1/*
2 * Double-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 "sv_math.h"
9#include "pl_sig.h"
10#include "pl_test.h"
11#include "poly_sve_f64.h"
12
13static const struct data
14{
15  float64_t poly[20];
16  float64_t pi_over_2;
17} data = {
18  /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
19     [2**-1022, 1.0].  */
20  .poly = { -0x1.5555555555555p-2,  0x1.99999999996c1p-3, -0x1.2492492478f88p-3,
21            0x1.c71c71bc3951cp-4,   -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4,
22            -0x1.11100ee084227p-4,  0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5,
23            0x1.842dbe9b0d916p-5,   -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5,
24            -0x1.00e6eece7de8p-5,   0x1.860897b29e5efp-6, -0x1.0051381722a59p-6,
25            0x1.14e9dc19a4a4ep-7,  -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10,
26            -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, },
27  .pi_over_2 = 0x1.921fb54442d18p+0,
28};
29
30/* Useful constants.  */
31#define SignMask sv_u64 (0x8000000000000000)
32
33/* Special cases i.e. 0, infinity, nan (fall back to scalar calls).  */
34static svfloat64_t NOINLINE
35special_case (svfloat64_t y, svfloat64_t x, svfloat64_t ret,
36	      const svbool_t cmp)
37{
38  return sv_call2_f64 (atan2, y, x, ret, cmp);
39}
40
41/* Returns a predicate indicating true if the input is the bit representation
42   of 0, infinity or nan.  */
43static inline svbool_t
44zeroinfnan (svuint64_t i, const svbool_t pg)
45{
46  return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
47		  sv_u64 (2 * asuint64 (INFINITY) - 1));
48}
49
50/* Fast implementation of SVE atan2. Errors are greatest when y and
51   x are reasonably close together. The greatest observed error is 2.28 ULP:
52   _ZGVsMxvv_atan2 (-0x1.5915b1498e82fp+732, 0x1.54d11ef838826p+732)
53   got -0x1.954f42f1fa841p-1 want -0x1.954f42f1fa843p-1.  */
54svfloat64_t SV_NAME_D2 (atan2) (svfloat64_t y, svfloat64_t x, const svbool_t pg)
55{
56  const struct data *data_ptr = ptr_barrier (&data);
57
58  svuint64_t ix = svreinterpret_u64 (x);
59  svuint64_t iy = svreinterpret_u64 (y);
60
61  svbool_t cmp_x = zeroinfnan (ix, pg);
62  svbool_t cmp_y = zeroinfnan (iy, pg);
63  svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y);
64
65  svuint64_t sign_x = svand_x (pg, ix, SignMask);
66  svuint64_t sign_y = svand_x (pg, iy, SignMask);
67  svuint64_t sign_xy = sveor_x (pg, sign_x, sign_y);
68
69  svfloat64_t ax = svabs_x (pg, x);
70  svfloat64_t ay = svabs_x (pg, y);
71
72  svbool_t pred_xlt0 = svcmplt (pg, x, 0.0);
73  svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
74
75  /* Set up z for call to atan.  */
76  svfloat64_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay);
77  svfloat64_t d = svsel (pred_aygtax, ay, ax);
78  svfloat64_t z = svdiv_x (pg, n, d);
79
80  /* Work out the correct shift.  */
81  svfloat64_t shift = svsel (pred_xlt0, sv_f64 (-2.0), sv_f64 (0.0));
82  shift = svsel (pred_aygtax, svadd_x (pg, shift, 1.0), shift);
83  shift = svmul_x (pg, shift, data_ptr->pi_over_2);
84
85  /* Use split Estrin scheme for P(z^2) with deg(P)=19.  */
86  svfloat64_t z2 = svmul_x (pg, z, z);
87  svfloat64_t x2 = svmul_x (pg, z2, z2);
88  svfloat64_t x4 = svmul_x (pg, x2, x2);
89  svfloat64_t x8 = svmul_x (pg, x4, x4);
90
91  svfloat64_t ret = svmla_x (
92      pg, sv_estrin_7_f64_x (pg, z2, x2, x4, data_ptr->poly),
93      sv_estrin_11_f64_x (pg, z2, x2, x4, x8, data_ptr->poly + 8), x8);
94
95  /* y = shift + z + z^3 * P(z^2).  */
96  svfloat64_t z3 = svmul_x (pg, z2, z);
97  ret = svmla_x (pg, z, z3, ret);
98
99  ret = svadd_m (pg, ret, shift);
100
101  /* Account for the sign of x and y.  */
102  ret = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy));
103
104  if (unlikely (svptest_any (pg, cmp_xy)))
105    return special_case (y, x, ret, cmp_xy);
106
107  return ret;
108}
109
110/* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h.  */
111PL_SIG (SV, D, 2, atan2)
112PL_TEST_ULP (SV_NAME_D2 (atan2), 1.78)
113PL_TEST_INTERVAL (SV_NAME_D2 (atan2), 0.0, 1.0, 40000)
114PL_TEST_INTERVAL (SV_NAME_D2 (atan2), 1.0, 100.0, 40000)
115PL_TEST_INTERVAL (SV_NAME_D2 (atan2), 100, inf, 40000)
116PL_TEST_INTERVAL (SV_NAME_D2 (atan2), -0, -inf, 40000)
117