1/* Double-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_f64.h"
22
23static const struct data
24{
25 float64_t poly[20];
26 float64_t pi_over_2;
27} data = {
28 /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
29 [2**-1022, 1.0]. */
30 .poly = { -0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3,
31 0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4,
32 -0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5,
33 0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5,
34 -0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6,
35 0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10,
36 -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, },
37 .pi_over_2 = 0x1.921fb54442d18p+0,
38};
39
40/* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */
41static svfloat64_t NOINLINE
42special_case (svfloat64_t y, svfloat64_t x, svfloat64_t ret,
43 const svbool_t cmp)
44{
45 return sv_call2_f64 (f: atan2, x1: y, x2: x, y: ret, cmp);
46}
47
48/* Returns a predicate indicating true if the input is the bit representation
49 of 0, infinity or nan. */
50static inline svbool_t
51zeroinfnan (svuint64_t i, const svbool_t pg)
52{
53 return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
54 sv_u64 (2 * asuint64 (INFINITY) - 1));
55}
56
57/* Fast implementation of SVE atan2. Errors are greatest when y and
58 x are reasonably close together. The greatest observed error is 2.28 ULP:
59 _ZGVsMxvv_atan2 (-0x1.5915b1498e82fp+732, 0x1.54d11ef838826p+732)
60 got -0x1.954f42f1fa841p-1 want -0x1.954f42f1fa843p-1. */
61svfloat64_t SV_NAME_D2 (atan2) (svfloat64_t y, svfloat64_t x, const svbool_t pg)
62{
63 const struct data *data_ptr = ptr_barrier (&data);
64
65 svuint64_t ix = svreinterpret_u64 (x);
66 svuint64_t iy = svreinterpret_u64 (y);
67
68 svbool_t cmp_x = zeroinfnan (i: ix, pg);
69 svbool_t cmp_y = zeroinfnan (i: iy, pg);
70 svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y);
71
72 svfloat64_t ax = svabs_x (pg, x);
73 svfloat64_t ay = svabs_x (pg, y);
74 svuint64_t iax = svreinterpret_u64 (ax);
75 svuint64_t iay = svreinterpret_u64 (ay);
76
77 svuint64_t sign_x = sveor_x (pg, ix, iax);
78 svuint64_t sign_y = sveor_x (pg, iy, iay);
79 svuint64_t sign_xy = sveor_x (pg, sign_x, sign_y);
80
81 svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
82
83 /* Set up z for call to atan. */
84 svfloat64_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay);
85 svfloat64_t d = svsel (pred_aygtax, ay, ax);
86 svfloat64_t z = svdiv_x (pg, n, d);
87
88 /* Work out the correct shift. */
89 svfloat64_t shift = svreinterpret_f64 (svlsr_x (pg, sign_x, 1));
90 shift = svsel (pred_aygtax, sv_f64 (x: 1.0), shift);
91 shift = svreinterpret_f64 (svorr_x (pg, sign_x, svreinterpret_u64 (shift)));
92 shift = svmul_x (pg, shift, data_ptr->pi_over_2);
93
94 /* Use split Estrin scheme for P(z^2) with deg(P)=19. */
95 svfloat64_t z2 = svmul_x (pg, z, z);
96 svfloat64_t x2 = svmul_x (pg, z2, z2);
97 svfloat64_t x4 = svmul_x (pg, x2, x2);
98 svfloat64_t x8 = svmul_x (pg, x4, x4);
99
100 svfloat64_t ret = svmla_x (
101 pg, sv_estrin_7_f64_x (pg, x: z2, x2, x4, poly: data_ptr->poly),
102 sv_estrin_11_f64_x (pg, x: z2, x2, x4, x8, poly: data_ptr->poly + 8), x8);
103
104 /* y = shift + z + z^3 * P(z^2). */
105 svfloat64_t z3 = svmul_x (pg, z2, z);
106 ret = svmla_x (pg, z, z3, ret);
107
108 ret = svadd_m (pg, ret, shift);
109
110 /* Account for the sign of x and y. */
111 if (__glibc_unlikely (svptest_any (pg, cmp_xy)))
112 return special_case (
113 y, x,
114 ret: svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy)),
115 cmp: cmp_xy);
116 return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy));
117}
118

source code of glibc/sysdeps/aarch64/fpu/atan2_sve.c