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/* Double-precision vector (SVE) atanh function
Copyright (C) 2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#define WANT_SV_LOG1P_K0_SHORTCUT 0
#include "sv_log1p_inline.h"
#define One (0x3ff0000000000000)
#define Half (0x3fe0000000000000)
static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
{
return sv_call_f64 (atanh, x, y, special);
}
/* SVE approximation for double-precision atanh, based on log1p.
The greatest observed error is 2.81 ULP:
_ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
want 0x1.ffd8ff31b501cp-6. */
svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
{
svfloat64_t ax = svabs_x (pg, x);
svuint64_t iax = svreinterpret_u64 (ax);
svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax);
svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));
/* It is special if iax >= 1. */
// svbool_t special = svcmpge (pg, iax, One);
svbool_t special = svacge (pg, x, 1.0);
/* Computation is performed based on the following sequence of equality:
(1+x)/(1-x) = 1 + 2x/(1-x). */
svfloat64_t y;
y = svadd_x (pg, ax, ax);
y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax));
/* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */
y = sv_log1p_inline (y, pg);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (x, svmul_x (pg, halfsign, y), special);
return svmul_x (pg, halfsign, y);
}
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