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/* Single-precision vector (AdvSIMD) exp10 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"
#define ScaleBound 192.0f
static const struct data
{
float32x4_t c0, c1, c3;
float log10_2_high, log10_2_low, c2, c4;
float32x4_t inv_log10_2, special_bound;
uint32x4_t exponent_bias, special_offset, special_bias;
#if !WANT_SIMD_EXCEPT
float32x4_t scale_thresh;
#endif
} data = {
/* Coefficients generated using Remez algorithm with minimisation of relative
error.
rel error: 0x1.89dafa3p-24
abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
maxerr: 1.85943 +0.5 ulp. */
.c0 = V4 (0x1.26bb16p+1f),
.c1 = V4 (0x1.5350d2p+1f),
.c2 = 0x1.04744ap+1f,
.c3 = V4 (0x1.2d8176p+0f),
.c4 = 0x1.12b41ap-1f,
.inv_log10_2 = V4 (0x1.a934fp+1),
.log10_2_high = 0x1.344136p-2,
.log10_2_low = 0x1.ec10cp-27,
/* rint (log2 (2^127 / (1 + sqrt (2)))). */
.special_bound = V4 (126.0f),
.exponent_bias = V4 (0x3f800000),
.special_offset = V4 (0x82000000),
.special_bias = V4 (0x7f000000),
#if !WANT_SIMD_EXCEPT
.scale_thresh = V4 (ScaleBound)
#endif
};
#if WANT_SIMD_EXCEPT
# define SpecialBound 38.0f /* rint(log10(2^127)). */
# define TinyBound v_u32 (0x20000000) /* asuint (0x1p-63). */
# define BigBound v_u32 (0x42180000) /* asuint (SpecialBound). */
# define Thres v_u32 (0x22180000) /* BigBound - TinyBound. */
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
{
/* If fenv exceptions are to be triggered correctly, fall back to the scalar
routine to special lanes. */
return v_call_f32 (exp10f, x, y, cmp);
}
#else
# define SpecialBound 126.0f
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t poly, float32x4_t n, uint32x4_t e, uint32x4_t cmp1,
float32x4_t scale, const struct data *d)
{
/* 2^n may overflow, break it up into s1*s2. */
uint32x4_t b = vandq_u32 (vclezq_f32 (n), d->special_offset);
float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, d->special_bias));
float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b));
uint32x4_t cmp2 = vcagtq_f32 (n, d->scale_thresh);
float32x4_t r2 = vmulq_f32 (s1, s1);
float32x4_t r1 = vmulq_f32 (vfmaq_f32 (s2, poly, s2), s1);
/* Similar to r1 but avoids double rounding in the subnormal range. */
float32x4_t r0 = vfmaq_f32 (scale, poly, scale);
float32x4_t r = vbslq_f32 (cmp1, r1, r0);
return vbslq_f32 (cmp2, r2, r);
}
#endif
/* Fast vector implementation of single-precision exp10.
Algorithm is accurate to 2.36 ULP.
_ZGVnN4v_exp10f(0x1.be2b36p+1) got 0x1.7e79c4p+11
want 0x1.7e79cp+11. */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (exp10) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
#if WANT_SIMD_EXCEPT
/* asuint(x) - TinyBound >= BigBound - TinyBound. */
uint32x4_t cmp = vcgeq_u32 (
vsubq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (x)), TinyBound), Thres);
float32x4_t xm = x;
/* If any lanes are special, mask them with 1 and retain a copy of x to allow
special case handler to fix special lanes later. This is only necessary if
fenv exceptions are to be triggered correctly. */
if (__glibc_unlikely (v_any_u32 (cmp)))
x = v_zerofy_f32 (x, cmp);
#endif
/* exp10(x) = 2^n * 10^r = 2^n * (1 + poly (r)),
with poly(r) in [1/sqrt(2), sqrt(2)] and
x = r + n * log10 (2), with r in [-log10(2)/2, log10(2)/2]. */
float32x4_t log10_2_c24 = vld1q_f32 (&d->log10_2_high);
float32x4_t n = vrndaq_f32 (vmulq_f32 (x, d->inv_log10_2));
float32x4_t r = vfmsq_laneq_f32 (x, n, log10_2_c24, 0);
r = vfmaq_laneq_f32 (r, n, log10_2_c24, 1);
uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (n)), 23);
float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, d->exponent_bias));
#if !WANT_SIMD_EXCEPT
uint32x4_t cmp = vcagtq_f32 (n, d->special_bound);
#endif
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t p12 = vfmaq_laneq_f32 (d->c1, r, log10_2_c24, 2);
float32x4_t p34 = vfmaq_laneq_f32 (d->c3, r, log10_2_c24, 3);
float32x4_t p14 = vfmaq_f32 (p12, r2, p34);
float32x4_t poly = vfmaq_f32 (vmulq_f32 (r, d->c0), p14, r2);
if (__glibc_unlikely (v_any_u32 (cmp)))
#if WANT_SIMD_EXCEPT
return special_case (xm, vfmaq_f32 (scale, poly, scale), cmp);
#else
return special_case (poly, n, e, cmp, scale, d);
#endif
return vfmaq_f32 (scale, poly, scale);
}
libmvec_hidden_def (V_NAME_F1 (exp10))
HALF_WIDTH_ALIAS_F1 (exp10)
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