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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
// Copyright (C) 2021 C. Antonio Sanchez <cantonios@google.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_COMPLEX_CUDA_H
#define EIGEN_COMPLEX_CUDA_H
// clang-format off
// Many std::complex methods such as operator+, operator-, operator* and
// operator/ are not constexpr. Due to this, GCC and older versions of clang do
// not treat them as device functions and thus Eigen functors making use of
// these operators fail to compile. Here, we manually specialize these
// operators and functors for complex types when building for CUDA to enable
// their use on-device.
#if defined(EIGEN_CUDACC) && defined(EIGEN_GPU_COMPILE_PHASE)
// ICC already specializes std::complex<float> and std::complex<double>
// operators, preventing us from making them device functions here.
// This will lead to silent runtime errors if the operators are used on device.
//
// To allow std::complex operator use on device, define _OVERRIDE_COMPLEX_SPECIALIZATION_
// prior to first inclusion of <complex>. This prevents ICC from adding
// its own specializations, so our custom ones below can be used instead.
#if !(defined(EIGEN_COMP_ICC) && defined(_USE_COMPLEX_SPECIALIZATION_))
// Import Eigen's internal operator specializations.
#define EIGEN_USING_STD_COMPLEX_OPERATORS \
using Eigen::complex_operator_detail::operator+; \
using Eigen::complex_operator_detail::operator-; \
using Eigen::complex_operator_detail::operator*; \
using Eigen::complex_operator_detail::operator/; \
using Eigen::complex_operator_detail::operator+=; \
using Eigen::complex_operator_detail::operator-=; \
using Eigen::complex_operator_detail::operator*=; \
using Eigen::complex_operator_detail::operator/=; \
using Eigen::complex_operator_detail::operator==; \
using Eigen::complex_operator_detail::operator!=;
namespace Eigen {
// Specialized std::complex overloads.
namespace complex_operator_detail {
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
std::complex<T> complex_multiply(const std::complex<T>& a, const std::complex<T>& b) {
const T a_real = numext::real(a);
const T a_imag = numext::imag(a);
const T b_real = numext::real(b);
const T b_imag = numext::imag(b);
return std::complex<T>(
a_real * b_real - a_imag * b_imag,
a_imag * b_real + a_real * b_imag);
}
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
std::complex<T> complex_divide_fast(const std::complex<T>& a, const std::complex<T>& b) {
const T a_real = numext::real(a);
const T a_imag = numext::imag(a);
const T b_real = numext::real(b);
const T b_imag = numext::imag(b);
const T norm = (b_real * b_real + b_imag * b_imag);
return std::complex<T>((a_real * b_real + a_imag * b_imag) / norm,
(a_imag * b_real - a_real * b_imag) / norm);
}
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
std::complex<T> complex_divide_stable(const std::complex<T>& a, const std::complex<T>& b) {
const T a_real = numext::real(a);
const T a_imag = numext::imag(a);
const T b_real = numext::real(b);
const T b_imag = numext::imag(b);
// Smith's complex division (https://arxiv.org/pdf/1210.4539.pdf),
// guards against over/under-flow.
const bool scale_imag = numext::abs(b_imag) <= numext::abs(b_real);
const T rscale = scale_imag ? T(1) : b_real / b_imag;
const T iscale = scale_imag ? b_imag / b_real : T(1);
const T denominator = b_real * rscale + b_imag * iscale;
return std::complex<T>((a_real * rscale + a_imag * iscale) / denominator,
(a_imag * rscale - a_real * iscale) / denominator);
}
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
std::complex<T> complex_divide(const std::complex<T>& a, const std::complex<T>& b) {
#if EIGEN_FAST_MATH
return complex_divide_fast(a, b);
#else
return complex_divide_stable(a, b);
#endif
}
// NOTE: We cannot specialize compound assignment operators with Scalar T,
// (i.e. operator@=(const T&), for @=+,-,*,/)
// since they are already specialized for float/double/long double within
// the standard <complex> header. We also do not specialize the stream
// operators.
#define EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(T) \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator+(const std::complex<T>& a) { return a; } \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator-(const std::complex<T>& a) { \
return std::complex<T>(-numext::real(a), -numext::imag(a)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator+(const std::complex<T>& a, const std::complex<T>& b) { \
return std::complex<T>(numext::real(a) + numext::real(b), numext::imag(a) + numext::imag(b)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator+(const std::complex<T>& a, const T& b) { \
return std::complex<T>(numext::real(a) + b, numext::imag(a)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator+(const T& a, const std::complex<T>& b) { \
return std::complex<T>(a + numext::real(b), numext::imag(b)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator-(const std::complex<T>& a, const std::complex<T>& b) { \
return std::complex<T>(numext::real(a) - numext::real(b), numext::imag(a) - numext::imag(b)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator-(const std::complex<T>& a, const T& b) { \
return std::complex<T>(numext::real(a) - b, numext::imag(a)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator-(const T& a, const std::complex<T>& b) { \
return std::complex<T>(a - numext::real(b), -numext::imag(b)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator*(const std::complex<T>& a, const std::complex<T>& b) { \
return complex_multiply(a, b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator*(const std::complex<T>& a, const T& b) { \
return std::complex<T>(numext::real(a) * b, numext::imag(a) * b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator*(const T& a, const std::complex<T>& b) { \
return std::complex<T>(a * numext::real(b), a * numext::imag(b)); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator/(const std::complex<T>& a, const std::complex<T>& b) { \
return complex_divide(a, b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator/(const std::complex<T>& a, const T& b) { \
return std::complex<T>(numext::real(a) / b, numext::imag(a) / b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T> operator/(const T& a, const std::complex<T>& b) { \
return complex_divide(std::complex<T>(a, 0), b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T>& operator+=(std::complex<T>& a, const std::complex<T>& b) { \
numext::real_ref(a) += numext::real(b); \
numext::imag_ref(a) += numext::imag(b); \
return a; \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T>& operator-=(std::complex<T>& a, const std::complex<T>& b) { \
numext::real_ref(a) -= numext::real(b); \
numext::imag_ref(a) -= numext::imag(b); \
return a; \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T>& operator*=(std::complex<T>& a, const std::complex<T>& b) { \
a = complex_multiply(a, b); \
return a; \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
std::complex<T>& operator/=(std::complex<T>& a, const std::complex<T>& b) { \
a = complex_divide(a, b); \
return a; \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
bool operator==(const std::complex<T>& a, const std::complex<T>& b) { \
return numext::real(a) == numext::real(b) && numext::imag(a) == numext::imag(b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
bool operator==(const std::complex<T>& a, const T& b) { \
return numext::real(a) == b && numext::imag(a) == 0; \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
bool operator==(const T& a, const std::complex<T>& b) { \
return a == numext::real(b) && 0 == numext::imag(b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
bool operator!=(const std::complex<T>& a, const std::complex<T>& b) { \
return !(a == b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
bool operator!=(const std::complex<T>& a, const T& b) { \
return !(a == b); \
} \
\
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
bool operator!=(const T& a, const std::complex<T>& b) { \
return !(a == b); \
}
// Do not specialize for long double, since that reduces to double on device.
EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(float)
EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(double)
#undef EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS
} // namespace complex_operator_detail
EIGEN_USING_STD_COMPLEX_OPERATORS
namespace numext {
EIGEN_USING_STD_COMPLEX_OPERATORS
} // namespace numext
namespace internal {
EIGEN_USING_STD_COMPLEX_OPERATORS
} // namespace internal
} // namespace Eigen
#endif // !(EIGEN_COMP_ICC && _USE_COMPLEX_SPECIALIZATION_)
#endif // EIGEN_CUDACC && EIGEN_GPU_COMPILE_PHASE
#endif // EIGEN_COMPLEX_CUDA_H
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