mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-03 02:11:08 +00:00
101 lines
3.7 KiB
C
101 lines
3.7 KiB
C
/* Single-precision SVE log1p
|
|
|
|
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"
|
|
|
|
static const struct data
|
|
{
|
|
float poly[8];
|
|
float ln2, exp_bias;
|
|
uint32_t four, three_quarters;
|
|
} data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as
|
|
this can be fmov-ed directly instead of including it in
|
|
the main load-and-mla polynomial schedule. */
|
|
0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
|
|
-0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f,
|
|
0x1.abcb6p-4f, -0x1.6f0d5ep-5f},
|
|
.ln2 = 0x1.62e43p-1f,
|
|
.exp_bias = 0x1p-23f,
|
|
.four = 0x40800000,
|
|
.three_quarters = 0x3f400000};
|
|
|
|
#define SignExponentMask 0xff800000
|
|
|
|
static svfloat32_t NOINLINE
|
|
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
|
|
{
|
|
return sv_call_f32 (log1pf, x, y, special);
|
|
}
|
|
|
|
/* Vector log1pf approximation using polynomial on reduced interval. Worst-case
|
|
error is 1.27 ULP very close to 0.5.
|
|
_ZGVsMxv_log1pf(0x1.fffffep-2) got 0x1.9f324p-2
|
|
want 0x1.9f323ep-2. */
|
|
svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg)
|
|
{
|
|
const struct data *d = ptr_barrier (&data);
|
|
/* x < -1, Inf/Nan. */
|
|
svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000);
|
|
special = svorn_z (pg, special, svcmpge (pg, x, -1));
|
|
|
|
/* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
|
|
is in [-0.25, 0.5]):
|
|
log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
|
|
|
|
We approximate log1p(m) with a polynomial, then scale by
|
|
k*log(2). Instead of doing this directly, we use an intermediate
|
|
scale factor s = 4*k*log(2) to ensure the scale is representable
|
|
as a normalised fp32 number. */
|
|
svfloat32_t m = svadd_x (pg, x, 1);
|
|
|
|
/* Choose k to scale x to the range [-1/4, 1/2]. */
|
|
svint32_t k
|
|
= svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters),
|
|
sv_s32 (SignExponentMask));
|
|
|
|
/* Scale x by exponent manipulation. */
|
|
svfloat32_t m_scale = svreinterpret_f32 (
|
|
svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k)));
|
|
|
|
/* Scale up to ensure that the scale factor is representable as normalised
|
|
fp32 number, and scale m down accordingly. */
|
|
svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four));
|
|
m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1), s, 0.25));
|
|
|
|
/* Evaluate polynomial on reduced interval. */
|
|
svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale),
|
|
ms4 = svmul_x (pg, ms2, ms2);
|
|
svfloat32_t p = sv_estrin_7_f32_x (pg, m_scale, ms2, ms4, d->poly);
|
|
p = svmad_x (pg, m_scale, p, -0.5);
|
|
p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p));
|
|
|
|
/* The scale factor to be applied back at the end - by multiplying float(k)
|
|
by 2^-23 we get the unbiased exponent of k. */
|
|
svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias);
|
|
|
|
/* Apply the scaling back. */
|
|
svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2);
|
|
|
|
if (__glibc_unlikely (svptest_any (pg, special)))
|
|
return special_case (x, y, special);
|
|
|
|
return y;
|
|
}
|