1 /////////////////////////////////////////////////////////////////////////////////////////////////// 2 // OpenGL Mathematics Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) 3 /////////////////////////////////////////////////////////////////////////////////////////////////// 4 // Created : 2006-01-09 5 // Updated : 2006-01-09 6 // Licence : This source is under MIT License 7 // File : glm/gtx/fast_exponential.inl 8 /////////////////////////////////////////////////////////////////////////////////////////////////// 9 10 namespace glm 11 { 12 // fastPow: 13 template <typename genType> 14 GLM_FUNC_QUALIFIER genType fastPow(genType const & x, genType const & y) 15 { 16 return exp(y * log(x)); 17 } 18 19 VECTORIZE_VEC_VEC(fastPow) 20 21 template <typename T> 22 GLM_FUNC_QUALIFIER T fastPow(const T x, int y) 23 { 24 T f = static_cast<T>(1); 25 for(int i = 0; i < y; ++i) 26 f *= x; 27 return f; 28 } 29 30 template <typename T, precision P> 31 GLM_FUNC_QUALIFIER detail::tvec2<T, P> fastPow( 32 const detail::tvec2<T, P>& x, 33 const detail::tvec2<int, P>& y) 34 { 35 return detail::tvec2<T, P>( 36 fastPow(x.x, y.x), 37 fastPow(x.y, y.y)); 38 } 39 40 template <typename T, precision P> 41 GLM_FUNC_QUALIFIER detail::tvec3<T, P> fastPow( 42 const detail::tvec3<T, P>& x, 43 const detail::tvec3<int, P>& y) 44 { 45 return detail::tvec3<T, P>( 46 fastPow(x.x, y.x), 47 fastPow(x.y, y.y), 48 fastPow(x.z, y.z)); 49 } 50 51 template <typename T, precision P> 52 GLM_FUNC_QUALIFIER detail::tvec4<T, P> fastPow( 53 const detail::tvec4<T, P>& x, 54 const detail::tvec4<int, P>& y) 55 { 56 return detail::tvec4<T, P>( 57 fastPow(x.x, y.x), 58 fastPow(x.y, y.y), 59 fastPow(x.z, y.z), 60 fastPow(x.w, y.w)); 61 } 62 63 // fastExp 64 // Note: This function provides accurate results only for value between -1 and 1, else avoid it. 65 template <typename T> 66 GLM_FUNC_QUALIFIER T fastExp(const T x) 67 { 68 // This has a better looking and same performance in release mode than the following code. However, in debug mode it's slower. 69 // return 1.0f + x * (1.0f + x * 0.5f * (1.0f + x * 0.3333333333f * (1.0f + x * 0.25 * (1.0f + x * 0.2f)))); 70 T x2 = x * x; 71 T x3 = x2 * x; 72 T x4 = x3 * x; 73 T x5 = x4 * x; 74 return T(1) + x + (x2 * T(0.5)) + (x3 * T(0.1666666667)) + (x4 * T(0.041666667)) + (x5 * T(0.008333333333)); 75 } 76 /* // Try to handle all values of float... but often shower than std::exp, glm::floor and the loop kill the performance 77 GLM_FUNC_QUALIFIER float fastExp(float x) 78 { 79 const float e = 2.718281828f; 80 const float IntegerPart = floor(x); 81 const float FloatPart = x - IntegerPart; 82 float z = 1.f; 83 84 for(int i = 0; i < int(IntegerPart); ++i) 85 z *= e; 86 87 const float x2 = FloatPart * FloatPart; 88 const float x3 = x2 * FloatPart; 89 const float x4 = x3 * FloatPart; 90 const float x5 = x4 * FloatPart; 91 return z * (1.0f + FloatPart + (x2 * 0.5f) + (x3 * 0.1666666667f) + (x4 * 0.041666667f) + (x5 * 0.008333333333f)); 92 } 93 94 // Increase accuracy on number bigger that 1 and smaller than -1 but it's not enough for high and negative numbers 95 GLM_FUNC_QUALIFIER float fastExp(float x) 96 { 97 // This has a better looking and same performance in release mode than the following code. However, in debug mode it's slower. 98 // return 1.0f + x * (1.0f + x * 0.5f * (1.0f + x * 0.3333333333f * (1.0f + x * 0.25 * (1.0f + x * 0.2f)))); 99 float x2 = x * x; 100 float x3 = x2 * x; 101 float x4 = x3 * x; 102 float x5 = x4 * x; 103 float x6 = x5 * x; 104 float x7 = x6 * x; 105 float x8 = x7 * x; 106 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);; 107 } 108 */ 109 110 VECTORIZE_VEC(fastExp) 111 112 // fastLog 113 template <typename genType> 114 GLM_FUNC_QUALIFIER genType fastLog(genType const & x) 115 { 116 return std::log(x); 117 } 118 119 /* Slower than the VC7.1 function... 120 GLM_FUNC_QUALIFIER float fastLog(float x) 121 { 122 float y1 = (x - 1.0f) / (x + 1.0f); 123 float y2 = y1 * y1; 124 return 2.0f * y1 * (1.0f + y2 * (0.3333333333f + y2 * (0.2f + y2 * 0.1428571429f))); 125 } 126 */ 127 128 VECTORIZE_VEC(fastLog) 129 130 //fastExp2, ln2 = 0.69314718055994530941723212145818f 131 template <typename genType> 132 GLM_FUNC_QUALIFIER genType fastExp2(genType const & x) 133 { 134 return fastExp(0.69314718055994530941723212145818f * x); 135 } 136 137 VECTORIZE_VEC(fastExp2) 138 139 // fastLog2, ln2 = 0.69314718055994530941723212145818f 140 template <typename genType> 141 GLM_FUNC_QUALIFIER genType fastLog2(genType const & x) 142 { 143 return fastLog(x) / 0.69314718055994530941723212145818f; 144 } 145 146 VECTORIZE_VEC(fastLog2) 147 148 }//namespace glm 149
