From 710e13a8e62015da18f7cbbfc9bc9d82b2807b54 Mon Sep 17 00:00:00 2001
From: Mathias Labeyrie <mathias.labeyrie@gmail.com>
Date: Wed, 5 Nov 2014 10:55:42 +0100
Subject: [PATCH] Much more precise fastCos and fastSin

fastCos and fastSin had a max error of ~0.2 on [-pi pi].
The updated version is ~0.000007.
---
 glm/gtx/fast_trigonometry.hpp | 10 +++++++---
 glm/gtx/fast_trigonometry.inl | 33 ++++++++++++++++++++++++++++-----
 2 files changed, 35 insertions(+), 8 deletions(-)

diff --git a/glm/gtx/fast_trigonometry.hpp b/glm/gtx/fast_trigonometry.hpp
index f89a6df6..17b04cfb 100644
--- a/glm/gtx/fast_trigonometry.hpp
+++ b/glm/gtx/fast_trigonometry.hpp
@@ -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);
diff --git a/glm/gtx/fast_trigonometry.inl b/glm/gtx/fast_trigonometry.inl
index b68e8fd5..632be5d2 100644
--- a/glm/gtx/fast_trigonometry.inl
+++ b/glm/gtx/fast_trigonometry.inl
@@ -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)