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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_atanpi(__CLC_GENTYPE x) {12 const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897932);13 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 xbypi = MATH_DIVIDE(x, pi);19 __CLC_GENTYPE shalf =20 __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(__CLC_FP_LIT(0.5)));21 22 __CLC_GENTYPE v = __CLC_AS_GENTYPE(aux);23 24 // Return for NaN25 __CLC_GENTYPE ret = x;26 27 // 2^26 <= |x| <= Inf => atan(x) is close to piby228 ret = aux <= PINFBITPATT_SP32 ? shalf : ret;29 30 // Reduce arguments 2^-19 <= |x| < 2^2631 32 // 39/16 <= x < 2^2633 x = -MATH_RECIP(v);34 __CLC_GENTYPE c = 1.57079632679489655800f; // atan(infinity)35 36 // 19/16 <= x < 39/1637 __CLC_INTN l = aux < 0x401c0000;38 __CLC_GENTYPE xx = MATH_DIVIDE(v - 1.5f, __clc_mad(v, 1.5f, 1.0f));39 x = l ? xx : x;40 c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)41 42 // 11/16 <= x < 19/1643 l = aux < 0x3f980000U;44 xx = MATH_DIVIDE(v - 1.0f, 1.0f + v);45 x = l ? xx : x;46 c = l ? 7.85398163397448278999e-01f : c; // atan(1)47 48 // 7/16 <= x < 11/1649 l = aux < 0x3f300000;50 xx = MATH_DIVIDE(__clc_mad(v, 2.0f, -1.0f), 2.0f + v);51 x = l ? xx : x;52 c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)53 54 // 2^-19 <= x < 7/1655 l = aux < 0x3ee00000;56 x = l ? v : x;57 c = l ? 0.0f : c;58 59 // Core approximation: Remez(2,2) on [-7/16,7/16]60 61 __CLC_GENTYPE s = x * x;62 __CLC_GENTYPE a = __clc_mad(s,63 __clc_mad(s, 0.470677934286149214138357545549e-2f,64 0.192324546402108583211697690500f),65 0.296528598819239217902158651186f);66 67 __CLC_GENTYPE b = __clc_mad(s,68 __clc_mad(s, 0.299309699959659728404442796915f,69 0.111072499995399550138837673349e1f),70 0.889585796862432286486651434570f);71 72 __CLC_GENTYPE q = x * s * MATH_DIVIDE(a, b);73 74 __CLC_GENTYPE z = c - (q - x);75 z = MATH_DIVIDE(z, pi);76 __CLC_GENTYPE zs = __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(z));77 78 ret = aux < 0x4c800000 ? zs : ret;79 80 // |x| < 2^-1981 ret = aux < 0x36000000 ? xbypi : ret;82 return ret;83}84 85#elif __CLC_FPSIZE == 6486 87_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) {88 const __CLC_GENTYPE pi = __CLC_FP_LIT(0x1.921fb54442d18p+1);89 90 __CLC_GENTYPE v = __clc_fabs(x);91 92 // 2^56 > v > 39/1693 __CLC_GENTYPE a = -1.0;94 __CLC_GENTYPE b = v;95 // (chi + clo) = arctan(infinity)96 __CLC_GENTYPE chi = 1.57079632679489655800e+00;97 __CLC_GENTYPE clo = 6.12323399573676480327e-17;98 99 __CLC_GENTYPE ta = v - 1.5;100 __CLC_GENTYPE tb = 1.0 + 1.5 * v;101 __CLC_LONGN l = v <= 0x1.38p+1; // 39/16 > v > 19/16102 a = l ? ta : a;103 b = l ? tb : b;104 // (chi + clo) = arctan(1.5)105 chi = l ? 9.82793723247329054082e-01 : chi;106 clo = l ? 1.39033110312309953701e-17 : clo;107 108 ta = v - 1.0;109 tb = 1.0 + v;110 l = v <= 0x1.3p+0; // 19/16 > v > 11/16111 a = l ? ta : a;112 b = l ? tb : b;113 // (chi + clo) = arctan(1.)114 chi = l ? 7.85398163397448278999e-01 : chi;115 clo = l ? 3.06161699786838240164e-17 : clo;116 117 ta = 2.0 * v - 1.0;118 tb = 2.0 + v;119 l = v <= 0x1.6p-1; // 11/16 > v > 7/16120 a = l ? ta : a;121 b = l ? tb : b;122 // (chi + clo) = arctan(0.5)123 chi = l ? 4.63647609000806093515e-01 : chi;124 clo = l ? 2.26987774529616809294e-17 : clo;125 126 l = v <= 0x1.cp-2; // v < 7/16127 a = l ? v : a;128 b = l ? 1.0 : b;129 ;130 chi = l ? 0.0 : chi;131 clo = l ? 0.0 : clo;132 133 // Core approximation: Remez(4,4) on [-7/16,7/16]134 __CLC_GENTYPE r = a / b;135 __CLC_GENTYPE s = r * r;136 __CLC_GENTYPE qn =137 __clc_fma(s,138 __clc_fma(s,139 __clc_fma(s,140 __clc_fma(s, 0.142316903342317766e-3,141 0.304455919504853031e-1),142 0.220638780716667420e0),143 0.447677206805497472e0),144 0.268297920532545909e0);145 146 __CLC_GENTYPE qd =147 __clc_fma(s,148 __clc_fma(s,149 __clc_fma(s,150 __clc_fma(s, 0.389525873944742195e-1,151 0.424602594203847109e0),152 0.141254259931958921e1),153 0.182596787737507063e1),154 0.804893761597637733e0);155 156 __CLC_GENTYPE q = r * s * qn / qd;157 r = (chi - ((q - clo) - r)) / pi;158 __CLC_GENTYPE vp = v / pi;159 160 __CLC_GENTYPE z = __clc_isnan(x) ? x : 0.5;161 z = v <= 0x1.0p+56 ? r : z;162 z = v < 0x1.0p-26 ? vp : z;163 return x == v ? z : -z;164}165 166#elif __CLC_FPSIZE == 16167 168_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) {169 return __CLC_CONVERT_GENTYPE(__clc_atanpi(__CLC_CONVERT_FLOATN(x)));170}171 172#endif173