libclc/generic/lib/math/atanpi.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 atanpi(float x) {
  29     const float pi = 3.1415926535897932f;
  30
  31     uint ux = as_uint(x);
  32     uint aux = ux & EXSIGNBIT_SP32;
  33     uint sx = ux ^ aux;
  34
  35     float xbypi = MATH_DIVIDE(x, pi);
  36     float shalf = as_float(sx | as_uint(0.5f));
  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  ? shalf : 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     z = MATH_DIVIDE(z, pi);
  90     float zs = as_float(sx | as_uint(z));
  91
  92     ret  = aux < 0x4c800000 ?  zs : ret;
  93
  94     // |x| < 2^-19
  95     ret = aux < 0x36000000 ? xbypi : ret;
  96     return ret;
  97 }
  98
  99 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atanpi, float)
 100
 101 #ifdef cl_khr_fp64
 102 #pragma OPENCL EXTENSION cl_khr_fp64 : enable
 103
 104 _CLC_OVERLOAD _CLC_DEF double atanpi(double x) {
 105     const double pi = 0x1.921fb54442d18p+1;
 106
 107     double v = fabs(x);
 108
 109     // 2^56 > v > 39/16
 110     double a = -1.0;
 111     double b = v;
 112     // (chi + clo) = arctan(infinity)
 113     double chi = 1.57079632679489655800e+00;
 114     double clo = 6.12323399573676480327e-17;
 115
 116     double ta = v - 1.5;
 117     double tb = 1.0 + 1.5 * v;
 118     int l = v <= 0x1.38p+1; // 39/16 > v > 19/16
 119     a = l ? ta : a;
 120     b = l ? tb : b;
 121     // (chi + clo) = arctan(1.5)
 122     chi = l ? 9.82793723247329054082e-01 : chi;
 123     clo = l ? 1.39033110312309953701e-17 : clo;
 124
 125     ta = v - 1.0;
 126     tb = 1.0 + v;
 127     l = v <= 0x1.3p+0; // 19/16 > v > 11/16
 128     a = l ? ta : a;
 129     b = l ? tb : b;
 130     // (chi + clo) = arctan(1.)
 131     chi = l ? 7.85398163397448278999e-01 : chi;
 132     clo = l ? 3.06161699786838240164e-17 : clo;
 133
 134     ta = 2.0 * v - 1.0;
 135     tb = 2.0 + v;
 136     l = v <= 0x1.6p-1; // 11/16 > v > 7/16
 137     a = l ? ta : a;
 138     b = l ? tb : b;
 139     // (chi + clo) = arctan(0.5)
 140     chi = l ? 4.63647609000806093515e-01 : chi;
 141     clo = l ? 2.26987774529616809294e-17 : clo;
 142
 143     l = v <= 0x1.cp-2; // v < 7/16
 144     a = l ? v : a;
 145     b = l ? 1.0 : b;;
 146     chi = l ? 0.0 : chi;
 147     clo = l ? 0.0 : clo;
 148
 149     // Core approximation: Remez(4,4) on [-7/16,7/16]
 150     double r = a / b;
 151     double s = r * r;
 152     double qn = fma(s,
 153                     fma(s,
 154                         fma(s,
 155                             fma(s, 0.142316903342317766e-3,
 156                                    0.304455919504853031e-1),
 157                             0.220638780716667420e0),
 158                         0.447677206805497472e0),
 159                     0.268297920532545909e0);
 160
 161     double qd = fma(s,
 162                     fma(s,
 163                         fma(s,
 164                             fma(s, 0.389525873944742195e-1,
 165                                    0.424602594203847109e0),
 166                             0.141254259931958921e1),
 167                         0.182596787737507063e1),
 168                     0.804893761597637733e0);
 169
 170     double q = r * s * qn / qd;
 171     r = (chi - ((q - clo) - r)) / pi;
 172     double vp = v / pi;
 173
 174     double z = isnan(x) ? x : 0.5;
 175     z = v <= 0x1.0p+56 ? r : z;
 176     z = v < 0x1.0p-26 ? vp : z;
 177     return x == v ? z : -z;
 178 }
 179
 180 _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atanpi, double)
 181
 182 #endif