1/*
2 * Double-precision SVE cospi(x) function.
3 *
4 * Copyright (c) 2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "mathlib.h"
9#include "sv_math.h"
10#include "pl_sig.h"
11#include "pl_test.h"
12#include "poly_sve_f64.h"
13
14static const struct data
15{
16  double poly[10];
17  double range_val;
18} data = {
19  /* Polynomial coefficients generated using Remez algorithm,
20     see sinpi.sollya for details.  */
21  .poly = { 0x1.921fb54442d184p1, -0x1.4abbce625be53p2, 0x1.466bc6775ab16p1,
22	    -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
23	    0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16,
24	    0x1.af86ae521260bp-21, -0x1.012a9870eeb7dp-25 },
25  .range_val = 0x1p53,
26};
27
28/* A fast SVE implementation of cospi.
29   Maximum error 3.20 ULP:
30   _ZGVsMxv_cospi(0x1.f18ba32c63159p-6) got 0x1.fdabf595f9763p-1
31				       want 0x1.fdabf595f9766p-1.  */
32svfloat64_t SV_NAME_D1 (cospi) (svfloat64_t x, const svbool_t pg)
33{
34  const struct data *d = ptr_barrier (&data);
35
36  /* Using cospi(x) = sinpi(0.5 - x)
37     range reduction and offset into sinpi range -1/2 .. 1/2
38     r = 0.5 - |x - rint(x)|.  */
39  svfloat64_t n = svrinta_x (pg, x);
40  svfloat64_t r = svsub_x (pg, x, n);
41  r = svsub_x (pg, sv_f64 (0.5), svabs_x (pg, r));
42
43  /* Result should be negated based on if n is odd or not.
44     If ax >= 2^53, the result will always be positive.  */
45  svbool_t cmp = svaclt (pg, x, d->range_val);
46  svuint64_t intn = svreinterpret_u64 (svcvt_s64_z (pg, n));
47  svuint64_t sign = svlsl_z (cmp, intn, 63);
48
49  /* y = sin(r).  */
50  svfloat64_t r2 = svmul_x (pg, r, r);
51  svfloat64_t r4 = svmul_x (pg, r2, r2);
52  svfloat64_t y = sv_pw_horner_9_f64_x (pg, r2, r4, d->poly);
53  y = svmul_x (pg, y, r);
54
55  return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
56}
57
58PL_SIG (SV, D, 1, cospi, -0.9, 0.9)
59PL_TEST_ULP (SV_NAME_D1 (cospi), 2.71)
60PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0, 0x1p-63, 5000)
61PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p-63, 0.5, 10000)
62PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0.5, 0x1p51, 10000)
63PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p51, inf, 100000)
64