5070880428
This allows building against the same version of GLM across all targets and not deal with API changes of newer GLM versions which introduce regressions. Long term we want to migrate away from GLM and stick to a minimal self-written subset.
476 lines
16 KiB
C++
476 lines
16 KiB
C++
///////////////////////////////////////////////////////////////////////////////////
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/// OpenGL Mathematics (glm.g-truc.net)
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///
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/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
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/// Permission is hereby granted, free of charge, to any person obtaining a copy
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/// of this software and associated documentation files (the "Software"), to deal
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/// in the Software without restriction, including without limitation the rights
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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/// copies of the Software, and to permit persons to whom the Software is
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/// furnished to do so, subject to the following conditions:
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///
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/// The above copyright notice and this permission notice shall be included in
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/// all copies or substantial portions of the Software.
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///
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/// Restrictions:
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/// By making use of the Software for military purposes, you choose to make
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/// a Bunny unhappy.
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///
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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/// THE SOFTWARE.
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///
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/// @file test/gtx/gtx_fast_trigonometry.cpp
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/// @date 2013-10-25 / 2014-11-25
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/// @author Christophe Riccio
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///////////////////////////////////////////////////////////////////////////////////
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#include <glm/gtc/type_precision.hpp>
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#include <glm/gtx/fast_trigonometry.hpp>
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#include <glm/gtx/integer.hpp>
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#include <glm/gtx/common.hpp>
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#include <glm/gtc/constants.hpp>
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#include <glm/gtc/ulp.hpp>
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#include <glm/gtc/vec1.hpp>
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#include <glm/trigonometric.hpp>
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#include <cmath>
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#include <ctime>
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#include <cstdio>
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#include <vector>
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namespace fastCos
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{
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int perf(bool NextFloat)
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{
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const float begin = -glm::pi<float>();
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const float end = glm::pi<float>();
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float result = 0.f;
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const std::clock_t timestamp1 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::fastCos(i);
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const std::clock_t timestamp2 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::cos(i);
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const std::clock_t timestamp3 = std::clock();
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const std::clock_t time_fast = timestamp2 - timestamp1;
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const std::clock_t time_default = timestamp3 - timestamp2;
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std::printf("fastCos Time %d clocks\n", static_cast<unsigned int>(time_fast));
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std::printf("cos Time %d clocks\n", static_cast<unsigned int>(time_default));
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return time_fast <= time_default ? 0 : 1;
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}
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}//namespace fastCos
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namespace fastSin
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{
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/*
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float sin(float x) {
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float temp;
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temp = (x + M_PI) / ((2 * M_PI) - M_PI);
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return limited_sin((x + M_PI) - ((2 * M_PI) - M_PI) * temp));
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}
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*/
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int perf(bool NextFloat)
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{
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const float begin = -glm::pi<float>();
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const float end = glm::pi<float>();
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float result = 0.f;
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const std::clock_t timestamp1 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::fastSin(i);
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const std::clock_t timestamp2 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::sin(i);
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const std::clock_t timestamp3 = std::clock();
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const std::clock_t time_fast = timestamp2 - timestamp1;
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const std::clock_t time_default = timestamp3 - timestamp2;
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std::printf("fastSin Time %d clocks\n", static_cast<unsigned int>(time_fast));
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std::printf("sin Time %d clocks\n", static_cast<unsigned int>(time_default));
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return time_fast <= time_default ? 0 : 1;
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}
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}//namespace fastSin
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namespace fastTan
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{
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int perf(bool NextFloat)
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{
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const float begin = -glm::pi<float>();
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const float end = glm::pi<float>();
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float result = 0.f;
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const std::clock_t timestamp1 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::fastTan(i);
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const std::clock_t timestamp2 = std::clock();
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for (float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::tan(i);
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const std::clock_t timestamp3 = std::clock();
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const std::clock_t time_fast = timestamp2 - timestamp1;
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const std::clock_t time_default = timestamp3 - timestamp2;
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std::printf("fastTan Time %d clocks\n", static_cast<unsigned int>(time_fast));
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std::printf("tan Time %d clocks\n", static_cast<unsigned int>(time_default));
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return time_fast <= time_default ? 0 : 1;
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}
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}//namespace fastTan
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namespace fastAcos
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{
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int perf(bool NextFloat)
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{
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const float begin = -glm::pi<float>();
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const float end = glm::pi<float>();
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float result = 0.f;
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const std::clock_t timestamp1 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::fastAcos(i);
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const std::clock_t timestamp2 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::acos(i);
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const std::clock_t timestamp3 = std::clock();
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const std::clock_t time_fast = timestamp2 - timestamp1;
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const std::clock_t time_default = timestamp3 - timestamp2;
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std::printf("fastAcos Time %d clocks\n", static_cast<unsigned int>(time_fast));
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std::printf("acos Time %d clocks\n", static_cast<unsigned int>(time_default));
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return time_fast <= time_default ? 0 : 1;
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}
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}//namespace fastAcos
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namespace fastAsin
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{
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int perf(bool NextFloat)
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{
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const float begin = -glm::pi<float>();
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const float end = glm::pi<float>();
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float result = 0.f;
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const std::clock_t timestamp1 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::fastAsin(i);
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const std::clock_t timestamp2 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::asin(i);
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const std::clock_t timestamp3 = std::clock();
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const std::clock_t time_fast = timestamp2 - timestamp1;
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const std::clock_t time_default = timestamp3 - timestamp2;
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std::printf("fastAsin Time %d clocks\n", static_cast<unsigned int>(time_fast));
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std::printf("asin Time %d clocks\n", static_cast<unsigned int>(time_default));
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return time_fast <= time_default ? 0 : 1;
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}
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}//namespace fastAsin
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namespace fastAtan
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{
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int perf(bool NextFloat)
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{
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const float begin = -glm::pi<float>();
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const float end = glm::pi<float>();
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float result = 0.f;
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const std::clock_t timestamp1 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::fastAtan(i);
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const std::clock_t timestamp2 = std::clock();
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for(float i = begin; i < end; i = NextFloat ? glm::next_float(i) : i += 0.1f)
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result = glm::atan(i);
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const std::clock_t timestamp3 = std::clock();
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const std::clock_t time_fast = timestamp2 - timestamp1;
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const std::clock_t time_default = timestamp3 - timestamp2;
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std::printf("fastAtan Time %d clocks\n", static_cast<unsigned int>(time_fast));
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std::printf("atan Time %d clocks\n", static_cast<unsigned int>(time_default));
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return time_fast <= time_default ? 0 : 1;
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}
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}//namespace fastAtan
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namespace taylorCos
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{
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glm::vec4 const AngleShift(0.0f, glm::pi<float>() * 0.5f, glm::pi<float>() * 1.0f, glm::pi<float>() * 1.5f);
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> taylorSeriesNewCos(vecType<T, P> const & x)
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{
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vecType<T, P> const Powed2(x * x);
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vecType<T, P> const Powed4(Powed2 * Powed2);
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vecType<T, P> const Powed6(Powed4 * Powed2);
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vecType<T, P> const Powed8(Powed4 * Powed4);
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return static_cast<T>(1)
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- Powed2 * static_cast<T>(0.5)
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+ Powed4 * static_cast<T>(0.04166666666666666666666666666667)
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- Powed6 * static_cast<T>(0.00138888888888888888888888888889)
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+ Powed8 * static_cast<T>(2.4801587301587301587301587301587e-5);
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}
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> taylorSeriesNewCos6(vecType<T, P> const & x)
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{
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vecType<T, P> const Powed2(x * x);
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vecType<T, P> const Powed4(Powed2 * Powed2);
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vecType<T, P> const Powed6(Powed4 * Powed2);
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return static_cast<T>(1)
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- Powed2 * static_cast<T>(0.5)
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+ Powed4 * static_cast<T>(0.04166666666666666666666666666667)
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- Powed6 * static_cast<T>(0.00138888888888888888888888888889);
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}
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template <glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<float, P> fastAbs(vecType<float, P> x)
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{
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int* Pointer = reinterpret_cast<int*>(&x[0]);
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Pointer[0] &= 0x7fffffff;
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Pointer[1] &= 0x7fffffff;
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Pointer[2] &= 0x7fffffff;
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Pointer[3] &= 0x7fffffff;
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return x;
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}
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> fastCosNew(vecType<T, P> const & x)
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{
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vecType<T, P> const Angle0_PI(fastAbs(fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
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return taylorSeriesNewCos6(x);
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/*
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vecType<bool, P> const FirstQuarterPi(lessThanEqual(Angle0_PI, vecType<T, P>(glm::half_pi<T>())));
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vecType<T, P> const RevertAngle(mix(vecType<T, P>(glm::pi<T>()), vecType<T, P>(0), FirstQuarterPi));
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vecType<T, P> const ReturnSign(mix(vecType<T, P>(-1), vecType<T, P>(1), FirstQuarterPi));
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vecType<T, P> const SectionAngle(RevertAngle - Angle0_PI);
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return ReturnSign * taylorSeriesNewCos(SectionAngle);
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*/
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}
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int perf_fastCosNew(float Begin, float End, std::size_t Samples)
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{
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std::vector<glm::vec4> Results;
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Results.resize(Samples);
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float Steps = (End - Begin) / Samples;
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std::clock_t const TimeStampBegin = std::clock();
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for(std::size_t i = 0; i < Samples; ++i)
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Results[i] = fastCosNew(AngleShift + glm::vec4(Begin + Steps * i));
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std::clock_t const TimeStampEnd = std::clock();
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std::printf("fastCosNew %ld clocks\n", TimeStampEnd - TimeStampBegin);
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int Error = 0;
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for(std::size_t i = 0; i < Samples; ++i)
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Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
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return Error;
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}
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> deterministic_fmod(vecType<T, P> const & x, T y)
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{
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return x - y * trunc(x / y);
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}
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> fastCosDeterminisctic(vecType<T, P> const & x)
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{
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vecType<T, P> const Angle0_PI(abs(deterministic_fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
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vecType<bool, P> const FirstQuarterPi(lessThanEqual(Angle0_PI, vecType<T, P>(glm::half_pi<T>())));
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vecType<T, P> const RevertAngle(mix(vecType<T, P>(glm::pi<T>()), vecType<T, P>(0), FirstQuarterPi));
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vecType<T, P> const ReturnSign(mix(vecType<T, P>(-1), vecType<T, P>(1), FirstQuarterPi));
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vecType<T, P> const SectionAngle(RevertAngle - Angle0_PI);
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return ReturnSign * taylorSeriesNewCos(SectionAngle);
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}
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int perf_fastCosDeterminisctic(float Begin, float End, std::size_t Samples)
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{
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std::vector<glm::vec4> Results;
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Results.resize(Samples);
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float Steps = (End - Begin) / Samples;
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std::clock_t const TimeStampBegin = std::clock();
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for(std::size_t i = 0; i < Samples; ++i)
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Results[i] = taylorCos::fastCosDeterminisctic(AngleShift + glm::vec4(Begin + Steps * i));
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std::clock_t const TimeStampEnd = std::clock();
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std::printf("fastCosDeterminisctic %ld clocks\n", TimeStampEnd - TimeStampBegin);
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int Error = 0;
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for(std::size_t i = 0; i < Samples; ++i)
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Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
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return Error;
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}
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> taylorSeriesRefCos(vecType<T, P> const & x)
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{
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return static_cast<T>(1)
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- (x * x) / glm::factorial(static_cast<T>(2))
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+ (x * x * x * x) / glm::factorial(static_cast<T>(4))
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- (x * x * x * x * x * x) / glm::factorial(static_cast<T>(6))
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+ (x * x * x * x * x * x * x * x) / glm::factorial(static_cast<T>(8));
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}
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template <typename T, glm::precision P, template <typename, glm::precision> class vecType>
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GLM_FUNC_QUALIFIER vecType<T, P> fastRefCos(vecType<T, P> const & x)
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{
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vecType<T, P> const Angle0_PI(glm::abs(fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
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// return taylorSeriesRefCos(Angle0_PI);
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vecType<bool, P> const FirstQuarterPi(lessThanEqual(Angle0_PI, vecType<T, P>(glm::half_pi<T>())));
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vecType<T, P> const RevertAngle(mix(vecType<T, P>(glm::pi<T>()), vecType<T, P>(0), FirstQuarterPi));
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vecType<T, P> const ReturnSign(mix(vecType<T, P>(-1), vecType<T, P>(1), FirstQuarterPi));
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vecType<T, P> const SectionAngle(RevertAngle - Angle0_PI);
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return ReturnSign * taylorSeriesRefCos(SectionAngle);
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}
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int perf_fastCosRef(float Begin, float End, std::size_t Samples)
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{
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std::vector<glm::vec4> Results;
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Results.resize(Samples);
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float Steps = (End - Begin) / Samples;
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std::clock_t const TimeStampBegin = std::clock();
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for(std::size_t i = 0; i < Samples; ++i)
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Results[i] = taylorCos::fastRefCos(AngleShift + glm::vec4(Begin + Steps * i));
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std::clock_t const TimeStampEnd = std::clock();
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std::printf("fastCosRef %ld clocks\n", TimeStampEnd - TimeStampBegin);
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int Error = 0;
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for(std::size_t i = 0; i < Samples; ++i)
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Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
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return Error;
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}
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int perf_fastCosOld(float Begin, float End, std::size_t Samples)
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{
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std::vector<glm::vec4> Results;
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Results.resize(Samples);
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float Steps = (End - Begin) / Samples;
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std::clock_t const TimeStampBegin = std::clock();
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for(std::size_t i = 0; i < Samples; ++i)
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Results[i] = glm::fastCos(AngleShift + glm::vec4(Begin + Steps * i));
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std::clock_t const TimeStampEnd = std::clock();
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std::printf("fastCosOld %ld clocks\n", TimeStampEnd - TimeStampBegin);
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int Error = 0;
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for(std::size_t i = 0; i < Samples; ++i)
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Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
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return Error;
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}
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int perf_cos(float Begin, float End, std::size_t Samples)
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{
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std::vector<glm::vec4> Results;
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Results.resize(Samples);
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float Steps = (End - Begin) / Samples;
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std::clock_t const TimeStampBegin = std::clock();
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for(std::size_t i = 0; i < Samples; ++i)
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Results[i] = glm::cos(AngleShift + glm::vec4(Begin + Steps * i));
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std::clock_t const TimeStampEnd = std::clock();
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std::printf("cos %ld clocks\n", TimeStampEnd - TimeStampBegin);
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int Error = 0;
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for(std::size_t i = 0; i < Samples; ++i)
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Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
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return Error;
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}
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int perf(std::size_t const Samples)
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{
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int Error = 0;
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float const Begin = -glm::pi<float>();
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float const End = glm::pi<float>();
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Error += perf_cos(Begin, End, Samples);
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Error += perf_fastCosOld(Begin, End, Samples);
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Error += perf_fastCosRef(Begin, End, Samples);
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//Error += perf_fastCosNew(Begin, End, Samples);
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Error += perf_fastCosDeterminisctic(Begin, End, Samples);
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|
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return Error;
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}
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|
|
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int test()
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{
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int Error = 0;
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|
|
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//for(float Angle = -4.0f * glm::pi<float>(); Angle < 4.0f * glm::pi<float>(); Angle += 0.1f)
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//for(float Angle = -720.0f; Angle < 720.0f; Angle += 0.1f)
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for(float Angle = 0.0f; Angle < 180.0f; Angle += 0.1f)
|
|
{
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float const modAngle = std::fmod(glm::abs(Angle), 360.f);
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assert(modAngle >= 0.0f && modAngle <= 360.f);
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float const radAngle = glm::radians(modAngle);
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float const Cos0 = std::cos(radAngle);
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|
|
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float const Cos1 = taylorCos::fastRefCos(glm::fvec1(radAngle)).x;
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Error += glm::abs(Cos1 - Cos0) < 0.1f ? 0 : 1;
|
|
|
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float const Cos2 = taylorCos::fastCosNew(glm::fvec1(radAngle)).x;
|
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//Error += glm::abs(Cos2 - Cos0) < 0.1f ? 0 : 1;
|
|
|
|
assert(!Error);
|
|
}
|
|
|
|
return Error;
|
|
}
|
|
}//namespace taylorCos
|
|
|
|
int main()
|
|
{
|
|
int Error(0);
|
|
|
|
Error += ::taylorCos::test();
|
|
Error += ::taylorCos::perf(1000);
|
|
|
|
# ifdef NDEBUG
|
|
::fastCos::perf(false);
|
|
::fastSin::perf(false);
|
|
::fastTan::perf(false);
|
|
::fastAcos::perf(false);
|
|
::fastAsin::perf(false);
|
|
::fastAtan::perf(false);
|
|
# endif//NDEBUG
|
|
|
|
return Error;
|
|
}
|