780 lines
22 KiB
C++
780 lines
22 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_MATHFUNCTIONS_H
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#define EIGEN_MATHFUNCTIONS_H
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namespace Eigen {
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namespace internal {
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/** \internal \struct global_math_functions_filtering_base
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*
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* What it does:
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* Defines a typedef 'type' as follows:
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* - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
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* global_math_functions_filtering_base<T>::type is a typedef for it.
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* - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
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*
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* How it's used:
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* To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
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* When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
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* is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
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* So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
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* won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
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*
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* How it's implemented:
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* SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace
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* the typename dummy by an integer template parameter, it doesn't work anymore!
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*/
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template<typename T, typename dummy = void>
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struct global_math_functions_filtering_base
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{
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typedef T type;
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};
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template<typename T> struct always_void { typedef void type; };
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template<typename T>
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struct global_math_functions_filtering_base
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<T,
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typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
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>
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{
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typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
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};
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#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
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#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
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/****************************************************************************
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* Implementation of real *
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****************************************************************************/
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template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
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struct real_default_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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return x;
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}
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};
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template<typename Scalar>
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struct real_default_impl<Scalar,true>
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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using std::real;
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return real(x);
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}
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};
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template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
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template<typename Scalar>
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struct real_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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/****************************************************************************
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* Implementation of imag *
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****************************************************************************/
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template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
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struct imag_default_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar&)
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{
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return RealScalar(0);
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}
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};
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template<typename Scalar>
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struct imag_default_impl<Scalar,true>
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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using std::imag;
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return imag(x);
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}
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};
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template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
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template<typename Scalar>
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struct imag_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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/****************************************************************************
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* Implementation of real_ref *
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****************************************************************************/
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template<typename Scalar>
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struct real_ref_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar& run(Scalar& x)
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{
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return reinterpret_cast<RealScalar*>(&x)[0];
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}
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static inline const RealScalar& run(const Scalar& x)
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{
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return reinterpret_cast<const RealScalar*>(&x)[0];
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}
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};
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template<typename Scalar>
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struct real_ref_retval
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{
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typedef typename NumTraits<Scalar>::Real & type;
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};
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/****************************************************************************
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* Implementation of imag_ref *
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****************************************************************************/
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template<typename Scalar, bool IsComplex>
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struct imag_ref_default_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar& run(Scalar& x)
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{
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return reinterpret_cast<RealScalar*>(&x)[1];
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}
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static inline const RealScalar& run(const Scalar& x)
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{
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return reinterpret_cast<RealScalar*>(&x)[1];
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}
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};
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template<typename Scalar>
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struct imag_ref_default_impl<Scalar, false>
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{
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static inline Scalar run(Scalar&)
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{
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return Scalar(0);
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}
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static inline const Scalar run(const Scalar&)
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{
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return Scalar(0);
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}
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};
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template<typename Scalar>
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struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
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template<typename Scalar>
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struct imag_ref_retval
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{
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typedef typename NumTraits<Scalar>::Real & type;
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};
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/****************************************************************************
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* Implementation of conj *
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****************************************************************************/
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template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
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struct conj_impl
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{
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static inline Scalar run(const Scalar& x)
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{
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return x;
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}
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};
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template<typename Scalar>
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struct conj_impl<Scalar,true>
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{
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static inline Scalar run(const Scalar& x)
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{
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using std::conj;
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return conj(x);
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}
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};
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template<typename Scalar>
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struct conj_retval
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{
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typedef Scalar type;
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};
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/****************************************************************************
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* Implementation of abs2 *
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****************************************************************************/
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template<typename Scalar,bool IsComplex>
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struct abs2_impl_default
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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return x*x;
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}
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};
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template<typename Scalar>
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struct abs2_impl_default<Scalar, true> // IsComplex
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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return real(x)*real(x) + imag(x)*imag(x);
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}
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};
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template<typename Scalar>
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struct abs2_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);
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}
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};
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template<typename Scalar>
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struct abs2_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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/****************************************************************************
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* Implementation of norm1 *
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****************************************************************************/
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template<typename Scalar, bool IsComplex>
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struct norm1_default_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x)
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{
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using std::abs;
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return abs(real(x)) + abs(imag(x));
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}
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};
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template<typename Scalar>
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struct norm1_default_impl<Scalar, false>
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{
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static inline Scalar run(const Scalar& x)
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{
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using std::abs;
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return abs(x);
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}
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};
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template<typename Scalar>
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struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
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template<typename Scalar>
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struct norm1_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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/****************************************************************************
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* Implementation of hypot *
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****************************************************************************/
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template<typename Scalar>
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struct hypot_impl
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline RealScalar run(const Scalar& x, const Scalar& y)
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{
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using std::max;
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using std::min;
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using std::abs;
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using std::sqrt;
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RealScalar _x = abs(x);
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RealScalar _y = abs(y);
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RealScalar p = (max)(_x, _y);
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if(p==RealScalar(0)) return RealScalar(0);
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RealScalar q = (min)(_x, _y);
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RealScalar qp = q/p;
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return p * sqrt(RealScalar(1) + qp*qp);
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}
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};
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template<typename Scalar>
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struct hypot_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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/****************************************************************************
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* Implementation of cast *
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****************************************************************************/
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template<typename OldType, typename NewType>
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struct cast_impl
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{
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static inline NewType run(const OldType& x)
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{
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return static_cast<NewType>(x);
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}
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};
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// here, for once, we're plainly returning NewType: we don't want cast to do weird things.
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template<typename OldType, typename NewType>
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inline NewType cast(const OldType& x)
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{
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return cast_impl<OldType, NewType>::run(x);
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}
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/****************************************************************************
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* Implementation of atanh2 *
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****************************************************************************/
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template<typename Scalar, bool IsInteger>
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struct atanh2_default_impl
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{
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typedef Scalar retval;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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static inline Scalar run(const Scalar& x, const Scalar& y)
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{
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using std::abs;
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using std::log;
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using std::sqrt;
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Scalar z = x / y;
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if (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon()))
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return RealScalar(0.5) * log((y + x) / (y - x));
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else
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return z + z*z*z / RealScalar(3);
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}
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};
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template<typename Scalar>
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struct atanh2_default_impl<Scalar, true>
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{
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static inline Scalar run(const Scalar&, const Scalar&)
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{
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EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
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return Scalar(0);
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}
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};
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template<typename Scalar>
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struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
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template<typename Scalar>
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struct atanh2_retval
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{
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typedef Scalar type;
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};
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/****************************************************************************
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* Implementation of pow *
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****************************************************************************/
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template<typename Scalar, bool IsInteger>
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struct pow_default_impl
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{
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typedef Scalar retval;
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static inline Scalar run(const Scalar& x, const Scalar& y)
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{
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using std::pow;
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return pow(x, y);
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}
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};
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template<typename Scalar>
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struct pow_default_impl<Scalar, true>
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{
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static inline Scalar run(Scalar x, Scalar y)
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{
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Scalar res(1);
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eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
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if(y & 1) res *= x;
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y >>= 1;
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while(y)
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{
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x *= x;
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if(y&1) res *= x;
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y >>= 1;
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}
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return res;
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}
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};
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template<typename Scalar>
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struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
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template<typename Scalar>
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struct pow_retval
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{
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typedef Scalar type;
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};
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/****************************************************************************
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* Implementation of random *
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****************************************************************************/
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template<typename Scalar,
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bool IsComplex,
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bool IsInteger>
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struct random_default_impl {};
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template<typename Scalar>
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struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
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template<typename Scalar>
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struct random_retval
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{
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typedef Scalar type;
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};
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template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
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template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
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template<typename Scalar>
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struct random_default_impl<Scalar, false, false>
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{
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static inline Scalar run(const Scalar& x, const Scalar& y)
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{
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return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
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}
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static inline Scalar run()
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{
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return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
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}
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};
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enum {
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floor_log2_terminate,
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floor_log2_move_up,
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floor_log2_move_down,
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floor_log2_bogus
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};
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template<unsigned int n, int lower, int upper> struct floor_log2_selector
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{
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enum { middle = (lower + upper) / 2,
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value = (upper <= lower + 1) ? int(floor_log2_terminate)
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: (n < (1 << middle)) ? int(floor_log2_move_down)
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: (n==0) ? int(floor_log2_bogus)
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: int(floor_log2_move_up)
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};
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};
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template<unsigned int n,
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int lower = 0,
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int upper = sizeof(unsigned int) * CHAR_BIT - 1,
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int selector = floor_log2_selector<n, lower, upper>::value>
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struct floor_log2 {};
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template<unsigned int n, int lower, int upper>
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struct floor_log2<n, lower, upper, floor_log2_move_down>
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{
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enum { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value };
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};
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template<unsigned int n, int lower, int upper>
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struct floor_log2<n, lower, upper, floor_log2_move_up>
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{
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enum { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value };
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};
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template<unsigned int n, int lower, int upper>
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struct floor_log2<n, lower, upper, floor_log2_terminate>
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{
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enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
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};
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template<unsigned int n, int lower, int upper>
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struct floor_log2<n, lower, upper, floor_log2_bogus>
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{
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// no value, error at compile time
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};
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template<typename Scalar>
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struct random_default_impl<Scalar, false, true>
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{
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typedef typename NumTraits<Scalar>::NonInteger NonInteger;
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static inline Scalar run(const Scalar& x, const Scalar& y)
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{
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return x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1)));
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}
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static inline Scalar run()
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{
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#ifdef EIGEN_MAKING_DOCS
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return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
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#else
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enum { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value,
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scalar_bits = sizeof(Scalar) * CHAR_BIT,
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shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
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offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
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};
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return Scalar((std::rand() >> shift) - offset);
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#endif
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}
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};
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template<typename Scalar>
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struct random_default_impl<Scalar, true, false>
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{
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static inline Scalar run(const Scalar& x, const Scalar& y)
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{
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return Scalar(random(real(x), real(y)),
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random(imag(x), imag(y)));
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}
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static inline Scalar run()
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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return Scalar(random<RealScalar>(), random<RealScalar>());
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}
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};
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
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{
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return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
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}
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
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{
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return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
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}
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} // end namespace internal
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/****************************************************************************
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* Generic math function *
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****************************************************************************/
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namespace numext {
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
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}
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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 *
|
|
****************************************************************************/
|
|
|
|
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>
|
|
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)
|
|
{
|
|
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>
|
|
static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
|
|
{
|
|
return x == Scalar(0);
|
|
}
|
|
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
|
|
{
|
|
return x == y;
|
|
}
|
|
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>
|
|
static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& 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 numext::abs2(x - y) <= (min)(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>
|
|
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>
|
|
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>
|
|
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>
|
|
static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
|
|
{
|
|
return !x;
|
|
}
|
|
|
|
static inline bool isApprox(bool x, bool y, bool)
|
|
{
|
|
return x == y;
|
|
}
|
|
|
|
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
|