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#include "poly_sve_f32.h"
12
13static const struct data
14{
15  float32_t poly[8];
16  float32_t pi_over_2;
17} data = {
18  /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
19     [2**-128, 1.0].  */
20  .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
21	    -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f },
22  .pi_over_2 = 0x1.921fb6p+0f,
23};
24
25#define SignMask sv_u32 (0x80000000)
26
27/* Special cases i.e. 0, infinity, nan (fall back to scalar calls).  */
28static inline svfloat32_t
29special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret,
30	      const svbool_t cmp)
31{
32  return sv_call2_f32 (atan2f, y, x, ret, cmp);
33}
34
35/* Returns a predicate indicating true if the input is the bit representation
36   of 0, infinity or nan.  */
37static inline svbool_t
38zeroinfnan (svuint32_t i, const svbool_t pg)
39{
40  return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
41		  sv_u32 (2 * 0x7f800000lu - 1));
42}
43
44/* Fast implementation of SVE atan2f based on atan(x) ~ shift + z + z^3 *
45   P(z^2) with reduction to [0,1] using z=1/x and shift = pi/2. Maximum
46   observed error is 2.95 ULP:
47   _ZGVsMxvv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1
48						 want 0x1.967f00p-1.  */
49svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, const svbool_t pg)
50{
51  const struct data *data_ptr = ptr_barrier (&data);
52
53  svuint32_t ix = svreinterpret_u32 (x);
54  svuint32_t iy = svreinterpret_u32 (y);
55
56  svbool_t cmp_x = zeroinfnan (ix, pg);
57  svbool_t cmp_y = zeroinfnan (iy, pg);
58  svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y);
59
60  svuint32_t sign_x = svand_x (pg, ix, SignMask);
61  svuint32_t sign_y = svand_x (pg, iy, SignMask);
62  svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y);
63
64  svfloat32_t ax = svabs_x (pg, x);
65  svfloat32_t ay = svabs_x (pg, y);
66
67  svbool_t pred_xlt0 = svcmplt (pg, x, 0.0);
68  svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
69
70  /* Set up z for call to atan.  */
71  svfloat32_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay);
72  svfloat32_t d = svsel (pred_aygtax, ay, ax);
73  svfloat32_t z = svdiv_x (pg, n, d);
74
75  /* Work out the correct shift.  */
76  svfloat32_t shift = svsel (pred_xlt0, sv_f32 (-2.0), sv_f32 (0.0));
77  shift = svsel (pred_aygtax, svadd_x (pg, shift, 1.0), shift);
78  shift = svmul_x (pg, shift, sv_f32 (data_ptr->pi_over_2));
79
80  /* Use split Estrin scheme for P(z^2) with deg(P)=7.  */
81  svfloat32_t z2 = svmul_x (pg, z, z);
82  svfloat32_t z4 = svmul_x (pg, z2, z2);
83  svfloat32_t z8 = svmul_x (pg, z4, z4);
84
85  svfloat32_t ret = sv_estrin_7_f32_x (pg, z2, z4, z8, data_ptr->poly);
86
87  /* ret = shift + z + z^3 * P(z^2).  */
88  svfloat32_t z3 = svmul_x (pg, z2, z);
89  ret = svmla_x (pg, z, z3, ret);
90
91  ret = svadd_m (pg, ret, shift);
92
93  /* Account for the sign of x and y.  */
94  ret = svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy));
95
96  if (unlikely (svptest_any (pg, cmp_xy)))
97    return special_case (y, x, ret, cmp_xy);
98
99  return ret;
100}
101
102/* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h.  */
103PL_SIG (SV, F, 2, atan2)
104PL_TEST_ULP (SV_NAME_F2 (atan2), 2.45)
105PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 0.0, 1.0, 40000)
106PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 1.0, 100.0, 40000)
107PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 100, inf, 40000)
108PL_TEST_INTERVAL (SV_NAME_F2 (atan2), -0, -inf, 40000)
109