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/* Single-precision SVE expm1
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"
/* Largest value of x for which expm1(x) should round to -1. */
#define SpecialBound 0x1.5ebc4p+6f
static const struct data
{
/* These 4 are grouped together so they can be loaded as one quadword, then
used with _lane forms of svmla/svmls. */
float c2, c4, ln2_hi, ln2_lo;
float c0, c1, c3, inv_ln2, special_bound, shift;
} data = {
/* Generated using fpminimax. */
.c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3,
.c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7,
.c4 = 0x1.6b55a2p-10,
.special_bound = SpecialBound, .shift = 0x1.8p23f,
.inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f,
.ln2_lo = 0x1.7f7d1cp-20f,
};
#define C(i) sv_f32 (d->c##i)
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svbool_t pg)
{
return sv_call_f32 (expm1f, x, x, pg);
}
/* Single-precision SVE exp(x) - 1. Maximum error is 1.52 ULP:
_ZGVsMxv_expm1f(0x1.8f4ebcp-2) got 0x1.e859dp-2
want 0x1.e859d4p-2. */
svfloat32_t SV_NAME_F1 (expm1) (svfloat32_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* Large, NaN/Inf. */
svbool_t special = svnot_z (pg, svaclt (pg, x, d->special_bound));
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (x, pg);
/* This vector is reliant on layout of data - it contains constants
that can be used with _lane forms of svmla/svmls. Values are:
[ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
/* Reduce argument to smaller range:
Let i = round(x / ln2)
and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
where 2^i is exact because i is an integer. */
svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2);
j = svsub_x (pg, j, d->shift);
svint32_t i = svcvt_s32_x (pg, j);
svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
f = svmls_lane (f, j, lane_constants, 3);
/* Approximate expm1(f) using polynomial.
Taylor expansion for expm1(x) has the form:
x + ax^2 + bx^3 + cx^4 ....
So we calculate the polynomial P(f) = a + bf + cf^2 + ...
and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
svfloat32_t f2 = svmul_x (pg, f, f);
svfloat32_t p = svmla_x (pg, p12, f2, p34);
p = svmla_x (pg, C (0), f, p);
p = svmla_x (pg, f, f2, p);
/* Assemble the result.
expm1(x) ~= 2^i * (p + 1) - 1
Let t = 2^i. */
svfloat32_t t = svreinterpret_f32 (
svadd_x (pg, svreinterpret_u32 (svlsl_x (pg, i, 23)), 0x3f800000));
return svmla_x (pg, svsub_x (pg, t, 1), p, t);
}
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