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563 lines
17 KiB
563 lines
17 KiB
#define GLM_ENABLE_EXPERIMENTAL
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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<int>(time_fast));
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std::printf("cos Time %d clocks\n", static_cast<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<int>(time_fast));
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std::printf("sin Time %d clocks\n", static_cast<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<int>(time_fast));
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std::printf("tan Time %d clocks\n", static_cast<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<int>(time_fast));
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std::printf("acos Time %d clocks\n", static_cast<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<int>(time_fast));
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std::printf("asin Time %d clocks\n", static_cast<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<int>(time_fast));
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std::printf("atan Time %d clocks\n", static_cast<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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using glm::qualifier;
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using glm::length_t;
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glm::vec4 const AngleShift(0.0f, glm::half_pi<float>(), glm::pi<float>(), glm::three_over_two_pi<float>());
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template<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> taylorSeriesNewCos(glm::vec<L, T, Q> const& x)
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{
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glm::vec<L, T, Q> const Powed2(x * x);
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glm::vec<L, T, Q> const Powed4(Powed2 * Powed2);
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glm::vec<L, T, Q> const Powed6(Powed4 * Powed2);
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glm::vec<L, T, Q> 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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> taylorSeriesNewCos6(glm::vec<L, T, Q> const& x)
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{
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glm::vec<L, T, Q> const Powed2(x * x);
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glm::vec<L, T, Q> const Powed4(Powed2 * Powed2);
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glm::vec<L, T, Q> 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::length_t L, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, float, Q> fastAbs(glm::vec<L, float, Q> 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<glm::length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> fastCosNew(glm::vec<L, T, Q> const& x)
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{
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glm::vec<L, T, Q> 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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vec<L, bool, Q> const FirstQuarterPi(lessThanEqual(Angle0_PI, vec<L, T, Q>(glm::half_pi<T>())));
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vec<L, T, Q> const RevertAngle(mix(vec<L, T, Q>(glm::pi<T>()), vec<L, T, Q>(0), FirstQuarterPi));
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vec<L, T, Q> const ReturnSign(mix(vec<L, T, Q>(-1), vec<L, T, Q>(1), FirstQuarterPi));
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vec<L, T, Q> 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 %d clocks\n", static_cast<int>(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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> deterministic_fmod(glm::vec<L, T, Q> 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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> fastCosDeterminisctic(glm::vec<L, T, Q> const& x)
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{
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glm::vec<L, T, Q> const Angle0_PI(abs(deterministic_fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
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glm::vec<L, bool, Q> const FirstQuarterPi(lessThanEqual(Angle0_PI, glm::vec<L, T, Q>(glm::half_pi<T>())));
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glm::vec<L, T, Q> const RevertAngle(mix(glm::vec<L, T, Q>(glm::pi<T>()), glm::vec<L, T, Q>(0), FirstQuarterPi));
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glm::vec<L, T, Q> const ReturnSign(mix(glm::vec<L, T, Q>(-1), glm::vec<L, T, Q>(1), FirstQuarterPi));
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glm::vec<L, T, Q> 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 %d clocks\n", static_cast<int>(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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> taylorSeriesRefCos(glm::vec<L, T, Q> 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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER glm::vec<L, T, Q> fastRefCos(glm::vec<L, T, Q> const& x)
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{
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glm::vec<L, T, Q> 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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glm::vec<L, bool, Q> const FirstQuarterPi(lessThanEqual(Angle0_PI, glm::vec<L, T, Q>(glm::half_pi<T>())));
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glm::vec<L, T, Q> const RevertAngle(mix(glm::vec<L, T, Q>(glm::pi<T>()), glm::vec<L, T, Q>(0), FirstQuarterPi));
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glm::vec<L, T, Q> const ReturnSign(mix(glm::vec<L, T, Q>(-1), glm::vec<L, T, Q>(1), FirstQuarterPi));
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glm::vec<L, T, Q> 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 %d clocks\n", static_cast<int>(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 %d clocks\n", static_cast<int>(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 %d clocks\n", static_cast<int>(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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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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|
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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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return Error;
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}
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}//namespace taylorCos
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|
|
|
namespace taylor2
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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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float taylorCosA(float x)
|
|
{
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|
return 1.f
|
|
- (x * x) * (1.f / 2.f)
|
|
+ (x * x * x * x) * (1.f / 24.f)
|
|
- (x * x * x * x * x * x) * (1.f / 720.f)
|
|
+ (x * x * x * x * x * x * x * x) * (1.f / 40320.f);
|
|
}
|
|
|
|
float taylorCosB(float x)
|
|
{
|
|
return 1.f
|
|
- (x * x) * (1.f / 2.f)
|
|
+ (x * x * x * x) * (1.f / 24.f)
|
|
- (x * x * x * x * x * x) * (1.f / 720.f)
|
|
+ (x * x * x * x * x * x * x * x) * (1.f / 40320.f);
|
|
}
|
|
|
|
float taylorCosC(float x)
|
|
{
|
|
return 1.f
|
|
- (x * x) * (1.f / 2.f)
|
|
+ ((x * x) * (x * x)) * (1.f / 24.f)
|
|
- (((x * x) * (x * x)) * (x * x)) * (1.f / 720.f)
|
|
+ (((x * x) * (x * x)) * ((x * x) * (x * x))) * (1.f / 40320.f);
|
|
}
|
|
|
|
int perf_taylorCosA(float Begin, float End, std::size_t Samples)
|
|
{
|
|
std::vector<float> Results;
|
|
Results.resize(Samples);
|
|
|
|
float Steps = (End - Begin) / Samples;
|
|
|
|
std::clock_t const TimeStampBegin = std::clock();
|
|
|
|
for(std::size_t i = 0; i < Samples; ++i)
|
|
Results[i] = taylorCosA(AngleShift.x + Begin + Steps * i);
|
|
|
|
std::clock_t const TimeStampEnd = std::clock();
|
|
|
|
std::printf("taylorCosA %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
|
|
|
|
int Error = 0;
|
|
for(std::size_t i = 0; i < Samples; ++i)
|
|
Error += Results[i] >= -1.0f && Results[i] <= 1.0f ? 0 : 1;
|
|
return Error;
|
|
}
|
|
|
|
int perf_taylorCosB(float Begin, float End, std::size_t Samples)
|
|
{
|
|
std::vector<float> Results;
|
|
Results.resize(Samples);
|
|
|
|
float Steps = (End - Begin) / Samples;
|
|
|
|
std::clock_t const TimeStampBegin = std::clock();
|
|
|
|
for(std::size_t i = 0; i < Samples; ++i)
|
|
Results[i] = taylorCosB(AngleShift.x + Begin + Steps * i);
|
|
|
|
std::clock_t const TimeStampEnd = std::clock();
|
|
|
|
std::printf("taylorCosB %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
|
|
|
|
int Error = 0;
|
|
for(std::size_t i = 0; i < Samples; ++i)
|
|
Error += Results[i] >= -1.0f && Results[i] <= 1.0f ? 0 : 1;
|
|
return Error;
|
|
}
|
|
|
|
int perf_taylorCosC(float Begin, float End, std::size_t Samples)
|
|
{
|
|
std::vector<float> Results;
|
|
Results.resize(Samples);
|
|
|
|
float Steps = (End - Begin) / Samples;
|
|
|
|
std::clock_t const TimeStampBegin = std::clock();
|
|
|
|
for(std::size_t i = 0; i < Samples; ++i)
|
|
Results[i] = taylorCosC(AngleShift.x + Begin + Steps * i);
|
|
|
|
std::clock_t const TimeStampEnd = std::clock();
|
|
|
|
std::printf("taylorCosC %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
|
|
|
|
int Error = 0;
|
|
for(std::size_t i = 0; i < Samples; ++i)
|
|
Error += Results[i] >= -1.0f && Results[i] <= 1.0f ? 0 : 1;
|
|
return Error;
|
|
}
|
|
|
|
int perf(std::size_t Samples)
|
|
{
|
|
int Error = 0;
|
|
|
|
float const Begin = -glm::pi<float>();
|
|
float const End = glm::pi<float>();
|
|
|
|
Error += perf_taylorCosA(Begin, End, Samples);
|
|
Error += perf_taylorCosB(Begin, End, Samples);
|
|
Error += perf_taylorCosC(Begin, End, Samples);
|
|
|
|
return Error;
|
|
}
|
|
|
|
}//namespace taylor2
|
|
|
|
int main()
|
|
{
|
|
int Error(0);
|
|
|
|
Error += ::taylor2::perf(1000);
|
|
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;
|
|
}
|