__(z) = __builtin_huge_val() * (__a * __c - __b * __d);
+ __imag__(z) = __builtin_huge_val() * (__a * __d + __b * __c);
+ }
+ }
+ return z;
+}
+
+__DEVICE__ float _Complex __mulsc3(float __a, float __b, float __c, float __d) {
+ float __ac = __a * __c;
+ float __bd = __b * __d;
+ float __ad = __a * __d;
+ float __bc = __b * __c;
+ float _Complex z;
+ __real__(z) = __ac - __bd;
+ __imag__(z) = __ad + __bc;
+ if (_ISNANf(__real__(z)) && _ISNANf(__imag__(z))) {
+ int __recalc = 0;
+ if (_ISINFf(__a) || _ISINFf(__b)) {
+ __a = _COPYSIGNf(_ISINFf(__a) ? 1 : 0, __a);
+ __b = _COPYSIGNf(_ISINFf(__b) ? 1 : 0, __b);
+ if (_ISNANf(__c))
+ __c = _COPYSIGNf(0, __c);
+ if (_ISNANf(__d))
+ __d = _COPYSIGNf(0, __d);
+ __recalc = 1;
+ }
+ if (_ISINFf(__c) || _ISINFf(__d)) {
+ __c = _COPYSIGNf(_ISINFf(__c) ? 1 : 0, __c);
+ __d = _COPYSIGNf(_ISINFf(__d) ? 1 : 0, __d);
+ if (_ISNANf(__a))
+ __a = _COPYSIGNf(0, __a);
+ if (_ISNANf(__b))
+ __b = _COPYSIGNf(0, __b);
+ __recalc = 1;
+ }
+ if (!__recalc &&
+ (_ISINFf(__ac) || _ISINFf(__bd) || _ISINFf(__ad) || _ISINFf(__bc))) {
+ if (_ISNANf(__a))
+ __a = _COPYSIGNf(0, __a);
+ if (_ISNANf(__b))
+ __b = _COPYSIGNf(0, __b);
+ if (_ISNANf(__c))
+ __c = _COPYSIGNf(0, __c);
+ if (_ISNANf(__d))
+ __d = _COPYSIGNf(0, __d);
+ __recalc = 1;
+ }
+ if (__recalc) {
+ __real__(z) = __builtin_huge_valf() * (__a * __c - __b * __d);
+ __imag__(z) = __builtin_huge_valf() * (__a * __d + __b * __c);
+ }
+ }
+ return z;
+}
+
+__DEVICE__ double _Complex __divdc3(double __a, double __b, double __c,
+ double __d) {
+ int __ilogbw = 0;
+ // Can't use std::max, because that's defined in <algorithm>, and we don't
+ // want to pull that in for every compile. The CUDA headers define
+ // ::max(float, float) and ::max(double, double), which is sufficient for us.
+ double __logbw = _LOGBd(_fmaxd(_ABSd(__c), _ABSd(__d)));
+ if (_ISFINITEd(__logbw)) {
+ __ilogbw = (int)__logbw;
+ __c = _SCALBNd(__c, -__ilogbw);
+ __d = _SCALBNd(__d, -__ilogbw);
+ }
+ double __denom = __c * __c + __d * __d;
+ double _Complex z;
+ __real__(z) = _SCALBNd((__a * __c + __b * __d) / __denom, -__ilogbw);
+ __imag__(z) = _SCALBNd((__b * __c - __a * __d) / __denom, -__ilogbw);
+ if (_ISNANd(__real__(z)) && _ISNANd(__imag__(z))) {
+ if ((__denom == 0.0) && (!_ISNANd(__a) || !_ISNANd(__b))) {
+ __real__(z) = _COPYSIGNd(__builtin_huge_val(), __c) * __a;
+ __imag__(z) = _COPYSIGNd(__builtin_huge_val(), __c) * __b;
+ } else if ((_ISINFd(__a) || _ISINFd(__b)) && _ISFINITEd(__c) &&
+ _ISFINITEd(__d)) {
+ __a = _COPYSIGNd(_ISINFd(__a) ? 1.0 : 0.0, __a);
+ __b = _COPYSIGNd(_ISINFd(__b) ? 1.0 : 0.0, __b);
+ __real__(z) = __builtin_huge_val() * (__a * __c + __b * __d);
+ __imag__(z) = __builtin_huge_val() * (__b * __c - __a * __d);
+ } else if (_ISINFd(__logbw) && __logbw > 0.0 && _ISFINITEd(__a) &&
+ _ISFINITEd(__b)) {
+ __c = _COPYSIGNd(_ISINFd(__c) ? 1.0 : 0.0, __c);
+ __d = _COPYSIGNd(_ISINFd(__d) ? 1.0 : 0.0, __d);
+ __real__(z) = 0.0 * (__a * __c + __b * __d);
+ __imag__(z) = 0.0 * (__b * __c - __a * __d);
+ }
+ }
+ return z;
+}
+
+__DEVICE__ float _Complex __divsc3(float __a, float __b, float __c, float __d) {
+ int __ilogbw = 0;
+ float __logbw = _LOGBf(_fmaxf(_ABSf(__c), _ABSf(__d)));
+ if (_ISFINITEf(__logbw)) {
+ __ilogbw = (int)__logbw;
+ __c = _SCALBNf(__c, -__ilogbw);
+ __d = _SCALBNf(__d, -__ilogbw);
+ }
+ float __denom = __c * __c + __d * __d;
+ float _Complex z;
+ __real__(z) = _SCALBNf((__a * __c + __b * __d) / __denom, -__ilogbw);
+ __imag__(z) = _SCALBNf((__b * __c - __a * __d) / __denom, -__ilogbw);
+ if (_ISNANf(__real__(z)) && _ISNANf(__imag__(z))) {
+ if ((__denom == 0) && (!_ISNANf(__a) || !_ISNANf(__b))) {
+ __real__(z) = _COPYSIGNf(__builtin_huge_valf(), __c) * __a;
+ __imag__(z) = _COPYSIGNf(__builtin_huge_valf(), __c) * __b;
+ } else if ((_ISINFf(__a) || _ISINFf(__b)) && _ISFINITEf(__c) &&
+ _ISFINITEf(__d)) {
+ __a = _COPYSIGNf(_ISINFf(__a) ? 1 : 0, __a);
+ __b = _COPYSIGNf(_ISINFf(__b) ? 1 : 0, __b);
+ __real__(z) = __builtin_huge_valf() * (__a * __c + __b * __d);
+ __imag__(z) = __builtin_huge_valf() * (__b * __c - __a * __d);
+ } else if (_ISINFf(__logbw) && __logbw > 0 && _ISFINITEf(__a) &&
+ _ISFINITEf(__b)) {
+ __c = _COPYSIGNf(_ISINFf(__c) ? 1 : 0, __c);
+ __d = _COPYSIGNf(_ISINFf(__d) ? 1 : 0, __d);
+ __real__(z) = 0 * (__a * __c + __b * __d);
+ __imag__(z) = 0 * (__b * __c - __a * __d);
+ }
+ }
+ return z;
+}
+
+#if defined(__cplusplus)
+} // extern "C"
+#endif
+
+#undef _ISNANd
+#undef _ISNANf
+#undef _ISINFd
+#undef _ISINFf
+#undef _COPYSIGNd
+#undef _COPYSIGNf
+#undef _ISFINITEd
+#undef _ISFINITEf
+#undef _SCALBNd
+#undef _SCALBNf
+#undef _ABSd
+#undef _ABSf
+#undef _LOGBd
+#undef _LOGBf
+#undef _fmaxd
+#undef _fmaxf
+
+#if defined(__OPENMP_NVPTX__) || defined(__OPENMP_AMDGCN__)
+#pragma omp end declare target
+#endif
+
+#pragma pop_macro("__DEVICE__")
+
+#endif // __CLANG_CUDA_COMPLEX_BUILTINS
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