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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>
//
// 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
#if defined(EIGEN_CUDACC) && defined(EIGEN_GPU_COMPILE_PHASE)
namespace Eigen {
namespace internal {
// Many std::complex methods such as operator+, operator-, operator* and
// operator/ are not constexpr. Due to this, clang does not treat them as device
// functions and thus Eigen functors making use of these operators fail to
// compile. Here, we manually specialize these functors for complex types when
// building for CUDA to avoid non-constexpr methods.
// Sum
template<typename T> struct scalar_sum_op<const std::complex<T>, const std::complex<T> > : binary_op_base<const std::complex<T>, const std::complex<T> > {
typedef typename std::complex<T> result_type;
EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {
return std::complex<T>(numext::real(a) + numext::real(b),
numext::imag(a) + numext::imag(b));
}
};
template<typename T> struct scalar_sum_op<std::complex<T>, std::complex<T> > : scalar_sum_op<const std::complex<T>, const std::complex<T> > {};
// Difference
template<typename T> struct scalar_difference_op<const std::complex<T>, const std::complex<T> > : binary_op_base<const std::complex<T>, const std::complex<T> > {
typedef typename std::complex<T> result_type;
EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {
return std::complex<T>(numext::real(a) - numext::real(b),
numext::imag(a) - numext::imag(b));
}
};
template<typename T> struct scalar_difference_op<std::complex<T>, std::complex<T> > : scalar_difference_op<const std::complex<T>, const std::complex<T> > {};
// Product
template<typename T> struct scalar_product_op<const std::complex<T>, const std::complex<T> > : binary_op_base<const std::complex<T>, const std::complex<T> > {
enum {
Vectorizable = packet_traits<std::complex<T> >::HasMul
};
typedef typename std::complex<T> result_type;
EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {
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_real * b_imag + a_imag * b_real);
}
};
template<typename T> struct scalar_product_op<std::complex<T>, std::complex<T> > : scalar_product_op<const std::complex<T>, const std::complex<T> > {};
// Quotient
template<typename T> struct scalar_quotient_op<const std::complex<T>, const std::complex<T> > : binary_op_base<const std::complex<T>, const std::complex<T> > {
enum {
Vectorizable = packet_traits<std::complex<T> >::HasDiv
};
typedef typename std::complex<T> result_type;
EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {
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 = T(1) / (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> struct scalar_quotient_op<std::complex<T>, std::complex<T> > : scalar_quotient_op<const std::complex<T>, const std::complex<T> > {};
template<typename T>
struct sqrt_impl<std::complex<T>> {
static EIGEN_DEVICE_FUNC std::complex<T> run(const std::complex<T>& z) {
// Computes the principal sqrt of the input.
//
// For a complex square root of the number x + i*y. We want to find real
// numbers u and v such that
// (u + i*v)^2 = x + i*y <=>
// u^2 - v^2 + i*2*u*v = x + i*v.
// By equating the real and imaginary parts we get:
// u^2 - v^2 = x
// 2*u*v = y.
//
// For x >= 0, this has the numerically stable solution
// u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))
// v = y / (2 * u)
// and for x < 0,
// v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2)))
// u = y / (2 * v)
//
// Letting w = sqrt(0.5 * (|x| + |z|)),
// if x == 0: u = w, v = sign(y) * w
// if x > 0: u = w, v = y / (2 * w)
// if x < 0: u = |y| / (2 * w), v = sign(y) * w
const T x = numext::real(z);
const T y = numext::imag(z);
const T zero = T(0);
const T cst_half = T(0.5);
// Special case of isinf(y)
if ((numext::isinf)(y)) {
const T inf = std::numeric_limits<T>::infinity();
return std::complex<T>(inf, y);
}
T w = numext::sqrt(cst_half * (numext::abs(x) + numext::abs(z)));
return
x == zero ? std::complex<T>(w, y < zero ? -w : w)
: x > zero ? std::complex<T>(w, y / (2 * w))
: std::complex<T>(numext::abs(y) / (2 * w), y < zero ? -w : w );
}
};
} // namespace internal
} // namespace Eigen
#endif
#endif // EIGEN_COMPLEX_CUDA_H
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