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
|
/* Single-precision vector (SVE) cos 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 neg_pio2_1, neg_pio2_2, neg_pio2_3, inv_pio2, shift;
} data = {
/* Polynomial coefficients are hard-wired in FTMAD instructions. */
.neg_pio2_1 = -0x1.921fb6p+0f,
.neg_pio2_2 = 0x1.777a5cp-25f,
.neg_pio2_3 = 0x1.ee59dap-50f,
.inv_pio2 = 0x1.45f306p-1f,
/* Original shift used in AdvSIMD cosf,
plus a contribution to set the bit #0 of q
as expected by trigonometric instructions. */
.shift = 0x1.800002p+23f
};
#define RangeVal 0x49800000 /* asuint32(0x1p20f). */
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t oob)
{
return sv_call_f32 (cosf, x, y, oob);
}
/* A fast SVE implementation of cosf based on trigonometric
instructions (FTMAD, FTSSEL, FTSMUL).
Maximum measured error: 2.06 ULPs.
SV_NAME_F1 (cos)(0x1.dea2f2p+19) got 0x1.fffe7ap-6
want 0x1.fffe76p-6. */
svfloat32_t SV_NAME_F1 (cos) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svfloat32_t r = svabs_x (pg, x);
svbool_t oob = svcmpge (pg, svreinterpret_u32 (r), RangeVal);
/* Load some constants in quad-word chunks to minimise memory access. */
svfloat32_t negpio2_and_invpio2 = svld1rq (svptrue_b32 (), &d->neg_pio2_1);
/* n = rint(|x|/(pi/2)). */
svfloat32_t q = svmla_lane (sv_f32 (d->shift), r, negpio2_and_invpio2, 3);
svfloat32_t n = svsub_x (pg, q, d->shift);
/* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
r = svmla_lane (r, n, negpio2_and_invpio2, 0);
r = svmla_lane (r, n, negpio2_and_invpio2, 1);
r = svmla_lane (r, n, negpio2_and_invpio2, 2);
/* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
svfloat32_t f = svtssel (r, svreinterpret_u32 (q));
/* cos(r) poly approx. */
svfloat32_t r2 = svtsmul (r, svreinterpret_u32 (q));
svfloat32_t y = sv_f32 (0.0f);
y = svtmad (y, r2, 4);
y = svtmad (y, r2, 3);
y = svtmad (y, r2, 2);
y = svtmad (y, r2, 1);
y = svtmad (y, r2, 0);
if (__glibc_unlikely (svptest_any (pg, oob)))
return special_case (x, svmul_x (svnot_z (pg, oob), f, y), oob);
/* Apply factor. */
return svmul_x (pg, f, y);
}
|
