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/* Single-precision vector (SVE) exp2 function
Copyright (C) 2023-2024 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_f32.h"
#define Thres 0x1.5d5e2ap+6f
static const struct data
{
float c0, c2, c4, c1, c3;
float shift, thres;
} data = {
/* Coefficients copied from the polynomial in AdvSIMD variant. */
.c0 = 0x1.62e422p-1f,
.c1 = 0x1.ebf9bcp-3f,
.c2 = 0x1.c6bd32p-5f,
.c3 = 0x1.3ce9e4p-7f,
.c4 = 0x1.59977ap-10f,
/* 1.5*2^17 + 127. */
.shift = 0x1.803f8p17f,
/* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
correctly by FEXPA. */
.thres = Thres,
};
static inline svfloat32_t
sv_exp2f_inline (svfloat32_t x, const svbool_t pg, const struct data *d)
{
/* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
x = n + r, with r in [-1/2, 1/2]. */
svfloat32_t z = svadd_x (svptrue_b32 (), x, d->shift);
svfloat32_t n = svsub_x (svptrue_b32 (), z, d->shift);
svfloat32_t r = svsub_x (svptrue_b32 (), x, n);
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* Polynomial evaluation: poly(r) ~ exp2(r)-1.
Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
coefficients 1 to 4, and apply most significant coefficient directly. */
svfloat32_t even_coeffs = svld1rq (svptrue_b32 (), &d->c0);
svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, even_coeffs, 1);
svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, even_coeffs, 2);
svfloat32_t p14 = svmla_x (pg, p12, r2, p34);
svfloat32_t p0 = svmul_lane (r, even_coeffs, 0);
svfloat32_t poly = svmla_x (pg, p0, r2, p14);
return svmla_x (pg, scale, scale, poly);
}
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svbool_t special, const struct data *d)
{
return sv_call_f32 (exp2f, x, sv_exp2f_inline (x, svptrue_b32 (), d),
special);
}
/* Single-precision SVE exp2f routine. Implements the same algorithm
as AdvSIMD exp2f.
Worst case error is 1.04 ULPs.
_ZGVsMxv_exp2f(-0x1.af994ap-3) got 0x1.ba6a66p-1
want 0x1.ba6a64p-1. */
svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svbool_t special = svacgt (pg, x, d->thres);
if (__glibc_unlikely (svptest_any (special, special)))
return special_case (x, special, d);
return sv_exp2f_inline (x, pg, d);
}
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