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
14 static 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. */
SV_NAME_D1(cospi)32 svfloat64_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
58 PL_SIG (SV, D, 1, cospi, -0.9, 0.9)
59 PL_TEST_ULP (SV_NAME_D1 (cospi), 2.71)
60 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0, 0x1p-63, 5000)
61 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p-63, 0.5, 10000)
62 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0.5, 0x1p51, 10000)
63 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p51, inf, 100000)
64