1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision vector tanpi(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "sv_math.h"
9*f3087befSAndrew Turner #include "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner const static struct v_tanpi_data
13*f3087befSAndrew Turner {
14*f3087befSAndrew Turner double c0, c2, c4, c6, c8, c10, c12;
15*f3087befSAndrew Turner double c1, c3, c5, c7, c9, c11, c13, c14;
16*f3087befSAndrew Turner } tanpi_data = {
17*f3087befSAndrew Turner /* Coefficents for tan(pi * x) computed with fpminimax
18*f3087befSAndrew Turner on [ 0x1p-1022 0x1p-2 ]
19*f3087befSAndrew Turner approx rel error: 0x1.7eap-55
20*f3087befSAndrew Turner approx abs error: 0x1.7eap-55. */
21*f3087befSAndrew Turner .c0 = 0x1.921fb54442d18p1, /* pi. */
22*f3087befSAndrew Turner .c1 = 0x1.4abbce625be52p3, .c2 = 0x1.466bc6775b0f9p5,
23*f3087befSAndrew Turner .c3 = 0x1.45fff9b426f5ep7, .c4 = 0x1.45f4730dbca5cp9,
24*f3087befSAndrew Turner .c5 = 0x1.45f3265994f85p11, .c6 = 0x1.45f4234b330cap13,
25*f3087befSAndrew Turner .c7 = 0x1.45dca11be79ebp15, .c8 = 0x1.47283fc5eea69p17,
26*f3087befSAndrew Turner .c9 = 0x1.3a6d958cdefaep19, .c10 = 0x1.927896baee627p21,
27*f3087befSAndrew Turner .c11 = -0x1.89333f6acd922p19, .c12 = 0x1.5d4e912bb8456p27,
28*f3087befSAndrew Turner .c13 = -0x1.a854d53ab6874p29, .c14 = 0x1.1b76de7681424p32,
29*f3087befSAndrew Turner };
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner /* Approximation for double-precision vector tanpi(x)
32*f3087befSAndrew Turner The maximum error is 3.06 ULP:
33*f3087befSAndrew Turner _ZGVsMxv_tanpi(0x1.0a4a07dfcca3ep-1) got -0x1.fa30112702c98p+3
34*f3087befSAndrew Turner want -0x1.fa30112702c95p+3. */
SV_NAME_D1(tanpi)35*f3087befSAndrew Turner svfloat64_t SV_NAME_D1 (tanpi) (svfloat64_t x, const svbool_t pg)
36*f3087befSAndrew Turner {
37*f3087befSAndrew Turner const struct v_tanpi_data *d = ptr_barrier (&tanpi_data);
38*f3087befSAndrew Turner
39*f3087befSAndrew Turner svfloat64_t n = svrintn_x (pg, x);
40*f3087befSAndrew Turner
41*f3087befSAndrew Turner /* inf produces nan that propagates. */
42*f3087befSAndrew Turner svfloat64_t xr = svsub_x (pg, x, n);
43*f3087befSAndrew Turner svfloat64_t ar = svabd_x (pg, x, n);
44*f3087befSAndrew Turner svbool_t flip = svcmpgt (pg, ar, 0.25);
45*f3087befSAndrew Turner svfloat64_t r = svsel (flip, svsubr_x (pg, ar, 0.5), ar);
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner /* Order-14 pairwise Horner. */
48*f3087befSAndrew Turner svfloat64_t r2 = svmul_x (pg, r, r);
49*f3087befSAndrew Turner svfloat64_t r4 = svmul_x (pg, r2, r2);
50*f3087befSAndrew Turner
51*f3087befSAndrew Turner svfloat64_t c_1_3 = svld1rq (pg, &d->c1);
52*f3087befSAndrew Turner svfloat64_t c_5_7 = svld1rq (pg, &d->c5);
53*f3087befSAndrew Turner svfloat64_t c_9_11 = svld1rq (pg, &d->c9);
54*f3087befSAndrew Turner svfloat64_t c_13_14 = svld1rq (pg, &d->c13);
55*f3087befSAndrew Turner svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r2, c_1_3, 0);
56*f3087befSAndrew Turner svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r2, c_1_3, 1);
57*f3087befSAndrew Turner svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), r2, c_5_7, 0);
58*f3087befSAndrew Turner svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), r2, c_5_7, 1);
59*f3087befSAndrew Turner svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), r2, c_9_11, 0);
60*f3087befSAndrew Turner svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), r2, c_9_11, 1);
61*f3087befSAndrew Turner svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), r2, c_13_14, 0);
62*f3087befSAndrew Turner
63*f3087befSAndrew Turner svfloat64_t p = svmla_lane (p1213, r4, c_13_14, 1);
64*f3087befSAndrew Turner p = svmad_x (pg, p, r4, p1011);
65*f3087befSAndrew Turner p = svmad_x (pg, p, r4, p89);
66*f3087befSAndrew Turner p = svmad_x (pg, p, r4, p67);
67*f3087befSAndrew Turner p = svmad_x (pg, p, r4, p45);
68*f3087befSAndrew Turner p = svmad_x (pg, p, r4, p23);
69*f3087befSAndrew Turner p = svmad_x (pg, p, r4, p01);
70*f3087befSAndrew Turner p = svmul_x (pg, r, p);
71*f3087befSAndrew Turner
72*f3087befSAndrew Turner svfloat64_t p_recip = svdivr_x (pg, p, 1.0);
73*f3087befSAndrew Turner svfloat64_t y = svsel (flip, p_recip, p);
74*f3087befSAndrew Turner
75*f3087befSAndrew Turner svuint64_t sign
76*f3087befSAndrew Turner = sveor_x (pg, svreinterpret_u64 (xr), svreinterpret_u64 (ar));
77*f3087befSAndrew Turner return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign));
78*f3087befSAndrew Turner }
79*f3087befSAndrew Turner
80*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS
81*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_D1 (tanpi))
82*f3087befSAndrew Turner TEST_ULP (SV_NAME_D1 (tanpi), 2.57)
83*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0, 0x1p-31, 50000)
84*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0x1p-31, 0.5, 50000)
85*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0.5, 1.0, 200000)
86*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 1.0, 0x1p23, 50000)
87*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0x1p23, inf, 50000)
88*f3087befSAndrew Turner #endif
89*f3087befSAndrew Turner CLOSE_SVE_ATTR
90