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/* Single-precision vector (AdvSIMD) 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 "v_math.h"
static const struct data
{
float32x4_t c0, c2, c4, c6, c8;
uint32x4_t off, offset_lower_bound;
uint16x8_t special_bound;
uint32x4_t mantissa_mask;
float c1, c3, c5, c7;
} data = {
/* Coefficients generated using Remez algorithm approximate
log2(1+r)/r for r in [ -1/3, 1/3 ].
rel error: 0x1.c4c4b0cp-26. */
.c0 = V4 (0x1.715476p0f), /* (float)(1 / ln(2)). */
.c1 = -0x1.715458p-1f,
.c2 = V4 (0x1.ec701cp-2f),
.c3 = -0x1.7171a4p-2f,
.c4 = V4 (0x1.27a0b8p-2f),
.c5 = -0x1.e5143ep-3f,
.c6 = V4 (0x1.9d8ecap-3f),
.c7 = -0x1.c675bp-3f,
.c8 = V4 (0x1.9e495p-3f),
/* Lower bound is the smallest positive normal float 0x00800000. For
optimised register use subnormals are detected after offset has been
subtracted, so lower bound is 0x0080000 - offset (which wraps around). */
.offset_lower_bound = V4 (0x00800000 - 0x3f2aaaab),
.special_bound = V8 (0x7f00), /* top16(asuint32(inf) - 0x00800000). */
.off = V4 (0x3f2aaaab), /* 0.666667. */
.mantissa_mask = V4 (0x007fffff),
};
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t n, uint32x4_t u_off, float32x4_t p, float32x4_t r,
uint16x4_t cmp, const struct data *d)
{
/* Fall back to scalar code. */
return v_call_f32 (log2f, vreinterpretq_f32_u32 (vaddq_u32 (u_off, d->off)),
vfmaq_f32 (n, p, r), vmovl_u16 (cmp));
}
/* Fast implementation for single precision AdvSIMD log2,
relies on same argument reduction as AdvSIMD logf.
Maximum error: 2.48 ULPs
_ZGVnN4v_log2f(0x1.558174p+0) got 0x1.a9be84p-2
want 0x1.a9be8p-2. */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log2) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
/* To avoid having to mov x out of the way, keep u after offset has been
applied, and recover x by adding the offset back in the special-case
handler. */
uint32x4_t u_off = vreinterpretq_u32_f32 (x);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
u_off = vsubq_u32 (u_off, d->off);
float32x4_t n = vcvtq_f32_s32 (
vshrq_n_s32 (vreinterpretq_s32_u32 (u_off), 23)); /* signextend. */
uint16x4_t special = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
vget_low_u16 (d->special_bound));
uint32x4_t u = vaddq_u32 (vandq_u32 (u_off, d->mantissa_mask), d->off);
float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
/* y = log2(1+r) + n. */
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t c1357 = vld1q_f32 (&d->c1);
float32x4_t c01 = vfmaq_laneq_f32 (d->c0, r, c1357, 0);
float32x4_t c23 = vfmaq_laneq_f32 (d->c2, r, c1357, 1);
float32x4_t c45 = vfmaq_laneq_f32 (d->c4, r, c1357, 2);
float32x4_t c67 = vfmaq_laneq_f32 (d->c6, r, c1357, 3);
float32x4_t p68 = vfmaq_f32 (c67, r2, d->c8);
float32x4_t p48 = vfmaq_f32 (c45, r2, p68);
float32x4_t p28 = vfmaq_f32 (c23, r2, p48);
float32x4_t p = vfmaq_f32 (c01, r2, p28);
if (__glibc_unlikely (v_any_u16h (special)))
return special_case (n, u_off, p, r, special, d);
return vfmaq_f32 (n, p, r);
}
libmvec_hidden_def (V_NAME_F1 (log2))
HALF_WIDTH_ALIAS_F1 (log2)
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