1/* 2 * Copyright (c) 2014 Advanced Micro Devices, Inc. 3 * 4 * Permission is hereby granted, free of charge, to any person obtaining a copy 5 * of this software and associated documentation files (the "Software"), to deal 6 * in the Software without restriction, including without limitation the rights 7 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 8 * copies of the Software, and to permit persons to whom the Software is 9 * furnished to do so, subject to the following conditions: 10 * 11 * The above copyright notice and this permission notice shall be included in 12 * all copies or substantial portions of the Software. 13 * 14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 17 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 18 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 19 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 20 * THE SOFTWARE. 21 */ 22 23#include <clc/clc.h> 24 25#include "math.h" 26#include "../clcmacro.h" 27 28_CLC_OVERLOAD _CLC_DEF float tanh(float x) 29{ 30 // The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent 31 // to the following three formulae: 32 // 1. (exp(x) - exp(-x))/(exp(x) + exp(-x)) 33 // 2. (1 - (2/(exp(2*x) + 1 ))) 34 // 3. (exp(2*x) - 1)/(exp(2*x) + 1) 35 // but computationally, some formulae are better on some ranges. 36 37 const float large_threshold = 0x1.0a2b24p+3f; 38 39 uint ux = as_uint(x); 40 uint aux = ux & EXSIGNBIT_SP32; 41 uint xs = ux ^ aux; 42 43 float y = as_float(aux); 44 float y2 = y*y; 45 46 float a1 = mad(y2, 47 mad(y2, 0.4891631088530669873e-4F, -0.14628356048797849e-2F), 48 -0.28192806108402678e0F); 49 float b1 = mad(y2, 0.3427017942262751343e0F, 0.845784192581041099e0F); 50 51 float a2 = mad(y2, 52 mad(y2, 0.3827534993599483396e-4F, -0.12325644183611929e-2F), 53 -0.24069858695196524e0F); 54 float b2 = mad(y2, 0.292529068698052819e0F, 0.72209738473684982e0F); 55 56 int c = y < 0.9f; 57 float a = c ? a1 : a2; 58 float b = c ? b1 : b2; 59 float zlo = mad(MATH_DIVIDE(a, b), y*y2, y); 60 61 float p = exp(2.0f * y) + 1.0f; 62 float zhi = 1.0F - MATH_DIVIDE(2.0F, p); 63 64 float z = y <= 1.0f ? zlo : zhi; 65 z = as_float(xs | as_uint(z)); 66 67 // Edge cases 68 float sone = as_float(0x3f800000U | xs); 69 z = y > large_threshold ? sone : z; 70 z = aux < 0x39000000 | aux > 0x7f800000 ? x : z; 71 72 return z; 73} 74 75_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, tanh, float); 76 77#ifdef cl_khr_fp64 78 79#pragma OPENCL EXTENSION cl_khr_fp64 : enable 80 81_CLC_OVERLOAD _CLC_DEF double tanh(double x) 82{ 83 // The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent 84 // to the following three formulae: 85 // 1. (exp(x) - exp(-x))/(exp(x) + exp(-x)) 86 // 2. (1 - (2/(exp(2*x) + 1 ))) 87 // 3. (exp(2*x) - 1)/(exp(2*x) + 1) 88 // but computationally, some formulae are better on some ranges. 89 90 // The point at which e^-x is insignificant compared to e^x = ln(2^27) 91 const double large_threshold = 0x1.2b708872320e2p+4; 92 93 ulong ux = as_ulong(x); 94 ulong ax = ux & ~SIGNBIT_DP64; 95 ulong sx = ux ^ ax; 96 double y = as_double(ax); 97 double y2 = y * y; 98 99 // y < 0.9 100 double znl = fma(y2, 101 fma(y2, 102 fma(y2, -0.142077926378834722618091e-7, -0.200047621071909498730453e-3), 103 -0.176016349003044679402273e-1), 104 -0.274030424656179760118928e0); 105 106 double zdl = fma(y2, 107 fma(y2, 108 fma(y2, 0.2091140262529164482568557e-3, 0.201562166026937652780575e-1), 109 0.381641414288328849317962e0), 110 0.822091273968539282568011e0); 111 112 // 0.9 <= y <= 1 113 double znm = fma(y2, 114 fma(y2, 115 fma(y2, -0.115475878996143396378318e-7, -0.165597043903549960486816e-3), 116 -0.146173047288731678404066e-1), 117 -0.227793870659088295252442e0); 118 119 double zdm = fma(y2, 120 fma(y2, 121 fma(y2, 0.173076050126225961768710e-3, 0.167358775461896562588695e-1), 122 0.317204558977294374244770e0), 123 0.683381611977295894959554e0); 124 125 int c = y < 0.9; 126 double zn = c ? znl : znm; 127 double zd = c ? zdl : zdm; 128 double z = y + y*y2 * MATH_DIVIDE(zn, zd); 129 130 // y > 1 131 double p = exp(2.0 * y) + 1.0; 132 double zg = 1.0 - 2.0 / p; 133 134 z = y > 1.0 ? zg : z; 135 136 // Other cases 137 z = y < 0x1.0p-28 | ax > PINFBITPATT_DP64 ? x : z; 138 139 z = y > large_threshold ? 1.0 : z; 140 141 return as_double(sx | as_ulong(z)); 142} 143 144_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, tanh, double); 145 146#endif // cl_khr_fp64 147