libclc/generic/lib/math/asinpi.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 asinpi(float x) {
  29     // Computes arcsin(x).
  30     // The argument is first reduced by noting that arcsin(x)
  31     // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
  32     // For denormal and small arguments arcsin(x) = x to machine
  33     // accuracy. Remaining argument ranges are handled as follows.
  34     // For abs(x) <= 0.5 use
  35     // arcsin(x) = x + x^3*R(x^2)
  36     // where R(x^2) is a rational minimax approximation to
  37     // (arcsin(x) - x)/x^3.
  38     // For abs(x) > 0.5 exploit the identity:
  39     // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
  40     // together with the above rational approximation, and
  41     // reconstruct the terms carefully.
  42
  43
  44     const float pi = 3.1415926535897933e+00f;
  45     const float piby2_tail = 7.5497894159e-08F;   /* 0x33a22168 */
  46     const float hpiby2_head = 7.8539812565e-01F;  /* 0x3f490fda */
  47
  48     uint ux = as_uint(x);
  49     uint aux = ux & EXSIGNBIT_SP32;
  50     uint xs = ux ^ aux;
  51     float shalf = as_float(xs | as_uint(0.5f));
  52
  53     int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
  54
  55     float y = as_float(aux);
  56
  57     // abs(x) >= 0.5
  58     int transform = xexp >= -1;
  59
  60     float y2 = y * y;
  61     float rt = 0.5f * (1.0f - y);
  62     float r = transform ? rt : y2;
  63
  64     // Use a rational approximation for [0.0, 0.5]
  65     float a = mad(r,
  66                   mad(r,
  67                       mad(r, -0.00396137437848476485201154797087F, -0.0133819288943925804214011424456F),
  68                       -0.0565298683201845211985026327361F),
  69                   0.184161606965100694821398249421F);
  70     float b = mad(r, -0.836411276854206731913362287293F, 1.10496961524520294485512696706F);
  71     float u = r * MATH_DIVIDE(a, b);
  72
  73     float s = MATH_SQRT(r);
  74     float s1 = as_float(as_uint(s) & 0xffff0000);
  75     float c = MATH_DIVIDE(mad(-s1, s1, r), s + s1);
  76     float p = mad(2.0f*s, u, -mad(c, -2.0f, piby2_tail));
  77     float q = mad(s1, -2.0f, hpiby2_head);
  78     float vt = hpiby2_head - (p - q);
  79     float v = mad(y, u, y);
  80     v = transform ? vt : v;
  81     v = MATH_DIVIDE(v, pi);
  82     float xbypi = MATH_DIVIDE(x, pi);
  83
  84     float ret = as_float(xs | as_uint(v));
  85     ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret;
  86     ret = aux == 0x3f800000U ? shalf : ret;
  87     ret = xexp < -14 ? xbypi : ret;
  88
  89     return ret;
  90 }
  91
  92 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, asinpi, float)
  93
  94 #ifdef cl_khr_fp64
  95 #pragma OPENCL EXTENSION cl_khr_fp64 : enable
  96
  97 _CLC_OVERLOAD _CLC_DEF double asinpi(double x) {
  98     // Computes arcsin(x).
  99     // The argument is first reduced by noting that arcsin(x)
 100     // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
 101     // For denormal and small arguments arcsin(x) = x to machine
 102     // accuracy. Remaining argument ranges are handled as follows.
 103     // For abs(x) <= 0.5 use
 104     // arcsin(x) = x + x^3*R(x^2)
 105     // where R(x^2) is a rational minimax approximation to
 106     // (arcsin(x) - x)/x^3.
 107     // For abs(x) > 0.5 exploit the identity:
 108     // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
 109     // together with the above rational approximation, and
 110     // reconstruct the terms carefully.
 111
 112     const double pi = 0x1.921fb54442d18p+1;
 113     const double piby2_tail = 6.1232339957367660e-17;   /* 0x3c91a62633145c07 */
 114     const double hpiby2_head = 7.8539816339744831e-01;  /* 0x3fe921fb54442d18 */
 115
 116     double y = fabs(x);
 117     int xneg = as_int2(x).hi < 0;
 118     int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64;
 119
 120     // abs(x) >= 0.5
 121     int transform = xexp >= -1;
 122
 123     double rt = 0.5 * (1.0 - y);
 124     double y2 = y * y;
 125     double r = transform ? rt : y2;
 126
 127     // Use a rational approximation for [0.0, 0.5]
 128     double un = fma(r,
 129                     fma(r,
 130                         fma(r,
 131                             fma(r,
 132                                 fma(r, 0.0000482901920344786991880522822991,
 133                                        0.00109242697235074662306043804220),
 134                                 -0.0549989809235685841612020091328),
 135                             0.275558175256937652532686256258),
 136                         -0.445017216867635649900123110649),
 137                     0.227485835556935010735943483075);
 138
 139     double ud = fma(r,
 140                     fma(r,
 141                         fma(r,
 142                             fma(r, 0.105869422087204370341222318533,
 143                                    -0.943639137032492685763471240072),
 144                             2.76568859157270989520376345954),
 145                         -3.28431505720958658909889444194),
 146                     1.36491501334161032038194214209);
 147
 148     double u = r * MATH_DIVIDE(un, ud);
 149
 150
 151     // Reconstruct asin carefully in transformed region
 152     double s = sqrt(r);
 153     double sh = as_double(as_ulong(s) & 0xffffffff00000000UL);
 154     double c = MATH_DIVIDE(fma(-sh, sh, r), s + sh);
 155     double p = fma(2.0*s, u, -fma(-2.0, c, piby2_tail));
 156     double q = fma(-2.0, sh, hpiby2_head);
 157     double vt = hpiby2_head - (p - q);
 158     double v = fma(y, u, y);
 159     v = transform ? vt : v;
 160
 161     v = xexp < -28 ? y : v;
 162     v = MATH_DIVIDE(v, pi);
 163     v = xexp >= 0 ? as_double(QNANBITPATT_DP64) : v;
 164     v = y == 1.0 ? 0.5 : v;
 165     return xneg ? -v : v;
 166 }
 167
 168 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, asinpi, double)
 169
 170 #endif