1 | /* Single-precision SVE atan2 |
2 | |
3 | Copyright (C) 2023-2024 Free Software Foundation, Inc. |
4 | This file is part of the GNU C Library. |
5 | |
6 | The GNU C Library is free software; you can redistribute it and/or |
7 | modify it under the terms of the GNU Lesser General Public |
8 | License as published by the Free Software Foundation; either |
9 | version 2.1 of the License, or (at your option) any later version. |
10 | |
11 | The GNU C Library is distributed in the hope that it will be useful, |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
14 | Lesser General Public License for more details. |
15 | |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with the GNU C Library; if not, see |
18 | <https://www.gnu.org/licenses/>. */ |
19 | |
20 | #include "sv_math.h" |
21 | #include "poly_sve_f32.h" |
22 | |
23 | static const struct data |
24 | { |
25 | float32_t poly[8]; |
26 | float32_t pi_over_2; |
27 | } data = { |
28 | /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on |
29 | [2**-128, 1.0]. */ |
30 | .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f, |
31 | -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f }, |
32 | .pi_over_2 = 0x1.921fb6p+0f, |
33 | }; |
34 | |
35 | /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ |
36 | static svfloat32_t NOINLINE |
37 | special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret, |
38 | const svbool_t cmp) |
39 | { |
40 | return sv_call2_f32 (f: atan2f, x1: y, x2: x, y: ret, cmp); |
41 | } |
42 | |
43 | /* Returns a predicate indicating true if the input is the bit representation |
44 | of 0, infinity or nan. */ |
45 | static inline svbool_t |
46 | zeroinfnan (svuint32_t i, const svbool_t pg) |
47 | { |
48 | return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1), |
49 | sv_u32 (x: 2 * 0x7f800000lu - 1)); |
50 | } |
51 | |
52 | /* Fast implementation of SVE atan2f based on atan(x) ~ shift + z + z^3 * |
53 | P(z^2) with reduction to [0,1] using z=1/x and shift = pi/2. Maximum |
54 | observed error is 2.95 ULP: |
55 | _ZGVsMxvv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1 |
56 | want 0x1.967f00p-1. */ |
57 | svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, const svbool_t pg) |
58 | { |
59 | const struct data *data_ptr = ptr_barrier (&data); |
60 | |
61 | svuint32_t ix = svreinterpret_u32 (x); |
62 | svuint32_t iy = svreinterpret_u32 (y); |
63 | |
64 | svbool_t cmp_x = zeroinfnan (i: ix, pg); |
65 | svbool_t cmp_y = zeroinfnan (i: iy, pg); |
66 | svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y); |
67 | |
68 | svfloat32_t ax = svabs_x (pg, x); |
69 | svfloat32_t ay = svabs_x (pg, y); |
70 | svuint32_t iax = svreinterpret_u32 (ax); |
71 | svuint32_t iay = svreinterpret_u32 (ay); |
72 | |
73 | svuint32_t sign_x = sveor_x (pg, ix, iax); |
74 | svuint32_t sign_y = sveor_x (pg, iy, iay); |
75 | svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y); |
76 | |
77 | svbool_t pred_aygtax = svcmpgt (pg, ay, ax); |
78 | |
79 | /* Set up z for call to atan. */ |
80 | svfloat32_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay); |
81 | svfloat32_t d = svsel (pred_aygtax, ay, ax); |
82 | svfloat32_t z = svdiv_x (pg, n, d); |
83 | |
84 | /* Work out the correct shift. */ |
85 | svfloat32_t shift = svreinterpret_f32 (svlsr_x (pg, sign_x, 1)); |
86 | shift = svsel (pred_aygtax, sv_f32 (x: 1.0), shift); |
87 | shift = svreinterpret_f32 (svorr_x (pg, sign_x, svreinterpret_u32 (shift))); |
88 | shift = svmul_x (pg, shift, sv_f32 (x: data_ptr->pi_over_2)); |
89 | |
90 | /* Use pure Estrin scheme for P(z^2) with deg(P)=7. */ |
91 | svfloat32_t z2 = svmul_x (pg, z, z); |
92 | svfloat32_t z4 = svmul_x (pg, z2, z2); |
93 | svfloat32_t z8 = svmul_x (pg, z4, z4); |
94 | |
95 | svfloat32_t ret = sv_estrin_7_f32_x (pg, x: z2, x2: z4, x4: z8, poly: data_ptr->poly); |
96 | |
97 | /* ret = shift + z + z^3 * P(z^2). */ |
98 | svfloat32_t z3 = svmul_x (pg, z2, z); |
99 | ret = svmla_x (pg, z, z3, ret); |
100 | |
101 | ret = svadd_m (pg, ret, shift); |
102 | |
103 | /* Account for the sign of x and y. */ |
104 | |
105 | if (__glibc_unlikely (svptest_any (pg, cmp_xy))) |
106 | return special_case ( |
107 | y, x, |
108 | ret: svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)), |
109 | cmp: cmp_xy); |
110 | |
111 | return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)); |
112 | } |
113 | |