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eigen/mirror/refs/heads/ci-smoketest-image-prereqs/./Eigen/src/Core/MathFunctions.h
blob: 879dff21491a9421616ce7257eedf015c0c09167 [file] [edit]
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
//
// 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/.
// SPDX-License-Identifier: MPL-2.0
#ifndef EIGEN_MATHFUNCTIONS_H
#define EIGEN_MATHFUNCTIONS_H
// TODO: consider moving these constants to NumTraits.
// Source: WolframAlpha
#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L
#define EIGEN_LOG2E 1.442695040888963407359924681001892137426645954152985934135449406931109219L
#define EIGEN_LN2 0.693147180559945309417232121458176568075500134360255254120680009493393621L
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
/** \internal \class global_math_functions_filtering_base
*
* What it does:
* Defines a typedef 'type' as follows:
* - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
* global_math_functions_filtering_base<T>::type is a typedef for it.
* - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
*
* How it's used:
* To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
* When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
* is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
* So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial
* specialization won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells
* it.
*
* How it's implemented:
* SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you
* replace the typename dummy by an integer template parameter, it doesn't work anymore!
*/
template <typename T, typename dummy = void>
struct global_math_functions_filtering_base {
using type = T;
};
template <typename T>
struct global_math_functions_filtering_base<T,
void_t<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>> {
using type = typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
};
#define EIGEN_MATHFUNC_IMPL(func, scalar) \
Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
/****************************************************************************
* Implementation of real *
****************************************************************************/
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct real_default_impl {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static constexpr RealScalar run(const Scalar& x) { return x; }
};
template <typename Scalar>
struct real_default_impl<Scalar, true> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
using std::real;
return real(x);
}
};
template <typename Scalar>
struct real_impl : real_default_impl<Scalar> {};
#if defined(EIGEN_GPU_COMPILE_PHASE)
template <typename T>
struct real_impl<std::complex<T>> {
using RealScalar = T;
EIGEN_DEVICE_FUNC static inline T run(const std::complex<T>& x) { return x.real(); }
};
#endif
/****************************************************************************
* Implementation of imag *
****************************************************************************/
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct imag_default_impl {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar&) { return RealScalar(0); }
};
template <typename Scalar>
struct imag_default_impl<Scalar, true> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
using std::imag;
return imag(x);
}
};
template <typename Scalar>
struct imag_impl : imag_default_impl<Scalar> {};
#if defined(EIGEN_GPU_COMPILE_PHASE)
template <typename T>
struct imag_impl<std::complex<T>> {
using RealScalar = T;
EIGEN_DEVICE_FUNC static inline T run(const std::complex<T>& x) { return x.imag(); }
};
#endif
/****************************************************************************
* Implementation of real_ref *
****************************************************************************/
template <typename Scalar>
struct real_ref_impl {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar& run(Scalar& x) { return reinterpret_cast<RealScalar*>(&x)[0]; }
EIGEN_DEVICE_FUNC static inline const RealScalar& run(const Scalar& x) {
return reinterpret_cast<const RealScalar*>(&x)[0];
}
};
/****************************************************************************
* Implementation of imag_ref *
****************************************************************************/
template <typename Scalar, bool IsComplex>
struct imag_ref_default_impl {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar& run(Scalar& x) { return reinterpret_cast<RealScalar*>(&x)[1]; }
EIGEN_DEVICE_FUNC static inline const RealScalar& run(const Scalar& x) {
return reinterpret_cast<const RealScalar*>(&x)[1];
}
};
template <typename Scalar>
struct imag_ref_default_impl<Scalar, false> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC constexpr static inline RealScalar run(Scalar&) { return RealScalar(0); }
EIGEN_DEVICE_FUNC constexpr static inline RealScalar run(const Scalar&) { return RealScalar(0); }
};
template <typename Scalar>
struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
} // namespace internal
namespace numext {
template <typename Scalar>
EIGEN_DEVICE_FUNC inline decltype(auto) real(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline auto real_ref(const Scalar& x)
-> internal::add_const_on_value_type_t<decltype(internal::real_ref_impl<Scalar>::run(x))> {
return internal::real_ref_impl<Scalar>::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline auto real_ref(Scalar& x)
-> decltype(EIGEN_MATHFUNC_IMPL(real_ref, std::remove_const_t<Scalar>)::run(x)) {
return EIGEN_MATHFUNC_IMPL(real_ref, std::remove_const_t<Scalar>)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline decltype(auto) imag(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar select(const Scalar& mask, const Scalar& a, const Scalar& b) {
return numext::is_exactly_zero(mask) ? b : a;
}
} // namespace numext
namespace internal {
/****************************************************************************
* Implementation of conj *
****************************************************************************/
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct conj_default_impl {
EIGEN_DEVICE_FUNC static constexpr Scalar run(const Scalar& x) { return x; }
};
template <typename Scalar>
struct conj_default_impl<Scalar, true> {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) {
using std::conj;
return conj(x);
}
};
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct conj_impl : conj_default_impl<Scalar, IsComplex> {};
/****************************************************************************
* Implementation of mul *
****************************************************************************/
// Unsigned operands narrower than int promote to int, where a product whose wrapped value is representable
// can still overflow: (unsigned short)0xffff squared is 0xfffe0001 > INT_MAX. Multiplying in unsigned int,
// wider than every such operand, wraps instead. Mixed operand types, signed types, and bool keep operator*.
template <typename Lhs, typename Rhs,
bool NarrowUnsigned = std::is_same<Lhs, Rhs>::value && std::is_unsigned<Lhs>::value &&
!std::is_same<Lhs, bool>::value && (sizeof(Lhs) < sizeof(int))>
struct mul_impl {
EIGEN_DEVICE_FUNC static constexpr EIGEN_ALWAYS_INLINE auto run(const Lhs& a, const Rhs& b) { return a * b; }
};
template <typename Scalar>
struct mul_impl<Scalar, Scalar, true> {
EIGEN_DEVICE_FUNC static constexpr EIGEN_ALWAYS_INLINE Scalar run(const Scalar& a, const Scalar& b) {
return static_cast<Scalar>(static_cast<unsigned int>(a) * static_cast<unsigned int>(b));
}
};
/** \internal \returns a * b, wrapping rather than overflowing the signed type that integral promotion
* would give narrow unsigned operands. The result keeps operator*'s type, which for an expression-template
* Scalar is a lazy expression: consume it rather than binding it to auto. */
template <typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE auto mul(const Lhs& a, const Rhs& b) {
return mul_impl<Lhs, Rhs>::run(a, b);
}
/****************************************************************************
* Implementation of abs2 *
****************************************************************************/
template <typename Scalar, bool IsComplex>
struct abs2_impl_default {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { return internal::mul(x, x); }
};
template <typename Scalar>
struct abs2_impl_default<Scalar, true> // IsComplex
{
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
return numext::real(x) * numext::real(x) + numext::imag(x) * numext::imag(x);
}
};
template <typename Scalar>
struct abs2_impl {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
return abs2_impl_default<Scalar, NumTraits<Scalar>::IsComplex>::run(x);
}
};
/****************************************************************************
* Implementation of sqrt/rsqrt *
****************************************************************************/
template <typename Scalar>
struct sqrt_impl {
EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE Scalar run(const Scalar& x) {
EIGEN_USING_STD(sqrt);
return sqrt(x);
}
};
// Complex sqrt defined in MathFunctionsImpl.h.
template <typename ComplexT>
EIGEN_DEVICE_FUNC constexpr ComplexT complex_sqrt(const ComplexT& a_x);
// Custom implementation is faster than `std::sqrt`, works on
// GPU, and correctly handles special cases (unlike MSVC).
template <typename T>
struct sqrt_impl<std::complex<T>> {
EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x) { return complex_sqrt(x); }
};
// Default implementation relies on numext::sqrt, at bottom of file.
template <typename T>
struct rsqrt_impl;
// Complex rsqrt defined in MathFunctionsImpl.h.
template <typename ComplexT>
EIGEN_DEVICE_FUNC constexpr ComplexT complex_rsqrt(const ComplexT& a_x);
template <typename T>
struct rsqrt_impl<std::complex<T>> {
EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x) {
return complex_rsqrt(x);
}
};
/****************************************************************************
* Implementation of norm1 *
****************************************************************************/
template <typename Scalar, bool IsComplex>
struct norm1_default_impl;
template <typename Scalar>
struct norm1_default_impl<Scalar, true> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
EIGEN_USING_STD(abs);
return abs(numext::real(x)) + abs(numext::imag(x));
}
};
template <typename Scalar>
struct norm1_default_impl<Scalar, false> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
EIGEN_USING_STD(abs);
return abs(x);
}
};
template <typename Scalar>
struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
/****************************************************************************
* Implementation of hypot *
****************************************************************************/
template <typename Scalar>
struct hypot_impl;
/****************************************************************************
* Implementation of cast *
****************************************************************************/
template <typename OldType, typename NewType, typename EnableIf = void>
struct cast_impl {
EIGEN_DEVICE_FUNC static inline NewType run(const OldType& x) { return static_cast<NewType>(x); }
};
template <typename OldType>
struct cast_impl<OldType, bool> {
EIGEN_DEVICE_FUNC static inline bool run(const OldType& x) { return x != OldType(0); }
};
// Casting from S -> Complex<T> leads to an implicit conversion from S to T,
// generating warnings on clang. Here we explicitly cast the real component.
template <typename OldType, typename NewType>
struct cast_impl<OldType, NewType, std::enable_if_t<!NumTraits<OldType>::IsComplex && NumTraits<NewType>::IsComplex>> {
EIGEN_DEVICE_FUNC static inline NewType run(const OldType& x) {
using NewReal = typename NumTraits<NewType>::Real;
return static_cast<NewType>(static_cast<NewReal>(x));
}
};
// Returns NewType directly to avoid unintended intermediate conversions.
template <typename OldType, typename NewType>
EIGEN_DEVICE_FUNC inline NewType cast(const OldType& x) {
return cast_impl<OldType, NewType>::run(x);
}
/****************************************************************************
* Implementation of arg *
****************************************************************************/
// Visual Studio 2017 has a bug where arg(float) returns 0 for negative inputs.
// This seems to be fixed in VS 2019.
#if (!EIGEN_COMP_MSVC || EIGEN_COMP_MSVC >= 1920)
// std::arg is only defined for types of std::complex, or integer types or float/double/long double
template <typename Scalar, bool HasStdImpl = NumTraits<Scalar>::IsComplex || std::is_integral<Scalar>::value ||
std::is_same<Scalar, float>::value ||
std::is_same<Scalar, double>::value ||
std::is_same<Scalar, long double>::value>
struct arg_default_impl;
template <typename Scalar>
struct arg_default_impl<Scalar, true> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
// There is no official ::arg on device in CUDA/HIP, so we always need to use std::arg.
using std::arg;
return static_cast<RealScalar>(arg(x));
}
};
// Must be non-complex floating-point type (e.g. half/bfloat16).
template <typename Scalar>
struct arg_default_impl<Scalar, false> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
return (x < Scalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0);
}
};
#else
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct arg_default_impl {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
return (x < RealScalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0);
}
};
template <typename Scalar>
struct arg_default_impl<Scalar, true> {
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
EIGEN_USING_STD(arg);
return arg(x);
}
};
#endif
template <typename Scalar>
struct arg_impl : arg_default_impl<Scalar> {};
/****************************************************************************
* Implementation of expm1 *
****************************************************************************/
// This implementation is based on GSL Math's expm1.
namespace std_fallback {
// fallback expm1 implementation in case there is no expm1(Scalar) function in namespace of Scalar,
// or that there is no suitable std::expm1 function available. Implementation
// attributed to Kahan. See: http://www.plunk.org/~hatch/rightway.php.
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar expm1(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_USING_STD(exp);
Scalar u = exp(x);
if (numext::equal_strict(u, Scalar(1))) {
return x;
}
Scalar um1 = u - RealScalar(1);
if (numext::equal_strict(um1, Scalar(-1))) {
return RealScalar(-1);
}
EIGEN_USING_STD(log);
Scalar logu = log(u);
return numext::equal_strict(u, logu) ? u : (u - RealScalar(1)) * x / logu;
}
} // namespace std_fallback
template <typename Scalar>
struct expm1_impl {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
EIGEN_USING_STD(expm1);
return expm1(x);
}
};
/****************************************************************************
* Implementation of log *
****************************************************************************/
// Complex log defined in MathFunctionsImpl.h.
template <typename ComplexT>
EIGEN_DEVICE_FUNC constexpr ComplexT complex_log(const ComplexT& z);
template <typename Scalar>
struct log_impl {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) {
EIGEN_USING_STD(log);
return static_cast<Scalar>(log(x));
}
};
template <typename Scalar>
struct log_impl<std::complex<Scalar>> {
EIGEN_DEVICE_FUNC static inline std::complex<Scalar> run(const std::complex<Scalar>& z) { return complex_log(z); }
};
/****************************************************************************
* Implementation of log1p *
****************************************************************************/
namespace std_fallback {
// fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar,
// or that there is no suitable std::log1p function available
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
using RealScalar = typename NumTraits<Scalar>::Real;
EIGEN_USING_STD(log);
Scalar x1p = RealScalar(1) + x;
Scalar log_1p = log_impl<Scalar>::run(x1p);
const bool is_small = numext::equal_strict(x1p, Scalar(1));
const bool is_inf = numext::equal_strict(x1p, log_1p);
return (is_small || is_inf) ? x : x * (log_1p / (x1p - RealScalar(1)));
}
} // namespace std_fallback
template <typename Scalar>
struct log1p_impl {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) {
EIGEN_USING_STD(log1p);
return log1p(x);
}
};
// Specialization for complex types that are not supported by std::log1p.
template <typename RealScalar>
struct log1p_impl<std::complex<RealScalar>> {
EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x) {
return std_fallback::log1p(x);
}
};
/****************************************************************************
* Implementation of pow *
****************************************************************************/
template <typename ScalarX, typename ScalarY,
bool IsInteger = NumTraits<ScalarX>::IsInteger && NumTraits<ScalarY>::IsInteger>
struct pow_impl {
using result_type =
typename ScalarBinaryOpTraits<ScalarX, ScalarY, internal::scalar_pow_op<ScalarX, ScalarY>>::ReturnType;
static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y) {
EIGEN_USING_STD(pow);
return pow(x, y);
}
};
template <typename ScalarX, typename ScalarY>
struct pow_impl<ScalarX, ScalarY, true> {
using result_type = ScalarX;
static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y) {
ScalarX res(1);
eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
if (y & 1) res = internal::mul(res, x);
y >>= 1;
while (y) {
x = internal::mul(x, x);
if (y & 1) res = internal::mul(res, x);
y >>= 1;
}
return res;
}
};
constexpr int floor_log2(unsigned int value) {
int result = 0;
while (value > 1) {
value >>= 1;
++result;
}
return result;
}
template <typename BitsType, typename EnableIf = void>
struct count_bits_impl {
static_assert(std::is_integral<BitsType>::value && std::is_unsigned<BitsType>::value,
"BitsType must be an unsigned integer");
static EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
int n = CHAR_BIT * sizeof(BitsType);
int shift = n / 2;
while (bits > 0 && shift > 0) {
BitsType y = bits >> shift;
if (y > 0) {
n -= shift;
bits = y;
}
shift /= 2;
}
if (shift == 0) {
--n;
}
return n;
}
static EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
int n = CHAR_BIT * sizeof(BitsType);
int shift = n / 2;
while (bits > 0 && shift > 0) {
BitsType y = bits << shift;
if (y > 0) {
n -= shift;
bits = y;
}
shift /= 2;
}
if (shift == 0) {
--n;
}
return n;
}
static EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
int n = 0;
while (bits) {
bits &= bits - 1;
++n;
}
return n;
}
};
// Count leading zeros.
template <typename BitsType>
EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
return count_bits_impl<BitsType>::clz(bits);
}
// Count trailing zeros.
template <typename BitsType>
EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
return count_bits_impl<BitsType>::ctz(bits);
}
// Count set bits (population count).
template <typename BitsType>
EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
return count_bits_impl<BitsType>::popcount(bits);
}
#if EIGEN_COMP_GNUC || EIGEN_COMP_CLANG
template <typename BitsType>
struct count_bits_impl<
BitsType, std::enable_if_t<std::is_integral<BitsType>::value && sizeof(BitsType) <= sizeof(unsigned int)>> {
static constexpr int kNumBits = static_cast<int>(sizeof(BitsType) * CHAR_BIT);
static EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
static constexpr int kLeadingBitsOffset = (sizeof(unsigned int) - sizeof(BitsType)) * CHAR_BIT;
return bits == 0 ? kNumBits : __builtin_clz(static_cast<unsigned int>(bits)) - kLeadingBitsOffset;
}
static EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
return bits == 0 ? kNumBits : __builtin_ctz(static_cast<unsigned int>(bits));
}
static EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
return __builtin_popcount(static_cast<unsigned int>(bits));
}
};
template <typename BitsType>
struct count_bits_impl<BitsType,
std::enable_if_t<std::is_integral<BitsType>::value && sizeof(unsigned int) < sizeof(BitsType) &&
sizeof(BitsType) <= sizeof(unsigned long)>> {
static constexpr int kNumBits = static_cast<int>(sizeof(BitsType) * CHAR_BIT);
static EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
static constexpr int kLeadingBitsOffset = (sizeof(unsigned long) - sizeof(BitsType)) * CHAR_BIT;
return bits == 0 ? kNumBits : __builtin_clzl(static_cast<unsigned long>(bits)) - kLeadingBitsOffset;
}
static EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
return bits == 0 ? kNumBits : __builtin_ctzl(static_cast<unsigned long>(bits));
}
static EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
return __builtin_popcountl(static_cast<unsigned long>(bits));
}
};
template <typename BitsType>
struct count_bits_impl<BitsType,
std::enable_if_t<std::is_integral<BitsType>::value && sizeof(unsigned long) < sizeof(BitsType) &&
sizeof(BitsType) <= sizeof(unsigned long long)>> {
static constexpr int kNumBits = static_cast<int>(sizeof(BitsType) * CHAR_BIT);
static EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
static constexpr int kLeadingBitsOffset = (sizeof(unsigned long long) - sizeof(BitsType)) * CHAR_BIT;
return bits == 0 ? kNumBits : __builtin_clzll(static_cast<unsigned long long>(bits)) - kLeadingBitsOffset;
}
static EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
return bits == 0 ? kNumBits : __builtin_ctzll(static_cast<unsigned long long>(bits));
}
static EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
return __builtin_popcountll(static_cast<unsigned long long>(bits));
}
};
#elif EIGEN_COMP_MSVC
// `__popcnt`/`__popcnt64` require `POPCNT` hardware support, which MSVC cannot guarantee
// at its default baseline (unlike `_BitScanReverse`/`_BitScanForward`, which lower to
// baseline `bsr`/`bsf`). Fall back to a portable count when building without SSE4.2
// enabled.
template <typename BitsType>
EIGEN_DEVICE_FUNC inline int popcount_fallback(BitsType bits) {
int n = 0;
while (bits) {
bits &= bits - 1;
++n;
}
return n;
}
template <typename BitsType>
struct count_bits_impl<
BitsType, std::enable_if_t<std::is_integral<BitsType>::value && sizeof(BitsType) <= sizeof(unsigned long)>> {
static constexpr int kNumBits = static_cast<int>(sizeof(BitsType) * CHAR_BIT);
static EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
unsigned long out;
_BitScanReverse(&out, static_cast<unsigned long>(bits));
return bits == 0 ? kNumBits : (kNumBits - 1) - static_cast<int>(out);
}
static EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
unsigned long out;
_BitScanForward(&out, static_cast<unsigned long>(bits));
return bits == 0 ? kNumBits : static_cast<int>(out);
}
static EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
#if defined(EIGEN_VECTORIZE_SSE4_2)
return static_cast<int>(__popcnt(static_cast<unsigned int>(bits)));
#else
return popcount_fallback(bits);
#endif
}
};
#ifdef _WIN64
template <typename BitsType>
struct count_bits_impl<BitsType,
std::enable_if_t<std::is_integral<BitsType>::value && sizeof(unsigned long) < sizeof(BitsType) &&
sizeof(BitsType) <= sizeof(__int64)>> {
static constexpr int kNumBits = static_cast<int>(sizeof(BitsType) * CHAR_BIT);
static EIGEN_DEVICE_FUNC inline int clz(BitsType bits) {
unsigned long out;
_BitScanReverse64(&out, static_cast<unsigned __int64>(bits));
return bits == 0 ? kNumBits : (kNumBits - 1) - static_cast<int>(out);
}
static EIGEN_DEVICE_FUNC inline int ctz(BitsType bits) {
unsigned long out;
_BitScanForward64(&out, static_cast<unsigned __int64>(bits));
return bits == 0 ? kNumBits : static_cast<int>(out);
}
static EIGEN_DEVICE_FUNC inline int popcount(BitsType bits) {
#if defined(EIGEN_VECTORIZE_SSE4_2)
return static_cast<int>(__popcnt64(static_cast<unsigned __int64>(bits)));
#else
return popcount_fallback(bits);
#endif
}
};
#endif // _WIN64
#endif // EIGEN_COMP_GNUC || EIGEN_COMP_CLANG
template <typename BitsType>
struct log_2_impl {
static constexpr int kTotalBits = sizeof(BitsType) * CHAR_BIT;
static EIGEN_DEVICE_FUNC inline int run_ceil(const BitsType& x) {
const int n = kTotalBits - clz(x);
bool power_of_two = (x & (x - 1)) == 0;
return x == 0 ? 0 : power_of_two ? (n - 1) : n;
}
static EIGEN_DEVICE_FUNC inline int run_floor(const BitsType& x) {
const int n = kTotalBits - clz(x);
return x == 0 ? 0 : n - 1;
}
};
template <typename BitsType>
int log2_ceil(const BitsType& x) {
return log_2_impl<BitsType>::run_ceil(x);
}
template <typename BitsType>
int log2_floor(const BitsType& x) {
return log_2_impl<BitsType>::run_floor(x);
}
// Implementation of is* functions
template <typename T>
EIGEN_DEVICE_FUNC std::enable_if_t<!(std::numeric_limits<T>::has_infinity || std::numeric_limits<T>::has_quiet_NaN ||
std::numeric_limits<T>::has_signaling_NaN),
bool>
isfinite_impl(const T&) {
return true;
}
template <typename T>
EIGEN_DEVICE_FUNC std::enable_if_t<(std::numeric_limits<T>::has_infinity || std::numeric_limits<T>::has_quiet_NaN ||
std::numeric_limits<T>::has_signaling_NaN) &&
(!NumTraits<T>::IsComplex),
bool>
isfinite_impl(const T& x) {
EIGEN_USING_STD(isfinite);
return isfinite EIGEN_NOT_A_MACRO(x);
}
template <typename T>
EIGEN_DEVICE_FUNC std::enable_if_t<!std::numeric_limits<T>::has_infinity, bool> isinf_impl(const T&) {
return false;
}
template <typename T>
EIGEN_DEVICE_FUNC std::enable_if_t<(std::numeric_limits<T>::has_infinity && !NumTraits<T>::IsComplex), bool> isinf_impl(
const T& x) {
EIGEN_USING_STD(isinf);
return isinf EIGEN_NOT_A_MACRO(x);
}
template <typename T>
EIGEN_DEVICE_FUNC
std::enable_if_t<!(std::numeric_limits<T>::has_quiet_NaN || std::numeric_limits<T>::has_signaling_NaN), bool>
isnan_impl(const T&) {
return false;
}
template <typename T>
EIGEN_DEVICE_FUNC std::enable_if_t<
(std::numeric_limits<T>::has_quiet_NaN || std::numeric_limits<T>::has_signaling_NaN) && (!NumTraits<T>::IsComplex),
bool>
isnan_impl(const T& x) {
EIGEN_USING_STD(isnan);
return isnan EIGEN_NOT_A_MACRO(x);
}
// The following overload are defined at the end of this file
template <typename T>
EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
template <typename T>
EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
template <typename T>
EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
template <typename T>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS T ptanh_float(const T& a_x);
/****************************************************************************
* Implementation of sign *
****************************************************************************/
template <typename Scalar, bool IsComplex = (NumTraits<Scalar>::IsComplex != 0),
bool IsInteger = (NumTraits<Scalar>::IsInteger != 0)>
struct sign_impl {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& a) { return Scalar((a > Scalar(0)) - (a < Scalar(0))); }
};
template <typename Scalar>
struct sign_impl<Scalar, false, false> {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& a) {
return (isnan_impl<Scalar>)(a) ? a : Scalar((a > Scalar(0)) - (a < Scalar(0)));
}
};
template <typename Scalar, bool IsInteger>
struct sign_impl<Scalar, true, IsInteger> {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& a) {
using real_type = typename NumTraits<Scalar>::Real;
EIGEN_USING_STD(abs);
real_type aa = abs(a);
if (aa == real_type(0)) return Scalar(0);
// Divide rather than multiply by 1/aa: the reciprocal overflows for subnormal aa and is itself
// subnormal, hence inexact, for aa near the top of the range. psign_impl for complex packets
// divides for the same reason.
return Scalar(numext::real(a) / aa, numext::imag(a) / aa);
}
};
// The sign function for bool is the identity.
template <>
struct sign_impl<bool, false, true> {
EIGEN_DEVICE_FUNC static inline bool run(const bool& a) { return a; }
};
template <typename Scalar, bool IsComplex = (NumTraits<Scalar>::IsComplex != 0),
bool IsInteger = (NumTraits<Scalar>::IsInteger != 0)>
struct copysign_impl {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& a, const Scalar& b) {
EIGEN_USING_STD(copysign);
return Scalar(copysign(a, b));
}
};
template <typename Scalar, bool IsInteger>
struct copysign_impl<Scalar, true, IsInteger> {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& a, const Scalar& b) {
EIGEN_USING_STD(copysign);
return Scalar(copysign(numext::real(a), numext::real(b)), copysign(numext::imag(a), numext::imag(b)));
}
};
template <typename Scalar>
struct copysign_impl<Scalar, false, true> {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& a, const Scalar& b) {
EIGEN_IF_CONSTEXPR (!NumTraits<Scalar>::IsSigned) return a;
const Scalar abs_a = a < Scalar(0) ? -a : a;
return b < Scalar(0) ? -abs_a : abs_a;
}
};
template <>
struct copysign_impl<bool, false, true> {
EIGEN_DEVICE_FUNC static inline bool run(const bool& a, const bool&) { return a; }
};
// suppress "unary minus operator applied to unsigned type, result still unsigned" warnings on MSVC
// note: `0 - a` is distinct from `-a` when Scalar is a floating point type and `a` is zero
template <typename Scalar, bool IsInteger = NumTraits<Scalar>::IsInteger>
struct negate_impl {
static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar run(const Scalar& a) { return -a; }
};
template <typename Scalar>
struct negate_impl<Scalar, true> {
EIGEN_STATIC_ASSERT((!std::is_same<Scalar, bool>::value), NEGATE IS NOT DEFINED FOR BOOLEAN TYPES)
static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar run(const Scalar& a) { return Scalar(0) - a; }
};
template <typename Scalar, bool IsInteger = NumTraits<typename unpacket_traits<Scalar>::type>::IsInteger>
struct nearest_integer_impl {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_floor(const Scalar& x) {
EIGEN_USING_STD(floor) return floor(x);
}
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_ceil(const Scalar& x) {
EIGEN_USING_STD(ceil) return ceil(x);
}
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_rint(const Scalar& x) {
EIGEN_USING_STD(rint) return rint(x);
}
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_round(const Scalar& x) {
EIGEN_USING_STD(round) return round(x);
}
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_trunc(const Scalar& x) {
EIGEN_USING_STD(trunc) return trunc(x);
}
};
template <typename Scalar>
struct nearest_integer_impl<Scalar, true> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_floor(const Scalar& x) { return x; }
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_ceil(const Scalar& x) { return x; }
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_rint(const Scalar& x) { return x; }
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_round(const Scalar& x) { return x; }
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_trunc(const Scalar& x) { return x; }
};
// Extra namespace to prevent leaking std::fma into Eigen::internal.
namespace has_fma_detail {
template <typename T, typename EnableIf = void>
struct has_fma_impl : public std::false_type {};
using std::fma;
template <typename T>
struct has_fma_impl<
T, std::enable_if_t<std::is_same<T, decltype(fma(std::declval<T>(), std::declval<T>(), std::declval<T>()))>::value>>
: public std::true_type {};
} // namespace has_fma_detail
template <typename T>
struct has_fma : public has_fma_detail::has_fma_impl<T> {};
// Default implementation.
template <typename T, typename Enable = void>
struct fma_impl {
static_assert(has_fma<T>::value, "No function fma(...) for type. Please provide an implementation.");
};
// STD or ADL version if it exists.
template <typename T>
struct fma_impl<T, std::enable_if_t<has_fma<T>::value>> {
static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T run(const T& a, const T& b, const T& c) {
using std::fma;
return fma(a, b, c);
}
};
#if defined(EIGEN_GPUCC)
template <>
struct has_fma<float> : public std::true_type {};
template <>
struct fma_impl<float, void> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float run(const float& a, const float& b, const float& c) {
return ::fmaf(a, b, c);
}
};
template <>
struct has_fma<double> : public std::true_type {};
template <>
struct fma_impl<double, void> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double run(const double& a, const double& b, const double& c) {
return ::fma(a, b, c);
}
};
#endif
// Basic multiply-add.
template <typename Scalar, typename EnableIf = void>
struct madd_impl {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Scalar& x, const Scalar& y, const Scalar& z) {
return x * y + z;
}
};
#if EIGEN_SCALAR_MADD_USE_FMA
template <typename Scalar>
struct madd_impl<Scalar, std::enable_if_t<has_fma<Scalar>::value>> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Scalar& x, const Scalar& y, const Scalar& z) {
return fma_impl<Scalar>::run(x, y, z);
}
};
#endif
// Representation properties shared by operations that inspect an IEEE-style binary floating-point value.
template <typename Scalar>
struct binary_floating_point_traits {
using Bits = typename numext::get_integer_by_size<sizeof(Scalar)>::unsigned_type;
static constexpr int kFractionBits = std::numeric_limits<Scalar>::digits - 1;
static constexpr int kExponentBits = int(sizeof(Scalar) * CHAR_BIT) - std::numeric_limits<Scalar>::digits;
static constexpr int kExponentBias = std::numeric_limits<Scalar>::max_exponent - 1;
static constexpr Bits kSignBit = Bits(1) << (sizeof(Scalar) * CHAR_BIT - 1);
static constexpr Bits kExponentUnit = Bits(1) << kFractionBits;
static constexpr Bits kFractionMask = kExponentUnit - 1;
static constexpr Bits kExponentMask = ((Bits(1) << kExponentBits) - 1) << kFractionBits;
static constexpr Bits kMaxFiniteExponentBits = kExponentMask - kExponentUnit;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Bits bits(const Scalar& value) { return numext::bit_cast<Bits>(value); }
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Bits magnitude(const Scalar& value) { return bits(value) & ~kSignBit; }
};
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool is_exactly_zero_no_flush_impl(const Scalar& value, false_type) {
return numext::is_exactly_zero(value);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE bool is_zero_magnitude_bits(
typename binary_floating_point_traits<Scalar>::Bits magnitude) {
// Keep the integer comparison out of line: Clang can otherwise fold it into a
// floating-point comparison that treats subnormals as zero under DAZ/FZ.
return magnitude == 0;
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool is_exactly_zero_no_flush_impl(const Scalar& value, true_type) {
return is_zero_magnitude_bits<Scalar>(binary_floating_point_traits<Scalar>::magnitude(value));
}
} // end namespace internal
/****************************************************************************
* Generic math functions *
****************************************************************************/
namespace numext {
template <typename X>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool is_exactly_zero_no_flush(const X& x) {
constexpr bool HasBinaryEncoding = (std::is_same<X, float>::value || std::is_same<X, double>::value) &&
std::numeric_limits<X>::is_iec559 && std::numeric_limits<X>::radix == 2 &&
(sizeof(X) == sizeof(uint32_t) || sizeof(X) == sizeof(uint64_t));
return internal::is_exactly_zero_no_flush_impl(x, internal::bool_constant<HasBinaryEncoding>());
}
#if !defined(EIGEN_GPUCC)
template <typename T>
EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) {
EIGEN_USING_STD(min)
return min EIGEN_NOT_A_MACRO(x, y);
}
template <typename T>
EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y) {
EIGEN_USING_STD(max)
return max EIGEN_NOT_A_MACRO(x, y);
}
#else
template <typename T>
EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) {
return y < x ? y : x;
}
#if !defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC)
// Without relaxed constexpr, numeric GPU scalars keep fmin/fmax's number-preferring
// NaN behavior. With relaxed constexpr, they use the constexpr ternary overloads,
// matching std::min/std::max behavior and supporting custom less-comparable scalars.
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float mini(const float& x, const float& y) {
return fminf(x, y);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double mini(const double& x, const double& y) {
return fmin(x, y);
}
#ifndef EIGEN_GPU_COMPILE_PHASE
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE long double mini(const long double& x, const long double& y) {
#if defined(EIGEN_HIPCC)
// no "fminl" on HIP yet
return (x < y) ? x : y;
#else
return fminl(x, y);
#endif
}
#endif
#endif
template <typename T>
EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y) {
return x < y ? y : x;
}
#if !defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y) {
return fmaxf(x, y);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double maxi(const double& x, const double& y) {
return fmax(x, y);
}
#ifndef EIGEN_GPU_COMPILE_PHASE
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE long double maxi(const long double& x, const long double& y) {
#if defined(EIGEN_HIPCC)
// no "fmaxl" on HIP yet
return (x > y) ? x : y;
#else
return fmaxl(x, y);
#endif
}
#endif
#endif
#endif
#if defined(SYCL_DEVICE_ONLY)
#define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_long)
#define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_long)
#define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong)
#define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong)
#define SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(NAME, FUNC) \
SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC)
#define SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(NAME, FUNC) \
SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC)
#define SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(NAME, FUNC) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \
SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_double)
#define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(NAME, FUNC) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \
SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_double)
#define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(NAME, FUNC, RET_TYPE) \
SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_float) \
SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_double)
#define SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \
template <> \
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE& x) { \
return cl::sycl::FUNC(x); \
}
#define SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, TYPE) SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, TYPE, TYPE)
#define SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE1, ARG_TYPE2) \
template <> \
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE1& x, const ARG_TYPE2& y) { \
return cl::sycl::FUNC(x, y); \
}
#define SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \
SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE, ARG_TYPE)
#define SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, TYPE) SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, TYPE, TYPE)
SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(mini, min)
SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(mini, fmin)
SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(maxi, max)
SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(maxi, fmax)
#endif
template <typename Scalar>
EIGEN_DEVICE_FUNC inline typename NumTraits<Scalar>::Real arg(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline auto imag_ref(const Scalar& x)
-> internal::add_const_on_value_type_t<decltype(internal::imag_ref_impl<Scalar>::run(x))> {
return internal::imag_ref_impl<Scalar>::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline auto imag_ref(Scalar& x)
-> decltype(EIGEN_MATHFUNC_IMPL(imag_ref, std::remove_const_t<Scalar>)::run(x)) {
return EIGEN_MATHFUNC_IMPL(imag_ref, std::remove_const_t<Scalar>)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar conj(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar sign(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(sign, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar copysign(const Scalar& x, const Scalar& y) {
return EIGEN_MATHFUNC_IMPL(copysign, Scalar)::run(x, y);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar negate(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(negate, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline decltype(auto) abs2(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
}
EIGEN_DEVICE_FUNC inline bool abs2(bool x) { return x; }
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T absdiff(const T& x, const T& y) {
return x > y ? x - y : y - x;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float absdiff(const float& x, const float& y) {
return fabsf(x - y);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double absdiff(const double& x, const double& y) {
return fabs(x - y);
}
// HIP and CUDA do not support long double.
#ifndef EIGEN_GPU_COMPILE_PHASE
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE long double absdiff(const long double& x, const long double& y) {
return fabsl(x - y);
}
#endif
template <typename Scalar>
EIGEN_DEVICE_FUNC inline typename NumTraits<Scalar>::Real norm1(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline typename NumTraits<Scalar>::Real hypot(const Scalar& x, const Scalar& y) {
return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(hypot, hypot)
#endif
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log1p, log1p)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float log1p(const float& x) {
return ::log1pf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double log1p(const double& x) {
return ::log1p(x);
}
#endif
template <typename ScalarX, typename ScalarY>
EIGEN_DEVICE_FUNC inline typename internal::pow_impl<ScalarX, ScalarY>::result_type pow(const ScalarX& x,
const ScalarY& y) {
return internal::pow_impl<ScalarX, ScalarY>::run(x, y);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(pow, pow)
#endif
template <typename T>
EIGEN_DEVICE_FUNC bool(isnan)(const T& x) {
return internal::isnan_impl(x);
}
template <typename T>
EIGEN_DEVICE_FUNC bool(isinf)(const T& x) {
return internal::isinf_impl(x);
}
template <typename T>
EIGEN_DEVICE_FUNC bool(isfinite)(const T& x) {
return internal::isfinite_impl(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isnan, isnan, bool)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isinf, isinf, bool)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isfinite, isfinite, bool)
#endif
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar rint(const Scalar& x) {
return internal::nearest_integer_impl<Scalar>::run_rint(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar round(const Scalar& x) {
return internal::nearest_integer_impl<Scalar>::run_round(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar(floor)(const Scalar& x) {
return internal::nearest_integer_impl<Scalar>::run_floor(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar(ceil)(const Scalar& x) {
return internal::nearest_integer_impl<Scalar>::run_ceil(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar(trunc)(const Scalar& x) {
return internal::nearest_integer_impl<Scalar>::run_trunc(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(round, round)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(floor, floor)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(ceil, ceil)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(trunc, trunc)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float floor(const float& x) {
return ::floorf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double floor(const double& x) {
return ::floor(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float ceil(const float& x) {
return ::ceilf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double ceil(const double& x) {
return ::ceil(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float trunc(const float& x) {
return ::truncf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double trunc(const double& x) {
return ::trunc(x);
}
#endif
// Integer division with rounding up.
// T is assumed to be an integer type with a>=0, and b>0
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE constexpr T div_ceil(T a, T b) {
using UnsignedT = std::make_unsigned_t<T>;
EIGEN_STATIC_ASSERT((NumTraits<T>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES)
// Note: explicitly declaring a and b as non-negative values allows the compiler to use better optimizations
const UnsignedT ua = UnsignedT(a);
const UnsignedT ub = UnsignedT(b);
// Note: This form is used because it cannot overflow.
return ua == 0 ? 0 : (ua - 1) / ub + 1;
}
// Integer round down to nearest power of b
// T is assumed to be an integer type with a>=0, and b>0
template <typename T, typename U>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE constexpr T round_down(T a, U b) {
using UnsignedT = std::make_unsigned_t<T>;
using UnsignedU = std::make_unsigned_t<U>;
EIGEN_STATIC_ASSERT((NumTraits<T>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES)
EIGEN_STATIC_ASSERT((NumTraits<U>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES)
// Note: explicitly declaring a and b as non-negative values allows the compiler to use better optimizations
const UnsignedT ua = UnsignedT(a);
const UnsignedU ub = UnsignedU(b);
return ub * (ua / ub);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T log2(T x) {
EIGEN_USING_STD(log2);
return log2(x);
}
/** Log base 2 for 32 bits positive integers.
* Conveniently returns 0 for x==0. */
constexpr int log2(int x) {
unsigned int v(x);
constexpr int table[32] = {0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30,
8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31};
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
return table[(v * 0x07C4ACDDU) >> 27];
}
/** \returns the square root of \a x.
*
* It is essentially equivalent to
* \code using std::sqrt; return sqrt(x); \endcode
* but slightly faster for float/double and some compilers (e.g., gcc), thanks to
* specializations when SSE is enabled.
*
* Its usage is justified in performance critical functions, like norm/normalize.
*/
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar sqrt(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
}
// Boolean specialization, avoids implicit float to bool conversion (-Wimplicit-conversion-floating-point-to-bool).
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC bool sqrt<bool>(const bool& x) {
return x;
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt)
#endif
/** \returns the cube root of \a x. **/
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<!NumTraits<T>::IsComplex, T> cbrt(const T& x) {
EIGEN_USING_STD(cbrt);
return static_cast<T>(cbrt(x));
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<NumTraits<T>::IsComplex, T> cbrt(const T& x) {
EIGEN_USING_STD(pow);
return pow(x, typename NumTraits<T>::Real(1.0 / 3.0));
}
/** \returns the reciprocal square root of \a x. **/
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T rsqrt(const T& x) {
return internal::rsqrt_impl<T>::run(x);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T log(const T& x) {
return internal::log_impl<T>::run(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log, log)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float log(const float& x) {
return ::logf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double log(const double& x) {
return ::log(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
std::enable_if_t<NumTraits<T>::IsSigned && !NumTraits<T>::IsComplex, typename NumTraits<T>::Real>
abs(const T& x) {
EIGEN_USING_STD(abs);
return abs(x);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<NumTraits<T>::IsComplex, typename NumTraits<T>::Real> abs(
const T& x) {
return numext::hypot(numext::real(x), numext::imag(x));
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
std::enable_if_t<!NumTraits<T>::IsSigned && !NumTraits<T>::IsComplex, typename NumTraits<T>::Real>
abs(const T& x) {
return x;
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(abs, abs)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(abs, fabs)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float abs(const float& x) {
return ::fabsf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double abs(const double& x) {
return ::fabs(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float abs(const std::complex<float>& x) {
return ::hypotf(x.real(), x.imag());
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double abs(const std::complex<double>& x) {
return ::hypot(x.real(), x.imag());
}
#endif
template <typename Scalar, bool IsInteger = NumTraits<Scalar>::IsInteger, bool IsSigned = NumTraits<Scalar>::IsSigned>
struct signbit_impl;
template <typename Scalar>
struct signbit_impl<Scalar, false, true> {
static constexpr size_t Size = sizeof(Scalar);
static constexpr size_t Shift = (CHAR_BIT * Size) - 1;
using intSize_t = typename get_integer_by_size<Size>::signed_type;
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static Scalar run(const Scalar& x) {
intSize_t a = bit_cast<intSize_t, Scalar>(x);
a = a >> Shift;
Scalar result = bit_cast<Scalar, intSize_t>(a);
return result;
}
};
template <typename Scalar>
struct signbit_impl<Scalar, true, true> {
static constexpr size_t Size = sizeof(Scalar);
static constexpr size_t Shift = (CHAR_BIT * Size) - 1;
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static constexpr Scalar run(const Scalar& x) { return x >> Shift; }
};
template <typename Scalar>
struct signbit_impl<Scalar, true, false> {
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static constexpr Scalar run(const Scalar&) { return Scalar(0); }
};
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static constexpr Scalar signbit(const Scalar& x) {
return signbit_impl<Scalar>::run(x);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T exp(const T& x) {
EIGEN_USING_STD(exp);
return exp(x);
}
// MSVC through at least 19.51 mishandles some finite-real, non-finite-imaginary inputs to std::exp(complex).
#if EIGEN_COMP_MSVC
template <typename RealScalar>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<RealScalar> exp(const std::complex<RealScalar>& x) {
// Evaluate eagerly to preserve the floating-point exceptions raised by std::exp before correcting its result.
const std::complex<RealScalar> result = std::exp(x);
// If z is (x,±∞) (for any finite x), the result is (NaN,NaN) and FE_INVALID is raised.
// If z is (x,NaN) (for any finite x), the result is (NaN,NaN) and FE_INVALID may be raised.
if ((isfinite)(real_ref(x)) && !(isfinite)(imag_ref(x))) {
return std::complex<RealScalar>(NumTraits<RealScalar>::quiet_NaN(), NumTraits<RealScalar>::quiet_NaN());
}
#if EIGEN_COMP_MSVC < 1931
// Before 19.31, MSVC also mishandles a positive-infinite real part with a non-finite imaginary part.
// If z is (+∞,±∞), the result is (±∞,NaN) and FE_INVALID is raised (the sign of the real part is unspecified)
// If z is (+∞,NaN), the result is (±∞,NaN) (the sign of the real part is unspecified)
if ((real_ref(x) == NumTraits<RealScalar>::infinity() && !(isfinite)(imag_ref(x)))) {
return std::complex<RealScalar>(NumTraits<RealScalar>::infinity(), NumTraits<RealScalar>::quiet_NaN());
}
#endif
return result;
}
#endif
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(exp, exp)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float exp(const float& x) {
return ::expf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double exp(const double& x) {
return ::exp(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<float> exp(const std::complex<float>& x) {
float com = ::expf(x.real());
float res_real = com * ::cosf(x.imag());
float res_imag = com * ::sinf(x.imag());
return std::complex<float>(res_real, res_imag);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<double> exp(const std::complex<double>& x) {
double com = ::exp(x.real());
double res_real = com * ::cos(x.imag());
double res_imag = com * ::sin(x.imag());
return std::complex<double>(res_real, res_imag);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T exp2(const T& x) {
EIGEN_USING_STD(exp2);
return exp2(x);
}
// MSVC screws up some edge-cases for std::exp2(complex).
#ifdef EIGEN_COMP_MSVC
template <typename RealScalar>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<RealScalar> exp2(const std::complex<RealScalar>& x) {
EIGEN_USING_STD(exp);
// If z is (x,±∞) (for any finite x), the result is (NaN,NaN) and FE_INVALID is raised.
// If z is (x,NaN) (for any finite x), the result is (NaN,NaN) and FE_INVALID may be raised.
if ((isfinite)(real_ref(x)) && !(isfinite)(imag_ref(x))) {
return std::complex<RealScalar>(NumTraits<RealScalar>::quiet_NaN(), NumTraits<RealScalar>::quiet_NaN());
}
// If z is (+∞,±∞), the result is (±∞,NaN) and FE_INVALID is raised (the sign of the real part is unspecified)
// If z is (+∞,NaN), the result is (±∞,NaN) (the sign of the real part is unspecified)
if ((real_ref(x) == NumTraits<RealScalar>::infinity() && !(isfinite)(imag_ref(x)))) {
return std::complex<RealScalar>(NumTraits<RealScalar>::infinity(), NumTraits<RealScalar>::quiet_NaN());
}
return exp2(x);
}
#endif
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(exp2, exp2)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float exp2(const float& x) {
return ::exp2f(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double exp2(const double& x) {
return ::exp2(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<float> exp2(const std::complex<float>& x) {
float com = ::exp2f(x.real());
float res_real = com * ::cosf(static_cast<float>(EIGEN_LN2) * x.imag());
float res_imag = com * ::sinf(static_cast<float>(EIGEN_LN2) * x.imag());
return std::complex<float>(res_real, res_imag);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<double> exp2(const std::complex<double>& x) {
double com = ::exp2(x.real());
double res_real = com * ::cos(static_cast<double>(EIGEN_LN2) * x.imag());
double res_imag = com * ::sin(static_cast<double>(EIGEN_LN2) * x.imag());
return std::complex<double>(res_real, res_imag);
}
#endif
// Exact scaling by 2^exponent, including denormals and unrepresentable scale factors.
// Results outside the finite range saturate to zero or infinity.
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T ldexp(const T& x, int exponent) {
EIGEN_USING_STD(ldexp);
return static_cast<T>(ldexp(x, exponent));
}
#if defined(SYCL_DEVICE_ONLY)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_float ldexp(const cl::sycl::cl_float& x, int exponent) {
return cl::sycl::ldexp(x, exponent);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_double ldexp(const cl::sycl::cl_double& x, int exponent) {
return cl::sycl::ldexp(x, exponent);
}
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float ldexp(const float& x, int exponent) {
return ::ldexpf(x, exponent);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double ldexp(const double& x, int exponent) {
return ::ldexp(x, exponent);
}
#endif
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar expm1(const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(expm1, Scalar)::run(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(expm1, expm1)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float expm1(const float& x) {
return ::expm1f(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double expm1(const double& x) {
return ::expm1(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T cos(const T& x) {
EIGEN_USING_STD(cos);
return cos(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cos, cos)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float cos(const float& x) {
return ::cosf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double cos(const double& x) {
return ::cos(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T sin(const T& x) {
EIGEN_USING_STD(sin);
return sin(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sin, sin)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float sin(const float& x) {
return ::sinf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double sin(const double& x) {
return ::sin(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T tan(const T& x) {
EIGEN_USING_STD(tan);
return tan(x);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tan, tan)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float tan(const float& x) {
return ::tanf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double tan(const double& x) {
return ::tan(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T acos(const T& x) {
EIGEN_USING_STD(acos);
return acos(x);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T acosh(const T& x) {
EIGEN_USING_STD(acosh);
return static_cast<T>(acosh(x));
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acos, acos)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acosh, acosh)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float acos(const float& x) {
return ::acosf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double acos(const double& x) {
return ::acos(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T asin(const T& x) {
EIGEN_USING_STD(asin);
return asin(x);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T asinh(const T& x) {
EIGEN_USING_STD(asinh);
return static_cast<T>(asinh(x));
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asin, asin)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asinh, asinh)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float asin(const float& x) {
return ::asinf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double asin(const double& x) {
return ::asin(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T atan(const T& x) {
EIGEN_USING_STD(atan);
return static_cast<T>(atan(x));
}
template <typename T, std::enable_if_t<!NumTraits<T>::IsComplex, int> = 0>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T atan2(const T& y, const T& x) {
EIGEN_USING_STD(atan2);
return static_cast<T>(atan2(y, x));
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T atanh(const T& x) {
EIGEN_USING_STD(atanh);
return static_cast<T>(atanh(x));
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atan, atan)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atanh, atanh)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float atan(const float& x) {
return ::atanf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double atan(const double& x) {
return ::atan(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T cosh(const T& x) {
EIGEN_USING_STD(cosh);
return static_cast<T>(cosh(x));
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cosh, cosh)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float cosh(const float& x) {
return ::coshf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double cosh(const double& x) {
return ::cosh(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T sinh(const T& x) {
EIGEN_USING_STD(sinh);
return static_cast<T>(sinh(x));
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sinh, sinh)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float sinh(const float& x) {
return ::sinhf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double sinh(const double& x) {
return ::sinh(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T tanh(const T& x) {
EIGEN_USING_STD(tanh);
return tanh(x);
}
#if (!defined(EIGEN_GPUCC)) && EIGEN_FAST_MATH && !defined(SYCL_DEVICE_ONLY)
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float tanh(float x) { return internal::ptanh_float(x); }
#endif
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tanh, tanh)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float tanh(const float& x) {
return ::tanhf(x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double tanh(const double& x) {
return ::tanh(x);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T fmod(const T& a, const T& b) {
EIGEN_USING_STD(fmod);
return fmod(a, b);
}
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(fmod, fmod)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float fmod(const float& a, const float& b) {
return ::fmodf(a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double fmod(const double& a, const double& b) {
return ::fmod(a, b);
}
#endif
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T nextafter(const T& from, const T& to) {
EIGEN_USING_STD(nextafter);
return nextafter(from, to);
}
/** Returns the smallest normal power of two greater than or equal to \a value.
*
* \pre \a value is finite and nonnegative.
* Zero is preserved. A value larger than the greatest finite power of two maps to infinity.
*/
template <typename Scalar,
std::enable_if_t<!std::is_same<Scalar, long double>::value && std::numeric_limits<Scalar>::is_iec559 &&
std::numeric_limits<Scalar>::radix == 2 &&
(sizeof(Scalar) == sizeof(uint16_t) || sizeof(Scalar) == sizeof(uint32_t) ||
sizeof(Scalar) == sizeof(uint64_t)),
int> = 0>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar ceil_power_of_two(const Scalar& value) {
using Binary = internal::binary_floating_point_traits<Scalar>;
using Bits = typename Binary::Bits;
const Bits valueBits = Binary::bits(value);
const Bits resultBits = Bits((valueBits + Binary::kFractionMask) & Binary::kExponentMask);
return bit_cast<Scalar>(resultBits);
}
// long double has no portable object representation: depending on the ABI it can be binary64, padded x87 extended
// precision, IEEE binary128, or IBM double-double. Construct the result arithmetically instead of inspecting its bits.
#if !defined(EIGEN_GPU_COMPILE_PHASE)
EIGEN_STRONG_INLINE long double ceil_power_of_two(const long double& value) {
EIGEN_USING_STD(frexp);
EIGEN_USING_STD(ldexp);
int exponent = 0;
const long double fraction = frexp(value, &exponent);
if (numext::is_exactly_zero(fraction)) return 0.0L;
if (numext::equal_strict(fraction, 0.5L)) --exponent;
if (exponent < std::numeric_limits<long double>::min_exponent - 1)
exponent = std::numeric_limits<long double>::min_exponent - 1;
return ldexp(1.0L, exponent);
}
#endif
#if defined(SYCL_DEVICE_ONLY)
SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(nextafter, nextafter)
#endif
#if defined(EIGEN_GPUCC)
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float nextafter(const float& from, const float& to) {
return ::nextafterf(from, to);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double nextafter(const double& from, const double& to) {
return ::nextafter(from, to);
}
#endif
#if defined(SYCL_DEVICE_ONLY)
#undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY
#undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY
#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY
#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY
#undef SYCL_SPECIALIZE_INTEGER_TYPES_BINARY
#undef SYCL_SPECIALIZE_INTEGER_TYPES_UNARY
#undef SYCL_SPECIALIZE_FLOATING_TYPES_BINARY
#undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY
#undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE
#undef SYCL_SPECIALIZE_GEN_UNARY_FUNC
#undef SYCL_SPECIALIZE_UNARY_FUNC
#undef SYCL_SPECIALIZE_GEN1_BINARY_FUNC
#undef SYCL_SPECIALIZE_GEN2_BINARY_FUNC
#undef SYCL_SPECIALIZE_BINARY_FUNC
#endif
// A logical shift is a shift of the bit pattern, so it goes through the unsigned type of the same
// width whatever Scalar's signedness. A Scalar narrower than int promotes to int for the shift
// itself, which the explicit truncation undoes: for the left shift the promoted value can carry set
// bits above Scalar's width, and dropping them is the operation rather than an accident of the cast.
template <typename Scalar, typename Enable = std::enable_if_t<std::is_integral<Scalar>::value>>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar logical_shift_left(const Scalar& a, int n) {
using UnsignedScalar = typename numext::get_integer_by_size<sizeof(Scalar)>::unsigned_type;
return bit_cast<Scalar, UnsignedScalar>(static_cast<UnsignedScalar>(bit_cast<UnsignedScalar, Scalar>(a) << n));
}
template <typename Scalar, typename Enable = std::enable_if_t<std::is_integral<Scalar>::value>>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar logical_shift_right(const Scalar& a, int n) {
using UnsignedScalar = typename numext::get_integer_by_size<sizeof(Scalar)>::unsigned_type;
return bit_cast<Scalar, UnsignedScalar>(static_cast<UnsignedScalar>(bit_cast<UnsignedScalar, Scalar>(a) >> n));
}
// An arithmetic shift propagates the sign bit, so it coincides with the logical shift when Scalar is
// unsigned and has none. Shifting through the signed type unconditionally would sign-extend an
// ordinary value bit, which is what every backend's parithmetic_shift_right on unsigned packets
// avoids, leaving the scalar and vectorized paths of one expression disagreeing. Scalar's own
// operator>> already selects on its signedness, so no reinterpretation is needed; the cast only
// undoes the integral promotion a Scalar narrower than int is subject to.
template <typename Scalar, typename Enable = std::enable_if_t<std::is_integral<Scalar>::value>>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar arithmetic_shift_right(const Scalar& a, int n) {
return static_cast<Scalar>(a >> n);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar fma(const Scalar& x, const Scalar& y, const Scalar& z) {
return internal::fma_impl<Scalar>::run(x, y, z);
}
// Multiply-add.
template <typename Scalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar madd(const Scalar& x, const Scalar& y, const Scalar& z) {
return internal::madd_impl<Scalar>::run(x, y, z);
}
} // end namespace numext
namespace internal {
template <typename T>
EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x) {
EIGEN_IF_CONSTEXPR ((std::is_floating_point<T>::value)) {
// Eager classification lets coefficient-wise loops remain branch-free.
return static_cast<unsigned int>((numext::isfinite)(numext::real(x))) & (numext::isfinite)(numext::imag(x));
} else {
return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
}
}
template <typename T>
EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x) {
EIGEN_IF_CONSTEXPR ((std::is_floating_point<T>::value)) {
return static_cast<unsigned int>((numext::isnan)(numext::real(x))) | (numext::isnan)(numext::imag(x));
} else {
return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
}
}
template <typename T>
EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x) {
EIGEN_IF_CONSTEXPR ((std::is_floating_point<T>::value)) {
const bool has_inf = static_cast<unsigned int>((numext::isinf)(numext::real(x))) | (numext::isinf)(numext::imag(x));
const bool has_nan = (numext::isnan)(x);
return has_inf & !has_nan;
} else {
return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
}
}
/****************************************************************************
* Implementation of fuzzy comparisons *
****************************************************************************/
template <typename Scalar, bool IsComplex, bool IsInteger>
struct scalar_fuzzy_default_impl {};
template <typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, false, false> {
using RealScalar = typename NumTraits<Scalar>::Real;
template <typename OtherScalar>
EIGEN_DEVICE_FUNC static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
const RealScalar& prec) {
return numext::abs(x) <= numext::abs(y) * prec;
}
EIGEN_DEVICE_FUNC static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec) {
return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
}
EIGEN_DEVICE_FUNC static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec) {
return x <= y || isApprox(x, y, prec);
}
};
template <typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, false, true> {
using RealScalar = typename NumTraits<Scalar>::Real;
template <typename OtherScalar>
EIGEN_DEVICE_FUNC static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&) {
return x == Scalar(0);
}
EIGEN_DEVICE_FUNC static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&) { return x == y; }
EIGEN_DEVICE_FUNC static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&) {
return x <= y;
}
};
template <typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, true, false> {
using RealScalar = typename NumTraits<Scalar>::Real;
template <typename OtherScalar>
EIGEN_DEVICE_FUNC static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
const RealScalar& prec) {
return numext::abs2(x) <= numext::abs2(y) * prec * prec;
}
EIGEN_DEVICE_FUNC static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec) {
return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;
}
};
template <typename Scalar>
struct scalar_fuzzy_impl
: scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
template <typename Scalar, typename OtherScalar>
EIGEN_DEVICE_FUNC inline bool isMuchSmallerThan(
const Scalar& x, const OtherScalar& y,
const typename NumTraits<Scalar>::Real& precision = NumTraits<Scalar>::dummy_precision()) {
return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline bool isApprox(
const Scalar& x, const Scalar& y,
const typename NumTraits<Scalar>::Real& precision = NumTraits<Scalar>::dummy_precision()) {
return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline bool isApproxOrLessThan(
const Scalar& x, const Scalar& y,
const typename NumTraits<Scalar>::Real& precision = NumTraits<Scalar>::dummy_precision()) {
return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
}
/******************************************
*** The special case of the bool type ***
******************************************/
template <>
struct scalar_fuzzy_impl<bool> {
using RealScalar = bool;
template <typename OtherScalar>
EIGEN_DEVICE_FUNC static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&) {
return !x;
}
EIGEN_DEVICE_FUNC static inline bool isApprox(bool x, bool y, bool) { return x == y; }
EIGEN_DEVICE_FUNC static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&) {
return (!x) || y;
}
};
} // end namespace internal
// Default implementations that rely on other numext implementations
namespace internal {
// Specialization for complex types that are not supported by std::expm1.
template <typename RealScalar>
struct expm1_impl<std::complex<RealScalar>> {
EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x) {
RealScalar xr = x.real();
RealScalar xi = x.imag();
// expm1(z) = exp(z) - 1
// = exp(x + i * y) - 1
// = exp(x) * (cos(y) + i * sin(y)) - 1
// = exp(x) * cos(y) - 1 + i * exp(x) * sin(y)
// Imag(expm1(z)) = exp(x) * sin(y)
// Real(expm1(z)) = exp(x) * cos(y) - 1
// = exp(x) * cos(y) - 1.
// = expm1(x) + exp(x) * (cos(y) - 1)
// = expm1(x) + exp(x) * (2 * sin(y / 2) ** 2)
RealScalar erm1 = numext::expm1<RealScalar>(xr);
RealScalar er = erm1 + RealScalar(1.);
RealScalar sin2 = numext::sin(xi / RealScalar(2.));
sin2 = sin2 * sin2;
RealScalar s = numext::sin(xi);
RealScalar real_part = erm1 - RealScalar(2.) * er * sin2;
return std::complex<RealScalar>(real_part, er * s);
}
};
template <typename T>
struct rsqrt_impl {
// C4804: unsafe use of type 'bool' in operation. Unavoidable when instantiated with T=bool.
#if EIGEN_COMP_MSVC
#pragma warning(push)
#pragma warning(disable : 4804)
#endif
EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE T run(const T& x) { return T(1) / numext::sqrt(x); }
#if EIGEN_COMP_MSVC
#pragma warning(pop)
#endif
};
#if defined(EIGEN_GPU_COMPILE_PHASE)
template <typename T>
struct conj_impl<std::complex<T>, true> {
EIGEN_DEVICE_FUNC static inline std::complex<T> run(const std::complex<T>& x) {
return std::complex<T>(numext::real(x), -numext::imag(x));
}
};
#endif
// Complex multiply and division operators.
// Note that these do not handle the case if inf+NaNi, which is considered an infinity.
// This is for consistency with our standard pmul, pdiv implementations.
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_smith(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_smith(a, b);
#endif
}
} // end namespace internal
namespace numext {
/** \internal
* \brief Scalar division that guards against intermediate overflow for complex types.
*
* For real types, this evaluates a / b.
* For complex types, this evaluates a / b using Smith's method to prevent intermediate
* overflow (c^2 + d^2) when b is near the boundary of the representable range, consistent
* with the vectorized complex division path in GenericPacketMathComplex.h.
*/
template <typename LhsScalar, typename RhsScalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE auto divide(const LhsScalar& a, const RhsScalar& b) -> decltype(a / b) {
return a / b;
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> divide(const std::complex<T>& a, const std::complex<T>& b) {
return internal::complex_divide_smith(a, b);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> divide(const T& a, const std::complex<T>& b) {
return internal::complex_divide_smith(std::complex<T>(a, T(0)), b);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> divide(const std::complex<T>& a, const T& b) {
return a / b;
}
} // end namespace numext
} // end namespace Eigen
#endif // EIGEN_MATHFUNCTIONS_H