/// @ref gtx_fast_exponential | |
/// @file glm/gtx/fast_exponential.inl | |
namespace glm | |
{ | |
// fastPow: | |
template <typename genType> | |
GLM_FUNC_QUALIFIER genType fastPow(genType x, genType y) | |
{ | |
return exp(y * log(x)); | |
} | |
template <typename T, precision P, template <typename, precision> class vecType> | |
GLM_FUNC_QUALIFIER vecType<T, P> fastPow(vecType<T, P> const & x, vecType<T, P> const & y) | |
{ | |
return exp(y * log(x)); | |
} | |
template <typename T> | |
GLM_FUNC_QUALIFIER T fastPow(T x, int y) | |
{ | |
T f = static_cast<T>(1); | |
for(int i = 0; i < y; ++i) | |
f *= x; | |
return f; | |
} | |
template <typename T, precision P, template <typename, precision> class vecType> | |
GLM_FUNC_QUALIFIER vecType<T, P> fastPow(vecType<T, P> const & x, vecType<int, P> const & y) | |
{ | |
vecType<T, P> Result(uninitialize); | |
for(length_t i = 0, n = x.length(); i < n; ++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 <typename T> | |
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 <typename T, precision P, template <typename, precision> class vecType> | |
GLM_FUNC_QUALIFIER vecType<T, P> fastExp(vecType<T, P> const & x) | |
{ | |
return detail::functor1<T, T, P, vecType>::call(fastExp, x); | |
} | |
// fastLog | |
template <typename genType> | |
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 <typename T, precision P, template <typename, precision> class vecType> | |
GLM_FUNC_QUALIFIER vecType<T, P> fastLog(vecType<T, P> const & x) | |
{ | |
return detail::functor1<T, T, P, vecType>::call(fastLog, x); | |
} | |
//fastExp2, ln2 = 0.69314718055994530941723212145818f | |
template <typename genType> | |
GLM_FUNC_QUALIFIER genType fastExp2(genType x) | |
{ | |
return fastExp(0.69314718055994530941723212145818f * x); | |
} | |
template <typename T, precision P, template <typename, precision> class vecType> | |
GLM_FUNC_QUALIFIER vecType<T, P> fastExp2(vecType<T, P> const & x) | |
{ | |
return detail::functor1<T, T, P, vecType>::call(fastExp2, x); | |
} | |
// fastLog2, ln2 = 0.69314718055994530941723212145818f | |
template <typename genType> | |
GLM_FUNC_QUALIFIER genType fastLog2(genType x) | |
{ | |
return fastLog(x) / 0.69314718055994530941723212145818f; | |
} | |
template <typename T, precision P, template <typename, precision> class vecType> | |
GLM_FUNC_QUALIFIER vecType<T, P> fastLog2(vecType<T, P> const & x) | |
{ | |
return detail::functor1<T, T, P, vecType>::call(fastLog2, x); | |
} | |
}//namespace glm |