1 /*
2 * Single-precision vector atan2f(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_atanf_common.h"
15
16 /* Useful constants. */
17 #define PiOver2 sv_f32 (0x1.921fb6p+0f)
18 #define SignMask sv_u32 (0x80000000)
19
20 /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */
21 static inline sv_f32_t
specialcase(sv_f32_t y,sv_f32_t x,sv_f32_t ret,const svbool_t cmp)22 specialcase (sv_f32_t y, sv_f32_t x, sv_f32_t ret, const svbool_t cmp)
23 {
24 return sv_call2_f32 (atan2f, y, x, ret, cmp);
25 }
26
27 /* Returns a predicate indicating true if the input is the bit representation of
28 0, infinity or nan. */
29 static inline svbool_t
zeroinfnan(sv_u32_t i,const svbool_t pg)30 zeroinfnan (sv_u32_t i, const svbool_t pg)
31 {
32 return svcmpge_u32 (pg, svsub_n_u32_x (pg, svlsl_n_u32_x (pg, i, 1), 1),
33 sv_u32 (2 * 0x7f800000lu - 1));
34 }
35
36 /* Fast implementation of SVE atan2f based on atan(x) ~ shift + z + z^3 * P(z^2)
37 with reduction to [0,1] using z=1/x and shift = pi/2.
38 Maximum observed error is 2.95 ULP:
39 __sv_atan2f(0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1
40 want 0x1.967f00p-1. */
41 sv_f32_t
__sv_atan2f_x(sv_f32_t y,sv_f32_t x,const svbool_t pg)42 __sv_atan2f_x (sv_f32_t y, sv_f32_t x, const svbool_t pg)
43 {
44 sv_u32_t ix = sv_as_u32_f32 (x);
45 sv_u32_t iy = sv_as_u32_f32 (y);
46
47 svbool_t cmp_x = zeroinfnan (ix, pg);
48 svbool_t cmp_y = zeroinfnan (iy, pg);
49 svbool_t cmp_xy = svorr_b_z (pg, cmp_x, cmp_y);
50
51 sv_u32_t sign_x = svand_u32_x (pg, ix, SignMask);
52 sv_u32_t sign_y = svand_u32_x (pg, iy, SignMask);
53 sv_u32_t sign_xy = sveor_u32_x (pg, sign_x, sign_y);
54
55 sv_f32_t ax = svabs_f32_x (pg, x);
56 sv_f32_t ay = svabs_f32_x (pg, y);
57
58 svbool_t pred_xlt0 = svcmplt_f32 (pg, x, sv_f32 (0.0));
59 svbool_t pred_aygtax = svcmpgt_f32 (pg, ay, ax);
60
61 /* Set up z for call to atan. */
62 sv_f32_t n = svsel_f32 (pred_aygtax, svneg_f32_x (pg, ax), ay);
63 sv_f32_t d = svsel_f32 (pred_aygtax, ay, ax);
64 sv_f32_t z = svdiv_f32_x (pg, n, d);
65
66 /* Work out the correct shift. */
67 sv_f32_t shift = svsel_f32 (pred_xlt0, sv_f32 (-2.0), sv_f32 (0.0));
68 shift = svsel_f32 (pred_aygtax, svadd_n_f32_x (pg, shift, 1.0), shift);
69 shift = svmul_f32_x (pg, shift, PiOver2);
70
71 sv_f32_t ret = __sv_atanf_common (pg, pg, z, z, shift);
72
73 /* Account for the sign of x and y. */
74 ret = sv_as_f32_u32 (sveor_u32_x (pg, sv_as_u32_f32 (ret), sign_xy));
75
76 if (unlikely (svptest_any (pg, cmp_xy)))
77 {
78 return specialcase (y, x, ret, cmp_xy);
79 }
80
81 return ret;
82 }
83
84 PL_ALIAS (__sv_atan2f_x, _ZGVsMxvv_atan2f)
85
86 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */
87 PL_SIG (SV, F, 2, atan2)
88 PL_TEST_ULP (__sv_atan2f, 2.45)
89 PL_TEST_INTERVAL (__sv_atan2f, -10.0, 10.0, 50000)
90 PL_TEST_INTERVAL (__sv_atan2f, -1.0, 1.0, 40000)
91 PL_TEST_INTERVAL (__sv_atan2f, 0.0, 1.0, 40000)
92 PL_TEST_INTERVAL (__sv_atan2f, 1.0, 100.0, 40000)
93 PL_TEST_INTERVAL (__sv_atan2f, 1e6, 1e32, 40000)
94 #endif
95