1/* 2 * Copyright (c) 2014,2015 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#include <clc/clcmacro.h> 25#include <clc/math/math.h> 26#include <clc/math/tables.h> 27 28_CLC_OVERLOAD _CLC_DEF float cosh(float x) { 29 30 // After dealing with special cases the computation is split into regions as follows. 31 // abs(x) >= max_cosh_arg: 32 // cosh(x) = sign(x)*Inf 33 // abs(x) >= small_threshold: 34 // cosh(x) = sign(x)*exp(abs(x))/2 computed using the 35 // splitexp and scaleDouble functions as for exp_amd(). 36 // abs(x) < small_threshold: 37 // compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) 38 // cosh(x) is then z. 39 40 const float max_cosh_arg = 0x1.65a9fap+6f; 41 const float small_threshold = 0x1.0a2b24p+3f; 42 43 uint ux = as_uint(x); 44 uint aux = ux & EXSIGNBIT_SP32; 45 float y = as_float(aux); 46 47 // Find the integer part y0 of y and the increment dy = y - y0. We then compute 48 // z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy) 49 // z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy) 50 // where sinh(y0) and cosh(y0) are tabulated above. 51 52 int ind = (int)y; 53 ind = (uint)ind > 36U ? 0 : ind; 54 55 float dy = y - ind; 56 float dy2 = dy * dy; 57 58 float sdy = mad(dy2, 59 mad(dy2, 60 mad(dy2, 61 mad(dy2, 62 mad(dy2, 63 mad(dy2, 0.7746188980094184251527126e-12f, 0.160576793121939886190847e-9f), 64 0.250521176994133472333666e-7f), 65 0.275573191913636406057211e-5f), 66 0.198412698413242405162014e-3f), 67 0.833333333333329931873097e-2f), 68 0.166666666666666667013899e0f); 69 sdy = mad(sdy, dy*dy2, dy); 70 71 float cdy = mad(dy2, 72 mad(dy2, 73 mad(dy2, 74 mad(dy2, 75 mad(dy2, 76 mad(dy2, 0.1163921388172173692062032e-10f, 0.208744349831471353536305e-8f), 77 0.275573350756016588011357e-6f), 78 0.248015872460622433115785e-4f), 79 0.138888888889814854814536e-2f), 80 0.416666666666660876512776e-1f), 81 0.500000000000000005911074e0f); 82 cdy = mad(cdy, dy2, 1.0f); 83 84 float2 tv = USE_TABLE(sinhcosh_tbl, ind); 85 float z = mad(tv.s0, sdy, tv.s1 * cdy); 86 87 // When exp(-x) is insignificant compared to exp(x), return exp(x)/2 88 float t = exp(y - 0x1.62e500p-1f); 89 float zsmall = mad(0x1.a0210ep-18f, t, t); 90 z = y >= small_threshold ? zsmall : z; 91 92 // Corner cases 93 z = y >= max_cosh_arg ? as_float(PINFBITPATT_SP32) : z; 94 z = aux > PINFBITPATT_SP32 ? as_float(QNANBITPATT_SP32) : z; 95 z = aux < 0x38800000 ? 1.0f : z; 96 97 return z; 98} 99 100_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cosh, float); 101 102#ifdef cl_khr_fp64 103#pragma OPENCL EXTENSION cl_khr_fp64 : enable 104 105_CLC_OVERLOAD _CLC_DEF double cosh(double x) { 106 107 // After dealing with special cases the computation is split into 108 // regions as follows: 109 // 110 // abs(x) >= max_cosh_arg: 111 // cosh(x) = sign(x)*Inf 112 // 113 // abs(x) >= small_threshold: 114 // cosh(x) = sign(x)*exp(abs(x))/2 computed using the 115 // splitexp and scaleDouble functions as for exp_amd(). 116 // 117 // abs(x) < small_threshold: 118 // compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) 119 // cosh(x) is then sign(x)*z. 120 121 // This is ln(2^1025) 122 const double max_cosh_arg = 7.10475860073943977113e+02; // 0x408633ce8fb9f87e 123 124 // This is where exp(-x) is insignificant compared to exp(x) = ln(2^27) 125 const double small_threshold = 0x1.2b708872320e2p+4; 126 127 double y = fabs(x); 128 129 // In this range we find the integer part y0 of y 130 // and the increment dy = y - y0. We then compute 131 // z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy) 132 // where sinh(y0) and cosh(y0) are tabulated above. 133 134 int ind = min((int)y, 36); 135 double dy = y - ind; 136 double dy2 = dy * dy; 137 138 double sdy = dy * dy2 * 139 fma(dy2, 140 fma(dy2, 141 fma(dy2, 142 fma(dy2, 143 fma(dy2, 144 fma(dy2, 0.7746188980094184251527126e-12, 0.160576793121939886190847e-9), 145 0.250521176994133472333666e-7), 146 0.275573191913636406057211e-5), 147 0.198412698413242405162014e-3), 148 0.833333333333329931873097e-2), 149 0.166666666666666667013899e0); 150 151 double cdy = dy2 * fma(dy2, 152 fma(dy2, 153 fma(dy2, 154 fma(dy2, 155 fma(dy2, 156 fma(dy2, 0.1163921388172173692062032e-10, 0.208744349831471353536305e-8), 157 0.275573350756016588011357e-6), 158 0.248015872460622433115785e-4), 159 0.138888888889814854814536e-2), 160 0.416666666666660876512776e-1), 161 0.500000000000000005911074e0); 162 163 // At this point sinh(dy) is approximated by dy + sdy, 164 // and cosh(dy) is approximated by 1 + cdy. 165 double2 tv = USE_TABLE(cosh_tbl, ind); 166 double cl = tv.s0; 167 double ct = tv.s1; 168 tv = USE_TABLE(sinh_tbl, ind); 169 double sl = tv.s0; 170 double st = tv.s1; 171 172 double z = fma(sl, dy, fma(sl, sdy, fma(cl, cdy, fma(st, dy, fma(st, sdy, ct*cdy)) + ct))) + cl; 173 174 // Other cases 175 z = y < 0x1.0p-28 ? 1.0 : z; 176 177 double t = exp(y - 0x1.62e42fefa3800p-1); 178 t = fma(t, -0x1.ef35793c76641p-45, t); 179 z = y >= small_threshold ? t : z; 180 181 z = y >= max_cosh_arg ? as_double(PINFBITPATT_DP64) : z; 182 183 z = isinf(x) | isnan(x) ? y : z; 184 185 return z; 186 187} 188 189_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cosh, double) 190 191#endif 192 193#ifdef cl_khr_fp16 194 195#pragma OPENCL EXTENSION cl_khr_fp16 : enable 196 197_CLC_DEFINE_UNARY_BUILTIN_FP16(cosh) 198 199#endif 200