| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2006-2010 Benoit Jacob <[email protected]> |
| // |
| // 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 |
