mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-13 23:00:22 +00:00
131 lines
4.8 KiB
C
131 lines
4.8 KiB
C
/* Single-precision AdvSIMD log1p
|
|
|
|
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"
|
|
#include "poly_advsimd_f32.h"
|
|
|
|
const static struct data
|
|
{
|
|
float32x4_t poly[8], ln2;
|
|
uint32x4_t tiny_bound, minus_one, four, thresh;
|
|
int32x4_t three_quarters;
|
|
} data = {
|
|
.poly = { /* Generated using FPMinimax in [-0.25, 0.5]. First two coefficients
|
|
(1, -0.5) are not stored as they can be generated more
|
|
efficiently. */
|
|
V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f),
|
|
V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f),
|
|
V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) },
|
|
.ln2 = V4 (0x1.62e43p-1f),
|
|
.tiny_bound = V4 (0x34000000), /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23. */
|
|
.thresh = V4 (0x4b800000), /* asuint32(INFINITY) - tiny_bound. */
|
|
.minus_one = V4 (0xbf800000),
|
|
.four = V4 (0x40800000),
|
|
.three_quarters = V4 (0x3f400000)
|
|
};
|
|
|
|
static inline float32x4_t
|
|
eval_poly (float32x4_t m, const float32x4_t *p)
|
|
{
|
|
/* Approximate log(1+m) on [-0.25, 0.5] using split Estrin scheme. */
|
|
float32x4_t p_12 = vfmaq_f32 (v_f32 (-0.5), m, p[0]);
|
|
float32x4_t p_34 = vfmaq_f32 (p[1], m, p[2]);
|
|
float32x4_t p_56 = vfmaq_f32 (p[3], m, p[4]);
|
|
float32x4_t p_78 = vfmaq_f32 (p[5], m, p[6]);
|
|
|
|
float32x4_t m2 = vmulq_f32 (m, m);
|
|
float32x4_t p_02 = vfmaq_f32 (m, m2, p_12);
|
|
float32x4_t p_36 = vfmaq_f32 (p_34, m2, p_56);
|
|
float32x4_t p_79 = vfmaq_f32 (p_78, m2, p[7]);
|
|
|
|
float32x4_t m4 = vmulq_f32 (m2, m2);
|
|
float32x4_t p_06 = vfmaq_f32 (p_02, m4, p_36);
|
|
return vfmaq_f32 (p_06, m4, vmulq_f32 (m4, p_79));
|
|
}
|
|
|
|
static float32x4_t NOINLINE VPCS_ATTR
|
|
special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
|
|
{
|
|
return v_call_f32 (log1pf, x, y, special);
|
|
}
|
|
|
|
/* Vector log1pf approximation using polynomial on reduced interval. Accuracy
|
|
is roughly 2.02 ULP:
|
|
log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3. */
|
|
VPCS_ATTR float32x4_t V_NAME_F1 (log1p) (float32x4_t x)
|
|
{
|
|
const struct data *d = ptr_barrier (&data);
|
|
|
|
uint32x4_t ix = vreinterpretq_u32_f32 (x);
|
|
uint32x4_t ia = vreinterpretq_u32_f32 (vabsq_f32 (x));
|
|
uint32x4_t special_cases
|
|
= vorrq_u32 (vcgeq_u32 (vsubq_u32 (ia, d->tiny_bound), d->thresh),
|
|
vcgeq_u32 (ix, d->minus_one));
|
|
float32x4_t special_arg = x;
|
|
|
|
#if WANT_SIMD_EXCEPT
|
|
if (__glibc_unlikely (v_any_u32 (special_cases)))
|
|
/* Side-step special lanes so fenv exceptions are not triggered
|
|
inadvertently. */
|
|
x = v_zerofy_f32 (x, special_cases);
|
|
#endif
|
|
|
|
/* 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. */
|
|
|
|
float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
|
|
|
|
/* Choose k to scale x to the range [-1/4, 1/2]. */
|
|
int32x4_t k
|
|
= vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters),
|
|
v_s32 (0xff800000));
|
|
uint32x4_t ku = vreinterpretq_u32_s32 (k);
|
|
|
|
/* Scale x by exponent manipulation. */
|
|
float32x4_t m_scale
|
|
= vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
|
|
|
|
/* Scale up to ensure that the scale factor is representable as normalised
|
|
fp32 number, and scale m down accordingly. */
|
|
float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku));
|
|
m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
|
|
|
|
/* Evaluate polynomial on the reduced interval. */
|
|
float32x4_t p = eval_poly (m_scale, d->poly);
|
|
|
|
/* The scale factor to be applied back at the end - by multiplying float(k)
|
|
by 2^-23 we get the unbiased exponent of k. */
|
|
float32x4_t scale_back = vcvtq_f32_s32 (vshrq_n_s32 (k, 23));
|
|
|
|
/* Apply the scaling back. */
|
|
float32x4_t y = vfmaq_f32 (p, scale_back, d->ln2);
|
|
|
|
if (__glibc_unlikely (v_any_u32 (special_cases)))
|
|
return special_case (special_arg, y, special_cases);
|
|
return y;
|
|
}
|
|
libmvec_hidden_def (V_NAME_F1 (log1p))
|
|
HALF_WIDTH_ALIAS_F1 (log1p)
|