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#ifdef cl_khr_fp64 24 25#include <clc/clc.h> 26#include "ep_log.h" 27#include "math.h" 28#include "tables.h" 29 30#pragma OPENCL EXTENSION cl_khr_fp64 : enable 31 32#define LN0 8.33333333333317923934e-02 33#define LN1 1.25000000037717509602e-02 34#define LN2 2.23213998791944806202e-03 35#define LN3 4.34887777707614552256e-04 36 37#define LF0 8.33333333333333593622e-02 38#define LF1 1.24999999978138668903e-02 39#define LF2 2.23219810758559851206e-03 40 41_CLC_DEF void __clc_ep_log(double x, int *xexp, double *r1, double *r2) 42{ 43 // Computes natural log(x). Algorithm based on: 44 // Ping-Tak Peter Tang 45 // "Table-driven implementation of the logarithm function in IEEE 46 // floating-point arithmetic" 47 // ACM Transactions on Mathematical Software (TOMS) 48 // Volume 16, Issue 4 (December 1990) 49 int near_one = x >= 0x1.e0faap-1 & x <= 0x1.1082cp+0; 50 51 ulong ux = as_ulong(x); 52 ulong uxs = as_ulong(as_double(0x03d0000000000000UL | ux) - 0x1.0p-962); 53 int c = ux < IMPBIT_DP64; 54 ux = c ? uxs : ux; 55 int expadjust = c ? 60 : 0; 56 57 // Store the exponent of x in xexp and put f into the range [0.5,1) 58 int xexp1 = ((as_int2(ux).hi >> 20) & 0x7ff) - EXPBIAS_DP64 - expadjust; 59 double f = as_double(HALFEXPBITS_DP64 | (ux & MANTBITS_DP64)); 60 *xexp = near_one ? 0 : xexp1; 61 62 double r = x - 1.0; 63 double u1 = MATH_DIVIDE(r, 2.0 + r); 64 double ru1 = -r * u1; 65 u1 = u1 + u1; 66 67 int index = as_int2(ux).hi >> 13; 68 index = ((0x80 | (index & 0x7e)) >> 1) + (index & 0x1); 69 70 double f1 = index * 0x1.0p-7; 71 double f2 = f - f1; 72 double u2 = MATH_DIVIDE(f2, fma(0.5, f2, f1)); 73 74 double2 tv = USE_TABLE(ln_tbl, (index - 64)); 75 double z1 = tv.s0; 76 double q = tv.s1; 77 78 z1 = near_one ? r : z1; 79 q = near_one ? 0.0 : q; 80 double u = near_one ? u1 : u2; 81 double v = u*u; 82 83 double cc = near_one ? ru1 : u2; 84 85 double z21 = fma(v, fma(v, fma(v, LN3, LN2), LN1), LN0); 86 double z22 = fma(v, fma(v, LF2, LF1), LF0); 87 double z2 = near_one ? z21 : z22; 88 z2 = fma(u*v, z2, cc) + q; 89 90 *r1 = z1; 91 *r2 = z2; 92} 93 94#endif 95