libclc/generic/lib/math/clc_exp10.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 #include <clc/clc.h>
  24
  25 #include "config.h"
  26 #include "math.h"
  27 #include "tables.h"
  28 #include "../clcmacro.h"
  29
  30 //    Algorithm:
  31 //
  32 //    e^x = 2^(x/ln(2)) = 2^(x*(64/ln(2))/64)
  33 //
  34 //    x*(64/ln(2)) = n + f, |f| <= 0.5, n is integer
  35 //    n = 64*m + j,   0 <= j < 64
  36 //
  37 //    e^x = 2^((64*m + j + f)/64)
  38 //        = (2^m) * (2^(j/64)) * 2^(f/64)
  39 //        = (2^m) * (2^(j/64)) * e^(f*(ln(2)/64))
  40 //
  41 //    f = x*(64/ln(2)) - n
  42 //    r = f*(ln(2)/64) = x - n*(ln(2)/64)
  43 //
  44 //    e^x = (2^m) * (2^(j/64)) * e^r
  45 //
  46 //    (2^(j/64)) is precomputed
  47 //
  48 //    e^r = 1 + r + (r^2)/2! + (r^3)/3! + (r^4)/4! + (r^5)/5!
  49 //    e^r = 1 + q
  50 //
  51 //    q = r + (r^2)/2! + (r^3)/3! + (r^4)/4! + (r^5)/5!
  52 //
  53 //    e^x = (2^m) * ( (2^(j/64)) + q*(2^(j/64)) )
  54
  55 _CLC_DEF _CLC_OVERLOAD float __clc_exp10(float x)
  56 {
  57     const float X_MAX =  0x1.344134p+5f; // 128*log2/log10 : 38.53183944498959
  58     const float X_MIN = -0x1.66d3e8p+5f; // -149*log2/log10 : -44.8534693539332
  59
  60     const float R_64_BY_LOG10_2 = 0x1.a934f0p+7f; // 64*log10/log2 : 212.6033980727912
  61     const float R_LOG10_2_BY_64_LD = 0x1.340000p-8f; // log2/(64 * log10) lead : 0.004699707
  62     const float R_LOG10_2_BY_64_TL = 0x1.04d426p-18f; // log2/(64 * log10) tail : 0.00000388665057
  63     const float R_LN10 = 0x1.26bb1cp+1f;
  64
  65     int return_nan = isnan(x);
  66     int return_inf = x > X_MAX;
  67     int return_zero = x < X_MIN;
  68
  69     int n = convert_int(x * R_64_BY_LOG10_2);
  70
  71     float fn = (float)n;
  72     int j = n & 0x3f;
  73     int m = n >> 6;
  74     int m2 = m << EXPSHIFTBITS_SP32;
  75     float r;
  76
  77     r = R_LN10 * mad(fn, -R_LOG10_2_BY_64_TL, mad(fn, -R_LOG10_2_BY_64_LD, x));
  78
  79     // Truncated Taylor series for e^r
  80     float z2 = mad(mad(mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 0x1.000000p-1f), r*r, r);
  81
  82     float two_to_jby64 = USE_TABLE(exp_tbl, j);
  83     z2 = mad(two_to_jby64, z2, two_to_jby64);
  84
  85     float z2s = z2 * as_float(0x1 << (m + 149));
  86     float z2n = as_float(as_int(z2) + m2);
  87     z2 = m <= -126 ? z2s : z2n;
  88
  89
  90     z2 = return_inf ? as_float(PINFBITPATT_SP32) : z2;
  91     z2 = return_zero ? 0.0f : z2;
  92     z2 = return_nan ? x : z2;
  93     return z2;
  94 }
  95 _CLC_UNARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_exp10, float)
  96
  97 #ifdef cl_khr_fp64
  98 _CLC_DEF _CLC_OVERLOAD double __clc_exp10(double x)
  99 {
 100     const double X_MAX = 0x1.34413509f79ffp+8; // 1024*ln(2)/ln(10)
 101     const double X_MIN = -0x1.434e6420f4374p+8; // -1074*ln(2)/ln(10)
 102
 103     const double R_64_BY_LOG10_2 = 0x1.a934f0979a371p+7; // 64*ln(10)/ln(2)
 104     const double R_LOG10_2_BY_64_LD = 0x1.3441350000000p-8; // head ln(2)/(64*ln(10))
 105     const double R_LOG10_2_BY_64_TL = 0x1.3ef3fde623e25p-37; // tail ln(2)/(64*ln(10))
 106     const double R_LN10 = 0x1.26bb1bbb55516p+1; // ln(10)
 107
 108     int n = convert_int(x * R_64_BY_LOG10_2);
 109
 110     double dn = (double)n;
 111
 112     int j = n & 0x3f;
 113     int m = n >> 6;
 114
 115     double r = R_LN10 * fma(-R_LOG10_2_BY_64_TL, dn, fma(-R_LOG10_2_BY_64_LD, dn, x));
 116
 117     // 6 term tail of Taylor expansion of e^r
 118     double z2 = r * fma(r,
 119                         fma(r,
 120                             fma(r,
 121                                 fma(r,
 122                                     fma(r, 0x1.6c16c16c16c17p-10, 0x1.1111111111111p-7),
 123                                     0x1.5555555555555p-5),
 124                                 0x1.5555555555555p-3),
 125                             0x1.0000000000000p-1),
 126                         1.0);
 127
 128     double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j);
 129     z2 = fma(tv.s0 + tv.s1, z2, tv.s1) + tv.s0;
 130
 131     int small_value = (m < -1022) || ((m == -1022) && (z2 < 1.0));
 132
 133         int n1 = m >> 2;
 134         int n2 = m-n1;
 135         double z3= z2 * as_double(((long)n1 + 1023) << 52);
 136         z3 *= as_double(((long)n2 + 1023) << 52);
 137
 138     z2 = ldexp(z2, m);
 139     z2 = small_value ? z3: z2;
 140
 141     z2 = isnan(x) ? x : z2;
 142
 143     z2 = x > X_MAX ? as_double(PINFBITPATT_DP64) : z2;
 144     z2 = x < X_MIN ? 0.0 : z2;
 145
 146     return z2;
 147 }
 148 _CLC_UNARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_exp10, double)
 149 #endif