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Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/Core/MathFunctions.h')
| -rw-r--r-- | runtimes/nn/depend/external/eigen/Eigen/src/Core/MathFunctions.h | 1431 |
1 files changed, 1431 insertions, 0 deletions
diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/Core/MathFunctions.h b/runtimes/nn/depend/external/eigen/Eigen/src/Core/MathFunctions.h new file mode 100644 index 000000000..a648aa0fa --- /dev/null +++ b/runtimes/nn/depend/external/eigen/Eigen/src/Core/MathFunctions.h @@ -0,0 +1,1431 @@ +// 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> +// +// 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 + +// source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html +// TODO this should better be moved to NumTraits +#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L + + +namespace Eigen { + +// On WINCE, std::abs is defined for int only, so let's defined our own overloads: +// This issue has been confirmed with MSVC 2008 only, but the issue might exist for more recent versions too. +#if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC<=1500 +long abs(long x) { return (labs(x)); } +double abs(double x) { return (fabs(x)); } +float abs(float x) { return (fabsf(x)); } +long double abs(long double x) { return (fabsl(x)); } +#endif + +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> {}; + +#ifdef __CUDA_ARCH__ +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> {}; + +#ifdef __CUDA_ARCH__ +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<RealScalar*>(&x)[1]; + } +}; + +template<typename Scalar> +struct imag_ref_default_impl<Scalar, false> +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(Scalar&) + { + return Scalar(0); + } + EIGEN_DEVICE_FUNC + 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_impl +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + return x; + } +}; + +template<typename Scalar> +struct conj_impl<Scalar,true> +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + using std::conj; + return conj(x); + } +}; + +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 real(x)*real(x) + imag(x)*imag(x); + } +}; + +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 norm1 * +****************************************************************************/ + +template<typename Scalar, bool IsComplex> +struct norm1_default_impl +{ + typedef typename NumTraits<Scalar>::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + EIGEN_USING_STD_MATH(abs); + return abs(real(x)) + abs(imag(x)); + } +}; + +template<typename Scalar> +struct norm1_default_impl<Scalar, false> +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + EIGEN_USING_STD_MATH(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 +{ + typedef typename NumTraits<Scalar>::Real RealScalar; + static inline RealScalar run(const Scalar& x, const Scalar& y) + { + EIGEN_USING_STD_MATH(abs); + EIGEN_USING_STD_MATH(sqrt); + RealScalar _x = abs(x); + RealScalar _y = abs(y); + Scalar p, qp; + if(_x>_y) + { + p = _x; + qp = _y / p; + } + else + { + p = _y; + qp = _x / p; + } + if(p==RealScalar(0)) return RealScalar(0); + return p * sqrt(RealScalar(1) + qp*qp); + } +}; + +template<typename Scalar> +struct hypot_retval +{ + typedef typename NumTraits<Scalar>::Real type; +}; + +/**************************************************************************** +* Implementation of cast * +****************************************************************************/ + +template<typename OldType, typename NewType> +struct cast_impl +{ + EIGEN_DEVICE_FUNC + static inline NewType run(const OldType& x) + { + return static_cast<NewType>(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 round * +****************************************************************************/ + +#if EIGEN_HAS_CXX11_MATH + template<typename Scalar> + struct round_impl { + static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL) + using std::round; + return round(x); + } + }; +#else + template<typename Scalar> + struct round_impl + { + static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL) + EIGEN_USING_STD_MATH(floor); + EIGEN_USING_STD_MATH(ceil); + return (x > Scalar(0)) ? floor(x + Scalar(0.5)) : ceil(x - Scalar(0.5)); + } + }; +#endif + +template<typename Scalar> +struct round_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of arg * +****************************************************************************/ + +#if EIGEN_HAS_CXX11_MATH + template<typename Scalar> + struct arg_impl { + static inline Scalar run(const Scalar& x) + { + EIGEN_USING_STD_MATH(arg); + return arg(x); + } + }; +#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 < Scalar(0)) ? Scalar(EIGEN_PI) : Scalar(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_MATH(arg); + return arg(x); + } + }; + + template<typename Scalar> struct arg_impl : arg_default_impl<Scalar> {}; +#endif + +template<typename Scalar> +struct arg_retval +{ + typedef typename NumTraits<Scalar>::Real type; +}; + +/**************************************************************************** +* 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_MATH(log); + Scalar x1p = RealScalar(1) + x; + return ( x1p == Scalar(1) ) ? x : x * ( log(x1p) / (x1p - RealScalar(1)) ); + } +} + +template<typename Scalar> +struct log1p_impl { + static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) + #if EIGEN_HAS_CXX11_MATH + using std::log1p; + #endif + using std_fallback::log1p; + return 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_MATH(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; + } +}; + +/**************************************************************************** +* Implementation of random * +****************************************************************************/ + +template<typename Scalar, + bool IsComplex, + bool IsInteger> +struct random_default_impl {}; + +template<typename Scalar> +struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {}; + +template<typename Scalar> +struct random_retval +{ + typedef Scalar type; +}; + +template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y); +template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(); + +template<typename Scalar> +struct random_default_impl<Scalar, false, false> +{ + static inline Scalar run(const Scalar& x, const Scalar& y) + { + return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX); + } + static inline Scalar run() + { + return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1)); + } +}; + +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 Scalar> +struct random_default_impl<Scalar, false, true> +{ + static inline Scalar run(const Scalar& x, const Scalar& y) + { + typedef typename conditional<NumTraits<Scalar>::IsSigned,std::ptrdiff_t,std::size_t>::type ScalarX; + if(y<x) + return x; + // the following difference might overflow on a 32 bits system, + // but since y>=x the result converted to an unsigned long is still correct. + std::size_t range = ScalarX(y)-ScalarX(x); + std::size_t offset = 0; + // rejection sampling + std::size_t divisor = 1; + std::size_t multiplier = 1; + if(range<RAND_MAX) divisor = (std::size_t(RAND_MAX)+1)/(range+1); + else multiplier = 1 + range/(std::size_t(RAND_MAX)+1); + do { + offset = (std::size_t(std::rand()) * multiplier) / divisor; + } while (offset > range); + return Scalar(ScalarX(x) + offset); + } + + static inline Scalar run() + { +#ifdef EIGEN_MAKING_DOCS + return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10)); +#else + enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value, + scalar_bits = sizeof(Scalar) * CHAR_BIT, + shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)), + offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0 + }; + return Scalar((std::rand() >> shift) - offset); +#endif + } +}; + +template<typename Scalar> +struct random_default_impl<Scalar, true, false> +{ + static inline Scalar run(const Scalar& x, const Scalar& y) + { + return Scalar(random(real(x), real(y)), + random(imag(x), imag(y))); + } + static inline Scalar run() + { + typedef typename NumTraits<Scalar>::Real RealScalar; + return Scalar(random<RealScalar>(), random<RealScalar>()); + } +}; + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y) +{ + return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y); +} + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random() +{ + return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(); +} + +// Implementatin of is* functions + +// std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang. +#if (EIGEN_HAS_CXX11_MATH && !(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC>=1800) || (EIGEN_COMP_CLANG) +#define EIGEN_USE_STD_FPCLASSIFY 1 +#else +#define EIGEN_USE_STD_FPCLASSIFY 0 +#endif + +template<typename T> +EIGEN_DEVICE_FUNC +typename internal::enable_if<internal::is_integral<T>::value,bool>::type +isnan_impl(const T&) { return false; } + +template<typename T> +EIGEN_DEVICE_FUNC +typename internal::enable_if<internal::is_integral<T>::value,bool>::type +isinf_impl(const T&) { return false; } + +template<typename T> +EIGEN_DEVICE_FUNC +typename internal::enable_if<internal::is_integral<T>::value,bool>::type +isfinite_impl(const T&) { return true; } + +template<typename T> +EIGEN_DEVICE_FUNC +typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type +isfinite_impl(const T& x) +{ + #ifdef __CUDA_ARCH__ + return (::isfinite)(x); + #elif EIGEN_USE_STD_FPCLASSIFY + using std::isfinite; + return isfinite EIGEN_NOT_A_MACRO (x); + #else + return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest(); + #endif +} + +template<typename T> +EIGEN_DEVICE_FUNC +typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type +isinf_impl(const T& x) +{ + #ifdef __CUDA_ARCH__ + return (::isinf)(x); + #elif EIGEN_USE_STD_FPCLASSIFY + using std::isinf; + return isinf EIGEN_NOT_A_MACRO (x); + #else + return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest(); + #endif +} + +template<typename T> +EIGEN_DEVICE_FUNC +typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type +isnan_impl(const T& x) +{ + #ifdef __CUDA_ARCH__ + return (::isnan)(x); + #elif EIGEN_USE_STD_FPCLASSIFY + using std::isnan; + return isnan EIGEN_NOT_A_MACRO (x); + #else + return x != x; + #endif +} + +#if (!EIGEN_USE_STD_FPCLASSIFY) + +#if EIGEN_COMP_MSVC + +template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x) +{ + return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF; +} + +//MSVC defines a _isnan builtin function, but for double only +EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; } +EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) { return _isnan(x)!=0; } +EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) { return _isnan(x)!=0; } + +EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); } +EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) { return isinf_msvc_helper(x); } +EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) { return isinf_msvc_helper(x); } + +#elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC) + +#if EIGEN_GNUC_AT_LEAST(5,0) + #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only"))) +#else + // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol), + // while the second prevent too aggressive optimizations in fast-math mode: + #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only"))) +#endif + +template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) { return __builtin_isnan(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) { return __builtin_isnan(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) { return __builtin_isinf(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) { return __builtin_isinf(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); } + +#undef EIGEN_TMP_NOOPT_ATTRIB + +#endif + +#endif + +// 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> T generic_fast_tanh_float(const T& a_x); + +} // end namespace internal + +/**************************************************************************** +* Generic math functions * +****************************************************************************/ + +namespace numext { + +#ifndef __CUDA_ARCH__ +template<typename T> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) +{ + EIGEN_USING_STD_MATH(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_MATH(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<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); +} +#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 typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type 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 typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type 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(abs2, Scalar) abs2(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x); +} + +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); +} + +template<typename Scalar> +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x); +} + +#ifdef __CUDACC__ +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); +} + +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); } + +template<typename Scalar> +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x); +} + +template<typename T> +EIGEN_DEVICE_FUNC +T (floor)(const T& x) +{ + EIGEN_USING_STD_MATH(floor); + return floor(x); +} + +#ifdef __CUDACC__ +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); } +#endif + +template<typename T> +EIGEN_DEVICE_FUNC +T (ceil)(const T& x) +{ + EIGEN_USING_STD_MATH(ceil); + return ceil(x); +} + +#ifdef __CUDACC__ +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); } +#endif + + +/** Log base 2 for 32 bits positive integers. + * Conveniently returns 0 for x==0. */ +inline int log2(int x) +{ + eigen_assert(x>=0); + unsigned int v(x); + static const 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 T> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T sqrt(const T &x) +{ + EIGEN_USING_STD_MATH(sqrt); + return sqrt(x); +} + +template<typename T> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T log(const T &x) { + EIGEN_USING_STD_MATH(log); + return log(x); +} + +#ifdef __CUDACC__ +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 +typename internal::enable_if<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex,typename NumTraits<T>::Real>::type +abs(const T &x) { + EIGEN_USING_STD_MATH(abs); + return abs(x); +} + +template<typename T> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +typename internal::enable_if<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex),typename NumTraits<T>::Real>::type +abs(const T &x) { + return x; +} + +#if defined(__SYCL_DEVICE_ONLY__) +EIGEN_ALWAYS_INLINE float abs(float x) { return cl::sycl::fabs(x); } +EIGEN_ALWAYS_INLINE double abs(double x) { return cl::sycl::fabs(x); } +#endif // defined(__SYCL_DEVICE_ONLY__) + +#ifdef __CUDACC__ +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 T> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T exp(const T &x) { + EIGEN_USING_STD_MATH(exp); + return exp(x); +} + +#ifdef __CUDACC__ +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); } +#endif + +template<typename T> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T cos(const T &x) { + EIGEN_USING_STD_MATH(cos); + return cos(x); +} + +#ifdef __CUDACC__ +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_MATH(sin); + return sin(x); +} + +#ifdef __CUDACC__ +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_MATH(tan); + return tan(x); +} + +#ifdef __CUDACC__ +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_MATH(acos); + return acos(x); +} + +#ifdef __CUDACC__ +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_MATH(asin); + return asin(x); +} + +#ifdef __CUDACC__ +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_MATH(atan); + return atan(x); +} + +#ifdef __CUDACC__ +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_MATH(cosh); + return cosh(x); +} + +#ifdef __CUDACC__ +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_MATH(sinh); + return sinh(x); +} + +#ifdef __CUDACC__ +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_MATH(tanh); + return tanh(x); +} + +#if (!defined(__CUDACC__)) && EIGEN_FAST_MATH +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float tanh(float x) { return internal::generic_fast_tanh_float(x); } +#endif + +#ifdef __CUDACC__ +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_MATH(fmod); + return fmod(a, b); +} + +#ifdef __CUDACC__ +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 + +} // 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 random_impl<bool> +{ + static inline bool run() + { + return random<int>(0,1)==0 ? false : true; + } +}; + +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 + +} // end namespace Eigen + +#endif // EIGEN_MATHFUNCTIONS_H |