1/* Single-precision vector (Advanced SIMD) log 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
22static const struct data
23{
24 uint32x4_t min_norm;
25 uint16x8_t special_bound;
26 float32x4_t poly[7];
27 float32x4_t ln2, tiny_bound;
28 uint32x4_t off, mantissa_mask;
29} data = {
30 /* 3.34 ulp error. */
31 .poly = { V4 (-0x1.3e737cp-3f), V4 (0x1.5a9aa2p-3f), V4 (-0x1.4f9934p-3f),
32 V4 (0x1.961348p-3f), V4 (-0x1.00187cp-2f), V4 (0x1.555d7cp-2f),
33 V4 (-0x1.ffffc8p-2f) },
34 .ln2 = V4 (0x1.62e43p-1f),
35 .tiny_bound = V4 (0x1p-126),
36 .min_norm = V4 (0x00800000),
37 .special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
38 .off = V4 (0x3f2aaaab), /* 0.666667. */
39 .mantissa_mask = V4 (0x007fffff)
40};
41
42#define P(i) d->poly[7 - i]
43
44static float32x4_t VPCS_ATTR NOINLINE
45special_case (float32x4_t x, float32x4_t y, float32x4_t r2, float32x4_t p,
46 uint16x4_t cmp)
47{
48 /* Fall back to scalar code. */
49 return v_call_f32 (logf, x, vfmaq_f32 (p, y, r2), vmovl_u16 (cmp));
50}
51
52float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log) (float32x4_t x)
53{
54 const struct data *d = ptr_barrier (&data);
55 float32x4_t n, p, q, r, r2, y;
56 uint32x4_t u;
57 uint16x4_t cmp;
58
59 u = vreinterpretq_u32_f32 (x);
60 cmp = vcge_u16 (vsubhn_u32 (u, d->min_norm),
61 vget_low_u16 (d->special_bound));
62
63 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
64 u = vsubq_u32 (u, d->off);
65 n = vcvtq_f32_s32 (
66 vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
67 u = vandq_u32 (u, d->mantissa_mask);
68 u = vaddq_u32 (u, d->off);
69 r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
70
71 /* y = log(1+r) + n*ln2. */
72 r2 = vmulq_f32 (r, r);
73 /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */
74 p = vfmaq_f32 (P (5), P (6), r);
75 q = vfmaq_f32 (P (3), P (4), r);
76 y = vfmaq_f32 (P (1), P (2), r);
77 p = vfmaq_f32 (p, P (7), r2);
78 q = vfmaq_f32 (q, p, r2);
79 y = vfmaq_f32 (y, q, r2);
80 p = vfmaq_f32 (r, d->ln2, n);
81
82 if (__glibc_unlikely (v_any_u16h (cmp)))
83 return special_case (x, y, r2, p, cmp);
84 return vfmaq_f32 (p, y, r2);
85}
86libmvec_hidden_def (V_NAME_F1 (log))
87HALF_WIDTH_ALIAS_F1 (log)
88

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