libclc/generic/lib/math/atan.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 "math.h"
  24 #include "../clcmacro.h"
  25
  26 #include <clc/clc.h>
  27
  28 _CLC_OVERLOAD _CLC_DEF float atan(float x)
  29 {
  30     const float piby2 = 1.5707963267948966f; // 0x3ff921fb54442d18
  31
  32     uint ux = as_uint(x);
  33     uint aux = ux & EXSIGNBIT_SP32;
  34     uint sx = ux ^ aux;
  35
  36     float spiby2 = as_float(sx | as_uint(piby2));
  37
  38     float v = as_float(aux);
  39
  40     // Return for NaN
  41     float ret = x;
  42
  43     // 2^26 <= |x| <= Inf => atan(x) is close to piby2
  44     ret = aux <= PINFBITPATT_SP32  ? spiby2 : ret;
  45
  46     // Reduce arguments 2^-19 <= |x| < 2^26
  47
  48     // 39/16 <= x < 2^26
  49     x = -MATH_RECIP(v);
  50     float c = 1.57079632679489655800f; // atan(infinity)
  51
  52     // 19/16 <= x < 39/16
  53     int l = aux < 0x401c0000;
  54     float xx = MATH_DIVIDE(v - 1.5f, mad(v, 1.5f, 1.0f));
  55     x = l ? xx : x;
  56     c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)
  57
  58     // 11/16 <= x < 19/16
  59     l = aux < 0x3f980000U;
  60     xx =  MATH_DIVIDE(v - 1.0f, 1.0f + v);
  61     x = l ? xx : x;
  62     c = l ? 7.85398163397448278999e-01f : c; // atan(1)
  63
  64     // 7/16 <= x < 11/16
  65     l = aux < 0x3f300000;
  66     xx = MATH_DIVIDE(mad(v, 2.0f, -1.0f), 2.0f + v);
  67     x = l ? xx : x;
  68     c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)
  69
  70     // 2^-19 <= x < 7/16
  71     l = aux < 0x3ee00000;
  72     x = l ? v : x;
  73     c = l ? 0.0f : c;
  74
  75     // Core approximation: Remez(2,2) on [-7/16,7/16]
  76
  77     float s = x * x;
  78     float a = mad(s,
  79                   mad(s, 0.470677934286149214138357545549e-2f, 0.192324546402108583211697690500f),
  80                   0.296528598819239217902158651186f);
  81
  82     float b = mad(s,
  83                   mad(s, 0.299309699959659728404442796915f, 0.111072499995399550138837673349e1f),
  84                   0.889585796862432286486651434570f);
  85
  86     float q = x * s * MATH_DIVIDE(a, b);
  87
  88     float z = c - (q - x);
  89     float zs = as_float(sx | as_uint(z));
  90
  91     ret  = aux < 0x4c800000 ?  zs : ret;
  92
  93     // |x| < 2^-19
  94     ret = aux < 0x36000000 ? as_float(ux) : ret;
  95     return ret;
  96 }
  97
  98 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan, float);
  99
 100 #ifdef cl_khr_fp64
 101
 102 #pragma OPENCL EXTENSION cl_khr_fp64 : enable
 103
 104
 105 _CLC_OVERLOAD _CLC_DEF double atan(double x)
 106 {
 107     const double piby2 = 1.5707963267948966e+00; // 0x3ff921fb54442d18
 108
 109     double v = fabs(x);
 110
 111     // 2^56 > v > 39/16
 112     double a = -1.0;
 113     double b = v;
 114     // (chi + clo) = arctan(infinity)
 115     double chi = 1.57079632679489655800e+00;
 116     double clo = 6.12323399573676480327e-17;
 117
 118     double ta = v - 1.5;
 119     double tb = 1.0 + 1.5 * v;
 120     int l = v <= 0x1.38p+1; // 39/16 > v > 19/16
 121     a = l ? ta : a;
 122     b = l ? tb : b;
 123     // (chi + clo) = arctan(1.5)
 124     chi = l ? 9.82793723247329054082e-01 : chi;
 125     clo = l ? 1.39033110312309953701e-17 : clo;
 126
 127     ta = v - 1.0;
 128     tb = 1.0 + v;
 129     l = v <= 0x1.3p+0; // 19/16 > v > 11/16
 130     a = l ? ta : a;
 131     b = l ? tb : b;
 132     // (chi + clo) = arctan(1.)
 133     chi = l ? 7.85398163397448278999e-01 : chi;
 134     clo = l ? 3.06161699786838240164e-17 : clo;
 135
 136     ta = 2.0 * v - 1.0;
 137     tb = 2.0 + v;
 138     l = v <= 0x1.6p-1; // 11/16 > v > 7/16
 139     a = l ? ta : a;
 140     b = l ? tb : b;
 141     // (chi + clo) = arctan(0.5)
 142     chi = l ? 4.63647609000806093515e-01 : chi;
 143     clo = l ? 2.26987774529616809294e-17 : clo;
 144
 145     l = v <= 0x1.cp-2; // v < 7/16
 146     a = l ? v : a;
 147     b = l ? 1.0 : b;;
 148     chi = l ? 0.0 : chi;
 149     clo = l ? 0.0 : clo;
 150
 151     // Core approximation: Remez(4,4) on [-7/16,7/16]
 152     double r = a / b;
 153     double s = r * r;
 154     double qn = fma(s,
 155                     fma(s,
 156                         fma(s,
 157                             fma(s, 0.142316903342317766e-3,
 158                                    0.304455919504853031e-1),
 159                             0.220638780716667420e0),
 160                         0.447677206805497472e0),
 161                     0.268297920532545909e0);
 162
 163     double qd = fma(s,
 164                     fma(s,
 165                         fma(s,
 166                             fma(s, 0.389525873944742195e-1,
 167                                    0.424602594203847109e0),
 168                             0.141254259931958921e1),
 169                         0.182596787737507063e1),
 170                     0.804893761597637733e0);
 171
 172     double q = r * s * qn / qd;
 173     r = chi - ((q - clo) - r);
 174
 175     double z = isnan(x) ? x : piby2;
 176     z = v <= 0x1.0p+56 ? r : z;
 177     z = v < 0x1.0p-26 ? v : z;
 178     return x == v ? z : -z;
 179 }
 180
 181 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan, double);
 182
 183 #endif // cl_khr_fp64