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Much more precise fastCos and fastSin

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fastCos and fastSin had a max error of ~0.2 on [-pi pi].
The updated version is ~0.000007.
This commit is contained in:
Mathias Labeyrie 2014-11-05 10:55:42 +01:00
parent b0c1777b57
commit 710e13a8e6
2 changed files with 35 additions and 8 deletions
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10
glm/gtx/fast_trigonometry.hpp
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@ -39,6 +39,7 @@
// Dependency:
#include "../glm.hpp"
#include "../gtc/constants.hpp"
#if(defined(GLM_MESSAGES) && !defined(GLM_EXT_INCLUDED))
# pragma message("GLM: GLM_GTX_fast_trigonometry extension included")
@ -49,14 +50,17 @@ namespace glm
/// @addtogroup gtx_fast_trigonometry
/// @{
//! Faster than the common sin function but less accurate.
//! Defined between -2pi and 2pi.
//! Wrap an angle to [0 2pi[
//! From GLM_GTX_fast_trigonometry extension.
template <typename T>
GLM_FUNC_DECL T wrapAngle(const T& angle);
//! Faster than the common sin function but less accurate.
//! From GLM_GTX_fast_trigonometry extension.
template <typename T>
GLM_FUNC_DECL T fastSin(const T& angle);
//! Faster than the common cos function but less accurate.
//! Defined between -2pi and 2pi.
//! From GLM_GTX_fast_trigonometry extension.
template <typename T>
GLM_FUNC_DECL T fastCos(const T& angle);

33
glm/gtx/fast_trigonometry.inl
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@ -9,24 +9,47 @@
namespace glm
{
// sin
template <typename T>
GLM_FUNC_QUALIFIER T fastSin(T const & x)
GLM_FUNC_QUALIFIER T wrapAngle(T const & angle)
{
return x - ((x * x * x) / T(6)) + ((x * x * x * x * x) / T(120)) - ((x * x * x * x * x * x * x) / T(5040));
T result = angle - floor<T>(angle * one_over_two_pi<T>()) * two_pi<T>();
result = result > T(0) ? result : -result;
return result;
}
VECTORIZE_VEC(fastSin)
VECTORIZE_VEC(wrapAngle)
template <typename T>
GLM_FUNC_QUALIFIER T cos_52s(T const & x)
{
T const xx(x * x);
return (T(0.9999932946) + xx * (T(-0.4999124376) + xx * (T(0.0414877472) + xx * T(-0.0012712095))));
}
VECTORIZE_VEC(cos_52s)
// cos
template <typename T>
GLM_FUNC_QUALIFIER T fastCos(T const & x)
{
return T(1) - (x * x * T(0.5)) + (x * x * x * x * T(0.041666666666)) - (x * x * x * x * x * x * T(0.00138888888888));
T const angle(wrapAngle<T>(x));
if(angle<half_pi<T>()) return cos_52s(angle);
if(angle<pi<T>()) return -cos_52s(pi<T>() - angle);
if(angle<(T(3) * half_pi<T>())) return -cos_52s(angle - pi<T>());
return cos_52s(two_pi<T>() - angle);
}
VECTORIZE_VEC(fastCos)
// sin
template <typename T>
GLM_FUNC_QUALIFIER T fastSin(T const & x)
{
return fastCos<T>(half_pi<T>() - x);
}
VECTORIZE_VEC(fastSin)
// tan
template <typename T>
GLM_FUNC_QUALIFIER T fastTan(T const & x)