1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-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 "v_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_tanpif_data
13*f3087befSAndrew Turner {
14*f3087befSAndrew Turner float32x4_t c0, c2, c4, c6;
15*f3087befSAndrew Turner float c1, c3, c5, c7;
16*f3087befSAndrew Turner } tanpif_data = {
17*f3087befSAndrew Turner /* Coefficents for tan(pi * x). */
18*f3087befSAndrew Turner .c0 = V4 (0x1.921fb4p1f), .c1 = 0x1.4abbcep3f, .c2 = V4 (0x1.466b8p5f),
19*f3087befSAndrew Turner .c3 = 0x1.461c72p7f, .c4 = V4 (0x1.42e9d4p9f), .c5 = 0x1.69e2c4p11f,
20*f3087befSAndrew Turner .c6 = V4 (0x1.e85558p11f), .c7 = 0x1.a52e08p16f,
21*f3087befSAndrew Turner };
22*f3087befSAndrew Turner
23*f3087befSAndrew Turner /* Approximation for single-precision vector tanpi(x)
24*f3087befSAndrew Turner The maximum error is 3.34 ULP:
25*f3087befSAndrew Turner _ZGVnN4v_tanpif(0x1.d6c09ap-2) got 0x1.f70aacp+2
26*f3087befSAndrew Turner want 0x1.f70aa6p+2. */
V_NAME_F1(tanpi)27*f3087befSAndrew Turner float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tanpi) (float32x4_t x)
28*f3087befSAndrew Turner {
29*f3087befSAndrew Turner const struct v_tanpif_data *d = ptr_barrier (&tanpif_data);
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner float32x4_t n = vrndnq_f32 (x);
32*f3087befSAndrew Turner
33*f3087befSAndrew Turner /* inf produces nan that propagates. */
34*f3087befSAndrew Turner float32x4_t xr = vsubq_f32 (x, n);
35*f3087befSAndrew Turner float32x4_t ar = vabdq_f32 (x, n);
36*f3087befSAndrew Turner uint32x4_t flip = vcgtq_f32 (ar, v_f32 (0.25f));
37*f3087befSAndrew Turner float32x4_t r = vbslq_f32 (flip, vsubq_f32 (v_f32 (0.5f), ar), ar);
38*f3087befSAndrew Turner
39*f3087befSAndrew Turner /* Order-7 pairwise Horner polynomial evaluation scheme. */
40*f3087befSAndrew Turner float32x4_t r2 = vmulq_f32 (r, r);
41*f3087befSAndrew Turner float32x4_t r4 = vmulq_f32 (r2, r2);
42*f3087befSAndrew Turner
43*f3087befSAndrew Turner float32x4_t odd_coeffs = vld1q_f32 (&d->c1);
44*f3087befSAndrew Turner float32x4_t p01 = vfmaq_laneq_f32 (d->c0, r2, odd_coeffs, 0);
45*f3087befSAndrew Turner float32x4_t p23 = vfmaq_laneq_f32 (d->c2, r2, odd_coeffs, 1);
46*f3087befSAndrew Turner float32x4_t p45 = vfmaq_laneq_f32 (d->c4, r2, odd_coeffs, 2);
47*f3087befSAndrew Turner float32x4_t p67 = vfmaq_laneq_f32 (d->c6, r2, odd_coeffs, 3);
48*f3087befSAndrew Turner float32x4_t p = vfmaq_f32 (p45, r4, p67);
49*f3087befSAndrew Turner p = vfmaq_f32 (p23, r4, p);
50*f3087befSAndrew Turner p = vfmaq_f32 (p01, r4, p);
51*f3087befSAndrew Turner
52*f3087befSAndrew Turner p = vmulq_f32 (r, p);
53*f3087befSAndrew Turner float32x4_t p_recip = vdivq_f32 (v_f32 (1.0f), p);
54*f3087befSAndrew Turner float32x4_t y = vbslq_f32 (flip, p_recip, p);
55*f3087befSAndrew Turner
56*f3087befSAndrew Turner uint32x4_t sign
57*f3087befSAndrew Turner = veorq_u32 (vreinterpretq_u32_f32 (xr), vreinterpretq_u32_f32 (ar));
58*f3087befSAndrew Turner return vreinterpretq_f32_u32 (vorrq_u32 (vreinterpretq_u32_f32 (y), sign));
59*f3087befSAndrew Turner }
60*f3087befSAndrew Turner
61*f3087befSAndrew Turner HALF_WIDTH_ALIAS_F1 (tanpi)
62*f3087befSAndrew Turner
63*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS
64*f3087befSAndrew Turner TEST_DISABLE_FENV (V_NAME_F1 (tanpi))
65*f3087befSAndrew Turner TEST_ULP (V_NAME_F1 (tanpi), 2.84)
66*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0, 0x1p-31, 50000)
67*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0x1p-31, 0.5, 100000)
68*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0.5, 0x1p23f, 100000)
69*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0x1p23f, inf, 100000)
70*f3087befSAndrew Turner #endif
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