Merge pull request #264 from Nojan/fast_trigonometry

More precision for fastCos and fastSin #264

glm/gtc/constants.hpp

@@ -71,6 +71,11 @@ namespace glm
 	template <typename genType>
 	GLM_FUNC_DECL genType pi();
 
+	/// Return pi * 2.
+	/// @see gtc_constants
+	template <typename genType>
+	GLM_FUNC_DECL genType two_pi();
+
 	/// Return square root of pi.
 	/// @see gtc_constants
 	template <typename genType>
@@ -81,6 +86,11 @@ namespace glm
 	template <typename genType>
 	GLM_FUNC_DECL genType half_pi();
 
+	/// Return pi / 2 * 3.
+	/// @see gtc_constants
+	template <typename genType>
+	GLM_FUNC_DECL genType three_over_two_pi();
+
 	/// Return pi / 4.
 	/// @see gtc_constants
 	template <typename genType>
@@ -91,11 +101,21 @@ namespace glm
 	template <typename genType>
 	GLM_FUNC_DECL genType one_over_pi();
 
+	/// Return 1 / (pi * 2).
+	/// @see gtc_constants
+	template <typename genType>
+	GLM_FUNC_DECL genType one_over_two_pi();
+
 	/// Return 2 / pi.
 	/// @see gtc_constants
 	template <typename genType>
 	GLM_FUNC_DECL genType two_over_pi();
 
+	/// Return 4 / pi.
+	/// @see gtc_constants
+	template <typename genType>
+	GLM_FUNC_DECL genType four_over_pi();
+
 	/// Return 2 / sqrt(pi).
 	/// @see gtc_constants
 	template <typename genType>

glm/gtc/constants.inl

@@ -54,6 +54,12 @@ namespace glm
 		return genType(3.14159265358979323846264338327950288);
 	}
 
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType two_pi()
+	{
+		return genType(6.28318530717958647692528676655900576);
+	}
+
 	template <typename genType>
 	GLM_FUNC_QUALIFIER genType root_pi()
 	{
@@ -66,6 +72,12 @@ namespace glm
 		return genType(1.57079632679489661923132169163975144);
 	}
 
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType three_over_two_pi()
+	{
+		return genType(4.71238898038468985769396507491925432);           
+	}
+
 	template <typename genType>
 	GLM_FUNC_QUALIFIER genType quarter_pi()
 	{
@@ -78,12 +90,24 @@ namespace glm
 		return genType(0.318309886183790671537767526745028724);
 	}
 
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType one_over_two_pi()
+	{
+		return genType(0.159154943091895335768883763372514362);
+	}
+
 	template <typename genType>
 	GLM_FUNC_QUALIFIER genType two_over_pi()
 	{
 		return genType(0.636619772367581343075535053490057448);
 	}
 
+	template <typename genType>
+	GLM_FUNC_QUALIFIER genType four_over_pi()
+	{
+		return genType(1.273239544735162686151070106980114898);
+	}
+
 	template <typename genType>
 	GLM_FUNC_QUALIFIER genType two_over_root_pi()
 	{

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);

glm/gtx/fast_trigonometry.inl

@@ -9,24 +9,45 @@
 
 namespace glm
 {
-	// sin
-	template <typename T> 
-	GLM_FUNC_QUALIFIER T fastSin(T const & x)
+	template <typename T>
+	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));
+		return abs<T>(mod<T>(angle, two_pi<T>()));
 	}
 
-	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)