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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_atanh(__CLC_GENTYPE x) {12 __CLC_UINTN ux = __CLC_AS_UINTN(x);13 __CLC_UINTN ax = ux & EXSIGNBIT_SP32;14 __CLC_UINTN xs = ux ^ ax;15 16 // |x| > 1 or NaN17 __CLC_GENTYPE z = __CLC_GENTYPE_NAN;18 19 // |x| == 120 __CLC_GENTYPE t = __CLC_AS_GENTYPE(xs | PINFBITPATT_SP32);21 z = ax == 0x3f800000U ? t : z;22 23 // 1/2 <= |x| < 124 t = __CLC_AS_GENTYPE(ax);25 t = MATH_DIVIDE(2.0f * t, 1.0f - t);26 t = 0.5f * __clc_log1p(t);27 t = __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN(t));28 z = ax < 0x3f800000U ? t : z;29 30 // |x| < 1/231 t = x * x;32 __CLC_GENTYPE a = __clc_mad(33 __clc_mad(0.92834212715e-2f, t, -0.28120347286e0f), t, 0.39453629046e0f);34 __CLC_GENTYPE b = __clc_mad(__clc_mad(0.45281890445e0f, t, -0.15537744551e1f),35 t, 0.11836088638e1f);36 __CLC_GENTYPE p = MATH_DIVIDE(a, b);37 t = __clc_mad(x * t, p, x);38 z = ax < 0x3f000000 ? t : z;39 40 // |x| < 2^-1341 z = ax < 0x39000000U ? x : z;42 43 return z;44}45 46#elif __CLC_FPSIZE == 6447 48_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanh(__CLC_GENTYPE x) {49 __CLC_GENTYPE absx = __clc_fabs(x);50 51 __CLC_GENTYPE ret = absx == 1.052 ? __CLC_AS_GENTYPE((__CLC_ULONGN)PINFBITPATT_DP64)53 : __CLC_GENTYPE_NAN;54 55 // |x| >= 0.556 // Note that atanh(x) = 0.5 * ln((1+x)/(1-x))57 // For greater accuracy we use58 // ln((1+x)/(1-x)) = ln(1 + 2x/(1-x)) = log1p(2x/(1-x)).59 __CLC_GENTYPE r = 0.5 * __clc_log1p(2.0 * absx / (1.0 - absx));60 ret = absx < 1.0 ? r : ret;61 62 r = -ret;63 ret = x < 0.0 ? r : ret;64 65 // Arguments up to 0.5 in magnitude are66 // approximated by a [5,5] minimax polynomial67 __CLC_GENTYPE t = x * x;68 69 __CLC_GENTYPE pn = __clc_fma(70 t,71 __clc_fma(t,72 __clc_fma(t,73 __clc_fma(t,74 __clc_fma(t, -0.10468158892753136958e-3,75 0.28728638600548514553e-1),76 -0.28180210961780814148e0),77 0.88468142536501647470e0),78 -0.11028356797846341457e1),79 0.47482573589747356373e0);80 81 __CLC_GENTYPE pd = __clc_fma(82 t,83 __clc_fma(t,84 __clc_fma(t,85 __clc_fma(t,86 __clc_fma(t, -0.35861554370169537512e-1,87 0.49561196555503101989e0),88 -0.22608883748988489342e1),89 0.45414700626084508355e1),90 -0.41631933639693546274e1),91 0.14244772076924206909e1);92 93 r = __clc_fma(x * t, pn / pd, x);94 ret = absx < 0.5 ? r : ret;95 96 return ret;97}98 99#elif __CLC_FPSIZE == 16100 101_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanh(__CLC_GENTYPE x) {102 return __CLC_CONVERT_GENTYPE(__clc_atanh(__CLC_CONVERT_FLOATN(x)));103}104 105#endif106