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
|
/* Single-precision SVE inverse cos
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"
#include "poly_sve_f32.h"
static const struct data
{
float32_t poly[5];
float32_t pi, pi_over_2;
} data = {
/* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
[ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
.poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6,
0x1.3af7d8p-5, },
.pi = 0x1.921fb6p+1f,
.pi_over_2 = 0x1.921fb6p+0f,
};
/* Single-precision SVE implementation of vector acos(x).
For |x| in [0, 0.5], use order 4 polynomial P such that the final
approximation of asin is an odd polynomial:
acos(x) ~ pi/2 - (x + x^3 P(x^2)).
The largest observed error in this region is 1.16 ulps,
_ZGVsMxv_acosf(0x1.ffbeccp-2) got 0x1.0c27f8p+0
want 0x1.0c27f6p+0.
For |x| in [0.5, 1.0], use same approximation with a change of variable
acos(x) = y + y * z * P(z), with z = (1-x)/2 and y = sqrt(z).
The largest observed error in this region is 1.32 ulps,
_ZGVsMxv_acosf (0x1.15ba56p-1) got 0x1.feb33p-1
want 0x1.feb32ep-1. */
svfloat32_t SV_NAME_F1 (acos) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000);
svfloat32_t ax = svabs_x (pg, x);
svbool_t a_gt_half = svacgt (pg, x, 0.5);
/* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with
z2 = x ^ 2 and z = |x| , if |x| < 0.5
z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */
svfloat32_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5),
svmul_x (pg, x, x));
svfloat32_t z = svsqrt_m (ax, a_gt_half, z2);
/* Use a single polynomial approximation P for both intervals. */
svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly);
/* Finalize polynomial: z + z * z2 * P(z2). */
p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
/* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5
= 2 Q(|x|) , for 0.5 < x < 1.0
= pi - 2 Q(|x|) , for -1.0 < x < -0.5. */
svfloat32_t y
= svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (p), sign));
svbool_t is_neg = svcmplt (pg, x, 0.0);
svfloat32_t off = svdup_f32_z (is_neg, d->pi);
svfloat32_t mul = svsel (a_gt_half, sv_f32 (2.0), sv_f32 (-1.0));
svfloat32_t add = svsel (a_gt_half, off, sv_f32 (d->pi_over_2));
return svmla_x (pg, add, mul, y);
}
|
