295 lines
11 KiB
C++
295 lines
11 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2006-2008 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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template<typename T> inline typename NumTraits<T>::Real precision();
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template<typename T> inline typename NumTraits<T>::Real machine_epsilon();
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template<typename T> inline T ei_random(T a, T b);
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template<typename T> inline T ei_random();
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template<typename T> inline T ei_random_amplitude()
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{
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if(NumTraits<T>::HasFloatingPoint) return static_cast<T>(1);
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else return static_cast<T>(10);
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}
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template<typename T> inline T ei_hypot(T x, T y)
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{
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T _x = ei_abs(x);
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T _y = ei_abs(y);
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T p = std::max(_x, _y);
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T q = std::min(_x, _y);
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T qp = q/p;
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return p * ei_sqrt(T(1) + qp*qp);
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}
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/**************
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*** int ***
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**************/
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template<> inline int precision<int>() { return 0; }
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template<> inline int machine_epsilon<int>() { return 0; }
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inline int ei_real(int x) { return x; }
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inline int ei_imag(int) { return 0; }
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inline int ei_conj(int x) { return x; }
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inline int ei_abs(int x) { return abs(x); }
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inline int ei_abs2(int x) { return x*x; }
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inline int ei_sqrt(int) { ei_assert(false); return 0; }
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inline int ei_exp(int) { ei_assert(false); return 0; }
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inline int ei_log(int) { ei_assert(false); return 0; }
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inline int ei_sin(int) { ei_assert(false); return 0; }
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inline int ei_cos(int) { ei_assert(false); return 0; }
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#if EIGEN_GNUC_AT_LEAST(4,3)
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inline int ei_pow(int x, int y) { return int(std::pow(x, y)); }
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#else
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inline int ei_pow(int x, int y) { return int(std::pow(double(x), y)); }
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#endif
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template<> inline int ei_random(int a, int b)
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{
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// We can't just do rand()%n as only the high-order bits are really random
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return a + static_cast<int>((b-a+1) * (rand() / (RAND_MAX + 1.0)));
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}
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template<> inline int ei_random()
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{
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return ei_random<int>(-ei_random_amplitude<int>(), ei_random_amplitude<int>());
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}
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inline bool ei_isMuchSmallerThan(int a, int, int = precision<int>())
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{
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return a == 0;
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}
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inline bool ei_isApprox(int a, int b, int = precision<int>())
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{
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return a == b;
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}
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inline bool ei_isApproxOrLessThan(int a, int b, int = precision<int>())
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{
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return a <= b;
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}
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/**************
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*** float ***
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**************/
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template<> inline float precision<float>() { return 1e-5f; }
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template<> inline float machine_epsilon<float>() { return 1.192e-07f; }
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inline float ei_real(float x) { return x; }
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inline float ei_imag(float) { return 0.f; }
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inline float ei_conj(float x) { return x; }
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inline float ei_abs(float x) { return std::abs(x); }
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inline float ei_abs2(float x) { return x*x; }
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inline float ei_sqrt(float x) { return std::sqrt(x); }
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inline float ei_exp(float x) { return std::exp(x); }
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inline float ei_log(float x) { return std::log(x); }
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inline float ei_sin(float x) { return std::sin(x); }
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inline float ei_cos(float x) { return std::cos(x); }
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inline float ei_pow(float x, float y) { return std::pow(x, y); }
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template<> inline float ei_random(float a, float b)
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{
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#ifdef EIGEN_NICE_RANDOM
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int i;
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do { i = ei_random<int>(256*int(a),256*int(b));
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} while(i==0);
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return float(i)/256.f;
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#else
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return a + (b-a) * float(std::rand()) / float(RAND_MAX);
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#endif
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}
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template<> inline float ei_random()
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{
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return ei_random<float>(-ei_random_amplitude<float>(), ei_random_amplitude<float>());
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}
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inline bool ei_isMuchSmallerThan(float a, float b, float prec = precision<float>())
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{
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return ei_abs(a) <= ei_abs(b) * prec;
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}
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inline bool ei_isApprox(float a, float b, float prec = precision<float>())
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{
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return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
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}
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inline bool ei_isApproxOrLessThan(float a, float b, float prec = precision<float>())
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{
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return a <= b || ei_isApprox(a, b, prec);
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}
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/**************
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*** double ***
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**************/
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template<> inline double precision<double>() { return 1e-11; }
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template<> inline double machine_epsilon<double>() { return 2.220e-16; }
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inline double ei_real(double x) { return x; }
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inline double ei_imag(double) { return 0.; }
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inline double ei_conj(double x) { return x; }
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inline double ei_abs(double x) { return std::abs(x); }
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inline double ei_abs2(double x) { return x*x; }
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inline double ei_sqrt(double x) { return std::sqrt(x); }
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inline double ei_exp(double x) { return std::exp(x); }
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inline double ei_log(double x) { return std::log(x); }
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inline double ei_sin(double x) { return std::sin(x); }
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inline double ei_cos(double x) { return std::cos(x); }
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inline double ei_pow(double x, double y) { return std::pow(x, y); }
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template<> inline double ei_random(double a, double b)
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{
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#ifdef EIGEN_NICE_RANDOM
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int i;
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do { i= ei_random<int>(256*int(a),256*int(b));
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} while(i==0);
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return i/256.;
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#else
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return a + (b-a) * std::rand() / RAND_MAX;
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#endif
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}
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template<> inline double ei_random()
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{
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return ei_random<double>(-ei_random_amplitude<double>(), ei_random_amplitude<double>());
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}
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inline bool ei_isMuchSmallerThan(double a, double b, double prec = precision<double>())
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{
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return ei_abs(a) <= ei_abs(b) * prec;
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}
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inline bool ei_isApprox(double a, double b, double prec = precision<double>())
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{
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return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
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}
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inline bool ei_isApproxOrLessThan(double a, double b, double prec = precision<double>())
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{
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return a <= b || ei_isApprox(a, b, prec);
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}
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/*********************
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*** complex<float> ***
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*********************/
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template<> inline float precision<std::complex<float> >() { return precision<float>(); }
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template<> inline float machine_epsilon<std::complex<float> >() { return machine_epsilon<float>(); }
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inline float ei_real(const std::complex<float>& x) { return std::real(x); }
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inline float ei_imag(const std::complex<float>& x) { return std::imag(x); }
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inline std::complex<float> ei_conj(const std::complex<float>& x) { return std::conj(x); }
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inline float ei_abs(const std::complex<float>& x) { return std::abs(x); }
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inline float ei_abs2(const std::complex<float>& x) { return std::norm(x); }
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inline std::complex<float> ei_exp(std::complex<float> x) { return std::exp(x); }
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inline std::complex<float> ei_sin(std::complex<float> x) { return std::sin(x); }
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inline std::complex<float> ei_cos(std::complex<float> x) { return std::cos(x); }
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template<> inline std::complex<float> ei_random()
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{
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return std::complex<float>(ei_random<float>(), ei_random<float>());
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}
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inline bool ei_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
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{
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return ei_abs2(a) <= ei_abs2(b) * prec * prec;
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}
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inline bool ei_isMuchSmallerThan(const std::complex<float>& a, float b, float prec = precision<float>())
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{
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return ei_abs2(a) <= ei_abs2(b) * prec * prec;
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}
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inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
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{
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return ei_isApprox(ei_real(a), ei_real(b), prec)
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&& ei_isApprox(ei_imag(a), ei_imag(b), prec);
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}
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// ei_isApproxOrLessThan wouldn't make sense for complex numbers
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/**********************
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*** complex<double> ***
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**********************/
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template<> inline double precision<std::complex<double> >() { return precision<double>(); }
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template<> inline double machine_epsilon<std::complex<double> >() { return machine_epsilon<double>(); }
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inline double ei_real(const std::complex<double>& x) { return std::real(x); }
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inline double ei_imag(const std::complex<double>& x) { return std::imag(x); }
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inline std::complex<double> ei_conj(const std::complex<double>& x) { return std::conj(x); }
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inline double ei_abs(const std::complex<double>& x) { return std::abs(x); }
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inline double ei_abs2(const std::complex<double>& x) { return std::norm(x); }
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inline std::complex<double> ei_exp(std::complex<double> x) { return std::exp(x); }
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inline std::complex<double> ei_sin(std::complex<double> x) { return std::sin(x); }
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inline std::complex<double> ei_cos(std::complex<double> x) { return std::cos(x); }
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template<> inline std::complex<double> ei_random()
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{
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return std::complex<double>(ei_random<double>(), ei_random<double>());
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}
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inline bool ei_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
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{
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return ei_abs2(a) <= ei_abs2(b) * prec * prec;
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}
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inline bool ei_isMuchSmallerThan(const std::complex<double>& a, double b, double prec = precision<double>())
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{
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return ei_abs2(a) <= ei_abs2(b) * prec * prec;
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}
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inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
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{
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return ei_isApprox(ei_real(a), ei_real(b), prec)
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&& ei_isApprox(ei_imag(a), ei_imag(b), prec);
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}
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// ei_isApproxOrLessThan wouldn't make sense for complex numbers
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/******************
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*** long double ***
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******************/
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template<> inline long double precision<long double>() { return precision<double>(); }
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template<> inline long double machine_epsilon<long double>() { return 1.084e-19l; }
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inline long double ei_real(long double x) { return x; }
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inline long double ei_imag(long double) { return 0.; }
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inline long double ei_conj(long double x) { return x; }
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inline long double ei_abs(long double x) { return std::abs(x); }
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inline long double ei_abs2(long double x) { return x*x; }
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inline long double ei_sqrt(long double x) { return std::sqrt(x); }
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inline long double ei_exp(long double x) { return std::exp(x); }
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inline long double ei_log(long double x) { return std::log(x); }
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inline long double ei_sin(long double x) { return std::sin(x); }
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inline long double ei_cos(long double x) { return std::cos(x); }
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inline long double ei_pow(long double x, long double y) { return std::pow(x, y); }
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template<> inline long double ei_random(long double a, long double b)
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{
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return ei_random<double>(static_cast<double>(a),static_cast<double>(b));
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}
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template<> inline long double ei_random()
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{
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return ei_random<double>(-ei_random_amplitude<double>(), ei_random_amplitude<double>());
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}
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inline bool ei_isMuchSmallerThan(long double a, long double b, long double prec = precision<long double>())
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{
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return ei_abs(a) <= ei_abs(b) * prec;
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}
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inline bool ei_isApprox(long double a, long double b, long double prec = precision<long double>())
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{
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return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
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}
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inline bool ei_isApproxOrLessThan(long double a, long double b, long double prec = precision<long double>())
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{
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return a <= b || ei_isApprox(a, b, prec);
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}
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#endif // EIGEN_MATHFUNCTIONS_H
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