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///////////////////////////////////////////////////////////////////////////////////////////////////
// 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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