| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /** | ||
| 2 | * \file | ||
| 3 | * \brief Low level math functions and compatibility wrappers | ||
| 4 | *//* | ||
| 5 | * Authors: | ||
| 6 | * Johan Engelen <goejendaagh@zonnet.nl> | ||
| 7 | * Michael G. Sloan <mgsloan@gmail.com> | ||
| 8 | * Krzysztof Kosiński <tweenk.pl@gmail.com> | ||
| 9 | * Copyright 2006-2009 Authors | ||
| 10 | * | ||
| 11 | * This library is free software; you can redistribute it and/or | ||
| 12 | * modify it either under the terms of the GNU Lesser General Public | ||
| 13 | * License version 2.1 as published by the Free Software Foundation | ||
| 14 | * (the "LGPL") or, at your option, under the terms of the Mozilla | ||
| 15 | * Public License Version 1.1 (the "MPL"). If you do not alter this | ||
| 16 | * notice, a recipient may use your version of this file under either | ||
| 17 | * the MPL or the LGPL. | ||
| 18 | * | ||
| 19 | * You should have received a copy of the LGPL along with this library | ||
| 20 | * in the file COPYING-LGPL-2.1; if not, write to the Free Software | ||
| 21 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | ||
| 22 | * You should have received a copy of the MPL along with this library | ||
| 23 | * in the file COPYING-MPL-1.1 | ||
| 24 | * | ||
| 25 | * The contents of this file are subject to the Mozilla Public License | ||
| 26 | * Version 1.1 (the "License"); you may not use this file except in | ||
| 27 | * compliance with the License. You may obtain a copy of the License at | ||
| 28 | * http://www.mozilla.org/MPL/ | ||
| 29 | * | ||
| 30 | * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY | ||
| 31 | * OF ANY KIND, either express or implied. See the LGPL or the MPL for | ||
| 32 | * the specific language governing rights and limitations. | ||
| 33 | * | ||
| 34 | */ | ||
| 35 | |||
| 36 | #ifndef LIB2GEOM_SEEN_MATH_UTILS_H | ||
| 37 | #define LIB2GEOM_SEEN_MATH_UTILS_H | ||
| 38 | |||
| 39 | #include <math.h> // sincos is usually only available in math.h | ||
| 40 | #include <array> | ||
| 41 | #include <cmath> | ||
| 42 | #include <utility> // for std::pair | ||
| 43 | #include <boost/math/special_functions/fpclassify.hpp> | ||
| 44 | |||
| 45 | namespace Geom { | ||
| 46 | |||
| 47 | /** @brief Sign function - indicates the sign of a numeric type. | ||
| 48 | * Mathsy people will know this is basically the derivative of abs, except for the fact | ||
| 49 | * that it is defined on 0. | ||
| 50 | * @return -1 when x is negative, 1 when positive, and 0 if equal to 0. */ | ||
| 51 | 4243330 | template <class T> inline int sgn(const T& x) { | |
| 52 |
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4243330 | return (x < 0 ? -1 : (x > 0 ? 1 : 0) ); |
| 53 | // can we 'optimize' this with: | ||
| 54 | // return ( (T(0) < x) - (x < T(0)) ); | ||
| 55 | } | ||
| 56 | |||
| 57 | 2461 | template <class T> inline T sqr(const T& x) {return x * x;} | |
| 58 | template <class T> inline T cube(const T& x) {return x * x * x;} | ||
| 59 | |||
| 60 | /** Between function - returns true if a number x is within a range: (min < x) && (max > x). | ||
| 61 | * The values delimiting the range and the number must have the same type. | ||
| 62 | */ | ||
| 63 | template <class T> inline const T& between (const T& min, const T& max, const T& x) | ||
| 64 | { return (min < x) && (max > x); } | ||
| 65 | |||
| 66 | /** @brief Returns @a x rounded to the nearest multiple of \f$10^{p}\f$. | ||
| 67 | |||
| 68 | Implemented in terms of round, i.e. we make no guarantees as to what happens if x is | ||
| 69 | half way between two rounded numbers. | ||
| 70 | |||
| 71 | Note: places is the number of decimal places without using scientific (e) notation, not the | ||
| 72 | number of significant figures. This function may not be suitable for values of x whose | ||
| 73 | magnitude is so far from 1 that one would want to use scientific (e) notation. | ||
| 74 | |||
| 75 | places may be negative: e.g. places = -2 means rounding to a multiple of .01 | ||
| 76 | **/ | ||
| 77 | inline double decimal_round(double x, int p) { | ||
| 78 | //TODO: possibly implement with modulus instead? | ||
| 79 | double const multiplier = ::pow(10.0, p); | ||
| 80 | return ::round( x * multiplier ) / multiplier; | ||
| 81 | } | ||
| 82 | |||
| 83 | /** @brief Simultaneously compute a sine and a cosine of the same angle. | ||
| 84 | * This function can be up to 2 times faster than separate computation, depending | ||
| 85 | * on the platform. It uses the standard library function sincos() if available. | ||
| 86 | * @param angle Angle | ||
| 87 | * @param sin_ Variable that will store the sine | ||
| 88 | * @param cos_ Variable that will store the cosine */ | ||
| 89 | 422624 | inline void sincos(double angle, double &sin_, double &cos_) { | |
| 90 | #ifdef HAVE_SINCOS | ||
| 91 | 422624 | ::sincos(angle, &sin_, &cos_); | |
| 92 | #else | ||
| 93 | sin_ = ::sin(angle); | ||
| 94 | cos_ = ::cos(angle); | ||
| 95 | #endif | ||
| 96 | 422624 | } | |
| 97 | |||
| 98 | /** @brief Scale the doubles in the passed array to make them "reasonably large". | ||
| 99 | * | ||
| 100 | * All doubles in the passed array will get scaled by the same power of 2 (which is | ||
| 101 | * a lossless operation) in such a way that their geometric average gets closer to 1. | ||
| 102 | * | ||
| 103 | * @tparam N The size of the passed array. | ||
| 104 | * @param[in,out] values The doubles to be rescaled in place. | ||
| 105 | * @return The exponent in the power of two by which the doubles got scaled. | ||
| 106 | */ | ||
| 107 | template <size_t N> | ||
| 108 | 40166 | inline int rescale_homogenous(std::array<double, N> &values) | |
| 109 | { | ||
| 110 | if constexpr (N == 0) { | ||
| 111 | return 0; | ||
| 112 | } | ||
| 113 | 40166 | std::array<int, N> exponents; | |
| 114 | 40166 | std::array<double, N> mantissas; | |
| 115 | 40166 | int average = 0; | |
| 116 | 220940 | for (size_t i = 0; i < N; i++) { | |
| 117 | 180774 | mantissas[i] = std::frexp(values[i], &exponents[i]); | |
| 118 | 180774 | average += exponents[i]; | |
| 119 | } | ||
| 120 | 40166 | average /= (int)N; | |
| 121 | 220940 | for (size_t i = 0; i < N; i++) { | |
| 122 | 180774 | values[i] = std::ldexp(mantissas[i], exponents[i] - average); | |
| 123 | } | ||
| 124 | 40166 | return -average; | |
| 125 | } | ||
| 126 | |||
| 127 | } // end namespace Geom | ||
| 128 | |||
| 129 | #endif // LIB2GEOM_SEEN_MATH_UTILS_H | ||
| 130 | |||
| 131 | /* | ||
| 132 | Local Variables: | ||
| 133 | mode:c++ | ||
| 134 | c-file-style:"stroustrup" | ||
| 135 | c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) | ||
| 136 | indent-tabs-mode:nil | ||
| 137 | fill-column:99 | ||
| 138 | End: | ||
| 139 | */ | ||
| 140 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : | ||
| 141 |