1*412f47f9SXin Li /*
2*412f47f9SXin Li * Double-precision SVE cos(x) function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2019-2023, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "sv_math.h"
9*412f47f9SXin Li #include "pl_sig.h"
10*412f47f9SXin Li #include "pl_test.h"
11*412f47f9SXin Li
12*412f47f9SXin Li static const struct data
13*412f47f9SXin Li {
14*412f47f9SXin Li double inv_pio2, pio2_1, pio2_2, pio2_3, shift;
15*412f47f9SXin Li } data = {
16*412f47f9SXin Li /* Polynomial coefficients are hardwired in FTMAD instructions. */
17*412f47f9SXin Li .inv_pio2 = 0x1.45f306dc9c882p-1,
18*412f47f9SXin Li .pio2_1 = 0x1.921fb50000000p+0,
19*412f47f9SXin Li .pio2_2 = 0x1.110b460000000p-26,
20*412f47f9SXin Li .pio2_3 = 0x1.1a62633145c07p-54,
21*412f47f9SXin Li /* Original shift used in AdvSIMD cos,
22*412f47f9SXin Li plus a contribution to set the bit #0 of q
23*412f47f9SXin Li as expected by trigonometric instructions. */
24*412f47f9SXin Li .shift = 0x1.8000000000001p52
25*412f47f9SXin Li };
26*412f47f9SXin Li
27*412f47f9SXin Li #define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */
28*412f47f9SXin Li
29*412f47f9SXin Li static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t oob)30*412f47f9SXin Li special_case (svfloat64_t x, svfloat64_t y, svbool_t oob)
31*412f47f9SXin Li {
32*412f47f9SXin Li return sv_call_f64 (cos, x, y, oob);
33*412f47f9SXin Li }
34*412f47f9SXin Li
35*412f47f9SXin Li /* A fast SVE implementation of cos based on trigonometric
36*412f47f9SXin Li instructions (FTMAD, FTSSEL, FTSMUL).
37*412f47f9SXin Li Maximum measured error: 2.108 ULPs.
38*412f47f9SXin Li SV_NAME_D1 (cos)(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3
39*412f47f9SXin Li want -0x1.fddd4c65c7f05p-3. */
SV_NAME_D1(cos)40*412f47f9SXin Li svfloat64_t SV_NAME_D1 (cos) (svfloat64_t x, const svbool_t pg)
41*412f47f9SXin Li {
42*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
43*412f47f9SXin Li
44*412f47f9SXin Li svfloat64_t r = svabs_x (pg, x);
45*412f47f9SXin Li svbool_t oob = svcmpge (pg, svreinterpret_u64 (r), RangeVal);
46*412f47f9SXin Li
47*412f47f9SXin Li /* Load some constants in quad-word chunks to minimise memory access. */
48*412f47f9SXin Li svbool_t ptrue = svptrue_b64 ();
49*412f47f9SXin Li svfloat64_t invpio2_and_pio2_1 = svld1rq (ptrue, &d->inv_pio2);
50*412f47f9SXin Li svfloat64_t pio2_23 = svld1rq (ptrue, &d->pio2_2);
51*412f47f9SXin Li
52*412f47f9SXin Li /* n = rint(|x|/(pi/2)). */
53*412f47f9SXin Li svfloat64_t q = svmla_lane (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0);
54*412f47f9SXin Li svfloat64_t n = svsub_x (pg, q, d->shift);
55*412f47f9SXin Li
56*412f47f9SXin Li /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
57*412f47f9SXin Li r = svmls_lane (r, n, invpio2_and_pio2_1, 1);
58*412f47f9SXin Li r = svmls_lane (r, n, pio2_23, 0);
59*412f47f9SXin Li r = svmls_lane (r, n, pio2_23, 1);
60*412f47f9SXin Li
61*412f47f9SXin Li /* cos(r) poly approx. */
62*412f47f9SXin Li svfloat64_t r2 = svtsmul (r, svreinterpret_u64 (q));
63*412f47f9SXin Li svfloat64_t y = sv_f64 (0.0);
64*412f47f9SXin Li y = svtmad (y, r2, 7);
65*412f47f9SXin Li y = svtmad (y, r2, 6);
66*412f47f9SXin Li y = svtmad (y, r2, 5);
67*412f47f9SXin Li y = svtmad (y, r2, 4);
68*412f47f9SXin Li y = svtmad (y, r2, 3);
69*412f47f9SXin Li y = svtmad (y, r2, 2);
70*412f47f9SXin Li y = svtmad (y, r2, 1);
71*412f47f9SXin Li y = svtmad (y, r2, 0);
72*412f47f9SXin Li
73*412f47f9SXin Li /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
74*412f47f9SXin Li svfloat64_t f = svtssel (r, svreinterpret_u64 (q));
75*412f47f9SXin Li
76*412f47f9SXin Li if (unlikely (svptest_any (pg, oob)))
77*412f47f9SXin Li return special_case (x, svmul_x (svnot_z (pg, oob), y, f), oob);
78*412f47f9SXin Li
79*412f47f9SXin Li /* Apply factor. */
80*412f47f9SXin Li return svmul_x (pg, f, y);
81*412f47f9SXin Li }
82*412f47f9SXin Li
83*412f47f9SXin Li PL_SIG (SV, D, 1, cos, -3.1, 3.1)
84*412f47f9SXin Li PL_TEST_ULP (SV_NAME_D1 (cos), 1.61)
85*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (cos), 0, 0xffff0000, 10000)
86*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (cos), 0x1p-4, 0x1p4, 500000)
87