1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision SVE asin(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2023-2024, 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 "sv_poly_f32.h"
10*f3087befSAndrew Turner #include "test_sig.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner
13*f3087befSAndrew Turner static const struct data
14*f3087befSAndrew Turner {
15*f3087befSAndrew Turner float32_t poly[5];
16*f3087befSAndrew Turner float32_t pi_over_2f;
17*f3087befSAndrew Turner } data = {
18*f3087befSAndrew Turner /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
19*f3087befSAndrew Turner [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
20*f3087befSAndrew Turner .poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6,
21*f3087befSAndrew Turner 0x1.3af7d8p-5, },
22*f3087befSAndrew Turner .pi_over_2f = 0x1.921fb6p+0f,
23*f3087befSAndrew Turner };
24*f3087befSAndrew Turner
25*f3087befSAndrew Turner /* Single-precision SVE implementation of vector asin(x).
26*f3087befSAndrew Turner
27*f3087befSAndrew Turner For |x| in [0, 0.5], use order 4 polynomial P such that the final
28*f3087befSAndrew Turner approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
29*f3087befSAndrew Turner
30*f3087befSAndrew Turner The largest observed error in this region is 0.83 ulps,
31*f3087befSAndrew Turner _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2
32*f3087befSAndrew Turner want 0x1.fef15cp-2.
33*f3087befSAndrew Turner
34*f3087befSAndrew Turner For |x| in [0.5, 1.0], use same approximation with a change of variable
35*f3087befSAndrew Turner
36*f3087befSAndrew Turner asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
37*f3087befSAndrew Turner
38*f3087befSAndrew Turner The largest observed error in this region is 2.41 ulps,
39*f3087befSAndrew Turner _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1
40*f3087befSAndrew Turner want -0x1.0c3a6p-1. */
SV_NAME_F1(asin)41*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (asin) (svfloat32_t x, const svbool_t pg)
42*f3087befSAndrew Turner {
43*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
44*f3087befSAndrew Turner
45*f3087befSAndrew Turner svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000);
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner svfloat32_t ax = svabs_x (pg, x);
48*f3087befSAndrew Turner svbool_t a_ge_half = svacge (pg, x, 0.5);
49*f3087befSAndrew Turner
50*f3087befSAndrew Turner /* Evaluate polynomial Q(x) = y + y * z * P(z) with
51*f3087befSAndrew Turner z = x ^ 2 and y = |x| , if |x| < 0.5
52*f3087befSAndrew Turner z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */
53*f3087befSAndrew Turner svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5),
54*f3087befSAndrew Turner svmul_x (pg, x, x));
55*f3087befSAndrew Turner svfloat32_t z = svsqrt_m (ax, a_ge_half, z2);
56*f3087befSAndrew Turner
57*f3087befSAndrew Turner /* Use a single polynomial approximation P for both intervals. */
58*f3087befSAndrew Turner svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly);
59*f3087befSAndrew Turner /* Finalize polynomial: z + z * z2 * P(z2). */
60*f3087befSAndrew Turner p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner /* asin(|x|) = Q(|x|) , for |x| < 0.5
63*f3087befSAndrew Turner = pi/2 - 2 Q(|x|), for |x| >= 0.5. */
64*f3087befSAndrew Turner svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f);
65*f3087befSAndrew Turner
66*f3087befSAndrew Turner /* Copy sign. */
67*f3087befSAndrew Turner return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign));
68*f3087befSAndrew Turner }
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner TEST_SIG (SV, F, 1, asin, -1.0, 1.0)
71*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (asin), 1.91)
72*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (asin))
73*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (asin), 0, 0.5, 50000)
74*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (asin), 0.5, 1.0, 50000)
75*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (asin), 1.0, 0x1p11, 50000)
76*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (asin), 0x1p11, inf, 20000)
77*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (asin), -0, -inf, 20000)
78*f3087befSAndrew Turner CLOSE_SVE_ATTR
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