1/* Single-precision vector (AdvSIMD) log10 function
2
3 Copyright (C) 2023-2024 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20#include "v_math.h"
21#include "poly_advsimd_f32.h"
22
23static const struct data
24{
25 uint32x4_t min_norm;
26 uint16x8_t special_bound;
27 float32x4_t poly[8];
28 float32x4_t inv_ln10, ln2;
29 uint32x4_t off, mantissa_mask;
30} data = {
31 /* Use order 9 for log10(1+x), i.e. order 8 for log10(1+x)/x, with x in
32 [-1/3, 1/3] (offset=2/3). Max. relative error: 0x1.068ee468p-25. */
33 .poly = { V4 (-0x1.bcb79cp-3f), V4 (0x1.2879c8p-3f), V4 (-0x1.bcd472p-4f),
34 V4 (0x1.6408f8p-4f), V4 (-0x1.246f8p-4f), V4 (0x1.f0e514p-5f),
35 V4 (-0x1.0fc92cp-4f), V4 (0x1.f5f76ap-5f) },
36 .ln2 = V4 (0x1.62e43p-1f),
37 .inv_ln10 = V4 (0x1.bcb7b2p-2f),
38 .min_norm = V4 (0x00800000),
39 .special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
40 .off = V4 (0x3f2aaaab), /* 0.666667. */
41 .mantissa_mask = V4 (0x007fffff),
42};
43
44static float32x4_t VPCS_ATTR NOINLINE
45special_case (float32x4_t x, float32x4_t y, float32x4_t p, float32x4_t r2,
46 uint16x4_t cmp)
47{
48 /* Fall back to scalar code. */
49 return v_call_f32 (log10f, x, vfmaq_f32 (y, p, r2), vmovl_u16 (cmp));
50}
51
52/* Fast implementation of AdvSIMD log10f,
53 uses a similar approach as AdvSIMD logf with the same offset (i.e., 2/3) and
54 an order 9 polynomial.
55 Maximum error: 3.305ulps (nearest rounding.)
56 _ZGVnN4v_log10f(0x1.555c16p+0) got 0x1.ffe2fap-4
57 want 0x1.ffe2f4p-4. */
58float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log10) (float32x4_t x)
59{
60 const struct data *d = ptr_barrier (&data);
61 uint32x4_t u = vreinterpretq_u32_f32 (x);
62 uint16x4_t special = vcge_u16 (vsubhn_u32 (u, d->min_norm),
63 vget_low_u16 (d->special_bound));
64
65 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
66 u = vsubq_u32 (u, d->off);
67 float32x4_t n = vcvtq_f32_s32 (
68 vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
69 u = vaddq_u32 (vandq_u32 (u, d->mantissa_mask), d->off);
70 float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
71
72 /* y = log10(1+r) + n * log10(2). */
73 float32x4_t r2 = vmulq_f32 (r, r);
74 float32x4_t poly = v_pw_horner_7_f32 (r, r2, d->poly);
75 /* y = Log10(2) * n + poly * InvLn(10). */
76 float32x4_t y = vfmaq_f32 (r, d->ln2, n);
77 y = vmulq_f32 (y, d->inv_ln10);
78
79 if (__glibc_unlikely (v_any_u16h (special)))
80 return special_case (x, y, poly, r2, special);
81 return vfmaq_f32 (y, poly, r2);
82}
83libmvec_hidden_def (V_NAME_F1 (log10))
84HALF_WIDTH_ALIAS_F1 (log10)
85

source code of glibc/sysdeps/aarch64/fpu/log10f_advsimd.c