libclc/generic/lib/math/atanh.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 "../clcmacro.h"
  27
  28 _CLC_OVERLOAD _CLC_DEF float atanh(float x) {
  29     uint ux = as_uint(x);
  30     uint ax = ux & EXSIGNBIT_SP32;
  31     uint xs = ux ^ ax;
  32
  33     // |x| > 1 or NaN
  34     float z = as_float(QNANBITPATT_SP32);
  35
  36     // |x| == 1
  37     float t = as_float(xs | PINFBITPATT_SP32);
  38     z = ax == 0x3f800000U ? t : z;
  39
  40     // 1/2 <= |x| < 1
  41     t = as_float(ax);
  42     t = MATH_DIVIDE(2.0f*t, 1.0f - t);
  43     t = 0.5f * log1p(t);
  44     t = as_float(xs | as_uint(t));
  45     z = ax < 0x3f800000U ? t : z;
  46
  47     // |x| < 1/2
  48     t = x * x;
  49     float a = mad(mad(0.92834212715e-2f, t, -0.28120347286e0f), t, 0.39453629046e0f);
  50     float b = mad(mad(0.45281890445e0f, t, -0.15537744551e1f), t, 0.11836088638e1f);
  51     float p = MATH_DIVIDE(a, b);
  52     t = mad(x*t, p, x);
  53     z = ax < 0x3f000000 ? t : z;
  54
  55     // |x| < 2^-13
  56     z = ax < 0x39000000U ? x : z;
  57
  58     return z;
  59 }
  60
  61 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atanh, float)
  62
  63 #ifdef cl_khr_fp64
  64 #pragma OPENCL EXTENSION cl_khr_fp64 : enable
  65
  66 _CLC_OVERLOAD _CLC_DEF double atanh(double x) {
  67     double absx = fabs(x);
  68
  69     double ret = absx == 1.0 ? as_double(PINFBITPATT_DP64) : as_double(QNANBITPATT_DP64);
  70
  71     // |x| >= 0.5
  72     // Note that atanh(x) = 0.5 * ln((1+x)/(1-x))
  73     // For greater accuracy we use
  74     // ln((1+x)/(1-x)) = ln(1 + 2x/(1-x)) = log1p(2x/(1-x)).
  75     double r = 0.5 * log1p(2.0 * absx / (1.0 - absx));
  76     ret = absx < 1.0 ? r : ret;
  77
  78     r = -ret;
  79     ret = x < 0.0 ? r : ret;
  80
  81     // Arguments up to 0.5 in magnitude are
  82     // approximated by a [5,5] minimax polynomial
  83     double t = x * x;
  84
  85     double pn = fma(t,
  86                     fma(t,
  87                         fma(t,
  88                             fma(t,
  89                                 fma(t, -0.10468158892753136958e-3, 0.28728638600548514553e-1),
  90                                 -0.28180210961780814148e0),
  91                             0.88468142536501647470e0),
  92                         -0.11028356797846341457e1),
  93                     0.47482573589747356373e0);
  94
  95     double pd = fma(t,
  96                     fma(t,
  97                         fma(t,
  98                             fma(t,
  99                                 fma(t, -0.35861554370169537512e-1, 0.49561196555503101989e0),
 100                                 -0.22608883748988489342e1),
 101                             0.45414700626084508355e1),
 102                         -0.41631933639693546274e1),
 103                     0.14244772076924206909e1);
 104
 105     r = fma(x*t, pn/pd, x);
 106     ret = absx < 0.5 ? r : ret;
 107
 108     return ret;
 109 }
 110
 111 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atanh, double)
 112
 113 #endif