approx_math.h 2.34 KB
 Matthieu Schaller committed Feb 09, 2016 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ``````/******************************************************************************* * This file is part of SWIFT. * Copyright (c) 2016 Matthieu Schaller matthieu.schaller@durham.ac.uk) * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as published * by the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU Lesser General Public License * along with this program. If not, see . * ******************************************************************************/ #ifndef SWIFT_APPROX_MATH_H #define SWIFT_APPROX_MATH_H `````` Matthieu Schaller committed Jun 15, 2016 22 23 ``````#include "inline.h" `````` Matthieu Schaller committed Feb 09, 2016 24 25 26 ``````/** * @brief Approximate version of expf(x) using a 4th order Taylor expansion * `````` Matthieu Schaller committed Jul 28, 2016 27 28 29 30 31 `````` * The absolute error is smaller than 3 * 10^-6 for -0.2 < x < 0.2. * The absolute error is smaller than 2 * 10^-7 for -0.1 < x < 0.1. * The relative error is smaller than 1 * 10^-6 for -0.2 < x < 0.2. * The relative error is smaller than 4 * 10^-8 for -0.1 < x < 0.1. `````` Matthieu Schaller committed Feb 09, 2016 32 33 34 `````` * * @param x The number to take the exponential of. */ `````` 35 ``````__attribute__((always_inline, const)) INLINE static float approx_expf(float x) { `````` Matthieu Schaller committed Jul 28, 2016 36 `````` return 1.f + x * (1.f + x * (0.5f + x * (1.f / 6.f + 1.f / 24.f * x))); `````` Matthieu Schaller committed Feb 09, 2016 37 38 ``````} `````` 39 40 41 42 ``````/** * @brief Approximate version of expf(x) using a 6th order Taylor expansion * */ `````` 43 44 ``````__attribute__((always_inline, const)) INLINE static float good_approx_expf( float x) { `````` 45 46 47 48 49 50 51 52 `````` return 1.f + x * (1.f + x * (0.5f + x * ((1.f / 6.f) + x * ((1.f / 24.f) + x * ((1.f / 120.f) + (1.f / 720.f) * x))))); } `````` 53 54 55 ``````/** * @brief Approximate version of exp(x) using a 6th order Taylor expansion */ `````` 56 57 ``````__attribute__((always_inline, const)) INLINE static double good_approx_exp( double x) { `````` 58 59 60 61 62 63 64 65 `````` return 1. + x * (1. + x * (0.5 + x * ((1. / 6.) + x * ((1. / 24.) + x * ((1. / 120.) + (1. / 720.) * x))))); } `````` Matthieu Schaller committed Feb 09, 2016 66 ``#endif /* SWIFT_APPROX_MATH_H */``