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/* Helper for single-precision SVE routines which depend on log1p
Copyright (C) 2024-2025 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/>. */
#ifndef AARCH64_FPU_SV_LOG1PF_INLINE_H
#define AARCH64_FPU_SV_LOG1PF_INLINE_H
#include "sv_math.h"
#include "vecmath_config.h"
#define SignExponentMask 0xff800000
static const struct sv_log1pf_data
{
float c0, c2, c4, c6;
float c1, c3, c5, c7;
float ln2, exp_bias, quarter;
uint32_t four, three_quarters;
} sv_log1pf_data = {
/* 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. */
.c0 = 0x1.5555aap-2f, .c1 = -0x1.000038p-2f, .c2 = 0x1.99675cp-3f,
.c3 = -0x1.54ef78p-3f, .c4 = 0x1.28a1f4p-3f, .c5 = -0x1.0da91p-3f,
.c6 = 0x1.abcb6p-4f, .c7 = -0x1.6f0d5ep-5f, .ln2 = 0x1.62e43p-1f,
.exp_bias = 0x1p-23f, .quarter = 0x1p-2f, .four = 0x40800000,
.three_quarters = 0x3f400000,
};
static inline svfloat32_t
sv_log1pf_inline (svfloat32_t x, svbool_t pg)
{
const struct sv_log1pf_data *d = ptr_barrier (&sv_log1pf_data);
/* 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));
svfloat32_t fconst = svld1rq_f32 (svptrue_b32 (), &d->ln2);
m_scale = svadd_x (pg, m_scale, svmla_lane_f32 (sv_f32 (-1), s, fconst, 2));
/* Evaluate polynomial on reduced interval. */
svfloat32_t ms2 = svmul_x (svptrue_b32 (), m_scale, m_scale);
svfloat32_t c1357 = svld1rq_f32 (svptrue_b32 (), &d->c1);
svfloat32_t p01 = svmla_lane_f32 (sv_f32 (d->c0), m_scale, c1357, 0);
svfloat32_t p23 = svmla_lane_f32 (sv_f32 (d->c2), m_scale, c1357, 1);
svfloat32_t p45 = svmla_lane_f32 (sv_f32 (d->c4), m_scale, c1357, 2);
svfloat32_t p67 = svmla_lane_f32 (sv_f32 (d->c6), m_scale, c1357, 3);
svfloat32_t p = svmla_x (pg, p45, p67, ms2);
p = svmla_x (pg, p23, p, ms2);
p = svmla_x (pg, p01, p, ms2);
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_lane_f32 (svcvt_f32_x (pg, k), fconst, 1);
return svmla_lane_f32 (p, scale_back, fconst, 0);
}
#endif
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