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
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
|
/* Double-precision vector (Advanced SIMD) log function.
Copyright (C) 2023-2024 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/>. */
#include "v_math.h"
static const struct data
{
uint64x2_t min_norm;
uint32x4_t special_bound;
float64x2_t poly[5];
float64x2_t ln2;
uint64x2_t sign_exp_mask;
} data = {
/* Worst-case error: 1.17 + 0.5 ulp.
Rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */
.poly = { V2 (-0x1.ffffffffffff7p-2), V2 (0x1.55555555170d4p-2),
V2 (-0x1.0000000399c27p-2), V2 (0x1.999b2e90e94cap-3),
V2 (-0x1.554e550bd501ep-3) },
.ln2 = V2 (0x1.62e42fefa39efp-1),
.min_norm = V2 (0x0010000000000000),
.special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm. */
.sign_exp_mask = V2 (0xfff0000000000000)
};
#define A(i) d->poly[i]
#define N (1 << V_LOG_TABLE_BITS)
#define IndexMask (N - 1)
#define Off v_u64 (0x3fe6900900000000)
struct entry
{
float64x2_t invc;
float64x2_t logc;
};
static inline struct entry
lookup (uint64x2_t i)
{
/* Since N is a power of 2, n % N = n & (N - 1). */
struct entry e;
uint64_t i0 = (i[0] >> (52 - V_LOG_TABLE_BITS)) & IndexMask;
uint64_t i1 = (i[1] >> (52 - V_LOG_TABLE_BITS)) & IndexMask;
float64x2_t e0 = vld1q_f64 (&__v_log_data.table[i0].invc);
float64x2_t e1 = vld1q_f64 (&__v_log_data.table[i1].invc);
#if __BYTE_ORDER == __LITTLE_ENDIAN
e.invc = vuzp1q_f64 (e0, e1);
e.logc = vuzp2q_f64 (e0, e1);
#else
e.invc = vuzp1q_f64 (e1, e0);
e.logc = vuzp2q_f64 (e1, e0);
#endif
return e;
}
static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, float64x2_t y, float64x2_t hi, float64x2_t r2,
uint32x2_t cmp)
{
return v_call_f64 (log, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (cmp));
}
float64x2_t VPCS_ATTR V_NAME_D1 (log) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
float64x2_t z, r, r2, p, y, kd, hi;
uint64x2_t ix, iz, tmp;
uint32x2_t cmp;
int64x2_t k;
struct entry e;
ix = vreinterpretq_u64_f64 (x);
cmp = vcge_u32 (vsubhn_u64 (ix, d->min_norm),
vget_low_u32 (d->special_bound));
/* x = 2^k z; where z is in range [Off,2*Off) and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
tmp = vsubq_u64 (ix, Off);
k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); /* arithmetic shift. */
iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask));
z = vreinterpretq_f64_u64 (iz);
e = lookup (tmp);
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
kd = vcvtq_f64_s64 (k);
/* hi = r + log(c) + k*Ln2. */
hi = vfmaq_f64 (vaddq_f64 (e.logc, r), kd, d->ln2);
/* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
r2 = vmulq_f64 (r, r);
y = vfmaq_f64 (A (2), A (3), r);
p = vfmaq_f64 (A (0), A (1), r);
y = vfmaq_f64 (y, A (4), r2);
y = vfmaq_f64 (p, y, r2);
if (__glibc_unlikely (v_any_u32h (cmp)))
return special_case (x, y, hi, r2, cmp);
return vfmaq_f64 (hi, y, r2);
}
|
