///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 – 2015 G-Truc Creation (www.g-truc.net)
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/// furnished to do so, subject to the following conditions:
///
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
///
/// Restrictions:
/// By making use of the Software for military purposes, you choose to make
/// a Bunny unhappy.
///
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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///
/// @ref gtx_fast_exponential
/// @file glm/gtx/fast_exponential.inl
/// @date 2006-01-09 / 2011-06-07
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////////////////////
namespace glm
{
// fastPow:
template
GLM_FUNC_QUALIFIER genType fastPow(genType x, genType y)
{
return exp(y * log(x));
}
template
GLM_FUNC_QUALIFIER vecType
{
return exp(y * log(x));
}
template
GLM_FUNC_QUALIFIER T fastPow(T x, int y)
{
T f = static_cast
for(int i = 0; i < y; ++i)
f *= x;
return f;
}
template
GLM_FUNC_QUALIFIER vecType
{
vecType
for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
Result[i] = fastPow(x[i], y[i]);
return Result;
}
// fastExp
// Note: This function provides accurate results only for value between -1 and 1, else avoid it.
template
GLM_FUNC_QUALIFIER T fastExp(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
GLM_FUNC_QUALIFIER vecType
{
return detail::functor1
}
// fastLog
template
GLM_FUNC_QUALIFIER genType fastLog(genType 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
GLM_FUNC_QUALIFIER vecType
{
return detail::functor1
}
//fastExp2, ln2 = 0.69314718055994530941723212145818f
template
GLM_FUNC_QUALIFIER genType fastExp2(genType x)
{
return fastExp(0.69314718055994530941723212145818f * x);
}
template
GLM_FUNC_QUALIFIER vecType
{
return detail::functor1
}
// fastLog2, ln2 = 0.69314718055994530941723212145818f
template
GLM_FUNC_QUALIFIER genType fastLog2(genType x)
{
return fastLog(x) / 0.69314718055994530941723212145818f;
}
template
GLM_FUNC_QUALIFIER vecType
{
return detail::functor1
}
}//namespace glm