1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision vector erf(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 "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner static const struct data
13*f3087befSAndrew Turner {
14*f3087befSAndrew Turner float min, max, scale, shift, third;
15*f3087befSAndrew Turner } data = {
16*f3087befSAndrew Turner .min = 0x1.cp-7f, /* 1/64 - 1/512. */
17*f3087befSAndrew Turner .max = 3.9375, /* 4 - 8/128. */
18*f3087befSAndrew Turner .scale = 0x1.20dd76p+0f, /* 2/sqrt(pi). */
19*f3087befSAndrew Turner .shift = 0x1p16f,
20*f3087befSAndrew Turner .third = 0x1.555556p-2f, /* 1/3. */
21*f3087befSAndrew Turner };
22*f3087befSAndrew Turner
23*f3087befSAndrew Turner #define SignMask (0x80000000)
24*f3087befSAndrew Turner
25*f3087befSAndrew Turner /* Single-precision implementation of vector erf(x).
26*f3087befSAndrew Turner Approximation based on series expansion near x rounded to
27*f3087befSAndrew Turner nearest multiple of 1/128.
28*f3087befSAndrew Turner Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
29*f3087befSAndrew Turner
30*f3087befSAndrew Turner erf(x) ~ erf(r) + scale * d * [1 - r * d - 1/3 * d^2]
31*f3087befSAndrew Turner
32*f3087befSAndrew Turner Values of erf(r) and scale are read from lookup tables.
33*f3087befSAndrew Turner For |x| < 0x1.cp-7, the algorithm sets r = 0, erf(r) = 0, and scale = 2 /
34*f3087befSAndrew Turner sqrt(pi), so it simply boils down to a Taylor series expansion near 0. For
35*f3087befSAndrew Turner |x| > 3.9375, erf(|x|) rounds to 1.0f.
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner Maximum error on each interval:
38*f3087befSAndrew Turner - [0, 0x1.cp-7]: 1.93 ULP
39*f3087befSAndrew Turner _ZGVsMxv_erff(0x1.c373e6p-9) got 0x1.fd686cp-9 want 0x1.fd6868p-9
40*f3087befSAndrew Turner - [0x1.cp-7, 4.0]: 1.26 ULP
41*f3087befSAndrew Turner _ZGVsMxv_erff(0x1.1d002ep+0) got 0x1.c4eb9ap-1 want 0x1.c4eb98p-1. */
SV_NAME_F1(erf)42*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (erf) (svfloat32_t x, const svbool_t pg)
43*f3087befSAndrew Turner {
44*f3087befSAndrew Turner const struct data *dat = ptr_barrier (&data);
45*f3087befSAndrew Turner
46*f3087befSAndrew Turner /* |x| > 1/64 - 1/512. */
47*f3087befSAndrew Turner svbool_t a_gt_min = svacgt (pg, x, dat->min);
48*f3087befSAndrew Turner
49*f3087befSAndrew Turner /* |x| >= 4.0 - 8/128. */
50*f3087befSAndrew Turner svbool_t a_ge_max = svacge (pg, x, dat->max);
51*f3087befSAndrew Turner svfloat32_t a = svabs_x (pg, x);
52*f3087befSAndrew Turner
53*f3087befSAndrew Turner svfloat32_t shift = sv_f32 (dat->shift);
54*f3087befSAndrew Turner svfloat32_t z = svadd_x (pg, a, shift);
55*f3087befSAndrew Turner svuint32_t i = svand_x (pg, svreinterpret_u32 (z), 0xfff);
56*f3087befSAndrew Turner i = svadd_x (pg, i, i);
57*f3087befSAndrew Turner
58*f3087befSAndrew Turner /* r and erf(r) set to 0 for |x| below min. */
59*f3087befSAndrew Turner svfloat32_t r = svsub_z (a_gt_min, z, shift);
60*f3087befSAndrew Turner svfloat32_t erfr
61*f3087befSAndrew Turner = svld1_gather_index (a_gt_min, &__v_erff_data.tab[0].erf, i);
62*f3087befSAndrew Turner
63*f3087befSAndrew Turner /* scale set to 2/sqrt(pi) for |x| below min. */
64*f3087befSAndrew Turner svfloat32_t scale
65*f3087befSAndrew Turner = svld1_gather_index (a_gt_min, &__v_erff_data.tab[0].scale, i);
66*f3087befSAndrew Turner scale = svsel (a_gt_min, scale, sv_f32 (dat->scale));
67*f3087befSAndrew Turner
68*f3087befSAndrew Turner /* erf(x) ~ erf(r) + scale * d * (1 - r * d + 1/3 * d^2). */
69*f3087befSAndrew Turner svfloat32_t d = svsub_x (pg, a, r);
70*f3087befSAndrew Turner svfloat32_t d2 = svmul_x (pg, d, d);
71*f3087befSAndrew Turner svfloat32_t y = svmla_x (pg, r, d, dat->third);
72*f3087befSAndrew Turner y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y));
73*f3087befSAndrew Turner
74*f3087befSAndrew Turner /* Solves the |x| = inf case. */
75*f3087befSAndrew Turner y = svsel (a_ge_max, sv_f32 (1.0f), y);
76*f3087befSAndrew Turner
77*f3087befSAndrew Turner /* Copy sign. */
78*f3087befSAndrew Turner svuint32_t ix = svreinterpret_u32 (x);
79*f3087befSAndrew Turner svuint32_t iy = svreinterpret_u32 (y);
80*f3087befSAndrew Turner svuint32_t sign = svand_x (pg, ix, SignMask);
81*f3087befSAndrew Turner return svreinterpret_f32 (svorr_x (pg, sign, iy));
82*f3087befSAndrew Turner }
83*f3087befSAndrew Turner
84*f3087befSAndrew Turner TEST_SIG (SV, F, 1, erf, -4.0, 4.0)
85*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (erf), 1.43)
86*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (erf))
87*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (erf), 0, 0x1.cp-7, 40000)
88*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (erf), 0x1.cp-7, 3.9375, 40000)
89*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (erf), 3.9375, inf, 40000)
90*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (erf), 0, inf, 4000)
91*f3087befSAndrew Turner CLOSE_SVE_ATTR
92