1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
|
/* Single-precision vector (SVE) log10 function
Copyright (C) 2023 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 "sv_math.h"
static const struct data
{
float poly_0246[4];
float poly_1357[4];
float ln2, inv_ln10;
} data = {
.poly_1357 = {
/* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs
1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane
variant of MLA intrinsic. */
0x1.2879c8p-3f, 0x1.6408f8p-4f, 0x1.f0e514p-5f, 0x1.f5f76ap-5f
},
.poly_0246 = { -0x1.bcb79cp-3f, -0x1.bcd472p-4f, -0x1.246f8p-4f,
-0x1.0fc92cp-4f },
.ln2 = 0x1.62e43p-1f,
.inv_ln10 = 0x1.bcb7b2p-2f,
};
#define Min 0x00800000
#define Max 0x7f800000
#define Thres 0x7f000000 /* Max - Min. */
#define Offset 0x3f2aaaab /* 0.666667. */
#define MantissaMask 0x007fffff
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
{
return sv_call_f32 (log10f, x, y, special);
}
/* Optimised implementation of SVE log10f using the same algorithm and
polynomial as AdvSIMD log10f.
Maximum error is 3.31ulps:
SV_NAME_F1 (log10)(0x1.555c16p+0) got 0x1.ffe2fap-4
want 0x1.ffe2f4p-4. */
svfloat32_t SV_NAME_F1 (log10) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svuint32_t ix = svreinterpret_u32 (x);
svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
ix = svsub_x (pg, ix, Offset);
svfloat32_t n = svcvt_f32_x (
pg, svasr_x (pg, svreinterpret_s32 (ix), 23)); /* signextend. */
ix = svand_x (pg, ix, MantissaMask);
ix = svadd_x (pg, ix, Offset);
svfloat32_t r = svsub_x (pg, svreinterpret_f32 (ix), 1.0f);
/* y = log10(1+r) + n*log10(2)
log10(1+r) ~ r * InvLn(10) + P(r)
where P(r) is a polynomial. Use order 9 for log10(1+x), i.e. order 8 for
log10(1+x)/x, with x in [-1/3, 1/3] (offset=2/3). */
svfloat32_t r2 = svmul_x (pg, r, r);
svfloat32_t r4 = svmul_x (pg, r2, r2);
svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]);
svfloat32_t q_01 = svmla_lane (sv_f32 (d->poly_0246[0]), r, p_1357, 0);
svfloat32_t q_23 = svmla_lane (sv_f32 (d->poly_0246[1]), r, p_1357, 1);
svfloat32_t q_45 = svmla_lane (sv_f32 (d->poly_0246[2]), r, p_1357, 2);
svfloat32_t q_67 = svmla_lane (sv_f32 (d->poly_0246[3]), r, p_1357, 3);
svfloat32_t q_47 = svmla_x (pg, q_45, r2, q_67);
svfloat32_t q_03 = svmla_x (pg, q_01, r2, q_23);
svfloat32_t y = svmla_x (pg, q_03, r4, q_47);
/* Using hi = Log10(2)*n + r*InvLn(10) is faster but less accurate. */
svfloat32_t hi = svmla_x (pg, r, n, d->ln2);
hi = svmul_x (pg, hi, d->inv_ln10);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y),
special);
return svmla_x (pg, hi, r2, y);
}
|
