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glm/test/gtx/gtx_fast_trigonometry.cpp

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#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/ulp.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::next_float(i) : i += 0.1f)
result = glm::fastCos(i);
const std::clock_t timestamp2 = std::clock();
for(float i = begin; i < end; i = NextFloat ? glm::next_float(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::next_float(i) : i += 0.1f)
result = glm::fastSin(i);
const std::clock_t timestamp2 = std::clock();
for(float i = begin; i < end; i = NextFloat ? glm::next_float(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::next_float(i) : i += 0.1f)
result = glm::fastTan(i);
const std::clock_t timestamp2 = std::clock();
for (float i = begin; i < end; i = NextFloat ? glm::next_float(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::next_float(i) : i += 0.1f)
result = glm::fastAcos(i);
const std::clock_t timestamp2 = std::clock();
for(float i = begin; i < end; i = NextFloat ? glm::next_float(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::next_float(i) : i += 0.1f)
result = glm::fastAsin(i);
const std::clock_t timestamp2 = std::clock();
for(float i = begin; i < end; i = NextFloat ? glm::next_float(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::next_float(i) : i += 0.1f)
result = glm::fastAtan(i);
const std::clock_t timestamp2 = std::clock();
for(float i = begin; i < end; i = NextFloat ? glm::next_float(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 Steps = (End - Begin) / 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 * 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 Steps = (End - Begin) / 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 * 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 Steps = (End - Begin) / 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 * 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 Steps = (End - Begin) / 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 * 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 Steps = (End - Begin) / 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 * 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 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;
}