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/* Double-precision vector (SVE) asinh 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/>. */
#include "sv_math.h"
#include "poly_sve_f64.h"
#define SignMask (0x8000000000000000)
#define One (0x3ff0000000000000)
#define Thres (0x5fe0000000000000) /* asuint64 (0x1p511). */
static const struct data
{
double poly[18];
double ln2, p3, p1, p4, p0, p2;
uint64_t n;
uint64_t off;
} data = {
/* Polynomial generated using Remez on [2^-26, 1]. */
.poly
= { -0x1.55555555554a7p-3, 0x1.3333333326c7p-4, -0x1.6db6db68332e6p-5,
0x1.f1c71b26fb40dp-6, -0x1.6e8b8b654a621p-6, 0x1.1c4daa9e67871p-6,
-0x1.c9871d10885afp-7, 0x1.7a16e8d9d2ecfp-7, -0x1.3ddca533e9f54p-7,
0x1.0becef748dafcp-7, -0x1.b90c7099dd397p-8, 0x1.541f2bb1ffe51p-8,
-0x1.d217026a669ecp-9, 0x1.0b5c7977aaf7p-9, -0x1.e0f37daef9127p-11,
0x1.388b5fe542a6p-12, -0x1.021a48685e287p-14, 0x1.93d4ba83d34dap-18 },
.ln2 = 0x1.62e42fefa39efp-1,
.p0 = -0x1.ffffffffffff7p-2,
.p1 = 0x1.55555555170d4p-2,
.p2 = -0x1.0000000399c27p-2,
.p3 = 0x1.999b2e90e94cap-3,
.p4 = -0x1.554e550bd501ep-3,
.n = 1 << V_LOG_TABLE_BITS,
.off = 0x3fe6900900000000
};
static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
{
return sv_call_f64 (asinh, x, y, special);
}
static inline svfloat64_t
__sv_log_inline (svfloat64_t x, const struct data *d, const svbool_t pg)
{
/* Double-precision SVE log, copied from SVE log implementation with some
cosmetic modification and special-cases removed. See that file for details
of the algorithm used. */
svuint64_t ix = svreinterpret_u64 (x);
svuint64_t tmp = svsub_x (pg, ix, d->off);
svuint64_t i = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)),
(d->n - 1) << 1);
svint64_t k = svasr_x (pg, svreinterpret_s64 (tmp), 52);
svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
svfloat64_t z = svreinterpret_f64 (iz);
svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
svfloat64_t ln2_p3 = svld1rq (svptrue_b64 (), &d->ln2);
svfloat64_t p1_p4 = svld1rq (svptrue_b64 (), &d->p1);
svfloat64_t r = svmla_x (pg, sv_f64 (-1.0), invc, z);
svfloat64_t kd = svcvt_f64_x (pg, k);
svfloat64_t hi = svmla_lane (svadd_x (pg, logc, r), kd, ln2_p3, 0);
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t y = svmla_lane (sv_f64 (d->p2), r, ln2_p3, 1);
svfloat64_t p = svmla_lane (sv_f64 (d->p0), r, p1_p4, 0);
y = svmla_lane (y, r2, p1_p4, 1);
y = svmla_x (pg, p, r2, y);
y = svmla_x (pg, hi, r2, y);
return y;
}
/* Double-precision implementation of SVE asinh(x).
asinh is very sensitive around 1, so it is impractical to devise a single
low-cost algorithm which is sufficiently accurate on a wide range of input.
Instead we use two different algorithms:
asinh(x) = sign(x) * log(|x| + sqrt(x^2 + 1) if |x| >= 1
= sign(x) * (|x| + |x|^3 * P(x^2)) otherwise
where log(x) is an optimized log approximation, and P(x) is a polynomial
shared with the scalar routine. The greatest observed error 2.51 ULP, in
|x| >= 1:
_ZGVsMxv_asinh(0x1.170469d024505p+0) got 0x1.e3181c43b0f36p-1
want 0x1.e3181c43b0f39p-1. */
svfloat64_t SV_NAME_D1 (asinh) (svfloat64_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svuint64_t ix = svreinterpret_u64 (x);
svuint64_t iax = svbic_x (pg, ix, SignMask);
svuint64_t sign = svand_x (pg, ix, SignMask);
svfloat64_t ax = svreinterpret_f64 (iax);
svbool_t ge1 = svcmpge (pg, iax, One);
svbool_t special = svcmpge (pg, iax, Thres);
/* Option 1: |x| >= 1.
Compute asinh(x) according by asinh(x) = log(x + sqrt(x^2 + 1)). */
svfloat64_t option_1 = sv_f64 (0);
if (__glibc_likely (svptest_any (pg, ge1)))
{
svfloat64_t x2 = svmul_x (pg, ax, ax);
option_1 = __sv_log_inline (
svadd_x (pg, ax, svsqrt_x (pg, svadd_x (pg, x2, 1))), d, pg);
}
/* Option 2: |x| < 1.
Compute asinh(x) using a polynomial.
The largest observed error in this region is 1.51 ULPs:
_ZGVsMxv_asinh(0x1.fe12bf8c616a2p-1) got 0x1.c1e649ee2681bp-1
want 0x1.c1e649ee2681dp-1. */
svfloat64_t option_2 = sv_f64 (0);
if (__glibc_likely (svptest_any (pg, svnot_z (pg, ge1))))
{
svfloat64_t x2 = svmul_x (pg, ax, ax);
svfloat64_t x4 = svmul_x (pg, x2, x2);
svfloat64_t p = sv_pw_horner_17_f64_x (pg, x2, x4, d->poly);
option_2 = svmla_x (pg, ax, p, svmul_x (pg, x2, ax));
}
/* Choose the right option for each lane. */
svfloat64_t y = svsel (ge1, option_1, option_2);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (
x, svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)),
special);
return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
}
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