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
|
/*
* Double-precision SVE log(x) function.
*
* Copyright (c) 2020-2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.h"
#if SV_SUPPORTED
#define A(i) __sv_log_data.poly[i]
#define Ln2 (0x1.62e42fefa39efp-1)
#define N (1 << SV_LOG_TABLE_BITS)
#define OFF (0x3fe6900900000000)
double
optr_aor_log_f64 (double);
static NOINLINE sv_f64_t
__sv_log_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp)
{
return sv_call_f64 (optr_aor_log_f64, x, y, cmp);
}
/* SVE port of Neon log algorithm from math/.
Maximum measured error is 2.17 ulp:
__sv_log(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2
want 0x1.ffffff1cca045p-2. */
sv_f64_t
__sv_log_x (sv_f64_t x, const svbool_t pg)
{
sv_u64_t ix = sv_as_u64_f64 (x);
sv_u64_t top = svlsr_n_u64_x (pg, ix, 48);
svbool_t cmp = svcmpge_u64 (pg, svsub_n_u64_x (pg, top, 0x0010),
sv_u64 (0x7ff0 - 0x0010));
/* 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. */
sv_u64_t tmp = svsub_n_u64_x (pg, ix, OFF);
/* Equivalent to (tmp >> (52 - SV_LOG_TABLE_BITS)) % N, since N is a power
of 2. */
sv_u64_t i
= svand_n_u64_x (pg, svlsr_n_u64_x (pg, tmp, (52 - SV_LOG_TABLE_BITS)),
N - 1);
sv_s64_t k
= svasr_n_s64_x (pg, sv_as_s64_u64 (tmp), 52); /* Arithmetic shift. */
sv_u64_t iz = svsub_u64_x (pg, ix, svand_n_u64_x (pg, tmp, 0xfffULL << 52));
sv_f64_t z = sv_as_f64_u64 (iz);
/* Lookup in 2 global lists (length N). */
sv_f64_t invc = sv_lookup_f64_x (pg, __sv_log_data.invc, i);
sv_f64_t logc = sv_lookup_f64_x (pg, __sv_log_data.logc, i);
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
sv_f64_t r = sv_fma_f64_x (pg, z, invc, sv_f64 (-1.0));
sv_f64_t kd = sv_to_f64_s64_x (pg, k);
/* hi = r + log(c) + k*Ln2. */
sv_f64_t hi = sv_fma_n_f64_x (pg, Ln2, kd, svadd_f64_x (pg, logc, r));
/* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
sv_f64_t r2 = svmul_f64_x (pg, r, r);
sv_f64_t y = sv_fma_n_f64_x (pg, A (3), r, sv_f64 (A (2)));
sv_f64_t p = sv_fma_n_f64_x (pg, A (1), r, sv_f64 (A (0)));
y = sv_fma_n_f64_x (pg, A (4), r2, y);
y = sv_fma_f64_x (pg, y, r2, p);
y = sv_fma_f64_x (pg, y, r2, hi);
if (unlikely (svptest_any (pg, cmp)))
return __sv_log_specialcase (x, y, cmp);
return y;
}
PL_ALIAS (__sv_log_x, _ZGVsMxv_log)
PL_SIG (SV, D, 1, log, 0.01, 11.1)
PL_TEST_ULP (__sv_log, 1.68)
#endif // SV_SUPPORTED
|
