1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision SVE cos(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2019-2024, 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 static const struct data
13*f3087befSAndrew Turner {
14*f3087befSAndrew Turner float neg_pio2_1, neg_pio2_2, neg_pio2_3, inv_pio2, shift;
15*f3087befSAndrew Turner } data = {
16*f3087befSAndrew Turner /* Polynomial coefficients are hard-wired in FTMAD instructions. */
17*f3087befSAndrew Turner .neg_pio2_1 = -0x1.921fb6p+0f,
18*f3087befSAndrew Turner .neg_pio2_2 = 0x1.777a5cp-25f,
19*f3087befSAndrew Turner .neg_pio2_3 = 0x1.ee59dap-50f,
20*f3087befSAndrew Turner .inv_pio2 = 0x1.45f306p-1f,
21*f3087befSAndrew Turner /* Original shift used in AdvSIMD cosf,
22*f3087befSAndrew Turner plus a contribution to set the bit #0 of q
23*f3087befSAndrew Turner as expected by trigonometric instructions. */
24*f3087befSAndrew Turner .shift = 0x1.800002p+23f
25*f3087befSAndrew Turner };
26*f3087befSAndrew Turner
27*f3087befSAndrew Turner #define RangeVal 0x49800000 /* asuint32(0x1p20f). */
28*f3087befSAndrew Turner
29*f3087befSAndrew Turner static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t oob)30*f3087befSAndrew Turner special_case (svfloat32_t x, svfloat32_t y, svbool_t oob)
31*f3087befSAndrew Turner {
32*f3087befSAndrew Turner return sv_call_f32 (cosf, x, y, oob);
33*f3087befSAndrew Turner }
34*f3087befSAndrew Turner
35*f3087befSAndrew Turner /* A fast SVE implementation of cosf based on trigonometric
36*f3087befSAndrew Turner instructions (FTMAD, FTSSEL, FTSMUL).
37*f3087befSAndrew Turner Maximum measured error: 2.06 ULPs.
38*f3087befSAndrew Turner SV_NAME_F1 (cos)(0x1.dea2f2p+19) got 0x1.fffe7ap-6
39*f3087befSAndrew Turner want 0x1.fffe76p-6. */
SV_NAME_F1(cos)40*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (cos) (svfloat32_t x, const svbool_t pg)
41*f3087befSAndrew Turner {
42*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
43*f3087befSAndrew Turner
44*f3087befSAndrew Turner svfloat32_t r = svabs_x (pg, x);
45*f3087befSAndrew Turner svbool_t oob = svcmpge (pg, svreinterpret_u32 (r), RangeVal);
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner /* Load some constants in quad-word chunks to minimise memory access. */
48*f3087befSAndrew Turner svfloat32_t negpio2_and_invpio2 = svld1rq (svptrue_b32 (), &d->neg_pio2_1);
49*f3087befSAndrew Turner
50*f3087befSAndrew Turner /* n = rint(|x|/(pi/2)). */
51*f3087befSAndrew Turner svfloat32_t q = svmla_lane (sv_f32 (d->shift), r, negpio2_and_invpio2, 3);
52*f3087befSAndrew Turner svfloat32_t n = svsub_x (pg, q, d->shift);
53*f3087befSAndrew Turner
54*f3087befSAndrew Turner /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
55*f3087befSAndrew Turner r = svmla_lane (r, n, negpio2_and_invpio2, 0);
56*f3087befSAndrew Turner r = svmla_lane (r, n, negpio2_and_invpio2, 1);
57*f3087befSAndrew Turner r = svmla_lane (r, n, negpio2_and_invpio2, 2);
58*f3087befSAndrew Turner
59*f3087befSAndrew Turner /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
60*f3087befSAndrew Turner svfloat32_t f = svtssel (r, svreinterpret_u32 (q));
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner /* cos(r) poly approx. */
63*f3087befSAndrew Turner svfloat32_t r2 = svtsmul (r, svreinterpret_u32 (q));
64*f3087befSAndrew Turner svfloat32_t y = sv_f32 (0.0f);
65*f3087befSAndrew Turner y = svtmad (y, r2, 4);
66*f3087befSAndrew Turner y = svtmad (y, r2, 3);
67*f3087befSAndrew Turner y = svtmad (y, r2, 2);
68*f3087befSAndrew Turner y = svtmad (y, r2, 1);
69*f3087befSAndrew Turner y = svtmad (y, r2, 0);
70*f3087befSAndrew Turner
71*f3087befSAndrew Turner if (unlikely (svptest_any (pg, oob)))
72*f3087befSAndrew Turner return special_case (x, svmul_x (svnot_z (pg, oob), f, y), oob);
73*f3087befSAndrew Turner /* Apply factor. */
74*f3087befSAndrew Turner return svmul_x (pg, f, y);
75*f3087befSAndrew Turner }
76*f3087befSAndrew Turner
77*f3087befSAndrew Turner TEST_SIG (SV, F, 1, cos, -3.1, 3.1)
78*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (cos), 1.57)
79*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (cos))
80*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (cos), 0, 0xffff0000, 10000)
81*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (cos), 0x1p-4, 0x1p4, 500000)
82*f3087befSAndrew Turner CLOSE_SVE_ATTR
83