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576 lines
18 KiB
576 lines
18 KiB
#include <glm/ext/scalar_ulp.hpp> |
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#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/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::nextFloat(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::nextFloat(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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(void) result; // Silence set but not used warning |
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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::nextFloat(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::nextFloat(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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(void) result; // Silence set but not used warning |
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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::nextFloat(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::nextFloat(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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(void) result; // Silence set but not used warning |
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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::nextFloat(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::nextFloat(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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(void) result; // Silence set but not used warning |
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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::nextFloat(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::nextFloat(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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(void) result; // Silence set but not used warning |
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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::nextFloat(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::nextFloat(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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(void) result; // Silence set but not used warning |
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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 const Steps = (End - Begin) / static_cast<float>(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 * static_cast<float>(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 const Steps = (End - Begin) / static_cast<float>(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 * static_cast<float>(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 const Steps = (End - Begin) / static_cast<float>(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 * static_cast<float>(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 const Steps = (End - Begin) / static_cast<float>(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 * static_cast<float>(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 const Steps = (End - Begin) / static_cast<float>(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 * static_cast<float>(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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//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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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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{ |
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return 1.f |
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- (x * x) * (1.f / 2.f) |
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+ (x * x * x * x) * (1.f / 24.f) |
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- (x * x * x * x * x * x) * (1.f / 720.f) |
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+ (x * x * x * x * x * x * x * x) * (1.f / 40320.f); |
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} |
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float taylorCosB(float x) |
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{ |
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return 1.f |
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- (x * x) * (1.f / 2.f) |
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+ (x * x * x * x) * (1.f / 24.f) |
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- (x * x * x * x * x * x) * (1.f / 720.f) |
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+ (x * x * x * x * x * x * x * x) * (1.f / 40320.f); |
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} |
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|
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float taylorCosC(float x) |
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{ |
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return 1.f |
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- (x * x) * (1.f / 2.f) |
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+ ((x * x) * (x * x)) * (1.f / 24.f) |
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- (((x * x) * (x * x)) * (x * x)) * (1.f / 720.f) |
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+ (((x * x) * (x * x)) * ((x * x) * (x * x))) * (1.f / 40320.f); |
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} |
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|
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int perf_taylorCosA(float Begin, float End, std::size_t Samples) |
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{ |
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std::vector<float> Results; |
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Results.resize(Samples); |
|
|
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float const Steps = (End - Begin) / static_cast<float>(Samples); |
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|
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std::clock_t const TimeStampBegin = std::clock(); |
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|
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for(std::size_t i = 0; i < Samples; ++i) |
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Results[i] = taylorCosA(AngleShift.x + Begin + Steps * static_cast<float>(i)); |
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|
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std::clock_t const TimeStampEnd = std::clock(); |
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|
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std::printf("taylorCosA %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin)); |
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|
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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] >= -1.0f && Results[i] <= 1.0f ? 0 : 1; |
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return Error; |
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} |
|
|
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int perf_taylorCosB(float Begin, float End, std::size_t Samples) |
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{ |
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std::vector<float> Results; |
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Results.resize(Samples); |
|
|
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float const Steps = (End - Begin) / static_cast<float>(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] = taylorCosB(AngleShift.x + Begin + Steps * static_cast<float>(i)); |
|
|
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std::clock_t const TimeStampEnd = std::clock(); |
|
|
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std::printf("taylorCosB %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] >= -1.0f && Results[i] <= 1.0f ? 0 : 1; |
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return Error; |
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} |
|
|
|
int perf_taylorCosC(float Begin, float End, std::size_t Samples) |
|
{ |
|
std::vector<float> Results; |
|
Results.resize(Samples); |
|
|
|
float const Steps = (End - Begin) / static_cast<float>(Samples); |
|
|
|
std::clock_t const TimeStampBegin = std::clock(); |
|
|
|
for(std::size_t i = 0; i < Samples; ++i) |
|
Results[i] = taylorCosC(AngleShift.x + Begin + Steps * static_cast<float>(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; |
|
}
|
|
|