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 27_CLC_OVERLOAD _CLC_DEF float exp(float x) { 28 29 // Reduce x 30 const float ln2HI = 0x1.62e300p-1f; 31 const float ln2LO = 0x1.2fefa2p-17f; 32 const float invln2 = 0x1.715476p+0f; 33 34 float fhalF = x < 0.0f ? -0.5f : 0.5f; 35 int p = mad(x, invln2, fhalF); 36 float fp = (float)p; 37 float hi = mad(fp, -ln2HI, x); // t*ln2HI is exact here 38 float lo = -fp*ln2LO; 39 40 // Evaluate poly 41 float t = hi + lo; 42 float tt = t*t; 43 float v = mad(tt, 44 -mad(tt, 45 mad(tt, 46 mad(tt, 47 mad(tt, 0x1.637698p-25f, -0x1.bbd41cp-20f), 48 0x1.1566aap-14f), 49 -0x1.6c16c2p-9f), 50 0x1.555556p-3f), 51 t); 52 53 float y = 1.0f - (((-lo) - MATH_DIVIDE(t * v, 2.0f - v)) - hi); 54 55 // Scale by 2^p 56 float r = as_float(as_int(y) + (p << 23)); 57 58 const float ulim = 0x1.62e430p+6f; // ln(largest_normal) = 88.72283905206835305366 59 const float llim = -0x1.5d589ep+6f; // ln(smallest_normal) = -87.33654475055310898657 60 61 r = x < llim ? 0.0f : r; 62 r = x < ulim ? r : as_float(0x7f800000); 63 return isnan(x) ? x : r; 64} 65 66_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, exp, float) 67 68#ifdef cl_khr_fp64 69 70#include "exp_helper.h" 71 72#pragma OPENCL EXTENSION cl_khr_fp64 : enable 73 74_CLC_OVERLOAD _CLC_DEF double exp(double x) { 75 76 const double X_MIN = -0x1.74910d52d3051p+9; // -1075*ln(2) 77 const double X_MAX = 0x1.62e42fefa39efp+9; // 1024*ln(2) 78 const double R_64_BY_LOG2 = 0x1.71547652b82fep+6; // 64/ln(2) 79 const double R_LOG2_BY_64_LD = 0x1.62e42fefa0000p-7; // head ln(2)/64 80 const double R_LOG2_BY_64_TL = 0x1.cf79abc9e3b39p-46; // tail ln(2)/64 81 82 int n = convert_int(x * R_64_BY_LOG2); 83 double r = fma(-R_LOG2_BY_64_TL, (double)n, fma(-R_LOG2_BY_64_LD, (double)n, x)); 84 return __clc_exp_helper(x, X_MIN, X_MAX, r, n); 85} 86 87_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, exp, double) 88 89#endif 90 91#ifdef cl_khr_fp16 92 93#pragma OPENCL EXTENSION cl_khr_fp16 : enable 94 95_CLC_DEFINE_UNARY_BUILTIN_FP16(exp) 96 97#endif 98