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
|
/*
* Double-precision vector atan(x) function.
*
* Copyright (c) 2021-2023, 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
#include "sv_atan_common.h"
/* Useful constants. */
#define PiOver2 sv_f64 (0x1.921fb54442d18p+0)
#define AbsMask (0x7fffffffffffffff)
/* Fast implementation of SVE atan.
Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
error is 2.27 ulps:
__sv_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
want 0x1.9225645bdd7c3p-1. */
sv_f64_t
__sv_atan_x (sv_f64_t x, const svbool_t pg)
{
/* No need to trigger special case. Small cases, infs and nans
are supported by our approximation technique. */
sv_u64_t ix = sv_as_u64_f64 (x);
sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask);
/* Argument reduction:
y := arctan(x) for x < 1
y := pi/2 + arctan(-1/x) for x > 1
Hence, use z=-1/a if x>=1, otherwise z=a. */
svbool_t red = svacgt_n_f64 (pg, x, 1.0);
/* Avoid dependency in abs(x) in division (and comparison). */
sv_f64_t z = svsel_f64 (red, svdiv_f64_x (pg, sv_f64 (-1.0), x), x);
/* Use absolute value only when needed (odd powers of z). */
sv_f64_t az = svabs_f64_x (pg, z);
az = svneg_f64_m (az, red, az);
sv_f64_t y = __sv_atan_common (pg, red, z, az, PiOver2);
/* y = atan(x) if x>0, -atan(-x) otherwise. */
y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign));
return y;
}
PL_ALIAS (__sv_atan_x, _ZGVsMxv_atan)
PL_SIG (SV, D, 1, atan, -3.1, 3.1)
PL_TEST_ULP (__sv_atan, 1.78)
PL_TEST_INTERVAL (__sv_atan, -10.0, 10.0, 50000)
PL_TEST_INTERVAL (__sv_atan, -1.0, 1.0, 40000)
PL_TEST_INTERVAL (__sv_atan, 0.0, 1.0, 40000)
PL_TEST_INTERVAL (__sv_atan, 1.0, 100.0, 40000)
PL_TEST_INTERVAL (__sv_atan, 1e6, 1e32, 40000)
#endif
|
