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Diffstat (limited to 'src/glm/gtx/fast_exponential.inl')
| -rw-r--r-- | src/glm/gtx/fast_exponential.inl | 294 |
1 files changed, 294 insertions, 0 deletions
diff --git a/src/glm/gtx/fast_exponential.inl b/src/glm/gtx/fast_exponential.inl new file mode 100644 index 0000000..59c0397 --- /dev/null +++ b/src/glm/gtx/fast_exponential.inl @@ -0,0 +1,294 @@ +///////////////////////////////////////////////////////////////////////////////////////////////////
+// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Created : 2006-01-09
+// Updated : 2006-01-09
+// Licence : This source is under MIT License
+// File : glm/gtx/fast_exponential.h
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+namespace glm{
+namespace gtx{
+namespace fast_exponential
+{
+ // fastPow:
+ template <typename T>
+ GLM_FUNC_QUALIFIER T fastPow(const T x, const T y)
+ {
+ return exp(y * log(x));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec2<T> fastPow(
+ const detail::tvec2<T>& x,
+ const detail::tvec2<T>& y)
+ {
+ return detail::tvec2<T>(
+ fastPow(x.x, y.x),
+ fastPow(x.y, y.y));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec3<T> fastPow(
+ const detail::tvec3<T>& x,
+ const detail::tvec3<T>& y)
+ {
+ return detail::tvec3<T>(
+ fastPow(x.x, y.x),
+ fastPow(x.y, y.y),
+ fastPow(x.z, y.z));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec4<T> fastPow(
+ const detail::tvec4<T>& x,
+ const detail::tvec4<T>& y)
+ {
+ return detail::tvec4<T>(
+ fastPow(x.x, y.x),
+ fastPow(x.y, y.y),
+ fastPow(x.z, y.z),
+ fastPow(x.w, y.w));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER T fastPow(const T x, int y)
+ {
+ T f = T(1);
+ for(int i = 0; i < y; ++i)
+ f *= x;
+ return f;
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec2<T> fastPow(
+ const detail::tvec2<T>& x,
+ const detail::tvec2<int>& y)
+ {
+ return detail::tvec2<T>(
+ fastPow(x.x, y.x),
+ fastPow(x.y, y.y));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec3<T> fastPow(
+ const detail::tvec3<T>& x,
+ const detail::tvec3<int>& y)
+ {
+ return detail::tvec3<T>(
+ fastPow(x.x, y.x),
+ fastPow(x.y, y.y),
+ fastPow(x.z, y.z));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec4<T> fastPow(
+ const detail::tvec4<T>& x,
+ const detail::tvec4<int>& y)
+ {
+ return detail::tvec4<T>(
+ fastPow(x.x, y.x),
+ fastPow(x.y, y.y),
+ fastPow(x.z, y.z),
+ fastPow(x.w, y.w));
+ }
+
+ // fastExp
+ // Note: This function provides accurate results only for value between -1 and 1, else avoid it.
+ template <typename T>
+ GLM_FUNC_QUALIFIER T fastExp(const T x)
+ {
+ // This has a better looking and same performance in release mode than the following code. However, in debug mode it's slower.
+ // return 1.0f + x * (1.0f + x * 0.5f * (1.0f + x * 0.3333333333f * (1.0f + x * 0.25 * (1.0f + x * 0.2f))));
+ T x2 = x * x;
+ T x3 = x2 * x;
+ T x4 = x3 * x;
+ T x5 = x4 * x;
+ return T(1) + x + (x2 * T(0.5)) + (x3 * T(0.1666666667)) + (x4 * T(0.041666667)) + (x5 * T(0.008333333333));
+ }
+/* // Try to handle all values of float... but often shower than std::exp, glm::floor and the loop kill the performance
+ GLM_FUNC_QUALIFIER float fastExp(float x)
+ {
+ const float e = 2.718281828f;
+ const float IntegerPart = floor(x);
+ const float FloatPart = x - IntegerPart;
+ float z = 1.f;
+
+ for(int i = 0; i < int(IntegerPart); ++i)
+ z *= e;
+
+ const float x2 = FloatPart * FloatPart;
+ const float x3 = x2 * FloatPart;
+ const float x4 = x3 * FloatPart;
+ const float x5 = x4 * FloatPart;
+ return z * (1.0f + FloatPart + (x2 * 0.5f) + (x3 * 0.1666666667f) + (x4 * 0.041666667f) + (x5 * 0.008333333333f));
+ }
+
+ // Increase accuracy on number bigger that 1 and smaller than -1 but it's not enough for high and negative numbers
+ GLM_FUNC_QUALIFIER float fastExp(float x)
+ {
+ // This has a better looking and same performance in release mode than the following code. However, in debug mode it's slower.
+ // return 1.0f + x * (1.0f + x * 0.5f * (1.0f + x * 0.3333333333f * (1.0f + x * 0.25 * (1.0f + x * 0.2f))));
+ float x2 = x * x;
+ float x3 = x2 * x;
+ float x4 = x3 * x;
+ float x5 = x4 * x;
+ float x6 = x5 * x;
+ float x7 = x6 * x;
+ float x8 = x7 * x;
+ return 1.0f + x + (x2 * 0.5f) + (x3 * 0.1666666667f) + (x4 * 0.041666667f) + (x5 * 0.008333333333f)+ (x6 * 0.00138888888888f) + (x7 * 0.000198412698f) + (x8 * 0.0000248015873f);;
+ }
+*/
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec2<T> fastExp(
+ const detail::tvec2<T>& x)
+ {
+ return detail::tvec2<T>(
+ fastExp(x.x),
+ fastExp(x.y));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec3<T> fastExp(
+ const detail::tvec3<T>& x)
+ {
+ return detail::tvec3<T>(
+ fastExp(x.x),
+ fastExp(x.y),
+ fastExp(x.z));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec4<T> fastExp(
+ const detail::tvec4<T>& x)
+ {
+ return detail::tvec4<T>(
+ fastExp(x.x),
+ fastExp(x.y),
+ fastExp(x.z),
+ fastExp(x.w));
+ }
+
+ // fastLog
+ template <typename T>
+ GLM_FUNC_QUALIFIER T fastLog(const T x)
+ {
+ return std::log(x);
+ }
+
+ /* Slower than the VC7.1 function...
+ GLM_FUNC_QUALIFIER float fastLog(float x)
+ {
+ float y1 = (x - 1.0f) / (x + 1.0f);
+ float y2 = y1 * y1;
+ return 2.0f * y1 * (1.0f + y2 * (0.3333333333f + y2 * (0.2f + y2 * 0.1428571429f)));
+ }
+ */
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec2<T> fastLog(
+ const detail::tvec2<T>& x)
+ {
+ return detail::tvec2<T>(
+ fastLog(x.x),
+ fastLog(x.y));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec3<T> fastLog(
+ const detail::tvec3<T>& x)
+ {
+ return detail::tvec3<T>(
+ fastLog(x.x),
+ fastLog(x.y),
+ fastLog(x.z));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec4<T> fastLog(
+ const detail::tvec4<T>& x)
+ {
+ return detail::tvec4<T>(
+ fastLog(x.x),
+ fastLog(x.y),
+ fastLog(x.z),
+ fastLog(x.w));
+ }
+
+ //fastExp2, ln2 = 0.69314718055994530941723212145818f
+ template <typename T>
+ GLM_FUNC_QUALIFIER T fastExp2(const T x)
+ {
+ return fastExp(0.69314718055994530941723212145818f * x);
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec2<T> fastExp2(
+ const detail::tvec2<T>& x)
+ {
+ return detail::tvec2<T>(
+ fastExp2(x.x),
+ fastExp2(x.y));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec3<T> fastExp2(
+ const detail::tvec3<T>& x)
+ {
+ return detail::tvec3<T>(
+ fastExp2(x.x),
+ fastExp2(x.y),
+ fastExp2(x.z));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec4<T> fastExp2(
+ const detail::tvec4<T>& x)
+ {
+ return detail::tvec4<T>(
+ fastExp2(x.x),
+ fastExp2(x.y),
+ fastExp2(x.z),
+ fastExp2(x.w));
+ }
+
+ // fastLog2, ln2 = 0.69314718055994530941723212145818f
+ template <typename T>
+ GLM_FUNC_QUALIFIER T fastLog2(const T x)
+ {
+ return fastLog(x) / 0.69314718055994530941723212145818f;
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec2<T> fastLog2(
+ const detail::tvec2<T>& x)
+ {
+ return detail::tvec2<T>(
+ fastLog2(x.x),
+ fastLog2(x.y));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec3<T> fastLog2(
+ const detail::tvec3<T>& x)
+ {
+ return detail::tvec3<T>(
+ fastLog2(x.x),
+ fastLog2(x.y),
+ fastLog2(x.z));
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER detail::tvec4<T> fastLog2(
+ const detail::tvec4<T>& x)
+ {
+ return detail::tvec4<T>(
+ fastLog2(x.x),
+ fastLog2(x.y),
+ fastLog2(x.z),
+ fastLog2(x.w));
+ }
+
+}//namespace fast_exponential
+}//namespace gtx
+}//namespace glm
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