1 /*
2 * Double-precision SVE erf(x) function.
3 *
4 * Copyright (c) 2020-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #if SV_SUPPORTED
13
14 #define Scale (8.0)
15 #define AbsMask (0x7fffffffffffffff)
16
17 static NOINLINE sv_f64_t
__sv_erf_specialcase(sv_f64_t x,sv_f64_t y,svbool_t cmp)18 __sv_erf_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp)
19 {
20 return sv_call_f64 (erf, x, y, cmp);
21 }
22
23 /* Optimized double precision SVE error function erf.
24 Maximum observed error is 2.62 ULP:
25 __sv_erf(0x1.79cab7e3078fap+2) got 0x1.0000000000001p+0
26 want 0x1.fffffffffffffp-1. */
27 sv_f64_t
__sv_erf_x(sv_f64_t x,const svbool_t pg)28 __sv_erf_x (sv_f64_t x, const svbool_t pg)
29 {
30 /* Use top 16 bits to test for special cases and small values. */
31 sv_u64_t ix = sv_as_u64_f64 (x);
32 sv_u64_t atop = svand_n_u64_x (pg, svlsr_n_u64_x (pg, ix, 48), 0x7fff);
33
34 /* Handle both inf/nan as well as small values (|x|<2^-28). */
35 svbool_t cmp
36 = svcmpge_n_u64 (pg, svsub_n_u64_x (pg, atop, 0x3e30), 0x7ff0 - 0x3e30);
37
38 /* Get sign and absolute value. */
39 sv_f64_t a = sv_as_f64_u64 (svand_n_u64_x (pg, ix, AbsMask));
40 sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask);
41
42 /* i = trunc(Scale*x). */
43 sv_f64_t a_scale = svmul_n_f64_x (pg, a, Scale);
44 /* Saturate index of intervals. */
45 svbool_t a_lt_6 = svcmplt_n_u64 (pg, atop, 0x4018);
46 sv_u64_t i = svcvt_u64_f64_m (sv_u64 (V_ERF_NINTS - 1), a_lt_6, a_scale);
47
48 /* Load polynomial coefficients. */
49 sv_f64_t P_0 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[0], i);
50 sv_f64_t P_1 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[1], i);
51 sv_f64_t P_2 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[2], i);
52 sv_f64_t P_3 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[3], i);
53 sv_f64_t P_4 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[4], i);
54 sv_f64_t P_5 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[5], i);
55 sv_f64_t P_6 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[6], i);
56 sv_f64_t P_7 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[7], i);
57 sv_f64_t P_8 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[8], i);
58 sv_f64_t P_9 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[9], i);
59
60 /* Get shift and scale. */
61 sv_f64_t shift = sv_lookup_f64_x (pg, __v_erf_data.shifts, i);
62
63 /* Transform polynomial variable.
64 Set z = 0 in the boring domain to avoid overflow. */
65 sv_f64_t z = svmla_f64_m (a_lt_6, shift, sv_f64 (Scale), a);
66
67 /* Evaluate polynomial P(z) using level-2 Estrin. */
68 sv_f64_t r1 = sv_fma_f64_x (pg, z, P_1, P_0);
69 sv_f64_t r2 = sv_fma_f64_x (pg, z, P_3, P_2);
70 sv_f64_t r3 = sv_fma_f64_x (pg, z, P_5, P_4);
71 sv_f64_t r4 = sv_fma_f64_x (pg, z, P_7, P_6);
72 sv_f64_t r5 = sv_fma_f64_x (pg, z, P_9, P_8);
73
74 sv_f64_t z2 = svmul_f64_x (pg, z, z);
75 sv_f64_t z4 = svmul_f64_x (pg, z2, z2);
76
77 sv_f64_t q2 = sv_fma_f64_x (pg, r4, z2, r3);
78 sv_f64_t q1 = sv_fma_f64_x (pg, r2, z2, r1);
79
80 sv_f64_t y = sv_fma_f64_x (pg, z4, r5, q2);
81 y = sv_fma_f64_x (pg, z4, y, q1);
82
83 /* y = erf(x) if x > 0, -erf(-x) otherwise. */
84 y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign));
85
86 if (unlikely (svptest_any (pg, cmp)))
87 return __sv_erf_specialcase (x, y, cmp);
88 return y;
89 }
90
91 PL_ALIAS (__sv_erf_x, _ZGVsMxv_erf)
92
93 PL_SIG (SV, D, 1, erf, -4.0, 4.0)
94 PL_TEST_ULP (__sv_erf, 2.13)
95 PL_TEST_INTERVAL (__sv_erf, 0, 0x1p-28, 20000)
96 PL_TEST_INTERVAL (__sv_erf, 0x1p-28, 1, 60000)
97 PL_TEST_INTERVAL (__sv_erf, 1, 0x1p28, 60000)
98 PL_TEST_INTERVAL (__sv_erf, 0x1p28, inf, 20000)
99 PL_TEST_INTERVAL (__sv_erf, -0, -0x1p-28, 20000)
100 PL_TEST_INTERVAL (__sv_erf, -0x1p-28, -1, 60000)
101 PL_TEST_INTERVAL (__sv_erf, -1, -0x1p28, 60000)
102 PL_TEST_INTERVAL (__sv_erf, -0x1p28, -inf, 20000)
103 #endif
104