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/* Single-precision vector (Advanced SIMD) erf function
Copyright (C) 2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "v_math.h"
static const struct data
{
float32x4_t max, shift, third;
#if WANT_SIMD_EXCEPT
float32x4_t tiny_bound, scale_minus_one;
#endif
} data = {
.max = V4 (3.9375), /* 4 - 8/128. */
.shift = V4 (0x1p16f),
.third = V4 (0x1.555556p-2f), /* 1/3. */
#if WANT_SIMD_EXCEPT
.tiny_bound = V4 (0x1p-62f),
.scale_minus_one = V4 (0x1.06eba8p-3f), /* scale - 1.0. */
#endif
};
#define AbsMask 0x7fffffff
struct entry
{
float32x4_t erf;
float32x4_t scale;
};
static inline struct entry
lookup (uint32x4_t i)
{
struct entry e;
float32x2_t t0 = vld1_f32 (&__erff_data.tab[vgetq_lane_u32 (i, 0)].erf);
float32x2_t t1 = vld1_f32 (&__erff_data.tab[vgetq_lane_u32 (i, 1)].erf);
float32x2_t t2 = vld1_f32 (&__erff_data.tab[vgetq_lane_u32 (i, 2)].erf);
float32x2_t t3 = vld1_f32 (&__erff_data.tab[vgetq_lane_u32 (i, 3)].erf);
float32x4_t e1 = vcombine_f32 (t0, t1);
float32x4_t e2 = vcombine_f32 (t2, t3);
e.erf = vuzp1q_f32 (e1, e2);
e.scale = vuzp2q_f32 (e1, e2);
return e;
}
/* Single-precision implementation of vector erf(x).
Approximation based on series expansion near x rounded to
nearest multiple of 1/128.
Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
erf(x) ~ erf(r) + scale * d * [1 - r * d - 1/3 * d^2]
Values of erf(r) and scale are read from lookup tables.
For |x| > 3.9375, erf(|x|) rounds to 1.0f.
Maximum error: 1.93 ULP
_ZGVnN4v_erff(0x1.c373e6p-9) got 0x1.fd686cp-9
want 0x1.fd6868p-9. */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (erf) (float32x4_t x)
{
const struct data *dat = ptr_barrier (&data);
#if WANT_SIMD_EXCEPT
/* |x| < 2^-62. */
uint32x4_t cmp = vcaltq_f32 (x, dat->tiny_bound);
float32x4_t xm = x;
/* If any lanes are special, mask them with 1 and retain a copy of x to allow
special case handler to fix special lanes later. This is only necessary if
fenv exceptions are to be triggered correctly. */
if (__glibc_unlikely (v_any_u32 (cmp)))
x = vbslq_f32 (cmp, v_f32 (1), x);
#endif
float32x4_t a = vabsq_f32 (x);
uint32x4_t a_gt_max = vcgtq_f32 (a, dat->max);
/* Lookup erf(r) and scale(r) in tables, e.g. set erf(r) to 0 and scale to
2/sqrt(pi), when x reduced to r = 0. */
float32x4_t shift = dat->shift;
float32x4_t z = vaddq_f32 (a, shift);
uint32x4_t i
= vsubq_u32 (vreinterpretq_u32_f32 (z), vreinterpretq_u32_f32 (shift));
i = vminq_u32 (i, v_u32 (512));
struct entry e = lookup (i);
float32x4_t r = vsubq_f32 (z, shift);
/* erf(x) ~ erf(r) + scale * d * (1 - r * d - 1/3 * d^2). */
float32x4_t d = vsubq_f32 (a, r);
float32x4_t d2 = vmulq_f32 (d, d);
float32x4_t y = vfmaq_f32 (r, dat->third, d);
y = vfmaq_f32 (e.erf, e.scale, vfmsq_f32 (d, d2, y));
/* Solves the |x| = inf case. */
y = vbslq_f32 (a_gt_max, v_f32 (1.0f), y);
/* Copy sign. */
y = vbslq_f32 (v_u32 (AbsMask), y, x);
#if WANT_SIMD_EXCEPT
if (__glibc_unlikely (v_any_u32 (cmp)))
return vbslq_f32 (cmp, vfmaq_f32 (xm, dat->scale_minus_one, xm), y);
#endif
return y;
}
libmvec_hidden_def (V_NAME_F1 (erf))
HALF_WIDTH_ALIAS_F1 (erf)
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