173 lines
5.1 KiB
C++
173 lines
5.1 KiB
C++
//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#if __CLC_FPSIZE == 32
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_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) {
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const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897932);
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__CLC_UINTN ux = __CLC_AS_UINTN(x);
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__CLC_UINTN aux = ux & EXSIGNBIT_SP32;
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__CLC_UINTN sx = ux ^ aux;
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__CLC_GENTYPE xbypi = MATH_DIVIDE(x, pi);
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__CLC_GENTYPE shalf =
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__CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(__CLC_FP_LIT(0.5)));
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__CLC_GENTYPE v = __CLC_AS_GENTYPE(aux);
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// Return for NaN
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__CLC_GENTYPE ret = x;
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// 2^26 <= |x| <= Inf => atan(x) is close to piby2
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ret = aux <= PINFBITPATT_SP32 ? shalf : ret;
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// Reduce arguments 2^-19 <= |x| < 2^26
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// 39/16 <= x < 2^26
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x = -MATH_RECIP(v);
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__CLC_GENTYPE c = 1.57079632679489655800f; // atan(infinity)
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// 19/16 <= x < 39/16
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__CLC_INTN l = aux < 0x401c0000;
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__CLC_GENTYPE xx = MATH_DIVIDE(v - 1.5f, __clc_mad(v, 1.5f, 1.0f));
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x = l ? xx : x;
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c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)
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// 11/16 <= x < 19/16
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l = aux < 0x3f980000U;
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xx = MATH_DIVIDE(v - 1.0f, 1.0f + v);
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x = l ? xx : x;
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c = l ? 7.85398163397448278999e-01f : c; // atan(1)
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// 7/16 <= x < 11/16
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l = aux < 0x3f300000;
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xx = MATH_DIVIDE(__clc_mad(v, 2.0f, -1.0f), 2.0f + v);
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x = l ? xx : x;
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c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)
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// 2^-19 <= x < 7/16
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l = aux < 0x3ee00000;
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x = l ? v : x;
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c = l ? 0.0f : c;
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// Core approximation: Remez(2,2) on [-7/16,7/16]
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__CLC_GENTYPE s = x * x;
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__CLC_GENTYPE a = __clc_mad(s,
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__clc_mad(s, 0.470677934286149214138357545549e-2f,
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0.192324546402108583211697690500f),
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0.296528598819239217902158651186f);
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__CLC_GENTYPE b = __clc_mad(s,
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__clc_mad(s, 0.299309699959659728404442796915f,
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0.111072499995399550138837673349e1f),
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0.889585796862432286486651434570f);
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__CLC_GENTYPE q = x * s * MATH_DIVIDE(a, b);
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__CLC_GENTYPE z = c - (q - x);
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z = MATH_DIVIDE(z, pi);
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__CLC_GENTYPE zs = __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(z));
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ret = aux < 0x4c800000 ? zs : ret;
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// |x| < 2^-19
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ret = aux < 0x36000000 ? xbypi : ret;
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return ret;
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}
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#elif __CLC_FPSIZE == 64
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_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) {
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const __CLC_GENTYPE pi = __CLC_FP_LIT(0x1.921fb54442d18p+1);
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__CLC_GENTYPE v = __clc_fabs(x);
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// 2^56 > v > 39/16
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__CLC_GENTYPE a = -1.0;
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__CLC_GENTYPE b = v;
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// (chi + clo) = arctan(infinity)
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__CLC_GENTYPE chi = 1.57079632679489655800e+00;
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__CLC_GENTYPE clo = 6.12323399573676480327e-17;
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__CLC_GENTYPE ta = v - 1.5;
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__CLC_GENTYPE tb = 1.0 + 1.5 * v;
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__CLC_LONGN l = v <= 0x1.38p+1; // 39/16 > v > 19/16
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a = l ? ta : a;
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b = l ? tb : b;
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// (chi + clo) = arctan(1.5)
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chi = l ? 9.82793723247329054082e-01 : chi;
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clo = l ? 1.39033110312309953701e-17 : clo;
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ta = v - 1.0;
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tb = 1.0 + v;
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l = v <= 0x1.3p+0; // 19/16 > v > 11/16
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a = l ? ta : a;
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b = l ? tb : b;
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// (chi + clo) = arctan(1.)
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chi = l ? 7.85398163397448278999e-01 : chi;
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clo = l ? 3.06161699786838240164e-17 : clo;
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ta = 2.0 * v - 1.0;
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tb = 2.0 + v;
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l = v <= 0x1.6p-1; // 11/16 > v > 7/16
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a = l ? ta : a;
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b = l ? tb : b;
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// (chi + clo) = arctan(0.5)
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chi = l ? 4.63647609000806093515e-01 : chi;
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clo = l ? 2.26987774529616809294e-17 : clo;
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l = v <= 0x1.cp-2; // v < 7/16
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a = l ? v : a;
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b = l ? 1.0 : b;
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;
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chi = l ? 0.0 : chi;
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clo = l ? 0.0 : clo;
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// Core approximation: Remez(4,4) on [-7/16,7/16]
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__CLC_GENTYPE r = a / b;
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__CLC_GENTYPE s = r * r;
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__CLC_GENTYPE qn =
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__clc_fma(s,
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__clc_fma(s,
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__clc_fma(s,
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__clc_fma(s, 0.142316903342317766e-3,
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0.304455919504853031e-1),
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0.220638780716667420e0),
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0.447677206805497472e0),
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0.268297920532545909e0);
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__CLC_GENTYPE qd =
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__clc_fma(s,
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__clc_fma(s,
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__clc_fma(s,
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__clc_fma(s, 0.389525873944742195e-1,
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0.424602594203847109e0),
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0.141254259931958921e1),
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0.182596787737507063e1),
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0.804893761597637733e0);
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__CLC_GENTYPE q = r * s * qn / qd;
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r = (chi - ((q - clo) - r)) / pi;
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__CLC_GENTYPE vp = v / pi;
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__CLC_GENTYPE z = __clc_isnan(x) ? x : 0.5;
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z = v <= 0x1.0p+56 ? r : z;
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z = v < 0x1.0p-26 ? vp : z;
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return x == v ? z : -z;
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}
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#elif __CLC_FPSIZE == 16
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_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) {
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return __CLC_CONVERT_GENTYPE(__clc_atanpi(__CLC_CONVERT_FLOATN(x)));
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}
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#endif
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