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
|
/* Single-precision inline helper for vector (SVE) expm1 function
Copyright (C) 2024 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/>. */
#ifndef AARCH64_FPU_SV_EXPM1F_INLINE_H
#define AARCH64_FPU_SV_EXPM1F_INLINE_H
#include "sv_math.h"
struct sv_expm1f_data
{
/* These 4 are grouped together so they can be loaded as one quadword, then
used with _lane forms of svmla/svmls. */
float32_t c2, c4, ln2_hi, ln2_lo;
float32_t c0, c1, c3, inv_ln2, shift;
};
/* Coefficients generated using fpminimax. */
#define SV_EXPM1F_DATA \
{ \
.c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \
.c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
\
.shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \
.ln2_lo = 0x1.7f7d1cp-20f, \
}
#define C(i) sv_f32 (d->c##i)
static inline svfloat32_t
expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d)
{
/* This vector is reliant on layout of data - it contains constants
that can be used with _lane forms of svmla/svmls. Values are:
[ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
/* Reduce argument to smaller range:
Let i = round(x / ln2)
and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
where 2^i is exact because i is an integer. */
svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2);
j = svsub_x (pg, j, d->shift);
svint32_t i = svcvt_s32_x (pg, j);
svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
f = svmls_lane (f, j, lane_constants, 3);
/* Approximate expm1(f) using polynomial.
Taylor expansion for expm1(x) has the form:
x + ax^2 + bx^3 + cx^4 ....
So we calculate the polynomial P(f) = a + bf + cf^2 + ...
and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
svfloat32_t f2 = svmul_x (pg, f, f);
svfloat32_t p = svmla_x (pg, p12, f2, p34);
p = svmla_x (pg, C (0), f, p);
p = svmla_x (pg, f, f2, p);
/* Assemble the result.
expm1(x) ~= 2^i * (p + 1) - 1
Let t = 2^i. */
svfloat32_t t = svscale_x (pg, sv_f32 (1), i);
return svmla_x (pg, svsub_x (pg, t, 1), p, t);
}
#endif
|
