libclc/generic/lib/math/cosh.cl

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