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1//===----------------------------------------------------------------------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#if __CLC_FPSIZE == 3210 11_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atan(__CLC_GENTYPE x) {12 const __CLC_GENTYPE piby2 = 1.5707963267948966f; // 0x3ff921fb54442d1813 14 __CLC_UINTN ux = __CLC_AS_UINTN(x);15 __CLC_UINTN aux = ux & EXSIGNBIT_SP32;16 __CLC_UINTN sx = ux ^ aux;17 18 __CLC_GENTYPE spiby2 = __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(piby2));19 20 __CLC_GENTYPE v = __CLC_AS_GENTYPE(aux);21 22 // Return for NaN23 __CLC_GENTYPE ret = x;24 25 // 2^26 <= |x| <= Inf => atan(x) is close to piby226 ret = aux <= PINFBITPATT_SP32 ? spiby2 : ret;27 28 // Reduce arguments 2^-19 <= |x| < 2^2629 30 // 39/16 <= x < 2^2631 x = -MATH_RECIP(v);32 __CLC_GENTYPE c = 1.57079632679489655800f; // atan(infinity)33 34 // 19/16 <= x < 39/1635 __CLC_INTN l = aux < 0x401c0000;36 __CLC_GENTYPE xx = MATH_DIVIDE(v - 1.5f, __clc_mad(v, 1.5f, 1.0f));37 x = l ? xx : x;38 c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)39 40 // 11/16 <= x < 19/1641 l = aux < 0x3f980000U;42 xx = MATH_DIVIDE(v - 1.0f, 1.0f + v);43 x = l ? xx : x;44 c = l ? 7.85398163397448278999e-01f : c; // atan(1)45 46 // 7/16 <= x < 11/1647 l = aux < 0x3f300000;48 xx = MATH_DIVIDE(__clc_mad(v, 2.0f, -1.0f), 2.0f + v);49 x = l ? xx : x;50 c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)51 52 // 2^-19 <= x < 7/1653 l = aux < 0x3ee00000;54 x = l ? v : x;55 c = l ? 0.0f : c;56 57 // Core approximation: Remez(2,2) on [-7/16,7/16]58 59 __CLC_GENTYPE s = x * x;60 __CLC_GENTYPE a = __clc_mad(s,61 __clc_mad(s, 0.470677934286149214138357545549e-2f,62 0.192324546402108583211697690500f),63 0.296528598819239217902158651186f);64 65 __CLC_GENTYPE b = __clc_mad(s,66 __clc_mad(s, 0.299309699959659728404442796915f,67 0.111072499995399550138837673349e1f),68 0.889585796862432286486651434570f);69 70 __CLC_GENTYPE q = x * s * MATH_DIVIDE(a, b);71 72 __CLC_GENTYPE z = c - (q - x);73 __CLC_GENTYPE zs = __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(z));74 75 ret = aux < 0x4c800000 ? zs : ret;76 77 // |x| < 2^-1978 ret = aux < 0x36000000 ? __CLC_AS_GENTYPE(ux) : ret;79 return ret;80}81 82#elif __CLC_FPSIZE == 6483 84_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atan(__CLC_GENTYPE x) {85 const __CLC_GENTYPE piby2 = 1.5707963267948966e+00; // 0x3ff921fb54442d1886 87 __CLC_GENTYPE v = __clc_fabs(x);88 89 // 2^56 > v > 39/1690 __CLC_GENTYPE a = -1.0;91 __CLC_GENTYPE b = v;92 // (chi + clo) = arctan(infinity)93 __CLC_GENTYPE chi = 1.57079632679489655800e+00;94 __CLC_GENTYPE clo = 6.12323399573676480327e-17;95 96 __CLC_GENTYPE ta = v - 1.5;97 __CLC_GENTYPE tb = 1.0 + 1.5 * v;98 __CLC_LONGN l = v <= 0x1.38p+1; // 39/16 > v > 19/1699 a = l ? ta : a;100 b = l ? tb : b;101 // (chi + clo) = arctan(1.5)102 chi = l ? 9.82793723247329054082e-01 : chi;103 clo = l ? 1.39033110312309953701e-17 : clo;104 105 ta = v - 1.0;106 tb = 1.0 + v;107 l = v <= 0x1.3p+0; // 19/16 > v > 11/16108 a = l ? ta : a;109 b = l ? tb : b;110 // (chi + clo) = arctan(1.)111 chi = l ? 7.85398163397448278999e-01 : chi;112 clo = l ? 3.06161699786838240164e-17 : clo;113 114 ta = 2.0 * v - 1.0;115 tb = 2.0 + v;116 l = v <= 0x1.6p-1; // 11/16 > v > 7/16117 a = l ? ta : a;118 b = l ? tb : b;119 // (chi + clo) = arctan(0.5)120 chi = l ? 4.63647609000806093515e-01 : chi;121 clo = l ? 2.26987774529616809294e-17 : clo;122 123 l = v <= 0x1.cp-2; // v < 7/16124 a = l ? v : a;125 b = l ? 1.0 : b;126 ;127 chi = l ? 0.0 : chi;128 clo = l ? 0.0 : clo;129 130 // Core approximation: Remez(4,4) on [-7/16,7/16]131 __CLC_GENTYPE r = a / b;132 __CLC_GENTYPE s = r * r;133 __CLC_GENTYPE qn =134 __clc_fma(s,135 __clc_fma(s,136 __clc_fma(s,137 __clc_fma(s, 0.142316903342317766e-3,138 0.304455919504853031e-1),139 0.220638780716667420e0),140 0.447677206805497472e0),141 0.268297920532545909e0);142 143 __CLC_GENTYPE qd =144 __clc_fma(s,145 __clc_fma(s,146 __clc_fma(s,147 __clc_fma(s, 0.389525873944742195e-1,148 0.424602594203847109e0),149 0.141254259931958921e1),150 0.182596787737507063e1),151 0.804893761597637733e0);152 153 __CLC_GENTYPE q = r * s * qn / qd;154 r = chi - ((q - clo) - r);155 156 __CLC_GENTYPE z = __clc_isnan(x) ? x : piby2;157 z = v <= 0x1.0p+56 ? r : z;158 z = v < 0x1.0p-26 ? v : z;159 return x == v ? z : -z;160}161 162#elif __CLC_FPSIZE == 16163 164_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atan(__CLC_GENTYPE x) {165 return __CLC_CONVERT_GENTYPE(__clc_atan(__CLC_CONVERT_FLOATN(x)));166}167 168#endif169