1 files changed, 564 insertions, 0 deletions
diff --git a/3rdparty/glm/source/test/gtx/gtx_fast_trigonometry.cpp b/3rdparty/glm/source/test/gtx/gtx_fast_trigonometry.cpp
new file mode 100644
index 0000000..8bf86ba
--- /dev/null
+++ b/3rdparty/glm/source/test/gtx/gtx_fast_trigonometry.cpp
@@ -0,0 +1,564 @@
+#include <glm/ext/scalar_ulp.hpp>
+
+#define GLM_ENABLE_EXPERIMENTAL
+#include <glm/gtc/type_precision.hpp>
+#include <glm/gtx/fast_trigonometry.hpp>
+#include <glm/gtx/integer.hpp>
+#include <glm/gtx/common.hpp>
+#include <glm/gtc/constants.hpp>
+#include <glm/gtc/vec1.hpp>
+#include <glm/trigonometric.hpp>
+#include <cmath>
+#include <ctime>
+#include <cstdio>
+#include <vector>
+
+namespace fastCos
+{
+	int perf(bool NextFloat)
+	{
+		const float begin = -glm::pi<float>();
+		const float end = glm::pi<float>();
+		float result = 0.f;
+
+		const std::clock_t timestamp1 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::fastCos(i);
+
+		const std::clock_t timestamp2 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::cos(i);
+
+		const std::clock_t timestamp3 = std::clock();
+		const std::clock_t time_fast = timestamp2 - timestamp1;
+		const std::clock_t time_default = timestamp3 - timestamp2;
+		std::printf("fastCos Time %d clocks\n", static_cast<int>(time_fast));
+		std::printf("cos Time %d clocks\n", static_cast<int>(time_default));
+
+		return time_fast <= time_default ? 0 : 1;
+	}
+}//namespace fastCos
+
+namespace fastSin
+{
+	/*
+	float sin(float x) {
+	float temp;
+	temp = (x + M_PI) / ((2 * M_PI) - M_PI);
+	return limited_sin((x + M_PI) - ((2 * M_PI) - M_PI) * temp));
+	}
+	*/
+
+	int perf(bool NextFloat)
+	{
+		const float begin = -glm::pi<float>();
+		const float end = glm::pi<float>();
+		float result = 0.f;
+
+		const std::clock_t timestamp1 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::fastSin(i);
+
+		const std::clock_t timestamp2 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::sin(i);
+
+		const std::clock_t timestamp3 = std::clock();
+		const std::clock_t time_fast = timestamp2 - timestamp1;
+		const std::clock_t time_default = timestamp3 - timestamp2;
+		std::printf("fastSin Time %d clocks\n", static_cast<int>(time_fast));
+		std::printf("sin Time %d clocks\n", static_cast<int>(time_default));
+
+		return time_fast <= time_default ? 0 : 1;
+	}
+}//namespace fastSin
+
+namespace fastTan
+{
+	int perf(bool NextFloat)
+	{
+		const float begin = -glm::pi<float>();
+		const float end = glm::pi<float>();
+		float result = 0.f;
+
+		const std::clock_t timestamp1 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::fastTan(i);
+
+		const std::clock_t timestamp2 = std::clock();
+		for (float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::tan(i);
+
+		const std::clock_t timestamp3 = std::clock();
+		const std::clock_t time_fast = timestamp2 - timestamp1;
+		const std::clock_t time_default = timestamp3 - timestamp2;
+		std::printf("fastTan Time %d clocks\n", static_cast<int>(time_fast));
+		std::printf("tan Time %d clocks\n", static_cast<int>(time_default));
+
+		return time_fast <= time_default ? 0 : 1;
+	}
+}//namespace fastTan
+
+namespace fastAcos
+{
+	int perf(bool NextFloat)
+	{
+		const float begin = -glm::pi<float>();
+		const float end = glm::pi<float>();
+		float result = 0.f;
+
+		const std::clock_t timestamp1 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::fastAcos(i);
+
+		const std::clock_t timestamp2 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::acos(i);
+
+		const std::clock_t timestamp3 = std::clock();
+		const std::clock_t time_fast = timestamp2 - timestamp1;
+		const std::clock_t time_default = timestamp3 - timestamp2;
+
+		std::printf("fastAcos Time %d clocks\n", static_cast<int>(time_fast));
+		std::printf("acos Time %d clocks\n", static_cast<int>(time_default));
+
+		return time_fast <= time_default ? 0 : 1;
+	}
+}//namespace fastAcos
+
+namespace fastAsin
+{
+	int perf(bool NextFloat)
+	{
+		const float begin = -glm::pi<float>();
+		const float end = glm::pi<float>();
+		float result = 0.f;
+		const std::clock_t timestamp1 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::fastAsin(i);
+		const std::clock_t timestamp2 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::asin(i);
+		const std::clock_t timestamp3 = std::clock();
+		const std::clock_t time_fast = timestamp2 - timestamp1;
+		const std::clock_t time_default = timestamp3 - timestamp2;
+		std::printf("fastAsin Time %d clocks\n", static_cast<int>(time_fast));
+		std::printf("asin Time %d clocks\n", static_cast<int>(time_default));
+
+		return time_fast <= time_default ? 0 : 1;
+	}
+}//namespace fastAsin
+
+namespace fastAtan
+{
+	int perf(bool NextFloat)
+	{
+		const float begin = -glm::pi<float>();
+		const float end = glm::pi<float>();
+		float result = 0.f;
+		const std::clock_t timestamp1 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::fastAtan(i);
+		const std::clock_t timestamp2 = std::clock();
+		for(float i = begin; i < end; i = NextFloat ? glm::nextFloat(i) : i += 0.1f)
+			result = glm::atan(i);
+		const std::clock_t timestamp3 = std::clock();
+		const std::clock_t time_fast = timestamp2 - timestamp1;
+		const std::clock_t time_default = timestamp3 - timestamp2;
+		std::printf("fastAtan Time %d clocks\n", static_cast<int>(time_fast));
+		std::printf("atan Time %d clocks\n", static_cast<int>(time_default));
+
+		return time_fast <= time_default ? 0 : 1;
+	}
+}//namespace fastAtan
+
+namespace taylorCos
+{
+	using glm::qualifier;
+	using glm::length_t;
+	
+	glm::vec4 const AngleShift(0.0f, glm::half_pi<float>(), glm::pi<float>(), glm::three_over_two_pi<float>());
+
+	template<length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> taylorSeriesNewCos(glm::vec<L, T, Q> const& x)
+	{
+		glm::vec<L, T, Q> const Powed2(x * x);
+		glm::vec<L, T, Q> const Powed4(Powed2 * Powed2);
+		glm::vec<L, T, Q> const Powed6(Powed4 * Powed2);
+		glm::vec<L, T, Q> const Powed8(Powed4 * Powed4);
+
+		return static_cast<T>(1)
+			- Powed2 * static_cast<T>(0.5)
+			+ Powed4 * static_cast<T>(0.04166666666666666666666666666667)
+			- Powed6 * static_cast<T>(0.00138888888888888888888888888889)
+			+ Powed8 * static_cast<T>(2.4801587301587301587301587301587e-5);
+	}
+
+	template<length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> taylorSeriesNewCos6(glm::vec<L, T, Q> const& x)
+	{
+		glm::vec<L, T, Q> const Powed2(x * x);
+		glm::vec<L, T, Q> const Powed4(Powed2 * Powed2);
+		glm::vec<L, T, Q> const Powed6(Powed4 * Powed2);
+
+		return static_cast<T>(1)
+			- Powed2 * static_cast<T>(0.5)
+			+ Powed4 * static_cast<T>(0.04166666666666666666666666666667)
+			- Powed6 * static_cast<T>(0.00138888888888888888888888888889);
+	}
+
+	template<glm::length_t L, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, float, Q> fastAbs(glm::vec<L, float, Q> x)
+	{
+		int* Pointer = reinterpret_cast<int*>(&x[0]);
+		Pointer[0] &= 0x7fffffff;
+		Pointer[1] &= 0x7fffffff;
+		Pointer[2] &= 0x7fffffff;
+		Pointer[3] &= 0x7fffffff;
+		return x;
+	}
+
+	template<glm::length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> fastCosNew(glm::vec<L, T, Q> const& x)
+	{
+		glm::vec<L, T, Q> const Angle0_PI(fastAbs(fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
+		return taylorSeriesNewCos6(x);
+/*
+		vec<L, bool, Q> const FirstQuarterPi(lessThanEqual(Angle0_PI, vec<L, T, Q>(glm::half_pi<T>())));
+
+		vec<L, T, Q> const RevertAngle(mix(vec<L, T, Q>(glm::pi<T>()), vec<L, T, Q>(0), FirstQuarterPi));
+		vec<L, T, Q> const ReturnSign(mix(vec<L, T, Q>(-1), vec<L, T, Q>(1), FirstQuarterPi));
+		vec<L, T, Q> const SectionAngle(RevertAngle - Angle0_PI);
+
+		return ReturnSign * taylorSeriesNewCos(SectionAngle);
+*/
+	}
+
+	int perf_fastCosNew(float Begin, float End, std::size_t Samples)
+	{
+		std::vector<glm::vec4> 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] = fastCosNew(AngleShift + glm::vec4(Begin + Steps * static_cast<float>(i)));
+
+		std::clock_t const TimeStampEnd = std::clock();
+
+		std::printf("fastCosNew %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
+
+		int Error = 0;
+		for(std::size_t i = 0; i < Samples; ++i)
+			Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
+		return Error;
+	}
+
+	template<length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> deterministic_fmod(glm::vec<L, T, Q> const& x, T y)
+	{
+		return x - y * trunc(x / y);
+	}
+
+	template<length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> fastCosDeterminisctic(glm::vec<L, T, Q> const& x)
+	{
+		glm::vec<L, T, Q> const Angle0_PI(abs(deterministic_fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
+		glm::vec<L, bool, Q> const FirstQuarterPi(lessThanEqual(Angle0_PI, glm::vec<L, T, Q>(glm::half_pi<T>())));
+
+		glm::vec<L, T, Q> const RevertAngle(mix(glm::vec<L, T, Q>(glm::pi<T>()), glm::vec<L, T, Q>(0), FirstQuarterPi));
+		glm::vec<L, T, Q> const ReturnSign(mix(glm::vec<L, T, Q>(-1), glm::vec<L, T, Q>(1), FirstQuarterPi));
+		glm::vec<L, T, Q> const SectionAngle(RevertAngle - Angle0_PI);
+
+		return ReturnSign * taylorSeriesNewCos(SectionAngle);
+	}
+
+	int perf_fastCosDeterminisctic(float Begin, float End, std::size_t Samples)
+	{
+		std::vector<glm::vec4> 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] = taylorCos::fastCosDeterminisctic(AngleShift + glm::vec4(Begin + Steps * static_cast<float>(i)));
+
+		std::clock_t const TimeStampEnd = std::clock();
+
+		std::printf("fastCosDeterminisctic %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
+
+		int Error = 0;
+		for(std::size_t i = 0; i < Samples; ++i)
+			Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
+		return Error;
+	}
+
+	template<length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> taylorSeriesRefCos(glm::vec<L, T, Q> const& x)
+	{
+		return static_cast<T>(1)
+			- (x * x) / glm::factorial(static_cast<T>(2))
+			+ (x * x * x * x) / glm::factorial(static_cast<T>(4))
+			- (x * x * x * x * x * x) / glm::factorial(static_cast<T>(6))
+			+ (x * x * x * x * x * x * x * x) / glm::factorial(static_cast<T>(8));
+	}
+
+	template<length_t L, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER glm::vec<L, T, Q> fastRefCos(glm::vec<L, T, Q> const& x)
+	{
+		glm::vec<L, T, Q> const Angle0_PI(glm::abs(fmod(x + glm::pi<T>(), glm::two_pi<T>()) - glm::pi<T>()));
+//		return taylorSeriesRefCos(Angle0_PI);
+
+		glm::vec<L, bool, Q> const FirstQuarterPi(lessThanEqual(Angle0_PI, glm::vec<L, T, Q>(glm::half_pi<T>())));
+
+		glm::vec<L, T, Q> const RevertAngle(mix(glm::vec<L, T, Q>(glm::pi<T>()), glm::vec<L, T, Q>(0), FirstQuarterPi));
+		glm::vec<L, T, Q> const ReturnSign(mix(glm::vec<L, T, Q>(-1), glm::vec<L, T, Q>(1), FirstQuarterPi));
+		glm::vec<L, T, Q> const SectionAngle(RevertAngle - Angle0_PI);
+
+		return ReturnSign * taylorSeriesRefCos(SectionAngle);
+	}
+
+	int perf_fastCosRef(float Begin, float End, std::size_t Samples)
+	{
+		std::vector<glm::vec4> 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] = taylorCos::fastRefCos(AngleShift + glm::vec4(Begin + Steps * static_cast<float>(i)));
+
+		std::clock_t const TimeStampEnd = std::clock();
+
+		std::printf("fastCosRef %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
+
+		int Error = 0;
+		for(std::size_t i = 0; i < Samples; ++i)
+			Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
+		return Error;
+	}
+
+	int perf_fastCosOld(float Begin, float End, std::size_t Samples)
+	{
+		std::vector<glm::vec4> 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] = glm::fastCos(AngleShift + glm::vec4(Begin + Steps * static_cast<float>(i)));
+
+		std::clock_t const TimeStampEnd = std::clock();
+
+		std::printf("fastCosOld %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
+
+		int Error = 0;
+		for(std::size_t i = 0; i < Samples; ++i)
+			Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
+		return Error;
+	}
+
+	int perf_cos(float Begin, float End, std::size_t Samples)
+	{
+		std::vector<glm::vec4> 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] = glm::cos(AngleShift + glm::vec4(Begin + Steps * static_cast<float>(i)));
+
+		std::clock_t const TimeStampEnd = std::clock();
+
+		std::printf("cos %d clocks\n", static_cast<int>(TimeStampEnd - TimeStampBegin));
+
+		int Error = 0;
+		for(std::size_t i = 0; i < Samples; ++i)
+			Error += Results[i].x >= -1.0f && Results[i].x <= 1.0f ? 0 : 1;
+		return Error;
+	}
+
+	int perf(std::size_t const Samples)
+	{
+		int Error = 0;
+
+		float const Begin = -glm::pi<float>();
+		float const End = glm::pi<float>();
+
+		Error += perf_cos(Begin, End, Samples);
+		Error += perf_fastCosOld(Begin, End, Samples);
+		Error += perf_fastCosRef(Begin, End, Samples);
+		//Error += perf_fastCosNew(Begin, End, Samples);
+		Error += perf_fastCosDeterminisctic(Begin, End, Samples);
+
+		return Error;
+	}
+
+	int test()
+	{
+		int Error = 0;
+
+		//for(float Angle = -4.0f * glm::pi<float>(); Angle < 4.0f * glm::pi<float>(); Angle += 0.1f)
+		//for(float Angle = -720.0f; Angle < 720.0f; Angle += 0.1f)
+		for(float Angle = 0.0f; Angle < 180.0f; Angle += 0.1f)
+		{
+			float const modAngle = std::fmod(glm::abs(Angle), 360.f);
+			assert(modAngle >= 0.0f && modAngle <= 360.f);
+			float const radAngle = glm::radians(modAngle);
+			float const Cos0 = std::cos(radAngle);
+
+			float const Cos1 = taylorCos::fastRefCos(glm::fvec1(radAngle)).x;
+			Error += glm::abs(Cos1 - Cos0) < 0.1f ? 0 : 1;
+
+			//float const Cos2 = taylorCos::fastCosNew(glm::fvec1(radAngle)).x;
+			//Error += glm::abs(Cos2 - Cos0) < 0.1f ? 0 : 1;
+
+			assert(!Error);
+		}
+
+		return Error;
+	}
+}//namespace taylorCos
+
+namespace taylor2
+{
+	glm::vec4 const AngleShift(0.0f, glm::pi<float>() * 0.5f, glm::pi<float>() * 1.0f, glm::pi<float>() * 1.5f);
+
+	float taylorCosA(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 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 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] = taylorCosA(AngleShift.x + Begin + Steps * static_cast<float>(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 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] = taylorCosB(AngleShift.x + Begin + Steps * static_cast<float>(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 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;
+}