[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_MATHFUNCTIONS_H
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| 11 | #define EIGEN_MATHFUNCTIONS_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | namespace internal {
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| 16 |
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| 17 | /** \internal \struct global_math_functions_filtering_base
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| 18 | *
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| 19 | * What it does:
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| 20 | * Defines a typedef 'type' as follows:
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| 21 | * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
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| 22 | * global_math_functions_filtering_base<T>::type is a typedef for it.
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| 23 | * - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
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| 24 | *
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| 25 | * How it's used:
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| 26 | * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
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| 27 | * 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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| 28 | * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
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| 29 | * So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
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| 30 | * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
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| 31 | *
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| 32 | * How it's implemented:
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| 33 | * 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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| 34 | * the typename dummy by an integer template parameter, it doesn't work anymore!
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| 35 | */
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| 36 |
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| 37 | template<typename T, typename dummy = void>
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| 38 | struct global_math_functions_filtering_base
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| 39 | {
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| 40 | typedef T type;
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| 41 | };
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| 42 |
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| 43 | template<typename T> struct always_void { typedef void type; };
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| 44 |
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| 45 | template<typename T>
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| 46 | struct global_math_functions_filtering_base
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| 47 | <T,
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| 48 | typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
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| 49 | >
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| 50 | {
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| 51 | typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
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| 52 | };
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| 53 |
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| 54 | #define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
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| 55 | #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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| 56 |
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| 57 | /****************************************************************************
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| 58 | * Implementation of real *
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| 59 | ****************************************************************************/
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| 60 |
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| 61 | template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
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| 62 | struct real_default_impl
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| 63 | {
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| 64 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 65 | static inline RealScalar run(const Scalar& x)
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| 66 | {
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| 67 | return x;
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| 68 | }
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| 69 | };
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| 70 |
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| 71 | template<typename Scalar>
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| 72 | struct real_default_impl<Scalar,true>
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| 73 | {
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| 74 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 75 | static inline RealScalar run(const Scalar& x)
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| 76 | {
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| 77 | using std::real;
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| 78 | return real(x);
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| 79 | }
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| 80 | };
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| 81 |
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| 82 | template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
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| 83 |
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| 84 | template<typename Scalar>
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| 85 | struct real_retval
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| 86 | {
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| 87 | typedef typename NumTraits<Scalar>::Real type;
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| 88 | };
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| 89 |
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| 90 |
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| 91 | /****************************************************************************
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| 92 | * Implementation of imag *
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| 93 | ****************************************************************************/
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| 94 |
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| 95 | template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
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| 96 | struct imag_default_impl
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| 97 | {
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| 98 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 99 | static inline RealScalar run(const Scalar&)
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| 100 | {
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| 101 | return RealScalar(0);
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| 102 | }
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| 103 | };
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| 104 |
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| 105 | template<typename Scalar>
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| 106 | struct imag_default_impl<Scalar,true>
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| 107 | {
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| 108 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 109 | static inline RealScalar run(const Scalar& x)
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| 110 | {
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| 111 | using std::imag;
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| 112 | return imag(x);
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| 113 | }
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| 114 | };
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| 115 |
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| 116 | template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
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| 117 |
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| 118 | template<typename Scalar>
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| 119 | struct imag_retval
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| 120 | {
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| 121 | typedef typename NumTraits<Scalar>::Real type;
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| 122 | };
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| 123 |
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| 124 | /****************************************************************************
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| 125 | * Implementation of real_ref *
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| 126 | ****************************************************************************/
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| 127 |
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| 128 | template<typename Scalar>
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| 129 | struct real_ref_impl
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| 130 | {
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| 131 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 132 | static inline RealScalar& run(Scalar& x)
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| 133 | {
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| 134 | return reinterpret_cast<RealScalar*>(&x)[0];
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| 135 | }
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| 136 | static inline const RealScalar& run(const Scalar& x)
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| 137 | {
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| 138 | return reinterpret_cast<const RealScalar*>(&x)[0];
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| 139 | }
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| 140 | };
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| 141 |
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| 142 | template<typename Scalar>
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| 143 | struct real_ref_retval
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| 144 | {
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| 145 | typedef typename NumTraits<Scalar>::Real & type;
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| 146 | };
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| 147 |
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| 148 | /****************************************************************************
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| 149 | * Implementation of imag_ref *
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| 150 | ****************************************************************************/
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| 151 |
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| 152 | template<typename Scalar, bool IsComplex>
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| 153 | struct imag_ref_default_impl
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| 154 | {
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| 155 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 156 | static inline RealScalar& run(Scalar& x)
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| 157 | {
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| 158 | return reinterpret_cast<RealScalar*>(&x)[1];
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| 159 | }
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| 160 | static inline const RealScalar& run(const Scalar& x)
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| 161 | {
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| 162 | return reinterpret_cast<RealScalar*>(&x)[1];
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| 163 | }
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| 164 | };
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| 165 |
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| 166 | template<typename Scalar>
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| 167 | struct imag_ref_default_impl<Scalar, false>
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| 168 | {
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| 169 | static inline Scalar run(Scalar&)
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| 170 | {
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| 171 | return Scalar(0);
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| 172 | }
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| 173 | static inline const Scalar run(const Scalar&)
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| 174 | {
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| 175 | return Scalar(0);
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| 176 | }
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| 177 | };
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| 178 |
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| 179 | template<typename Scalar>
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| 180 | struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
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| 181 |
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| 182 | template<typename Scalar>
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| 183 | struct imag_ref_retval
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| 184 | {
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| 185 | typedef typename NumTraits<Scalar>::Real & type;
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| 186 | };
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| 187 |
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| 188 | /****************************************************************************
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| 189 | * Implementation of conj *
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| 190 | ****************************************************************************/
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| 191 |
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| 192 | template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
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| 193 | struct conj_impl
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| 194 | {
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| 195 | static inline Scalar run(const Scalar& x)
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| 196 | {
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| 197 | return x;
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| 198 | }
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| 199 | };
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| 200 |
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| 201 | template<typename Scalar>
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| 202 | struct conj_impl<Scalar,true>
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| 203 | {
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| 204 | static inline Scalar run(const Scalar& x)
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| 205 | {
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| 206 | using std::conj;
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| 207 | return conj(x);
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| 208 | }
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| 209 | };
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| 210 |
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| 211 | template<typename Scalar>
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| 212 | struct conj_retval
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| 213 | {
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| 214 | typedef Scalar type;
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| 215 | };
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| 216 |
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| 217 | /****************************************************************************
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| 218 | * Implementation of abs2 *
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| 219 | ****************************************************************************/
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| 220 |
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| 221 | template<typename Scalar,bool IsComplex>
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| 222 | struct abs2_impl_default
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| 223 | {
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| 224 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 225 | static inline RealScalar run(const Scalar& x)
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| 226 | {
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| 227 | return x*x;
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| 228 | }
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| 229 | };
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| 230 |
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| 231 | template<typename Scalar>
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| 232 | struct abs2_impl_default<Scalar, true> // IsComplex
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| 233 | {
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| 234 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 235 | static inline RealScalar run(const Scalar& x)
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| 236 | {
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| 237 | return real(x)*real(x) + imag(x)*imag(x);
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| 238 | }
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| 239 | };
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| 240 |
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| 241 | template<typename Scalar>
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| 242 | struct abs2_impl
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| 243 | {
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| 244 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 245 | static inline RealScalar run(const Scalar& x)
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| 246 | {
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| 247 | return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);
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| 248 | }
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| 249 | };
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| 250 |
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| 251 | template<typename Scalar>
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| 252 | struct abs2_retval
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| 253 | {
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| 254 | typedef typename NumTraits<Scalar>::Real type;
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| 255 | };
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| 256 |
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| 257 | /****************************************************************************
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| 258 | * Implementation of norm1 *
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| 259 | ****************************************************************************/
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| 260 |
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| 261 | template<typename Scalar, bool IsComplex>
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| 262 | struct norm1_default_impl
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| 263 | {
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| 264 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 265 | static inline RealScalar run(const Scalar& x)
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| 266 | {
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| 267 | using std::abs;
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| 268 | return abs(real(x)) + abs(imag(x));
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| 269 | }
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| 270 | };
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| 271 |
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| 272 | template<typename Scalar>
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| 273 | struct norm1_default_impl<Scalar, false>
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| 274 | {
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| 275 | static inline Scalar run(const Scalar& x)
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| 276 | {
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| 277 | using std::abs;
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| 278 | return abs(x);
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| 279 | }
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| 280 | };
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| 281 |
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| 282 | template<typename Scalar>
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| 283 | struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
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| 284 |
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| 285 | template<typename Scalar>
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| 286 | struct norm1_retval
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| 287 | {
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| 288 | typedef typename NumTraits<Scalar>::Real type;
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| 289 | };
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| 290 |
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| 291 | /****************************************************************************
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| 292 | * Implementation of hypot *
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| 293 | ****************************************************************************/
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| 294 |
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| 295 | template<typename Scalar>
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| 296 | struct hypot_impl
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| 297 | {
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| 298 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 299 | static inline RealScalar run(const Scalar& x, const Scalar& y)
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| 300 | {
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| 301 | using std::max;
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| 302 | using std::min;
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| 303 | using std::abs;
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| 304 | using std::sqrt;
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| 305 | RealScalar _x = abs(x);
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| 306 | RealScalar _y = abs(y);
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| 307 | RealScalar p = (max)(_x, _y);
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| 308 | if(p==RealScalar(0)) return RealScalar(0);
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| 309 | RealScalar q = (min)(_x, _y);
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| 310 | RealScalar qp = q/p;
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| 311 | return p * sqrt(RealScalar(1) + qp*qp);
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| 312 | }
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| 313 | };
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| 314 |
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| 315 | template<typename Scalar>
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| 316 | struct hypot_retval
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| 317 | {
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| 318 | typedef typename NumTraits<Scalar>::Real type;
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| 319 | };
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| 320 |
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| 321 | /****************************************************************************
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| 322 | * Implementation of cast *
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| 323 | ****************************************************************************/
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| 324 |
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| 325 | template<typename OldType, typename NewType>
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| 326 | struct cast_impl
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| 327 | {
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| 328 | static inline NewType run(const OldType& x)
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| 329 | {
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| 330 | return static_cast<NewType>(x);
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| 331 | }
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| 332 | };
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| 333 |
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| 334 | // here, for once, we're plainly returning NewType: we don't want cast to do weird things.
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| 335 |
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| 336 | template<typename OldType, typename NewType>
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| 337 | inline NewType cast(const OldType& x)
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| 338 | {
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| 339 | return cast_impl<OldType, NewType>::run(x);
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| 340 | }
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| 341 |
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| 342 | /****************************************************************************
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| 343 | * Implementation of atanh2 *
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| 344 | ****************************************************************************/
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| 345 |
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| 346 | template<typename Scalar, bool IsInteger>
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| 347 | struct atanh2_default_impl
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| 348 | {
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| 349 | typedef Scalar retval;
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| 350 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 351 | static inline Scalar run(const Scalar& x, const Scalar& y)
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| 352 | {
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| 353 | using std::abs;
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| 354 | using std::log;
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| 355 | using std::sqrt;
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| 356 | Scalar z = x / y;
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| 357 | if (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon()))
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| 358 | return RealScalar(0.5) * log((y + x) / (y - x));
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| 359 | else
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| 360 | return z + z*z*z / RealScalar(3);
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| 361 | }
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| 362 | };
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| 363 |
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| 364 | template<typename Scalar>
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| 365 | struct atanh2_default_impl<Scalar, true>
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| 366 | {
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| 367 | static inline Scalar run(const Scalar&, const Scalar&)
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| 368 | {
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| 369 | EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
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| 370 | return Scalar(0);
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| 371 | }
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| 372 | };
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| 373 |
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| 374 | template<typename Scalar>
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| 375 | struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
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| 376 |
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| 377 | template<typename Scalar>
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| 378 | struct atanh2_retval
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| 379 | {
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| 380 | typedef Scalar type;
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| 381 | };
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| 382 |
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| 383 | /****************************************************************************
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| 384 | * Implementation of pow *
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| 385 | ****************************************************************************/
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| 386 |
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| 387 | template<typename Scalar, bool IsInteger>
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| 388 | struct pow_default_impl
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| 389 | {
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| 390 | typedef Scalar retval;
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| 391 | static inline Scalar run(const Scalar& x, const Scalar& y)
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| 392 | {
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| 393 | using std::pow;
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| 394 | return pow(x, y);
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| 395 | }
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| 396 | };
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| 397 |
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| 398 | template<typename Scalar>
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| 399 | struct pow_default_impl<Scalar, true>
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| 400 | {
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| 401 | static inline Scalar run(Scalar x, Scalar y)
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| 402 | {
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| 403 | Scalar res(1);
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| 404 | eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
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| 405 | if(y & 1) res *= x;
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| 406 | y >>= 1;
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| 407 | while(y)
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| 408 | {
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| 409 | x *= x;
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| 410 | if(y&1) res *= x;
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| 411 | y >>= 1;
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| 412 | }
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| 413 | return res;
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| 414 | }
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| 415 | };
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| 416 |
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| 417 | template<typename Scalar>
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| 418 | struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
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| 419 |
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| 420 | template<typename Scalar>
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| 421 | struct pow_retval
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| 422 | {
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| 423 | typedef Scalar type;
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| 424 | };
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| 425 |
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| 426 | /****************************************************************************
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| 427 | * Implementation of random *
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| 428 | ****************************************************************************/
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| 429 |
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| 430 | template<typename Scalar,
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| 431 | bool IsComplex,
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| 432 | bool IsInteger>
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| 433 | struct random_default_impl {};
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| 434 |
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| 435 | template<typename Scalar>
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| 436 | struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
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| 437 |
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| 438 | template<typename Scalar>
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| 439 | struct random_retval
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| 440 | {
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| 441 | typedef Scalar type;
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| 442 | };
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| 443 |
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| 444 | template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
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| 445 | template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
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| 446 |
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| 447 | template<typename Scalar>
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| 448 | struct random_default_impl<Scalar, false, false>
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| 449 | {
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| 450 | static inline Scalar run(const Scalar& x, const Scalar& y)
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| 451 | {
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| 452 | return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
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| 453 | }
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| 454 | static inline Scalar run()
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| 455 | {
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| 456 | return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
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| 457 | }
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| 458 | };
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| 459 |
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| 460 | enum {
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| 461 | floor_log2_terminate,
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| 462 | floor_log2_move_up,
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| 463 | floor_log2_move_down,
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| 464 | floor_log2_bogus
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| 465 | };
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| 466 |
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| 467 | template<unsigned int n, int lower, int upper> struct floor_log2_selector
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| 468 | {
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| 469 | enum { middle = (lower + upper) / 2,
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| 470 | value = (upper <= lower + 1) ? int(floor_log2_terminate)
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| 471 | : (n < (1 << middle)) ? int(floor_log2_move_down)
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| 472 | : (n==0) ? int(floor_log2_bogus)
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| 473 | : int(floor_log2_move_up)
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| 474 | };
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| 475 | };
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| 476 |
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| 477 | template<unsigned int n,
|
---|
| 478 | int lower = 0,
|
---|
| 479 | int upper = sizeof(unsigned int) * CHAR_BIT - 1,
|
---|
| 480 | int selector = floor_log2_selector<n, lower, upper>::value>
|
---|
| 481 | struct floor_log2 {};
|
---|
| 482 |
|
---|
| 483 | template<unsigned int n, int lower, int upper>
|
---|
| 484 | struct floor_log2<n, lower, upper, floor_log2_move_down>
|
---|
| 485 | {
|
---|
| 486 | enum { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value };
|
---|
| 487 | };
|
---|
| 488 |
|
---|
| 489 | template<unsigned int n, int lower, int upper>
|
---|
| 490 | struct floor_log2<n, lower, upper, floor_log2_move_up>
|
---|
| 491 | {
|
---|
| 492 | enum { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value };
|
---|
| 493 | };
|
---|
| 494 |
|
---|
| 495 | template<unsigned int n, int lower, int upper>
|
---|
| 496 | struct floor_log2<n, lower, upper, floor_log2_terminate>
|
---|
| 497 | {
|
---|
| 498 | enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
|
---|
| 499 | };
|
---|
| 500 |
|
---|
| 501 | template<unsigned int n, int lower, int upper>
|
---|
| 502 | struct floor_log2<n, lower, upper, floor_log2_bogus>
|
---|
| 503 | {
|
---|
| 504 | // no value, error at compile time
|
---|
| 505 | };
|
---|
| 506 |
|
---|
| 507 | template<typename Scalar>
|
---|
| 508 | struct random_default_impl<Scalar, false, true>
|
---|
| 509 | {
|
---|
| 510 | typedef typename NumTraits<Scalar>::NonInteger NonInteger;
|
---|
| 511 |
|
---|
| 512 | static inline Scalar run(const Scalar& x, const Scalar& y)
|
---|
| 513 | {
|
---|
| 514 | return x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1)));
|
---|
| 515 | }
|
---|
| 516 |
|
---|
| 517 | static inline Scalar run()
|
---|
| 518 | {
|
---|
| 519 | #ifdef EIGEN_MAKING_DOCS
|
---|
| 520 | return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
|
---|
| 521 | #else
|
---|
| 522 | enum { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value,
|
---|
| 523 | scalar_bits = sizeof(Scalar) * CHAR_BIT,
|
---|
| 524 | shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
|
---|
| 525 | offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
|
---|
| 526 | };
|
---|
| 527 | return Scalar((std::rand() >> shift) - offset);
|
---|
| 528 | #endif
|
---|
| 529 | }
|
---|
| 530 | };
|
---|
| 531 |
|
---|
| 532 | template<typename Scalar>
|
---|
| 533 | struct random_default_impl<Scalar, true, false>
|
---|
| 534 | {
|
---|
| 535 | static inline Scalar run(const Scalar& x, const Scalar& y)
|
---|
| 536 | {
|
---|
| 537 | return Scalar(random(real(x), real(y)),
|
---|
| 538 | random(imag(x), imag(y)));
|
---|
| 539 | }
|
---|
| 540 | static inline Scalar run()
|
---|
| 541 | {
|
---|
| 542 | typedef typename NumTraits<Scalar>::Real RealScalar;
|
---|
| 543 | return Scalar(random<RealScalar>(), random<RealScalar>());
|
---|
| 544 | }
|
---|
| 545 | };
|
---|
| 546 |
|
---|
| 547 | template<typename Scalar>
|
---|
| 548 | inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
|
---|
| 549 | {
|
---|
| 550 | return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
|
---|
| 551 | }
|
---|
| 552 |
|
---|
| 553 | template<typename Scalar>
|
---|
| 554 | inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
|
---|
| 555 | {
|
---|
| 556 | return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
|
---|
| 557 | }
|
---|
| 558 |
|
---|
| 559 | } // end namespace internal
|
---|
| 560 |
|
---|
| 561 | /****************************************************************************
|
---|
| 562 | * Generic math function *
|
---|
| 563 | ****************************************************************************/
|
---|
| 564 |
|
---|
| 565 | namespace numext {
|
---|
| 566 |
|
---|
| 567 | template<typename Scalar>
|
---|
| 568 | inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
|
---|
| 569 | {
|
---|
| 570 | return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
|
---|
| 571 | }
|
---|
| 572 |
|
---|
| 573 | template<typename Scalar>
|
---|
| 574 | inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
|
---|
| 575 | {
|
---|
| 576 | return internal::real_ref_impl<Scalar>::run(x);
|
---|
| 577 | }
|
---|
| 578 |
|
---|
| 579 | template<typename Scalar>
|
---|
| 580 | inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
|
---|
| 581 | {
|
---|
| 582 | return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
|
---|
| 583 | }
|
---|
| 584 |
|
---|
| 585 | template<typename Scalar>
|
---|
| 586 | inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
|
---|
| 587 | {
|
---|
| 588 | return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
|
---|
| 589 | }
|
---|
| 590 |
|
---|
| 591 | template<typename Scalar>
|
---|
| 592 | inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
|
---|
| 593 | {
|
---|
| 594 | return internal::imag_ref_impl<Scalar>::run(x);
|
---|
| 595 | }
|
---|
| 596 |
|
---|
| 597 | template<typename Scalar>
|
---|
| 598 | inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
|
---|
| 599 | {
|
---|
| 600 | return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
|
---|
| 601 | }
|
---|
| 602 |
|
---|
| 603 | template<typename Scalar>
|
---|
| 604 | inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
|
---|
| 605 | {
|
---|
| 606 | return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
|
---|
| 607 | }
|
---|
| 608 |
|
---|
| 609 | template<typename Scalar>
|
---|
| 610 | inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
|
---|
| 611 | {
|
---|
| 612 | return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
|
---|
| 613 | }
|
---|
| 614 |
|
---|
| 615 | template<typename Scalar>
|
---|
| 616 | inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
|
---|
| 617 | {
|
---|
| 618 | return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
|
---|
| 619 | }
|
---|
| 620 |
|
---|
| 621 | template<typename Scalar>
|
---|
| 622 | inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
|
---|
| 623 | {
|
---|
| 624 | return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
|
---|
| 625 | }
|
---|
| 626 |
|
---|
| 627 | template<typename Scalar>
|
---|
| 628 | inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)
|
---|
| 629 | {
|
---|
| 630 | return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);
|
---|
| 631 | }
|
---|
| 632 |
|
---|
| 633 | template<typename Scalar>
|
---|
| 634 | inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
|
---|
| 635 | {
|
---|
| 636 | return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
|
---|
| 637 | }
|
---|
| 638 |
|
---|
| 639 | // std::isfinite is non standard, so let's define our own version,
|
---|
| 640 | // even though it is not very efficient.
|
---|
| 641 | template<typename T> bool (isfinite)(const T& x)
|
---|
| 642 | {
|
---|
| 643 | return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
|
---|
| 644 | }
|
---|
| 645 |
|
---|
| 646 | } // end namespace numext
|
---|
| 647 |
|
---|
| 648 | namespace internal {
|
---|
| 649 |
|
---|
| 650 | /****************************************************************************
|
---|
| 651 | * Implementation of fuzzy comparisons *
|
---|
| 652 | ****************************************************************************/
|
---|
| 653 |
|
---|
| 654 | template<typename Scalar,
|
---|
| 655 | bool IsComplex,
|
---|
| 656 | bool IsInteger>
|
---|
| 657 | struct scalar_fuzzy_default_impl {};
|
---|
| 658 |
|
---|
| 659 | template<typename Scalar>
|
---|
| 660 | struct scalar_fuzzy_default_impl<Scalar, false, false>
|
---|
| 661 | {
|
---|
| 662 | typedef typename NumTraits<Scalar>::Real RealScalar;
|
---|
| 663 | template<typename OtherScalar>
|
---|
| 664 | static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
|
---|
| 665 | {
|
---|
| 666 | using std::abs;
|
---|
| 667 | return abs(x) <= abs(y) * prec;
|
---|
| 668 | }
|
---|
| 669 | static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
|
---|
| 670 | {
|
---|
| 671 | using std::min;
|
---|
| 672 | using std::abs;
|
---|
| 673 | return abs(x - y) <= (min)(abs(x), abs(y)) * prec;
|
---|
| 674 | }
|
---|
| 675 | static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
|
---|
| 676 | {
|
---|
| 677 | return x <= y || isApprox(x, y, prec);
|
---|
| 678 | }
|
---|
| 679 | };
|
---|
| 680 |
|
---|
| 681 | template<typename Scalar>
|
---|
| 682 | struct scalar_fuzzy_default_impl<Scalar, false, true>
|
---|
| 683 | {
|
---|
| 684 | typedef typename NumTraits<Scalar>::Real RealScalar;
|
---|
| 685 | template<typename OtherScalar>
|
---|
| 686 | static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
|
---|
| 687 | {
|
---|
| 688 | return x == Scalar(0);
|
---|
| 689 | }
|
---|
| 690 | static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
|
---|
| 691 | {
|
---|
| 692 | return x == y;
|
---|
| 693 | }
|
---|
| 694 | static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
|
---|
| 695 | {
|
---|
| 696 | return x <= y;
|
---|
| 697 | }
|
---|
| 698 | };
|
---|
| 699 |
|
---|
| 700 | template<typename Scalar>
|
---|
| 701 | struct scalar_fuzzy_default_impl<Scalar, true, false>
|
---|
| 702 | {
|
---|
| 703 | typedef typename NumTraits<Scalar>::Real RealScalar;
|
---|
| 704 | template<typename OtherScalar>
|
---|
| 705 | static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
|
---|
| 706 | {
|
---|
| 707 | return numext::abs2(x) <= numext::abs2(y) * prec * prec;
|
---|
| 708 | }
|
---|
| 709 | static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
|
---|
| 710 | {
|
---|
| 711 | using std::min;
|
---|
| 712 | return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec;
|
---|
| 713 | }
|
---|
| 714 | };
|
---|
| 715 |
|
---|
| 716 | template<typename Scalar>
|
---|
| 717 | struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
|
---|
| 718 |
|
---|
| 719 | template<typename Scalar, typename OtherScalar>
|
---|
| 720 | inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
|
---|
| 721 | const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
|
---|
| 722 | {
|
---|
| 723 | return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
|
---|
| 724 | }
|
---|
| 725 |
|
---|
| 726 | template<typename Scalar>
|
---|
| 727 | inline bool isApprox(const Scalar& x, const Scalar& y,
|
---|
| 728 | const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
|
---|
| 729 | {
|
---|
| 730 | return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
|
---|
| 731 | }
|
---|
| 732 |
|
---|
| 733 | template<typename Scalar>
|
---|
| 734 | inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
|
---|
| 735 | const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
|
---|
| 736 | {
|
---|
| 737 | return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
|
---|
| 738 | }
|
---|
| 739 |
|
---|
| 740 | /******************************************
|
---|
| 741 | *** The special case of the bool type ***
|
---|
| 742 | ******************************************/
|
---|
| 743 |
|
---|
| 744 | template<> struct random_impl<bool>
|
---|
| 745 | {
|
---|
| 746 | static inline bool run()
|
---|
| 747 | {
|
---|
| 748 | return random<int>(0,1)==0 ? false : true;
|
---|
| 749 | }
|
---|
| 750 | };
|
---|
| 751 |
|
---|
| 752 | template<> struct scalar_fuzzy_impl<bool>
|
---|
| 753 | {
|
---|
| 754 | typedef bool RealScalar;
|
---|
| 755 |
|
---|
| 756 | template<typename OtherScalar>
|
---|
| 757 | static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
|
---|
| 758 | {
|
---|
| 759 | return !x;
|
---|
| 760 | }
|
---|
| 761 |
|
---|
| 762 | static inline bool isApprox(bool x, bool y, bool)
|
---|
| 763 | {
|
---|
| 764 | return x == y;
|
---|
| 765 | }
|
---|
| 766 |
|
---|
| 767 | static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
|
---|
| 768 | {
|
---|
| 769 | return (!x) || y;
|
---|
| 770 | }
|
---|
| 771 |
|
---|
| 772 | };
|
---|
| 773 |
|
---|
| 774 |
|
---|
| 775 | } // end namespace internal
|
---|
| 776 |
|
---|
| 777 | } // end namespace Eigen
|
---|
| 778 |
|
---|
| 779 | #endif // EIGEN_MATHFUNCTIONS_H
|
---|