1/* Single-precision vector (SVE) 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 "sv_math.h"
21
22static const struct data
23{
24 float poly_0246[4];
25 float poly_1357[4];
26 float ln2, inv_ln10;
27} data = {
28 .poly_1357 = {
29 /* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs
30 1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane
31 variant of MLA intrinsic. */
32 0x1.2879c8p-3f, 0x1.6408f8p-4f, 0x1.f0e514p-5f, 0x1.f5f76ap-5f
33 },
34 .poly_0246 = { -0x1.bcb79cp-3f, -0x1.bcd472p-4f, -0x1.246f8p-4f,
35 -0x1.0fc92cp-4f },
36 .ln2 = 0x1.62e43p-1f,
37 .inv_ln10 = 0x1.bcb7b2p-2f,
38};
39
40#define Min 0x00800000
41#define Max 0x7f800000
42#define Thres 0x7f000000 /* Max - Min. */
43#define Offset 0x3f2aaaab /* 0.666667. */
44#define MantissaMask 0x007fffff
45
46static svfloat32_t NOINLINE
47special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
48{
49 return sv_call_f32 (f: log10f, x, y, cmp: special);
50}
51
52/* Optimised implementation of SVE log10f using the same algorithm and
53 polynomial as AdvSIMD log10f.
54 Maximum error is 3.31ulps:
55 SV_NAME_F1 (log10)(0x1.555c16p+0) got 0x1.ffe2fap-4
56 want 0x1.ffe2f4p-4. */
57svfloat32_t SV_NAME_F1 (log10) (svfloat32_t x, const svbool_t pg)
58{
59 const struct data *d = ptr_barrier (&data);
60 svuint32_t ix = svreinterpret_u32 (x);
61 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
62
63 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
64 ix = svsub_x (pg, ix, Offset);
65 svfloat32_t n = svcvt_f32_x (
66 pg, svasr_x (pg, svreinterpret_s32 (ix), 23)); /* signextend. */
67 ix = svand_x (pg, ix, MantissaMask);
68 ix = svadd_x (pg, ix, Offset);
69 svfloat32_t r = svsub_x (pg, svreinterpret_f32 (ix), 1.0f);
70
71 /* y = log10(1+r) + n*log10(2)
72 log10(1+r) ~ r * InvLn(10) + P(r)
73 where P(r) is a polynomial. Use order 9 for log10(1+x), i.e. order 8 for
74 log10(1+x)/x, with x in [-1/3, 1/3] (offset=2/3). */
75 svfloat32_t r2 = svmul_x (pg, r, r);
76 svfloat32_t r4 = svmul_x (pg, r2, r2);
77 svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]);
78 svfloat32_t q_01 = svmla_lane (sv_f32 (x: d->poly_0246[0]), r, p_1357, 0);
79 svfloat32_t q_23 = svmla_lane (sv_f32 (x: d->poly_0246[1]), r, p_1357, 1);
80 svfloat32_t q_45 = svmla_lane (sv_f32 (x: d->poly_0246[2]), r, p_1357, 2);
81 svfloat32_t q_67 = svmla_lane (sv_f32 (x: d->poly_0246[3]), r, p_1357, 3);
82 svfloat32_t q_47 = svmla_x (pg, q_45, r2, q_67);
83 svfloat32_t q_03 = svmla_x (pg, q_01, r2, q_23);
84 svfloat32_t y = svmla_x (pg, q_03, r4, q_47);
85
86 /* Using hi = Log10(2)*n + r*InvLn(10) is faster but less accurate. */
87 svfloat32_t hi = svmla_x (pg, r, n, d->ln2);
88 hi = svmul_x (pg, hi, d->inv_ln10);
89
90 if (__glibc_unlikely (svptest_any (pg, special)))
91 return special_case (x, y: svmla_x (svnot_z (pg, special), hi, r2, y),
92 special);
93 return svmla_x (pg, hi, r2, y);
94}
95

source code of glibc/sysdeps/aarch64/fpu/log10f_sve.c