1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision SVE acos(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, pi_over_2;
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 = 0x1.921fb6p+1f,
23*f3087befSAndrew Turner .pi_over_2 = 0x1.921fb6p+0f,
24*f3087befSAndrew Turner };
25*f3087befSAndrew Turner
26*f3087befSAndrew Turner /* Single-precision SVE implementation of vector acos(x).
27*f3087befSAndrew Turner
28*f3087befSAndrew Turner For |x| in [0, 0.5], use order 4 polynomial P such that the final
29*f3087befSAndrew Turner approximation of asin is an odd polynomial:
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner acos(x) ~ pi/2 - (x + x^3 P(x^2)).
32*f3087befSAndrew Turner
33*f3087befSAndrew Turner The largest observed error in this region is 1.16 ulps,
34*f3087befSAndrew Turner _ZGVsMxv_acosf(0x1.ffbeccp-2) got 0x1.0c27f8p+0
35*f3087befSAndrew Turner want 0x1.0c27f6p+0.
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner For |x| in [0.5, 1.0], use same approximation with a change of variable
38*f3087befSAndrew Turner
39*f3087befSAndrew Turner acos(x) = y + y * z * P(z), with z = (1-x)/2 and y = sqrt(z).
40*f3087befSAndrew Turner
41*f3087befSAndrew Turner The largest observed error in this region is 1.32 ulps,
42*f3087befSAndrew Turner _ZGVsMxv_acosf (0x1.15ba56p-1) got 0x1.feb33p-1
43*f3087befSAndrew Turner want 0x1.feb32ep-1. */
SV_NAME_F1(acos)44*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (acos) (svfloat32_t x, const svbool_t pg)
45*f3087befSAndrew Turner {
46*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
47*f3087befSAndrew Turner
48*f3087befSAndrew Turner svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000);
49*f3087befSAndrew Turner svfloat32_t ax = svabs_x (pg, x);
50*f3087befSAndrew Turner svbool_t a_gt_half = svacgt (pg, x, 0.5);
51*f3087befSAndrew Turner
52*f3087befSAndrew Turner /* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with
53*f3087befSAndrew Turner z2 = x ^ 2 and z = |x| , if |x| < 0.5
54*f3087befSAndrew Turner z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */
55*f3087befSAndrew Turner svfloat32_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5),
56*f3087befSAndrew Turner svmul_x (pg, x, x));
57*f3087befSAndrew Turner svfloat32_t z = svsqrt_m (ax, a_gt_half, z2);
58*f3087befSAndrew Turner
59*f3087befSAndrew Turner /* Use a single polynomial approximation P for both intervals. */
60*f3087befSAndrew Turner svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly);
61*f3087befSAndrew Turner /* Finalize polynomial: z + z * z2 * P(z2). */
62*f3087befSAndrew Turner p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
63*f3087befSAndrew Turner
64*f3087befSAndrew Turner /* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5
65*f3087befSAndrew Turner = 2 Q(|x|) , for 0.5 < x < 1.0
66*f3087befSAndrew Turner = pi - 2 Q(|x|) , for -1.0 < x < -0.5. */
67*f3087befSAndrew Turner svfloat32_t y
68*f3087befSAndrew Turner = svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (p), sign));
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner svbool_t is_neg = svcmplt (pg, x, 0.0);
71*f3087befSAndrew Turner svfloat32_t off = svdup_f32_z (is_neg, d->pi);
72*f3087befSAndrew Turner svfloat32_t mul = svsel (a_gt_half, sv_f32 (2.0), sv_f32 (-1.0));
73*f3087befSAndrew Turner svfloat32_t add = svsel (a_gt_half, off, sv_f32 (d->pi_over_2));
74*f3087befSAndrew Turner
75*f3087befSAndrew Turner return svmla_x (pg, add, mul, y);
76*f3087befSAndrew Turner }
77*f3087befSAndrew Turner
78*f3087befSAndrew Turner TEST_SIG (SV, F, 1, acos, -1.0, 1.0)
79*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (acos), 0.82)
80*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (acos))
81*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (acos), 0, 0.5, 50000)
82*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (acos), 0.5, 1.0, 50000)
83*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (acos), 1.0, 0x1p11, 50000)
84*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (acos), 0x1p11, inf, 20000)
85*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_F1 (acos), -0, -inf, 20000)
86*f3087befSAndrew Turner CLOSE_SVE_ATTR
87