1*5a02ffc3SAndrew Turner /*
2*5a02ffc3SAndrew Turner * Double-precision SVE cospi(x) function.
3*5a02ffc3SAndrew Turner *
4*5a02ffc3SAndrew Turner * Copyright (c) 2023, Arm Limited.
5*5a02ffc3SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*5a02ffc3SAndrew Turner */
7*5a02ffc3SAndrew Turner
8*5a02ffc3SAndrew Turner #include "mathlib.h"
9*5a02ffc3SAndrew Turner #include "sv_math.h"
10*5a02ffc3SAndrew Turner #include "pl_sig.h"
11*5a02ffc3SAndrew Turner #include "pl_test.h"
12*5a02ffc3SAndrew Turner #include "poly_sve_f64.h"
13*5a02ffc3SAndrew Turner
14*5a02ffc3SAndrew Turner static const struct data
15*5a02ffc3SAndrew Turner {
16*5a02ffc3SAndrew Turner double poly[10];
17*5a02ffc3SAndrew Turner double range_val;
18*5a02ffc3SAndrew Turner } data = {
19*5a02ffc3SAndrew Turner /* Polynomial coefficients generated using Remez algorithm,
20*5a02ffc3SAndrew Turner see sinpi.sollya for details. */
21*5a02ffc3SAndrew Turner .poly = { 0x1.921fb54442d184p1, -0x1.4abbce625be53p2, 0x1.466bc6775ab16p1,
22*5a02ffc3SAndrew Turner -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
23*5a02ffc3SAndrew Turner 0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16,
24*5a02ffc3SAndrew Turner 0x1.af86ae521260bp-21, -0x1.012a9870eeb7dp-25 },
25*5a02ffc3SAndrew Turner .range_val = 0x1p53,
26*5a02ffc3SAndrew Turner };
27*5a02ffc3SAndrew Turner
28*5a02ffc3SAndrew Turner /* A fast SVE implementation of cospi.
29*5a02ffc3SAndrew Turner Maximum error 3.20 ULP:
30*5a02ffc3SAndrew Turner _ZGVsMxv_cospi(0x1.f18ba32c63159p-6) got 0x1.fdabf595f9763p-1
31*5a02ffc3SAndrew Turner want 0x1.fdabf595f9766p-1. */
SV_NAME_D1(cospi)32*5a02ffc3SAndrew Turner svfloat64_t SV_NAME_D1 (cospi) (svfloat64_t x, const svbool_t pg)
33*5a02ffc3SAndrew Turner {
34*5a02ffc3SAndrew Turner const struct data *d = ptr_barrier (&data);
35*5a02ffc3SAndrew Turner
36*5a02ffc3SAndrew Turner /* Using cospi(x) = sinpi(0.5 - x)
37*5a02ffc3SAndrew Turner range reduction and offset into sinpi range -1/2 .. 1/2
38*5a02ffc3SAndrew Turner r = 0.5 - |x - rint(x)|. */
39*5a02ffc3SAndrew Turner svfloat64_t n = svrinta_x (pg, x);
40*5a02ffc3SAndrew Turner svfloat64_t r = svsub_x (pg, x, n);
41*5a02ffc3SAndrew Turner r = svsub_x (pg, sv_f64 (0.5), svabs_x (pg, r));
42*5a02ffc3SAndrew Turner
43*5a02ffc3SAndrew Turner /* Result should be negated based on if n is odd or not.
44*5a02ffc3SAndrew Turner If ax >= 2^53, the result will always be positive. */
45*5a02ffc3SAndrew Turner svbool_t cmp = svaclt (pg, x, d->range_val);
46*5a02ffc3SAndrew Turner svuint64_t intn = svreinterpret_u64 (svcvt_s64_z (pg, n));
47*5a02ffc3SAndrew Turner svuint64_t sign = svlsl_z (cmp, intn, 63);
48*5a02ffc3SAndrew Turner
49*5a02ffc3SAndrew Turner /* y = sin(r). */
50*5a02ffc3SAndrew Turner svfloat64_t r2 = svmul_x (pg, r, r);
51*5a02ffc3SAndrew Turner svfloat64_t r4 = svmul_x (pg, r2, r2);
52*5a02ffc3SAndrew Turner svfloat64_t y = sv_pw_horner_9_f64_x (pg, r2, r4, d->poly);
53*5a02ffc3SAndrew Turner y = svmul_x (pg, y, r);
54*5a02ffc3SAndrew Turner
55*5a02ffc3SAndrew Turner return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
56*5a02ffc3SAndrew Turner }
57*5a02ffc3SAndrew Turner
58*5a02ffc3SAndrew Turner PL_SIG (SV, D, 1, cospi, -0.9, 0.9)
59*5a02ffc3SAndrew Turner PL_TEST_ULP (SV_NAME_D1 (cospi), 2.71)
60*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0, 0x1p-63, 5000)
61*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p-63, 0.5, 10000)
62*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0.5, 0x1p51, 10000)
63*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p51, inf, 100000)
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