diff options
Diffstat (limited to 'extern/Eigen3/Eigen/src/Core/MathFunctions.h')
| -rw-r--r-- | extern/Eigen3/Eigen/src/Core/MathFunctions.h | 881 |
1 files changed, 764 insertions, 117 deletions
diff --git a/extern/Eigen3/Eigen/src/Core/MathFunctions.h b/extern/Eigen3/Eigen/src/Core/MathFunctions.h index adf2f9c511b..b249ce0c8b0 100644 --- a/extern/Eigen3/Eigen/src/Core/MathFunctions.h +++ b/extern/Eigen3/Eigen/src/Core/MathFunctions.h @@ -10,11 +10,25 @@ #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 \struct global_math_functions_filtering_base +/** \internal \class global_math_functions_filtering_base * * What it does: * Defines a typedef 'type' as follows: @@ -62,6 +76,7 @@ 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; @@ -72,6 +87,7 @@ 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; @@ -81,13 +97,25 @@ struct real_default_impl<Scalar,true> 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 * ****************************************************************************/ @@ -96,6 +124,7 @@ 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); @@ -106,6 +135,7 @@ 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; @@ -115,6 +145,19 @@ struct imag_default_impl<Scalar,true> 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 { @@ -129,10 +172,12 @@ 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]; @@ -153,10 +198,12 @@ 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]; @@ -166,10 +213,12 @@ struct imag_ref_default_impl 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); @@ -192,6 +241,7 @@ struct imag_ref_retval template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> struct conj_impl { + EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) { return x; @@ -201,6 +251,7 @@ struct conj_impl template<typename Scalar> struct conj_impl<Scalar,true> { + EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) { using std::conj; @@ -218,26 +269,40 @@ struct conj_retval * Implementation of abs2 * ****************************************************************************/ -template<typename Scalar> -struct abs2_impl +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 RealScalar> -struct abs2_impl<std::complex<RealScalar> > +template<typename Scalar> +struct abs2_impl_default<Scalar, true> // IsComplex { - static inline RealScalar run(const std::complex<RealScalar>& x) + 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; @@ -251,9 +316,10 @@ 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) { - using std::abs; + EIGEN_USING_STD_MATH(abs); return abs(real(x)) + abs(imag(x)); } }; @@ -261,9 +327,10 @@ struct norm1_default_impl template<typename Scalar> struct norm1_default_impl<Scalar, false> { + EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) { - using std::abs; + EIGEN_USING_STD_MATH(abs); return abs(x); } }; @@ -281,25 +348,7 @@ struct norm1_retval * 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) - { - using std::max; - using std::min; - using std::abs; - using std::sqrt; - RealScalar _x = abs(x); - RealScalar _y = abs(y); - RealScalar p = (max)(_x, _y); - if(p==RealScalar(0)) return RealScalar(0); - RealScalar q = (min)(_x, _y); - RealScalar qp = q/p; - return p * sqrt(RealScalar(1) + qp*qp); - } -}; +template<typename Scalar> struct hypot_impl; template<typename Scalar> struct hypot_retval @@ -314,6 +363,7 @@ struct hypot_retval template<typename OldType, typename NewType> struct cast_impl { + EIGEN_DEVICE_FUNC static inline NewType run(const OldType& x) { return static_cast<NewType>(x); @@ -323,48 +373,124 @@ struct cast_impl // 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 atanh2 * +* Implementation of round * ****************************************************************************/ -template<typename Scalar, bool IsInteger> -struct atanh2_default_impl -{ - typedef Scalar retval; - typedef typename NumTraits<Scalar>::Real RealScalar; - static inline Scalar run(const Scalar& x, const Scalar& y) +#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 { - using std::abs; - using std::log; - using std::sqrt; - Scalar z = x / y; - if (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon())) - return RealScalar(0.5) * log((y + x) / (y - x)); - else - return z + z*z*z / RealScalar(3); - } + 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 atanh2_default_impl<Scalar, true> +struct arg_retval { - static inline Scalar run(const Scalar&, const Scalar&) + 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 numext::equal_strict(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) - return Scalar(0); + #if EIGEN_HAS_CXX11_MATH + using std::log1p; + #endif + using std_fallback::log1p; + return log1p(x); } }; -template<typename Scalar> -struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {}; template<typename Scalar> -struct atanh2_retval +struct log1p_retval { typedef Scalar type; }; @@ -373,24 +499,26 @@ struct atanh2_retval * Implementation of pow * ****************************************************************************/ -template<typename Scalar, bool IsInteger> -struct pow_default_impl +template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger> +struct pow_impl { - typedef Scalar retval; - static inline Scalar run(const Scalar& x, const Scalar& y) + //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) { - using std::pow; + EIGEN_USING_STD_MATH(pow); return pow(x, y); } }; -template<typename Scalar> -struct pow_default_impl<Scalar, true> +template<typename ScalarX,typename ScalarY> +struct pow_impl<ScalarX,ScalarY, true> { - static inline Scalar run(Scalar x, Scalar y) + typedef ScalarX result_type; + static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y) { - Scalar res(1); - eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0); + ScalarX res(1); + eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0); if(y & 1) res *= x; y >>= 1; while(y) @@ -403,15 +531,6 @@ struct pow_default_impl<Scalar, true> } }; -template<typename Scalar> -struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {}; - -template<typename Scalar> -struct pow_retval -{ - typedef Scalar type; -}; - /**************************************************************************** * Implementation of random * ****************************************************************************/ @@ -447,48 +566,48 @@ struct random_default_impl<Scalar, false, false> }; enum { - floor_log2_terminate, - floor_log2_move_up, - floor_log2_move_down, - floor_log2_bogus + 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 floor_log2_selector +template<unsigned int n, int lower, int upper> struct meta_floor_log2_selector { enum { middle = (lower + upper) / 2, - value = (upper <= lower + 1) ? int(floor_log2_terminate) - : (n < (1 << middle)) ? int(floor_log2_move_down) - : (n==0) ? int(floor_log2_bogus) - : int(floor_log2_move_up) + 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 = floor_log2_selector<n, lower, upper>::value> -struct floor_log2 {}; + int selector = meta_floor_log2_selector<n, lower, upper>::value> +struct meta_floor_log2 {}; template<unsigned int n, int lower, int upper> -struct floor_log2<n, lower, upper, floor_log2_move_down> +struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down> { - enum { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value }; + 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 floor_log2<n, lower, upper, floor_log2_move_up> +struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up> { - enum { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value }; + 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 floor_log2<n, lower, upper, floor_log2_terminate> +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 floor_log2<n, lower, upper, floor_log2_bogus> +struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus> { // no value, error at compile time }; @@ -496,11 +615,31 @@ struct floor_log2<n, lower, upper, floor_log2_bogus> template<typename Scalar> struct random_default_impl<Scalar, false, true> { - typedef typename NumTraits<Scalar>::NonInteger NonInteger; - static inline Scalar run(const Scalar& x, const Scalar& y) { - return x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1))); + if (y <= x) + return x; + // ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself. + typedef typename make_unsigned<Scalar>::type ScalarU; + // ScalarX is the widest of ScalarU and unsigned int. + // We'll deal only with ScalarX and unsigned int below thus avoiding signed + // types and arithmetic and signed overflows (which are undefined behavior). + typedef typename conditional<(ScalarU(-1) > unsigned(-1)), ScalarU, unsigned>::type ScalarX; + // The following difference doesn't overflow, provided our integer types are two's + // complement and have the same number of padding bits in signed and unsigned variants. + // This is the case in most modern implementations of C++. + ScalarX range = ScalarX(y) - ScalarX(x); + ScalarX offset = 0; + ScalarX divisor = 1; + ScalarX multiplier = 1; + const unsigned rand_max = RAND_MAX; + if (range <= rand_max) divisor = (rand_max + 1) / (range + 1); + else multiplier = 1 + range / (rand_max + 1); + // Rejection sampling. + do { + offset = (unsigned(std::rand()) * multiplier) / divisor; + } while (offset > range); + return Scalar(ScalarX(x) + offset); } static inline Scalar run() @@ -508,7 +647,7 @@ struct random_default_impl<Scalar, false, true> #ifdef EIGEN_MAKING_DOCS return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10)); #else - enum { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value, + 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 @@ -545,97 +684,602 @@ 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 function * +* 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> -inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y) +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x) { - return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y); + 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> -inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y) +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) { - return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y); + 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]; } -// std::isfinite is non standard, so let's define our own version, -// even though it is not very efficient. -template<typename T> bool (isfinite)(const T& x) +/** \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) { - return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest(); + 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 * ****************************************************************************/ @@ -649,18 +1293,17 @@ template<typename Scalar> struct scalar_fuzzy_default_impl<Scalar, false, false> { typedef typename NumTraits<Scalar>::Real RealScalar; - template<typename OtherScalar> + template<typename OtherScalar> EIGEN_DEVICE_FUNC static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec) { - using std::abs; - return abs(x) <= abs(y) * 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) { - using std::min; - using std::abs; - return abs(x - y) <= (min)(abs(x), abs(y)) * 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); @@ -671,15 +1314,17 @@ template<typename Scalar> struct scalar_fuzzy_default_impl<Scalar, false, true> { typedef typename NumTraits<Scalar>::Real RealScalar; - template<typename OtherScalar> + 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; @@ -690,38 +1335,38 @@ template<typename Scalar> struct scalar_fuzzy_default_impl<Scalar, true, false> { typedef typename NumTraits<Scalar>::Real RealScalar; - template<typename OtherScalar> + 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) { - using std::min; - return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * 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> +template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, - typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) + const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision()) { return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision); } -template<typename Scalar> +template<typename Scalar> EIGEN_DEVICE_FUNC inline bool isApprox(const Scalar& x, const Scalar& y, - typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) + const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision()) { return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision); } -template<typename Scalar> +template<typename Scalar> EIGEN_DEVICE_FUNC inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, - typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) + const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision()) { return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision); } @@ -742,17 +1387,19 @@ template<> struct scalar_fuzzy_impl<bool> { typedef bool RealScalar; - template<typename OtherScalar> + 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; |