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843 lines
24 KiB
C++
843 lines
24 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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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_MATHFUNCTIONS_H
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#define EIGEN_MATHFUNCTIONS_H
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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) func##_impl<typename global_math_functions_filtering_base<scalar>::type>
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#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename func##_retval<typename 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>
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struct real_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 RealScalar>
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struct real_impl<std::complex<RealScalar> >
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{
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static inline RealScalar run(const std::complex<RealScalar>& 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>
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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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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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/****************************************************************************
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* Implementation of imag *
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****************************************************************************/
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template<typename Scalar>
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struct imag_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 RealScalar>
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struct imag_impl<std::complex<RealScalar> >
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{
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static inline RealScalar run(const std::complex<RealScalar>& 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>
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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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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
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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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template<typename Scalar>
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inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
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{
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return real_ref_impl<Scalar>::run(x);
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}
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
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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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template<typename Scalar>
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inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
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{
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return imag_ref_impl<Scalar>::run(x);
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}
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
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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>
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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 RealScalar>
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struct conj_impl<std::complex<RealScalar> >
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{
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static inline std::complex<RealScalar> run(const std::complex<RealScalar>& 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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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
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}
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/****************************************************************************
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* Implementation of abs *
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****************************************************************************/
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template<typename Scalar>
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struct abs_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(x);
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}
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};
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template<typename Scalar>
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struct abs_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(abs, Scalar) abs(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(abs, Scalar)::run(x);
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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>
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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 x*x;
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}
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};
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template<typename RealScalar>
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struct abs2_impl<std::complex<RealScalar> >
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{
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static inline RealScalar run(const std::complex<RealScalar>& 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_retval
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{
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typedef typename NumTraits<Scalar>::Real type;
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};
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
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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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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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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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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
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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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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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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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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
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{
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return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
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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 sqrt *
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****************************************************************************/
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template<typename Scalar, bool IsInteger>
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struct sqrt_default_impl
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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::sqrt;
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return sqrt(x);
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}
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};
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template<typename Scalar>
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struct sqrt_default_impl<Scalar, true>
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{
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static inline Scalar run(const Scalar&)
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{
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#ifdef EIGEN2_SUPPORT
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eigen_assert(!NumTraits<Scalar>::IsInteger);
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#else
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EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
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#endif
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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 sqrt_impl : sqrt_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
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template<typename Scalar>
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struct sqrt_retval
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{
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typedef Scalar type;
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};
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x)
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{
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return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
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}
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/****************************************************************************
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* Implementation of standard unary real functions (exp, log, sin, cos, ... *
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****************************************************************************/
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// This macro instanciate all the necessary template mechanism which is common to all unary real functions.
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#define EIGEN_MATHFUNC_STANDARD_REAL_UNARY(NAME) \
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template<typename Scalar, bool IsInteger> struct NAME##_default_impl { \
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static inline Scalar run(const Scalar& x) { using std::NAME; return NAME(x); } \
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}; \
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template<typename Scalar> struct NAME##_default_impl<Scalar, true> { \
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static inline Scalar run(const Scalar&) { \
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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> struct NAME##_impl \
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: NAME##_default_impl<Scalar, NumTraits<Scalar>::IsInteger> \
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{}; \
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template<typename Scalar> struct NAME##_retval { typedef Scalar type; }; \
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template<typename Scalar> \
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inline EIGEN_MATHFUNC_RETVAL(NAME, Scalar) NAME(const Scalar& x) { \
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return EIGEN_MATHFUNC_IMPL(NAME, Scalar)::run(x); \
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}
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(exp)
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(log)
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(sin)
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(cos)
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(tan)
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(asin)
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EIGEN_MATHFUNC_STANDARD_REAL_UNARY(acos)
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/****************************************************************************
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* Implementation of atan2 *
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****************************************************************************/
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template<typename Scalar, bool IsInteger>
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struct atan2_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::atan2;
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return atan2(x, y);
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}
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};
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template<typename Scalar>
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struct atan2_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 atan2_impl : atan2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
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template<typename Scalar>
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struct atan2_retval
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{
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typedef Scalar type;
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};
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template<typename Scalar>
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inline EIGEN_MATHFUNC_RETVAL(atan2, Scalar) atan2(const Scalar& x, const Scalar& y)
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{
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return EIGEN_MATHFUNC_IMPL(atan2, Scalar)::run(x, y);
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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>
|
|
struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
|
|
|
|
template<typename Scalar>
|
|
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 *
|
|
****************************************************************************/
|
|
|
|
template<typename Scalar,
|
|
bool IsComplex,
|
|
bool IsInteger>
|
|
struct random_default_impl {};
|
|
|
|
template<typename Scalar>
|
|
struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
|
|
|
|
template<typename Scalar>
|
|
struct random_retval
|
|
{
|
|
typedef Scalar type;
|
|
};
|
|
|
|
template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
|
|
template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
|
|
|
|
template<typename Scalar>
|
|
struct random_default_impl<Scalar, false, false>
|
|
{
|
|
static inline Scalar run(const Scalar& x, const Scalar& y)
|
|
{
|
|
return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
|
|
}
|
|
static inline Scalar run()
|
|
{
|
|
return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
|
|
}
|
|
};
|
|
|
|
enum {
|
|
floor_log2_terminate,
|
|
floor_log2_move_up,
|
|
floor_log2_move_down,
|
|
floor_log2_bogus
|
|
};
|
|
|
|
template<unsigned int n, int lower, int upper> struct 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)
|
|
};
|
|
};
|
|
|
|
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 {};
|
|
|
|
template<unsigned int n, int lower, int upper>
|
|
struct floor_log2<n, lower, upper, floor_log2_move_down>
|
|
{
|
|
enum { value = floor_log2<n, lower, 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>
|
|
{
|
|
enum { value = floor_log2<n, 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>
|
|
{
|
|
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>
|
|
{
|
|
// no value, error at compile time
|
|
};
|
|
|
|
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)));
|
|
}
|
|
|
|
static inline Scalar run()
|
|
{
|
|
#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,
|
|
scalar_bits = sizeof(Scalar) * CHAR_BIT,
|
|
shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits))
|
|
};
|
|
Scalar x = Scalar(std::rand() >> shift);
|
|
Scalar offset = NumTraits<Scalar>::IsSigned ? Scalar(1 << (rand_bits-1)) : Scalar(0);
|
|
return x - offset;
|
|
#endif
|
|
}
|
|
};
|
|
|
|
template<typename Scalar>
|
|
struct random_default_impl<Scalar, true, false>
|
|
{
|
|
static inline Scalar run(const Scalar& x, const Scalar& y)
|
|
{
|
|
return Scalar(random(real(x), real(y)),
|
|
random(imag(x), imag(y)));
|
|
}
|
|
static inline Scalar run()
|
|
{
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
return Scalar(random<RealScalar>(), random<RealScalar>());
|
|
}
|
|
};
|
|
|
|
template<typename Scalar>
|
|
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
|
|
{
|
|
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
|
|
}
|
|
|
|
template<typename Scalar>
|
|
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
|
|
{
|
|
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
|
|
}
|
|
|
|
/****************************************************************************
|
|
* 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)
|
|
{
|
|
return abs(x) <= abs(y) * prec;
|
|
}
|
|
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
|
|
{
|
|
using std::min;
|
|
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 abs2(x) <= 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;
|
|
}
|
|
};
|
|
|
|
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,
|
|
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,
|
|
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,
|
|
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
|
|
|
|
#endif // EIGEN_MATHFUNCTIONS_H
|