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
|
/* Single-precision vector (SVE) exp 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[5];
float inv_ln2, ln2_hi, ln2_lo, shift, thres;
} data = {
/* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
compatibility with polynomial helpers. */
.poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
0x1.0e4020p-7f },
.inv_ln2 = 0x1.715476p+0f,
.ln2_hi = 0x1.62e4p-1f,
.ln2_lo = 0x1.7f7d1cp-20f,
/* 1.5*2^17 + 127. */
.shift = 0x1.903f8p17f,
/* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
correctly by FEXPA. */
.thres = 0x1.5d5e2ap+6f,
};
#define C(i) sv_f32 (d->poly[i])
#define ExponentBias 0x3f800000
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
{
return sv_call_f32 (expf, x, y, special);
}
/* Optimised single-precision SVE exp function.
Worst-case error is 1.04 ulp:
SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
want 0x1.ba74bap+4. */
svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
/* Load some constants in quad-word chunks to minimise memory access (last
lane is wasted). */
svfloat32_t invln2_and_ln2 = svld1rq_f32 (svptrue_b32 (), &d->inv_ln2);
/* n = round(x/(ln2/N)). */
svfloat32_t z = svmla_lane_f32 (sv_f32 (d->shift), x, invln2_and_ln2, 0);
svfloat32_t n = svsub_n_f32_x (pg, z, d->shift);
/* r = x - n*ln2/N. */
svfloat32_t r = svmls_lane_f32 (x, n, invln2_and_ln2, 1);
r = svmls_lane_f32 (r, n, invln2_and_ln2, 2);
/* scale = 2^(n/N). */
svbool_t is_special_case = svacgt_n_f32 (pg, x, d->thres);
svfloat32_t scale = svexpa_f32 (svreinterpret_u32_f32 (z));
/* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
svfloat32_t p12 = svmla_f32_x (pg, C (1), C (2), r);
svfloat32_t p34 = svmla_f32_x (pg, C (3), C (4), r);
svfloat32_t r2 = svmul_f32_x (pg, r, r);
svfloat32_t p14 = svmla_f32_x (pg, p12, p34, r2);
svfloat32_t p0 = svmul_f32_x (pg, r, C (0));
svfloat32_t poly = svmla_f32_x (pg, p0, r2, p14);
if (__glibc_unlikely (svptest_any (pg, is_special_case)))
return special_case (x, svmla_f32_x (pg, scale, scale, poly),
is_special_case);
return svmla_f32_x (pg, scale, scale, poly);
}
|
