| // 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/. |
| |
| #ifndef EIGEN_MATHFUNCTIONS_H |
| #define EIGEN_MATHFUNCTIONS_H |
| |
| // TODO this should better be moved 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 { |
| typedef T type; |
| }; |
| |
| template <typename T> |
| struct always_void { |
| typedef void type; |
| }; |
| |
| template <typename T> |
| struct global_math_functions_filtering_base< |
| T, typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type> { |
| typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type; |
| }; |
| |
| #define EIGEN_MATHFUNC_IMPL(func, scalar) \ |
| Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type> |
| #define EIGEN_MATHFUNC_RETVAL(func, scalar) \ |
| typename Eigen::internal::func##_retval< \ |
| typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type |
| |
| /**************************************************************************** |
| * Implementation of real * |
| ****************************************************************************/ |
| |
| template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> |
| struct real_default_impl { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { return x; } |
| }; |
| |
| template <typename Scalar> |
| struct real_default_impl<Scalar, true> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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>> { |
| typedef T RealScalar; |
| EIGEN_DEVICE_FUNC static inline T run(const std::complex<T>& x) { return x.real(); } |
| }; |
| #endif |
| |
| template <typename Scalar> |
| struct real_retval { |
| typedef typename NumTraits<Scalar>::Real type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of imag * |
| ****************************************************************************/ |
| |
| template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> |
| struct imag_default_impl { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar&) { return RealScalar(0); } |
| }; |
| |
| template <typename Scalar> |
| struct imag_default_impl<Scalar, true> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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>> { |
| typedef T RealScalar; |
| EIGEN_DEVICE_FUNC static inline T run(const std::complex<T>& x) { return x.imag(); } |
| }; |
| #endif |
| |
| template <typename Scalar> |
| struct imag_retval { |
| typedef typename NumTraits<Scalar>::Real type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of real_ref * |
| ****************************************************************************/ |
| |
| template <typename Scalar> |
| struct real_ref_impl { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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]; |
| } |
| }; |
| |
| template <typename Scalar> |
| struct real_ref_retval { |
| typedef typename NumTraits<Scalar>::Real& type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of imag_ref * |
| ****************************************************************************/ |
| |
| template <typename Scalar, bool IsComplex> |
| struct imag_ref_default_impl { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Scalar run(Scalar&) { return Scalar(0); } |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline const Scalar run(const Scalar&) { return Scalar(0); } |
| }; |
| |
| template <typename Scalar> |
| struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {}; |
| |
| template <typename Scalar> |
| struct imag_ref_retval { |
| typedef typename NumTraits<Scalar>::Real& type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of conj * |
| ****************************************************************************/ |
| |
| template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> |
| struct conj_default_impl { |
| EIGEN_DEVICE_FUNC static inline 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> {}; |
| |
| template <typename Scalar> |
| struct conj_retval { |
| typedef Scalar type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of abs2 * |
| ****************************************************************************/ |
| |
| template <typename Scalar, bool IsComplex> |
| struct abs2_impl_default { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { return x * x; } |
| }; |
| |
| template <typename Scalar> |
| struct abs2_impl_default<Scalar, true> // IsComplex |
| { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { return x.real() * x.real() + x.imag() * x.imag(); } |
| }; |
| |
| template <typename Scalar> |
| struct abs2_impl { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { |
| return abs2_impl_default<Scalar, NumTraits<Scalar>::IsComplex>::run(x); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct abs2_retval { |
| typedef typename NumTraits<Scalar>::Real type; |
| }; |
| |
| /**************************************************************************** |
| * 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 T> |
| EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& 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<T>(x); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct sqrt_retval { |
| typedef Scalar type; |
| }; |
| |
| // Default implementation relies on numext::sqrt, at bottom of file. |
| template <typename T> |
| struct rsqrt_impl; |
| |
| // Complex rsqrt defined in MathFunctionsImpl.h. |
| template <typename T> |
| EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& 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<T>(x); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct rsqrt_retval { |
| typedef Scalar type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of norm1 * |
| ****************************************************************************/ |
| |
| template <typename Scalar, bool IsComplex> |
| struct norm1_default_impl; |
| |
| template <typename Scalar> |
| struct norm1_default_impl<Scalar, true> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { |
| EIGEN_USING_STD(abs); |
| return abs(x.real()) + abs(x.imag()); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct norm1_default_impl<Scalar, false> { |
| EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) { |
| EIGEN_USING_STD(abs); |
| return abs(x); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {}; |
| |
| template <typename Scalar> |
| struct norm1_retval { |
| typedef typename NumTraits<Scalar>::Real type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of hypot * |
| ****************************************************************************/ |
| |
| template <typename Scalar> |
| struct hypot_impl; |
| |
| template <typename Scalar> |
| struct hypot_retval { |
| typedef typename NumTraits<Scalar>::Real type; |
| }; |
| |
| /**************************************************************************** |
| * 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, |
| typename std::enable_if_t<!NumTraits<OldType>::IsComplex && NumTraits<NewType>::IsComplex>> { |
| EIGEN_DEVICE_FUNC static inline NewType run(const OldType& x) { |
| typedef typename NumTraits<NewType>::Real NewReal; |
| return static_cast<NewType>(static_cast<NewReal>(x)); |
| } |
| }; |
| |
| // here, for once, we're plainly returning NewType: we don't want cast to do weird things. |
| |
| 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 || is_integral<Scalar>::value || |
| is_same<Scalar, float>::value || is_same<Scalar, double>::value || |
| is_same<Scalar, long double>::value> |
| struct arg_default_impl; |
| |
| template <typename Scalar> |
| struct arg_default_impl<Scalar, true> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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 { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> {}; |
| |
| template <typename Scalar> |
| struct arg_retval { |
| typedef typename NumTraits<Scalar>::Real type; |
| }; |
| |
| /**************************************************************************** |
| * 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) |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| |
| 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); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct expm1_retval { |
| typedef Scalar type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of log * |
| ****************************************************************************/ |
| |
| // Complex log defined in MathFunctionsImpl.h. |
| template <typename T> |
| EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& 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) |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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); |
| } |
| }; |
| |
| template <typename Scalar> |
| struct log1p_retval { |
| typedef Scalar type; |
| }; |
| |
| /**************************************************************************** |
| * Implementation of pow * |
| ****************************************************************************/ |
| |
| template <typename ScalarX, typename ScalarY, |
| bool IsInteger = NumTraits<ScalarX>::IsInteger && NumTraits<ScalarY>::IsInteger> |
| struct pow_impl { |
| // typedef Scalar retval; |
| typedef typename ScalarBinaryOpTraits<ScalarX, ScalarY, internal::scalar_pow_op<ScalarX, ScalarY>>::ReturnType |
| result_type; |
| 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> { |
| typedef ScalarX result_type; |
| 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 *= x; |
| y >>= 1; |
| while (y) { |
| x *= x; |
| if (y & 1) res *= x; |
| y >>= 1; |
| } |
| return res; |
| } |
| }; |
| |
| enum { meta_floor_log2_terminate, meta_floor_log2_move_up, meta_floor_log2_move_down, meta_floor_log2_bogus }; |
| |
| template <unsigned int n, int lower, int upper> |
| struct meta_floor_log2_selector { |
| enum { |
| middle = (lower + upper) / 2, |
| value = (upper <= lower + 1) ? int(meta_floor_log2_terminate) |
| : (n < (1 << middle)) ? int(meta_floor_log2_move_down) |
| : (n == 0) ? int(meta_floor_log2_bogus) |
| : int(meta_floor_log2_move_up) |
| }; |
| }; |
| |
| template <unsigned int n, int lower = 0, int upper = sizeof(unsigned int) * CHAR_BIT - 1, |
| int selector = meta_floor_log2_selector<n, lower, upper>::value> |
| struct meta_floor_log2 {}; |
| |
| template <unsigned int n, int lower, int upper> |
| struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down> { |
| enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value }; |
| }; |
| |
| template <unsigned int n, int lower, int upper> |
| struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up> { |
| enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value }; |
| }; |
| |
| template <unsigned int n, int lower, int upper> |
| struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate> { |
| enum { value = (n >= ((unsigned int)(1) << (lower + 1))) ? lower + 1 : lower }; |
| }; |
| |
| template <unsigned int n, int lower, int upper> |
| struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus> { |
| // no value, error at compile time |
| }; |
| |
| 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; |
| } |
| }; |
| |
| // 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); |
| } |
| |
| #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)); |
| } |
| }; |
| |
| 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)); |
| } |
| }; |
| |
| 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)); |
| } |
| }; |
| |
| #elif EIGEN_COMP_MSVC |
| |
| 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); |
| } |
| }; |
| |
| #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); |
| } |
| }; |
| |
| #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); |
| aa = real_type(1) / aa; |
| return Scalar(a.real() * aa, a.imag() * 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> |
| struct sign_retval { |
| typedef Scalar type; |
| }; |
| |
| // 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((!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> |
| struct negate_retval { |
| typedef Scalar type; |
| }; |
| |
| 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; } |
| }; |
| |
| } // end namespace internal |
| |
| /**************************************************************************** |
| * Generic math functions * |
| ****************************************************************************/ |
| |
| namespace numext { |
| |
| #if (!defined(EIGEN_GPUCC) || defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC)) |
| template <typename T> |
| EIGEN_DEVICE_FUNC 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 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 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) { |
| return y < x ? y : x; |
| } |
| 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 |
| |
| template <typename T> |
| EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y) { |
| return x < y ? y : x; |
| } |
| 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 |
| |
| #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 EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline internal::add_const_on_value_type_t<EIGEN_MATHFUNC_RETVAL(real_ref, Scalar)> real_ref( |
| const Scalar& x) { |
| return internal::real_ref_impl<Scalar>::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline internal::add_const_on_value_type_t<EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar)> imag_ref( |
| const Scalar& x) { |
| return internal::imag_ref_impl<Scalar>::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(sign, Scalar) sign(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(sign, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(negate, Scalar) negate(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(negate, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) 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 EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x) { |
| return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x); |
| } |
| |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) 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 EIGEN_MATHFUNC_RETVAL(log1p, 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 EIGEN_CONSTEXPR T div_ceil(T a, T b) { |
| using UnsignedT = typename internal::make_unsigned<T>::type; |
| EIGEN_STATIC_ASSERT((NumTraits<T>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES) |
| eigen_assert(a >= 0); |
| eigen_assert(b > 0); |
| // 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 EIGEN_CONSTEXPR T round_down(T a, U b) { |
| using UnsignedT = typename internal::make_unsigned<T>::type; |
| using UnsignedU = typename internal::make_unsigned<U>::type; |
| EIGEN_STATIC_ASSERT((NumTraits<T>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES) |
| EIGEN_STATIC_ASSERT((NumTraits<U>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES) |
| eigen_assert(a >= 0); |
| eigen_assert(b > 0); |
| // 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); |
| } |
| |
| /** Log base 2 for 32 bits positive integers. |
| * Conveniently returns 0 for x==0. */ |
| EIGEN_CONSTEXPR inline int log2(int x) { |
| eigen_assert(x >= 0); |
| 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. |
| * |
| * It's usage is justified in performance critical functions, like norm/normalize. |
| */ |
| template <typename Scalar> |
| EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE EIGEN_MATHFUNC_RETVAL(sqrt, 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 T cbrt(const T& x) { |
| EIGEN_USING_STD(cbrt); |
| return static_cast<T>(cbrt(x)); |
| } |
| |
| /** \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>::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 screws up some edge-cases for std::exp(complex). |
| #ifdef EIGEN_COMP_MSVC |
| template <typename RealScalar> |
| EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<RealScalar> exp(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 exp(x); |
| } |
| #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 Scalar> |
| EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(expm1, 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 |
| |
| #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_UNSIGNED_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 |
| |
| 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) { |
| return 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>(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 arithmetic_shift_right(const Scalar& a, int n) { |
| using SignedScalar = typename numext::get_integer_by_size<sizeof(Scalar)>::signed_type; |
| return bit_cast<Scalar, SignedScalar>(bit_cast<SignedScalar, Scalar>(a) >> n); |
| } |
| |
| } // end namespace numext |
| |
| namespace internal { |
| |
| template <typename T> |
| EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x) { |
| 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) { |
| 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) { |
| 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> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| 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> { |
| typedef bool RealScalar; |
| |
| 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 { |
| EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE T run(const T& x) { return T(1) / numext::sqrt(x); } |
| }; |
| |
| #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 |
| |
| } // end namespace internal |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_MATHFUNCTIONS_H |
