16cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi/* 26cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * Copyright (C) 2013 The Android Open Source Project 36cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * 46cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * Licensed under the Apache License, Version 2.0 (the "License"); 56cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * you may not use this file except in compliance with the License. 66cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * You may obtain a copy of the License at 76cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * 86cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * http://www.apache.org/licenses/LICENSE-2.0 96cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * 106cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * Unless required by applicable law or agreed to in writing, software 116cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * distributed under the License is distributed on an "AS IS" BASIS, 126cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 136cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * See the License for the specific language governing permissions and 146cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi * limitations under the License. 156cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi */ 166cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 176cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#ifndef LE_FX_ENGINE_COMMON_CORE_MATH_H_ 186cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#define LE_FX_ENGINE_COMMON_CORE_MATH_H_ 196cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 206cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#include <math.h> 216cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#include <algorithm> 226cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviusing ::std::min; 236cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviusing ::std::max; 246cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviusing ::std::fill; 256cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviusing ::std::fill_n;using ::std::lower_bound; 266cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#include <cmath> 276cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#include <math.h> 286cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi//using ::std::fpclassify; 296cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 306cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#include "common/core/os.h" 316cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#include "common/core/types.h" 326cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 336cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivinamespace le_fx { 346cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivinamespace math { 356cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 366cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// A fast approximation to log2(.) 376cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviinline float fast_log2(float val) { 386cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi int* const exp_ptr = reinterpret_cast <int *> (&val); 396cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi int x = *exp_ptr; 406cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi const int log_2 = ((x >> 23) & 255) - 128; 416cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi x &= ~(255 << 23); 426cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi x += 127 << 23; 436cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi *exp_ptr = x; 446cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi val = ((-1.0f / 3) * val + 2) * val - 2.0f / 3; 456cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi return static_cast<float>(val + log_2); 466cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} 476cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 486cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// A fast approximation to log(.) 496cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviinline float fast_log(float val) { 506cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi return fast_log2(val) * 516cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 0.693147180559945286226763982995180413126945495605468750f; 526cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} 536cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 546cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// An approximation of the exp(.) function using a 5-th order Taylor expansion. 556cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// It's pretty accurate between +-0.1 and accurate to 10e-3 between +-1 566cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivitemplate <typename T> 576cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviinline T ExpApproximationViaTaylorExpansionOrder5(T x) { 586cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi const T x2 = x * x; 596cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi const T x3 = x2 * x; 606cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi const T x4 = x2 * x2; 616cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi const T x5 = x3 * x2; 626cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi return 1.0f + x + 0.5f * x2 + 636cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 0.16666666666666665741480812812369549646973609924316406250f * x3 + 646cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 0.0416666666666666643537020320309238741174340248107910156250f * x4 + 656cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 0.008333333333333333217685101601546193705871701240539550781250f * x5; 666cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} 676cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 686cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} // namespace math 696cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} // namespace le_fx 706cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 716cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// Math functions missing in Android NDK: 726cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#if defined(LE_FX_OS_ANDROID) 736cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 746cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivinamespace std { 756cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 766cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// 776cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// Round to the nearest integer: We need this implementation 786cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// since std::round is missing on android. 796cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi// 806cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivitemplate <typename T> 816cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Triviinline T round(const T &x) { 826cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi return static_cast<T>(std::floor(static_cast<double>(x) + 0.5)); 836cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} 846cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 856cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi} // namespace std 866cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 876cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#endif // LE_FX_OS_ANDROID 886cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi 896cc3a9948b51193dfdcb0c3527d7f3d1ca38aa3cJean-Michel Trivi#endif // LE_FX_ENGINE_COMMON_CORE_MATH_H_ 90