1 /*
2 * Double-precision vector atan(x) function.
3 *
4 * Copyright (c) 2021-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #if SV_SUPPORTED
13
14 #include "sv_atan_common.h"
15
16 /* Useful constants. */
17 #define PiOver2 sv_f64 (0x1.921fb54442d18p+0)
18 #define AbsMask (0x7fffffffffffffff)
19
20 /* Fast implementation of SVE atan.
21 Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
22 z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
23 error is 2.27 ulps:
24 __sv_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
25 want 0x1.9225645bdd7c3p-1. */
26 sv_f64_t
__sv_atan_x(sv_f64_t x,const svbool_t pg)27 __sv_atan_x (sv_f64_t x, const svbool_t pg)
28 {
29 /* No need to trigger special case. Small cases, infs and nans
30 are supported by our approximation technique. */
31 sv_u64_t ix = sv_as_u64_f64 (x);
32 sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask);
33
34 /* Argument reduction:
35 y := arctan(x) for x < 1
36 y := pi/2 + arctan(-1/x) for x > 1
37 Hence, use z=-1/a if x>=1, otherwise z=a. */
38 svbool_t red = svacgt_n_f64 (pg, x, 1.0);
39 /* Avoid dependency in abs(x) in division (and comparison). */
40 sv_f64_t z = svsel_f64 (red, svdiv_f64_x (pg, sv_f64 (-1.0), x), x);
41 /* Use absolute value only when needed (odd powers of z). */
42 sv_f64_t az = svabs_f64_x (pg, z);
43 az = svneg_f64_m (az, red, az);
44
45 sv_f64_t y = __sv_atan_common (pg, red, z, az, PiOver2);
46
47 /* y = atan(x) if x>0, -atan(-x) otherwise. */
48 y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign));
49
50 return y;
51 }
52
53 PL_ALIAS (__sv_atan_x, _ZGVsMxv_atan)
54
55 PL_SIG (SV, D, 1, atan, -3.1, 3.1)
56 PL_TEST_ULP (__sv_atan, 1.78)
57 PL_TEST_INTERVAL (__sv_atan, -10.0, 10.0, 50000)
58 PL_TEST_INTERVAL (__sv_atan, -1.0, 1.0, 40000)
59 PL_TEST_INTERVAL (__sv_atan, 0.0, 1.0, 40000)
60 PL_TEST_INTERVAL (__sv_atan, 1.0, 100.0, 40000)
61 PL_TEST_INTERVAL (__sv_atan, 1e6, 1e32, 40000)
62 #endif
63