|
@@ -2,267 +2,76 @@
|
|
|
// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
|
|
// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
// Created : 2006-01-08
|
|
// Created : 2006-01-08
|
|
|
-// Updated : 2006-01-08
|
|
|
|
|
|
|
+// Updated : 2011-10-14
|
|
|
// Licence : This source is under MIT License
|
|
// Licence : This source is under MIT License
|
|
|
// File : glm/gtx/fast_trigonometry.inl
|
|
// File : glm/gtx/fast_trigonometry.inl
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
|
|
|
|
-namespace glm{
|
|
|
|
|
|
|
+#include "../core/_vectorize.hpp"
|
|
|
|
|
|
|
|
-// sin
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastSin(const T x)
|
|
|
|
|
|
|
+namespace glm
|
|
|
{
|
|
{
|
|
|
- return x - ((x * x * x) / T(6)) + ((x * x * x * x * x) / T(120)) - ((x * x * x * x * x * x * x) / T(5040));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ // sin
|
|
|
|
|
+ template <typename T>
|
|
|
|
|
+ GLM_FUNC_QUALIFIER T fastSin(T const & x)
|
|
|
|
|
+ {
|
|
|
|
|
+ return x - ((x * x * x) / T(6)) + ((x * x * x * x * x) / T(120)) - ((x * x * x * x * x * x * x) / T(5040));
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec2<T> fastSin(
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastSin(x.x),
|
|
|
|
|
- fastSin(x.y));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC(fastSin)
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec3<T> fastSin(
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastSin(x.x),
|
|
|
|
|
- fastSin(x.y),
|
|
|
|
|
- fastSin(x.z));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ // 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));
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec4<T> fastSin(
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastSin(x.x),
|
|
|
|
|
- fastSin(x.y),
|
|
|
|
|
- fastSin(x.z),
|
|
|
|
|
- fastSin(x.w));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC(fastCos)
|
|
|
|
|
|
|
|
-// cos
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastCos(const T 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));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ // tan
|
|
|
|
|
+ template <typename T>
|
|
|
|
|
+ GLM_FUNC_QUALIFIER T fastTan(T const & x)
|
|
|
|
|
+ {
|
|
|
|
|
+ return x + (x * x * x * T(0.3333333333)) + (x * x * x * x * x * T(0.1333333333333)) + (x * x * x * x * x * x * x * T(0.0539682539));
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec2<T> fastCos(
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastCos(x.x),
|
|
|
|
|
- fastCos(x.y));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC(fastTan)
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec3<T> fastCos(
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastCos(x.x),
|
|
|
|
|
- fastCos(x.y),
|
|
|
|
|
- fastCos(x.z));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ // asin
|
|
|
|
|
+ template <typename T>
|
|
|
|
|
+ GLM_FUNC_QUALIFIER T fastAsin(T const & x)
|
|
|
|
|
+ {
|
|
|
|
|
+ return x + (x * x * x * T(0.166666667)) + (x * x * x * x * x * T(0.075)) + (x * x * x * x * x * x * x * T(0.0446428571)) + (x * x * x * x * x * x * x * x * x * T(0.0303819444));// + (x * x * x * x * x * x * x * x * x * x * x * T(0.022372159));
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec4<T> fastCos(
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastCos(x.x),
|
|
|
|
|
- fastCos(x.y),
|
|
|
|
|
- fastCos(x.z),
|
|
|
|
|
- fastCos(x.w));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC(fastAsin)
|
|
|
|
|
|
|
|
-// tan
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastTan(const T x)
|
|
|
|
|
-{
|
|
|
|
|
- return x + (x * x * x * T(0.3333333333)) + (x * x * x * x * x * T(0.1333333333333)) + (x * x * x * x * x * x * x * T(0.0539682539));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ // acos
|
|
|
|
|
+ template <typename T>
|
|
|
|
|
+ GLM_FUNC_QUALIFIER T fastAcos(T const & x)
|
|
|
|
|
+ {
|
|
|
|
|
+ return T(1.5707963267948966192313216916398) - fastAsin(x); //(PI / 2)
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec2<T> fastTan(
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastTan(x.x),
|
|
|
|
|
- fastTan(x.y));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC(fastAcos)
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec3<T> fastTan(
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastTan(x.x),
|
|
|
|
|
- fastTan(x.y),
|
|
|
|
|
- fastTan(x.z));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ // atan
|
|
|
|
|
+ template <typename T>
|
|
|
|
|
+ GLM_FUNC_QUALIFIER T fastAtan(T const & y, T const & x)
|
|
|
|
|
+ {
|
|
|
|
|
+ T sgn = sign(y) * sign(x);
|
|
|
|
|
+ return abs(fastAtan(y / x)) * sgn;
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec4<T> fastTan(
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastTan(x.x),
|
|
|
|
|
- fastTan(x.y),
|
|
|
|
|
- fastTan(x.z),
|
|
|
|
|
- fastTan(x.w));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC_VEC(fastAtan)
|
|
|
|
|
|
|
|
-// asin
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastAsin(const T x)
|
|
|
|
|
-{
|
|
|
|
|
- return x + (x * x * x * T(0.166666667)) + (x * x * x * x * x * T(0.075)) + (x * x * x * x * x * x * x * T(0.0446428571)) + (x * x * x * x * x * x * x * x * x * T(0.0303819444));// + (x * x * x * x * x * x * x * x * x * x * x * T(0.022372159));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T> detail::tvec2<T> fastAsin(
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastAsin(x.x),
|
|
|
|
|
- fastAsin(x.y));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T> detail::tvec3<T> fastAsin(
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastAsin(x.x),
|
|
|
|
|
- fastAsin(x.y),
|
|
|
|
|
- fastAsin(x.z));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ template <typename T>
|
|
|
|
|
+ GLM_FUNC_QUALIFIER T fastAtan(T const & x)
|
|
|
|
|
+ {
|
|
|
|
|
+ return x - (x * x * x * T(0.333333333333)) + (x * x * x * x * x * T(0.2)) - (x * x * x * x * x * x * x * T(0.1428571429)) + (x * x * x * x * x * x * x * x * x * T(0.111111111111)) - (x * x * x * x * x * x * x * x * x * x * x * T(0.0909090909));
|
|
|
|
|
+ }
|
|
|
|
|
|
|
|
-template <typename T> detail::tvec4<T> fastAsin(
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastAsin(x.x),
|
|
|
|
|
- fastAsin(x.y),
|
|
|
|
|
- fastAsin(x.z),
|
|
|
|
|
- fastAsin(x.w));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-// acos
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastAcos(const T x)
|
|
|
|
|
-{
|
|
|
|
|
- return T(1.5707963267948966192313216916398) - fastAsin(x); //(PI / 2)
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T> detail::tvec2<T> fastAcos(
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastAcos(x.x),
|
|
|
|
|
- fastAcos(x.y));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T> detail::tvec3<T> fastAcos(
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastAcos(x.x),
|
|
|
|
|
- fastAcos(x.y),
|
|
|
|
|
- fastAcos(x.z));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T> detail::tvec4<T> fastAcos(
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastAcos(x.x),
|
|
|
|
|
- fastAcos(x.y),
|
|
|
|
|
- fastAcos(x.z),
|
|
|
|
|
- fastAcos(x.w));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-// atan
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastAtan(const T y, const T x)
|
|
|
|
|
-{
|
|
|
|
|
- T sgn = sign(y) * sign(x);
|
|
|
|
|
- return abs(fastAtan(y / x)) * sgn;
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec2<T> fastAtan(
|
|
|
|
|
- const detail::tvec2<T>& y,
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastAtan(y.x, x.x),
|
|
|
|
|
- fastAtan(y.y, x.y));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec3<T> fastAtan(
|
|
|
|
|
- const detail::tvec3<T>& y,
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastAtan(y.x, x.x),
|
|
|
|
|
- fastAtan(y.y, x.y),
|
|
|
|
|
- fastAtan(y.z, x.z));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec4<T> fastAtan(
|
|
|
|
|
- const detail::tvec4<T>& y,
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastAtan(y.x, x.x),
|
|
|
|
|
- fastAtan(y.y, x.y),
|
|
|
|
|
- fastAtan(y.z, x.z),
|
|
|
|
|
- fastAtan(y.w, x.w));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER T fastAtan(const T x)
|
|
|
|
|
-{
|
|
|
|
|
- return x - (x * x * x * T(0.333333333333)) + (x * x * x * x * x * T(0.2)) - (x * x * x * x * x * x * x * T(0.1428571429)) + (x * x * x * x * x * x * x * x * x * T(0.111111111111)) - (x * x * x * x * x * x * x * x * x * x * x * T(0.0909090909));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec2<T> fastAtan(
|
|
|
|
|
- const detail::tvec2<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec2<T>(
|
|
|
|
|
- fastAtan(x.x),
|
|
|
|
|
- fastAtan(x.y));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec3<T> fastAtan(
|
|
|
|
|
- const detail::tvec3<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec3<T>(
|
|
|
|
|
- fastAtan(x.x),
|
|
|
|
|
- fastAtan(x.y),
|
|
|
|
|
- fastAtan(x.z));
|
|
|
|
|
-}
|
|
|
|
|
-
|
|
|
|
|
-template <typename T>
|
|
|
|
|
-GLM_FUNC_QUALIFIER detail::tvec4<T> fastAtan(
|
|
|
|
|
- const detail::tvec4<T>& x)
|
|
|
|
|
-{
|
|
|
|
|
- return detail::tvec4<T>(
|
|
|
|
|
- fastAtan(x.x),
|
|
|
|
|
- fastAtan(x.y),
|
|
|
|
|
- fastAtan(x.z),
|
|
|
|
|
- fastAtan(x.w));
|
|
|
|
|
-}
|
|
|
|
|
|
|
+ VECTORIZE_VEC(fastAtan)
|
|
|
|
|
|
|
|
}//namespace glm
|
|
}//namespace glm
|