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 183