/////////////////////////////////////////////////////////////////////////////////////////////////// // OpenGL Mathematics Copyright (c) 2005 - 2014 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.inl /////////////////////////////////////////////////////////////////////////////////////////////////// namespace glm { // fastPow: template <typename genType> GLM_FUNC_QUALIFIER genType fastPow(genType const & x, genType const & y) { return exp(y * log(x)); } VECTORIZE_VEC_VEC(fastPow) template <typename T> GLM_FUNC_QUALIFIER T fastPow(const 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> GLM_FUNC_QUALIFIER detail::tvec2<T, P> fastPow( const detail::tvec2<T, P>& x, const detail::tvec2<int, P>& y) { return detail::tvec2<T, P>( fastPow(x.x, y.x), fastPow(x.y, y.y)); } template <typename T, precision P> GLM_FUNC_QUALIFIER detail::tvec3<T, P> fastPow( const detail::tvec3<T, P>& x, const detail::tvec3<int, P>& y) { return detail::tvec3<T, P>( fastPow(x.x, y.x), fastPow(x.y, y.y), fastPow(x.z, y.z)); } template <typename T, precision P> GLM_FUNC_QUALIFIER detail::tvec4<T, P> fastPow( const detail::tvec4<T, P>& x, const detail::tvec4<int, P>& y) { return detail::tvec4<T, P>( 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);; } */ VECTORIZE_VEC(fastExp) // fastLog template <typename genType> GLM_FUNC_QUALIFIER genType fastLog(genType const & 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))); } */ VECTORIZE_VEC(fastLog) //fastExp2, ln2 = 0.69314718055994530941723212145818f template <typename genType> GLM_FUNC_QUALIFIER genType fastExp2(genType const & x) { return fastExp(0.69314718055994530941723212145818f * x); } VECTORIZE_VEC(fastExp2) // fastLog2, ln2 = 0.69314718055994530941723212145818f template <typename genType> GLM_FUNC_QUALIFIER genType fastLog2(genType const & x) { return fastLog(x) / 0.69314718055994530941723212145818f; } VECTORIZE_VEC(fastLog2) }//namespace glm