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/* Single-precision vector (SVE) exp10 function.
Copyright (C) 2023 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_f32.h"
/* For x < -SpecialBound, the result is subnormal and not handled correctly by
FEXPA. */
#define SpecialBound 37.9
static const struct data
{
float poly[5];
float shift, log10_2, log2_10_hi, log2_10_lo, special_bound;
} data = {
/* Coefficients generated using Remez algorithm with minimisation of relative
error.
rel error: 0x1.89dafa3p-24
abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
maxerr: 0.52 +0.5 ulp. */
.poly = { 0x1.26bb16p+1f, 0x1.5350d2p+1f, 0x1.04744ap+1f, 0x1.2d8176p+0f,
0x1.12b41ap-1f },
/* 1.5*2^17 + 127, a shift value suitable for FEXPA. */
.shift = 0x1.903f8p17f,
.log10_2 = 0x1.a934fp+1,
.log2_10_hi = 0x1.344136p-2,
.log2_10_lo = -0x1.ec10cp-27,
.special_bound = SpecialBound,
};
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
{
return sv_call_f32 (exp10f, x, y, special);
}
/* Single-precision SVE exp10f routine. Implements the same algorithm
as AdvSIMD exp10f.
Worst case error is 1.02 ULPs.
_ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
want 0x1.ba5f9cp-1. */
svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)),
with poly(r) in [1/sqrt(2), sqrt(2)] and
x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N]. */
/* Load some constants in quad-word chunks to minimise memory access (last
lane is wasted). */
svfloat32_t log10_2_and_inv = svld1rq (svptrue_b32 (), &d->log10_2);
/* n = round(x/(log10(2)/N)). */
svfloat32_t shift = sv_f32 (d->shift);
svfloat32_t z = svmla_lane (shift, x, log10_2_and_inv, 0);
svfloat32_t n = svsub_x (pg, z, shift);
/* r = x - n*log10(2)/N. */
svfloat32_t r = svmls_lane (x, n, log10_2_and_inv, 1);
r = svmls_lane (r, n, log10_2_and_inv, 2);
svbool_t special = svacgt (pg, x, d->special_bound);
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* Polynomial evaluation: poly(r) ~ exp10(r)-1. */
svfloat32_t r2 = svmul_x (pg, r, r);
svfloat32_t poly
= svmla_x (pg, svmul_x (pg, r, d->poly[0]),
sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1), r2);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (x, svmla_x (pg, scale, scale, poly), special);
return svmla_x (pg, scale, scale, poly);
}
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