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