1 /*
2 * Double-precision SVE asin(x) function.
3 *
4 * Copyright (c) 2023-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "sv_poly_f64.h"
10 #include "test_sig.h"
11 #include "test_defs.h"
12
13 static const struct data
14 {
15 float64_t poly[12];
16 float64_t pi_over_2f;
17 } data = {
18 /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x))
19 on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */
20 .poly = { 0x1.555555555554ep-3, 0x1.3333333337233p-4,
21 0x1.6db6db67f6d9fp-5, 0x1.f1c71fbd29fbbp-6,
22 0x1.6e8b264d467d6p-6, 0x1.1c5997c357e9dp-6,
23 0x1.c86a22cd9389dp-7, 0x1.856073c22ebbep-7,
24 0x1.fd1151acb6bedp-8, 0x1.087182f799c1dp-6,
25 -0x1.6602748120927p-7, 0x1.cfa0dd1f9478p-6, },
26 .pi_over_2f = 0x1.921fb54442d18p+0,
27 };
28
29 #define P(i) sv_f64 (d->poly[i])
30
31 /* Double-precision SVE implementation of vector asin(x).
32
33 For |x| in [0, 0.5], use an order 11 polynomial P such that the final
34 approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
35
36 The largest observed error in this region is 0.52 ulps,
37 _ZGVsMxv_asin(0x1.d95ae04998b6cp-2) got 0x1.ec13757305f27p-2
38 want 0x1.ec13757305f26p-2.
39
40 For |x| in [0.5, 1.0], use same approximation with a change of variable
41
42 asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
43
44 The largest observed error in this region is 2.69 ulps,
45 _ZGVsMxv_asin (0x1.044e8cefee301p-1) got 0x1.1111dd54ddf96p-1
46 want 0x1.1111dd54ddf99p-1. */
SV_NAME_D1(asin)47 svfloat64_t SV_NAME_D1 (asin) (svfloat64_t x, const svbool_t pg)
48 {
49 const struct data *d = ptr_barrier (&data);
50
51 svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000);
52 svfloat64_t ax = svabs_x (pg, x);
53 svbool_t a_ge_half = svacge (pg, x, 0.5);
54
55 /* Evaluate polynomial Q(x) = y + y * z * P(z) with
56 z = x ^ 2 and y = |x| , if |x| < 0.5
57 z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */
58 svfloat64_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5),
59 svmul_x (pg, x, x));
60 svfloat64_t z = svsqrt_m (ax, a_ge_half, z2);
61
62 /* Use a single polynomial approximation P for both intervals. */
63 svfloat64_t z4 = svmul_x (pg, z2, z2);
64 svfloat64_t z8 = svmul_x (pg, z4, z4);
65 svfloat64_t z16 = svmul_x (pg, z8, z8);
66 svfloat64_t p = sv_estrin_11_f64_x (pg, z2, z4, z8, z16, d->poly);
67 /* Finalize polynomial: z + z * z2 * P(z2). */
68 p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
69
70 /* asin(|x|) = Q(|x|) , for |x| < 0.5
71 = pi/2 - 2 Q(|x|), for |x| >= 0.5. */
72 svfloat64_t y = svmad_m (a_ge_half, p, sv_f64 (-2.0), d->pi_over_2f);
73
74 /* Copy sign. */
75 return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign));
76 }
77
78 TEST_SIG (SV, D, 1, asin, -1.0, 1.0)
79 TEST_ULP (SV_NAME_D1 (asin), 2.20)
80 TEST_DISABLE_FENV (SV_NAME_D1 (asin))
81 TEST_INTERVAL (SV_NAME_D1 (asin), 0, 0.5, 50000)
82 TEST_INTERVAL (SV_NAME_D1 (asin), 0.5, 1.0, 50000)
83 TEST_INTERVAL (SV_NAME_D1 (asin), 1.0, 0x1p11, 50000)
84 TEST_INTERVAL (SV_NAME_D1 (asin), 0x1p11, inf, 20000)
85 TEST_INTERVAL (SV_NAME_D1 (asin), -0, -inf, 20000)
86 CLOSE_SVE_ATTR
87