1 /*
2 * Single-precision vector atan2(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 "v_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #if V_SUPPORTED
13
14 #include "atanf_common.h"
15
16 /* Useful constants. */
17 #define PiOver2 v_f32 (0x1.921fb6p+0f)
18 #define SignMask v_u32 (0x80000000)
19
20 /* Special cases i.e. 0, infinity and nan (fall back to scalar calls). */
21 VPCS_ATTR
22 NOINLINE static v_f32_t
specialcase(v_f32_t y,v_f32_t x,v_f32_t ret,v_u32_t cmp)23 specialcase (v_f32_t y, v_f32_t x, v_f32_t ret, v_u32_t cmp)
24 {
25 return v_call2_f32 (atan2f, y, x, ret, cmp);
26 }
27
28 /* Returns 1 if input is the bit representation of 0, infinity or nan. */
29 static inline v_u32_t
zeroinfnan(v_u32_t i)30 zeroinfnan (v_u32_t i)
31 {
32 return v_cond_u32 (2 * i - 1 >= v_u32 (2 * 0x7f800000lu - 1));
33 }
34
35 /* Fast implementation of vector atan2f. Maximum observed error is
36 2.95 ULP in [0x1.9300d6p+6 0x1.93c0c6p+6] x [0x1.8c2dbp+6 0x1.8cea6p+6]:
37 v_atan2(0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1
38 want 0x1.967f00p-1. */
39 VPCS_ATTR
V_NAME(atan2f)40 v_f32_t V_NAME (atan2f) (v_f32_t y, v_f32_t x)
41 {
42 v_u32_t ix = v_as_u32_f32 (x);
43 v_u32_t iy = v_as_u32_f32 (y);
44
45 v_u32_t special_cases = zeroinfnan (ix) | zeroinfnan (iy);
46
47 v_u32_t sign_x = ix & SignMask;
48 v_u32_t sign_y = iy & SignMask;
49 v_u32_t sign_xy = sign_x ^ sign_y;
50
51 v_f32_t ax = v_abs_f32 (x);
52 v_f32_t ay = v_abs_f32 (y);
53
54 v_u32_t pred_xlt0 = x < 0.0f;
55 v_u32_t pred_aygtax = ay > ax;
56
57 /* Set up z for call to atanf. */
58 v_f32_t n = v_sel_f32 (pred_aygtax, -ax, ay);
59 v_f32_t d = v_sel_f32 (pred_aygtax, ay, ax);
60 v_f32_t z = v_div_f32 (n, d);
61
62 /* Work out the correct shift. */
63 v_f32_t shift = v_sel_f32 (pred_xlt0, v_f32 (-2.0f), v_f32 (0.0f));
64 shift = v_sel_f32 (pred_aygtax, shift + 1.0f, shift);
65 shift *= PiOver2;
66
67 v_f32_t ret = eval_poly (z, z, shift);
68
69 /* Account for the sign of y. */
70 ret = v_as_f32_u32 (v_as_u32_f32 (ret) ^ sign_xy);
71
72 if (unlikely (v_any_u32 (special_cases)))
73 {
74 return specialcase (y, x, ret, special_cases);
75 }
76
77 return ret;
78 }
79 VPCS_ALIAS
80
81 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */
82 PL_SIG (V, F, 2, atan2)
83 PL_TEST_ULP (V_NAME (atan2f), 2.46)
84 PL_TEST_INTERVAL (V_NAME (atan2f), -10.0, 10.0, 50000)
85 PL_TEST_INTERVAL (V_NAME (atan2f), -1.0, 1.0, 40000)
86 PL_TEST_INTERVAL (V_NAME (atan2f), 0.0, 1.0, 40000)
87 PL_TEST_INTERVAL (V_NAME (atan2f), 1.0, 100.0, 40000)
88 PL_TEST_INTERVAL (V_NAME (atan2f), 1e6, 1e32, 40000)
89 #endif
90