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
|
/* Double-precision vector (AdvSIMD) exp2 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"
#include "poly_advsimd_f64.h"
#define N (1 << V_LOG2_TABLE_BITS)
static const struct data
{
uint64x2_t min_norm;
uint32x4_t special_bound;
float64x2_t poly[5];
float64x2_t invln2;
uint64x2_t sign_exp_mask;
} data = {
/* Each coefficient was generated to approximate log(r) for |r| < 0x1.fp-9
and N = 128, then scaled by log2(e) in extended precision and rounded back
to double precision. */
.poly = { V2 (-0x1.71547652b83p-1), V2 (0x1.ec709dc340953p-2),
V2 (-0x1.71547651c8f35p-2), V2 (0x1.2777ebe12dda5p-2),
V2 (-0x1.ec738d616fe26p-3) },
.invln2 = V2 (0x1.71547652b82fep0),
.min_norm = V2 (0x0010000000000000), /* asuint64(0x1p-1022). */
.special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm. */
.sign_exp_mask = V2 (0xfff0000000000000),
};
#define Off v_u64 (0x3fe6900900000000)
#define IndexMask (N - 1)
struct entry
{
float64x2_t invc;
float64x2_t log2c;
};
static inline struct entry
lookup (uint64x2_t i)
{
struct entry e;
uint64_t i0
= (vgetq_lane_u64 (i, 0) >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
uint64_t i1
= (vgetq_lane_u64 (i, 1) >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
float64x2_t e0 = vld1q_f64 (&__v_log2_data.table[i0].invc);
float64x2_t e1 = vld1q_f64 (&__v_log2_data.table[i1].invc);
e.invc = vuzp1q_f64 (e0, e1);
e.log2c = vuzp2q_f64 (e0, e1);
return e;
}
static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, float64x2_t y, float64x2_t w, float64x2_t r2,
uint32x2_t special)
{
return v_call_f64 (log2, x, vfmaq_f64 (w, r2, y), vmovl_u32 (special));
}
/* Double-precision vector log2 routine. Implements the same algorithm as
vector log10, with coefficients and table entries scaled in extended
precision. The maximum observed error is 2.58 ULP:
_ZGVnN2v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
want 0x1.fffb34198d9ddp-5. */
float64x2_t VPCS_ATTR V_NAME_D1 (log2) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
uint64x2_t ix = vreinterpretq_u64_f64 (x);
uint32x2_t special = 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. */
uint64x2_t tmp = vsubq_u64 (ix, Off);
int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52);
uint64x2_t iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask));
float64x2_t z = vreinterpretq_f64_u64 (iz);
struct entry e = lookup (tmp);
/* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
float64x2_t kd = vcvtq_f64_s64 (k);
float64x2_t w = vfmaq_f64 (e.log2c, r, d->invln2);
float64x2_t r2 = vmulq_f64 (r, r);
float64x2_t y = v_pw_horner_4_f64 (r, r2, d->poly);
w = vaddq_f64 (kd, w);
if (__glibc_unlikely (v_any_u32h (special)))
return special_case (x, y, w, r2, special);
return vfmaq_f64 (w, r2, y);
}
|
