1/*
2 * Single-precision SVE cos(x) function.
3 *
4 * Copyright (c) 2019-2023, 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
12static const struct data
13{
14  float neg_pio2_1, neg_pio2_2, neg_pio2_3, inv_pio2, shift;
15} data = {
16  /* Polynomial coefficients are hard-wired in FTMAD instructions.  */
17  .neg_pio2_1 = -0x1.921fb6p+0f,
18  .neg_pio2_2 = 0x1.777a5cp-25f,
19  .neg_pio2_3 = 0x1.ee59dap-50f,
20  .inv_pio2 = 0x1.45f306p-1f,
21  /* Original shift used in AdvSIMD cosf,
22     plus a contribution to set the bit #0 of q
23     as expected by trigonometric instructions.  */
24  .shift = 0x1.800002p+23f
25};
26
27#define RangeVal 0x49800000 /* asuint32(0x1p20f).  */
28
29static svfloat32_t NOINLINE
30special_case (svfloat32_t x, svfloat32_t y, svbool_t oob)
31{
32  return sv_call_f32 (cosf, x, y, oob);
33}
34
35/* A fast SVE implementation of cosf based on trigonometric
36   instructions (FTMAD, FTSSEL, FTSMUL).
37   Maximum measured error: 2.06 ULPs.
38   SV_NAME_F1 (cos)(0x1.dea2f2p+19) got 0x1.fffe7ap-6
39				   want 0x1.fffe76p-6.  */
40svfloat32_t SV_NAME_F1 (cos) (svfloat32_t x, const svbool_t pg)
41{
42  const struct data *d = ptr_barrier (&data);
43
44  svfloat32_t r = svabs_x (pg, x);
45  svbool_t oob = svcmpge (pg, svreinterpret_u32 (r), RangeVal);
46
47  /* Load some constants in quad-word chunks to minimise memory access.  */
48  svfloat32_t negpio2_and_invpio2 = svld1rq (svptrue_b32 (), &d->neg_pio2_1);
49
50  /* n = rint(|x|/(pi/2)).  */
51  svfloat32_t q = svmla_lane (sv_f32 (d->shift), r, negpio2_and_invpio2, 3);
52  svfloat32_t n = svsub_x (pg, q, d->shift);
53
54  /* r = |x| - n*(pi/2)  (range reduction into -pi/4 .. pi/4).  */
55  r = svmla_lane (r, n, negpio2_and_invpio2, 0);
56  r = svmla_lane (r, n, negpio2_and_invpio2, 1);
57  r = svmla_lane (r, n, negpio2_and_invpio2, 2);
58
59  /* Final multiplicative factor: 1.0 or x depending on bit #0 of q.  */
60  svfloat32_t f = svtssel (r, svreinterpret_u32 (q));
61
62  /* cos(r) poly approx.  */
63  svfloat32_t r2 = svtsmul (r, svreinterpret_u32 (q));
64  svfloat32_t y = sv_f32 (0.0f);
65  y = svtmad (y, r2, 4);
66  y = svtmad (y, r2, 3);
67  y = svtmad (y, r2, 2);
68  y = svtmad (y, r2, 1);
69  y = svtmad (y, r2, 0);
70
71  if (unlikely (svptest_any (pg, oob)))
72    return special_case (x, svmul_x (svnot_z (pg, oob), f, y), oob);
73  /* Apply factor.  */
74  return svmul_x (pg, f, y);
75}
76
77PL_SIG (SV, F, 1, cos, -3.1, 3.1)
78PL_TEST_ULP (SV_NAME_F1 (cos), 1.57)
79PL_TEST_INTERVAL (SV_NAME_F1 (cos), 0, 0xffff0000, 10000)
80PL_TEST_INTERVAL (SV_NAME_F1 (cos), 0x1p-4, 0x1p4, 500000)
81