1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision SVE asin(x) function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 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 "poly_sve_f32.h"
10*412f47f9SXin Li #include "pl_sig.h"
11*412f47f9SXin Li #include "pl_test.h"
12*412f47f9SXin Li
13*412f47f9SXin Li static const struct data
14*412f47f9SXin Li {
15*412f47f9SXin Li float32_t poly[5];
16*412f47f9SXin Li float32_t pi_over_2f;
17*412f47f9SXin Li } data = {
18*412f47f9SXin Li /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
19*412f47f9SXin Li [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
20*412f47f9SXin Li .poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6,
21*412f47f9SXin Li 0x1.3af7d8p-5, },
22*412f47f9SXin Li .pi_over_2f = 0x1.921fb6p+0f,
23*412f47f9SXin Li };
24*412f47f9SXin Li
25*412f47f9SXin Li /* Single-precision SVE implementation of vector asin(x).
26*412f47f9SXin Li
27*412f47f9SXin Li For |x| in [0, 0.5], use order 4 polynomial P such that the final
28*412f47f9SXin Li approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
29*412f47f9SXin Li
30*412f47f9SXin Li The largest observed error in this region is 0.83 ulps,
31*412f47f9SXin Li _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2
32*412f47f9SXin Li want 0x1.fef15cp-2.
33*412f47f9SXin Li
34*412f47f9SXin Li For |x| in [0.5, 1.0], use same approximation with a change of variable
35*412f47f9SXin Li
36*412f47f9SXin Li asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
37*412f47f9SXin Li
38*412f47f9SXin Li The largest observed error in this region is 2.41 ulps,
39*412f47f9SXin Li _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1
40*412f47f9SXin Li want -0x1.0c3a6p-1. */
SV_NAME_F1(asin)41*412f47f9SXin Li svfloat32_t SV_NAME_F1 (asin) (svfloat32_t x, const svbool_t pg)
42*412f47f9SXin Li {
43*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
44*412f47f9SXin Li
45*412f47f9SXin Li svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000);
46*412f47f9SXin Li
47*412f47f9SXin Li svfloat32_t ax = svabs_x (pg, x);
48*412f47f9SXin Li svbool_t a_ge_half = svacge (pg, x, 0.5);
49*412f47f9SXin Li
50*412f47f9SXin Li /* Evaluate polynomial Q(x) = y + y * z * P(z) with
51*412f47f9SXin Li z = x ^ 2 and y = |x| , if |x| < 0.5
52*412f47f9SXin Li z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */
53*412f47f9SXin Li svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5),
54*412f47f9SXin Li svmul_x (pg, x, x));
55*412f47f9SXin Li svfloat32_t z = svsqrt_m (ax, a_ge_half, z2);
56*412f47f9SXin Li
57*412f47f9SXin Li /* Use a single polynomial approximation P for both intervals. */
58*412f47f9SXin Li svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly);
59*412f47f9SXin Li /* Finalize polynomial: z + z * z2 * P(z2). */
60*412f47f9SXin Li p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
61*412f47f9SXin Li
62*412f47f9SXin Li /* asin(|x|) = Q(|x|) , for |x| < 0.5
63*412f47f9SXin Li = pi/2 - 2 Q(|x|), for |x| >= 0.5. */
64*412f47f9SXin Li svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f);
65*412f47f9SXin Li
66*412f47f9SXin Li /* Copy sign. */
67*412f47f9SXin Li return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign));
68*412f47f9SXin Li }
69*412f47f9SXin Li
70*412f47f9SXin Li PL_SIG (SV, F, 1, asin, -1.0, 1.0)
71*412f47f9SXin Li PL_TEST_ULP (SV_NAME_F1 (asin), 1.91)
72*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (asin), 0, 0.5, 50000)
73*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (asin), 0.5, 1.0, 50000)
74*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (asin), 1.0, 0x1p11, 50000)
75*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (asin), 0x1p11, inf, 20000)
76*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (asin), -0, -inf, 20000)