478 lines
16 KiB
C++
478 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()
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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 = glm::next_float(i))
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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 = glm::next_float(i))
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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()
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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 = glm::next_float(i))
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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 = glm::next_float(i))
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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()
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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 = glm::next_float(i))
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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 = glm::next_float(i))
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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()
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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 = glm::next_float(i))
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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 = glm::next_float(i))
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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()
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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 = glm::next_float(i))
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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 = glm::next_float(i))
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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()
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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 = glm::next_float(i))
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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 = glm::next_float(i))
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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()
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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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std::size_t const Samples = 10000000;
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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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return Error;
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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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//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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{
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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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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;
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|
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assert(!Error);
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}
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|
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return Error;
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}
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}//namespace taylorCos
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|
|
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int main()
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|
{
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int Error(0);
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|
|
|
Error += ::taylorCos::test();
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|
Error += ::taylorCos::perf();
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|
|
|
# ifdef NDEBUG
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|
Error += ::fastCos::perf();
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|
Error += ::fastSin::perf();
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|
Error += ::fastTan::perf();
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|
Error += ::fastAcos::perf();
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|
Error += ::fastAsin::perf();
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Error += ::fastAtan::perf();
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# endif//NDEBUG
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|
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return Error;
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|
}
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