libclc/generic/lib/math/ep_log.cl

   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