diff options
Diffstat (limited to 'extern/Eigen3/Eigen/src/Core/MathFunctions.h')
| -rw-r--r-- | extern/Eigen3/Eigen/src/Core/MathFunctions.h | 354 |
1 files changed, 140 insertions, 214 deletions
diff --git a/extern/Eigen3/Eigen/src/Core/MathFunctions.h b/extern/Eigen3/Eigen/src/Core/MathFunctions.h index 05e913f2fec..2bfc5ebd98a 100644 --- a/extern/Eigen3/Eigen/src/Core/MathFunctions.h +++ b/extern/Eigen3/Eigen/src/Core/MathFunctions.h @@ -51,16 +51,15 @@ struct global_math_functions_filtering_base typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type; }; -#define EIGEN_MATHFUNC_IMPL(func, scalar) func##_impl<typename global_math_functions_filtering_base<scalar>::type> -#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename func##_retval<typename global_math_functions_filtering_base<scalar>::type>::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> -struct real_impl +template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> +struct real_default_impl { typedef typename NumTraits<Scalar>::Real RealScalar; static inline RealScalar run(const Scalar& x) @@ -69,34 +68,32 @@ struct real_impl } }; -template<typename RealScalar> -struct real_impl<std::complex<RealScalar> > +template<typename Scalar> +struct real_default_impl<Scalar,true> { - static inline RealScalar run(const std::complex<RealScalar>& x) + typedef typename NumTraits<Scalar>::Real RealScalar; + static inline RealScalar run(const Scalar& x) { using std::real; return real(x); } }; +template<typename Scalar> struct real_impl : real_default_impl<Scalar> {}; + template<typename Scalar> struct real_retval { typedef typename NumTraits<Scalar>::Real type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x); -} /**************************************************************************** * Implementation of imag * ****************************************************************************/ -template<typename Scalar> -struct imag_impl +template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> +struct imag_default_impl { typedef typename NumTraits<Scalar>::Real RealScalar; static inline RealScalar run(const Scalar&) @@ -105,28 +102,25 @@ struct imag_impl } }; -template<typename RealScalar> -struct imag_impl<std::complex<RealScalar> > +template<typename Scalar> +struct imag_default_impl<Scalar,true> { - static inline RealScalar run(const std::complex<RealScalar>& x) + typedef typename NumTraits<Scalar>::Real RealScalar; + static inline RealScalar run(const Scalar& x) { using std::imag; return imag(x); } }; +template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {}; + template<typename Scalar> struct imag_retval { typedef typename NumTraits<Scalar>::Real type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x); -} - /**************************************************************************** * Implementation of real_ref * ****************************************************************************/ @@ -151,18 +145,6 @@ struct real_ref_retval typedef typename NumTraits<Scalar>::Real & type; }; -template<typename Scalar> -inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x) -{ - return real_ref_impl<Scalar>::run(x); -} - -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x); -} - /**************************************************************************** * Implementation of imag_ref * ****************************************************************************/ @@ -203,23 +185,11 @@ struct imag_ref_retval typedef typename NumTraits<Scalar>::Real & type; }; -template<typename Scalar> -inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x) -{ - return imag_ref_impl<Scalar>::run(x); -} - -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x); -} - /**************************************************************************** * Implementation of conj * ****************************************************************************/ -template<typename Scalar> +template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> struct conj_impl { static inline Scalar run(const Scalar& x) @@ -228,10 +198,10 @@ struct conj_impl } }; -template<typename RealScalar> -struct conj_impl<std::complex<RealScalar> > +template<typename Scalar> +struct conj_impl<Scalar,true> { - static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x) + static inline Scalar run(const Scalar& x) { using std::conj; return conj(x); @@ -244,39 +214,6 @@ struct conj_retval typedef Scalar type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x); -} - -/**************************************************************************** -* Implementation of abs * -****************************************************************************/ - -template<typename Scalar> -struct abs_impl -{ - typedef typename NumTraits<Scalar>::Real RealScalar; - static inline RealScalar run(const Scalar& x) - { - using std::abs; - return abs(x); - } -}; - -template<typename Scalar> -struct abs_retval -{ - typedef typename NumTraits<Scalar>::Real type; -}; - -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(abs, Scalar) abs(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(abs, Scalar)::run(x); -} - /**************************************************************************** * Implementation of abs2 * ****************************************************************************/ @@ -306,12 +243,6 @@ struct abs2_retval typedef typename NumTraits<Scalar>::Real type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x); -} - /**************************************************************************** * Implementation of norm1 * ****************************************************************************/ @@ -322,6 +253,7 @@ struct norm1_default_impl typedef typename NumTraits<Scalar>::Real RealScalar; static inline RealScalar run(const Scalar& x) { + using std::abs; return abs(real(x)) + abs(imag(x)); } }; @@ -331,6 +263,7 @@ struct norm1_default_impl<Scalar, false> { static inline Scalar run(const Scalar& x) { + using std::abs; return abs(x); } }; @@ -344,12 +277,6 @@ struct norm1_retval typedef typename NumTraits<Scalar>::Real type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x); -} - /**************************************************************************** * Implementation of hypot * ****************************************************************************/ @@ -362,9 +289,12 @@ struct hypot_impl { 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 0; RealScalar q = (min)(_x, _y); RealScalar qp = q/p; return p * sqrt(RealScalar(1) + qp*qp); @@ -377,12 +307,6 @@ struct hypot_retval typedef typename NumTraits<Scalar>::Real type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y) -{ - return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y); -} - /**************************************************************************** * Implementation of cast * ****************************************************************************/ @@ -405,97 +329,29 @@ inline NewType cast(const OldType& x) } /**************************************************************************** -* Implementation of sqrt * +* Implementation of atanh2 * ****************************************************************************/ template<typename Scalar, bool IsInteger> -struct sqrt_default_impl -{ - static inline Scalar run(const Scalar& x) - { - using std::sqrt; - return sqrt(x); - } -}; - -template<typename Scalar> -struct sqrt_default_impl<Scalar, true> -{ - static inline Scalar run(const Scalar&) - { -#ifdef EIGEN2_SUPPORT - eigen_assert(!NumTraits<Scalar>::IsInteger); -#else - EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) -#endif - return Scalar(0); - } -}; - -template<typename Scalar> -struct sqrt_impl : sqrt_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {}; - -template<typename Scalar> -struct sqrt_retval -{ - typedef Scalar type; -}; - -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x) -{ - return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x); -} - -/**************************************************************************** -* Implementation of standard unary real functions (exp, log, sin, cos, ... * -****************************************************************************/ - -// This macro instanciate all the necessary template mechanism which is common to all unary real functions. -#define EIGEN_MATHFUNC_STANDARD_REAL_UNARY(NAME) \ - template<typename Scalar, bool IsInteger> struct NAME##_default_impl { \ - static inline Scalar run(const Scalar& x) { using std::NAME; return NAME(x); } \ - }; \ - template<typename Scalar> struct NAME##_default_impl<Scalar, true> { \ - static inline Scalar run(const Scalar&) { \ - EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) \ - return Scalar(0); \ - } \ - }; \ - template<typename Scalar> struct NAME##_impl \ - : NAME##_default_impl<Scalar, NumTraits<Scalar>::IsInteger> \ - {}; \ - template<typename Scalar> struct NAME##_retval { typedef Scalar type; }; \ - template<typename Scalar> \ - inline EIGEN_MATHFUNC_RETVAL(NAME, Scalar) NAME(const Scalar& x) { \ - return EIGEN_MATHFUNC_IMPL(NAME, Scalar)::run(x); \ - } - -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(exp) -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(log) -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(sin) -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(cos) -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(tan) -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(asin) -EIGEN_MATHFUNC_STANDARD_REAL_UNARY(acos) - -/**************************************************************************** -* Implementation of atan2 * -****************************************************************************/ - -template<typename Scalar, bool IsInteger> -struct atan2_default_impl +struct atanh2_default_impl { typedef Scalar retval; + typedef typename NumTraits<Scalar>::Real RealScalar; static inline Scalar run(const Scalar& x, const Scalar& y) { - using std::atan2; - return atan2(x, y); + 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); } }; template<typename Scalar> -struct atan2_default_impl<Scalar, true> +struct atanh2_default_impl<Scalar, true> { static inline Scalar run(const Scalar&, const Scalar&) { @@ -505,20 +361,14 @@ struct atan2_default_impl<Scalar, true> }; template<typename Scalar> -struct atan2_impl : atan2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {}; +struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {}; template<typename Scalar> -struct atan2_retval +struct atanh2_retval { typedef Scalar type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(atan2, Scalar) atan2(const Scalar& x, const Scalar& y) -{ - return EIGEN_MATHFUNC_IMPL(atan2, Scalar)::run(x, y); -} - /**************************************************************************** * Implementation of pow * ****************************************************************************/ @@ -562,12 +412,6 @@ struct pow_retval typedef Scalar type; }; -template<typename Scalar> -inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y) -{ - return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y); -} - /**************************************************************************** * Implementation of random * ****************************************************************************/ @@ -666,11 +510,10 @@ struct random_default_impl<Scalar, false, true> #else enum { rand_bits = 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)) + 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 }; - Scalar x = Scalar(std::rand() >> shift); - Scalar offset = NumTraits<Scalar>::IsSigned ? Scalar(1 << (rand_bits-1)) : Scalar(0); - return x - offset; + return Scalar((std::rand() >> shift) - offset); #endif } }; @@ -702,6 +545,97 @@ inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random() return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(); } +} // end namespace internal + +/**************************************************************************** +* Generic math function * +****************************************************************************/ + +namespace numext { + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x); +} + +template<typename Scalar> +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> +inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x); +} + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x); +} + +template<typename Scalar> +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> +inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x); +} + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x); +} + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x); +} + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x); +} + +template<typename Scalar> +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) +{ + return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y); +} + +template<typename Scalar> +inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y) +{ + return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y); +} + +// 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) +{ + return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest(); +} + +} // end namespace numext + +namespace internal { + /**************************************************************************** * Implementation of fuzzy comparisons * ****************************************************************************/ @@ -718,11 +652,13 @@ struct scalar_fuzzy_default_impl<Scalar, false, false> template<typename OtherScalar> static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec) { + using std::abs; return abs(x) <= abs(y) * prec; } 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; } static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec) @@ -757,12 +693,12 @@ struct scalar_fuzzy_default_impl<Scalar, true, false> template<typename OtherScalar> static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec) { - return abs2(x) <= abs2(y) * prec * prec; + return numext::abs2(x) <= numext::abs2(y) * prec * prec; } static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec) { using std::min; - return abs2(x - y) <= (min)(abs2(x), abs2(y)) * prec * prec; + return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec; } }; @@ -824,17 +760,7 @@ template<> struct scalar_fuzzy_impl<bool> }; -/**************************************************************************** -* Special functions * -****************************************************************************/ - -// 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) -{ - return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest(); -} - + } // end namespace internal } // end namespace Eigen |