1/*
2 * Double-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  double inv_pio2, pio2_1, pio2_2, pio2_3, shift;
15} data = {
16  /* Polynomial coefficients are hardwired in FTMAD instructions.  */
17  .inv_pio2 = 0x1.45f306dc9c882p-1,
18  .pio2_1 = 0x1.921fb50000000p+0,
19  .pio2_2 = 0x1.110b460000000p-26,
20  .pio2_3 = 0x1.1a62633145c07p-54,
21  /* Original shift used in AdvSIMD cos,
22     plus a contribution to set the bit #0 of q
23     as expected by trigonometric instructions.  */
24  .shift = 0x1.8000000000001p52
25};
26
27#define RangeVal 0x4160000000000000 /* asuint64 (0x1p23).  */
28
29static svfloat64_t NOINLINE
30special_case (svfloat64_t x, svfloat64_t y, svbool_t oob)
31{
32  return sv_call_f64 (cos, x, y, oob);
33}
34
35/* A fast SVE implementation of cos based on trigonometric
36   instructions (FTMAD, FTSSEL, FTSMUL).
37   Maximum measured error: 2.108 ULPs.
38   SV_NAME_D1 (cos)(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3
39					 want -0x1.fddd4c65c7f05p-3.  */
40svfloat64_t SV_NAME_D1 (cos) (svfloat64_t x, const svbool_t pg)
41{
42  const struct data *d = ptr_barrier (&data);
43
44  svfloat64_t r = svabs_x (pg, x);
45  svbool_t oob = svcmpge (pg, svreinterpret_u64 (r), RangeVal);
46
47  /* Load some constants in quad-word chunks to minimise memory access.  */
48  svbool_t ptrue = svptrue_b64 ();
49  svfloat64_t invpio2_and_pio2_1 = svld1rq (ptrue, &d->inv_pio2);
50  svfloat64_t pio2_23 = svld1rq (ptrue, &d->pio2_2);
51
52  /* n = rint(|x|/(pi/2)).  */
53  svfloat64_t q = svmla_lane (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0);
54  svfloat64_t n = svsub_x (pg, q, d->shift);
55
56  /* r = |x| - n*(pi/2)  (range reduction into -pi/4 .. pi/4).  */
57  r = svmls_lane (r, n, invpio2_and_pio2_1, 1);
58  r = svmls_lane (r, n, pio2_23, 0);
59  r = svmls_lane (r, n, pio2_23, 1);
60
61  /* cos(r) poly approx.  */
62  svfloat64_t r2 = svtsmul (r, svreinterpret_u64 (q));
63  svfloat64_t y = sv_f64 (0.0);
64  y = svtmad (y, r2, 7);
65  y = svtmad (y, r2, 6);
66  y = svtmad (y, r2, 5);
67  y = svtmad (y, r2, 4);
68  y = svtmad (y, r2, 3);
69  y = svtmad (y, r2, 2);
70  y = svtmad (y, r2, 1);
71  y = svtmad (y, r2, 0);
72
73  /* Final multiplicative factor: 1.0 or x depending on bit #0 of q.  */
74  svfloat64_t f = svtssel (r, svreinterpret_u64 (q));
75
76  if (unlikely (svptest_any (pg, oob)))
77    return special_case (x, svmul_x (svnot_z (pg, oob), y, f), oob);
78
79  /* Apply factor.  */
80  return svmul_x (pg, f, y);
81}
82
83PL_SIG (SV, D, 1, cos, -3.1, 3.1)
84PL_TEST_ULP (SV_NAME_D1 (cos), 1.61)
85PL_TEST_INTERVAL (SV_NAME_D1 (cos), 0, 0xffff0000, 10000)
86PL_TEST_INTERVAL (SV_NAME_D1 (cos), 0x1p-4, 0x1p4, 500000)
87