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/* Single-precision vector (SVE) erfc 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 "sv_math.h"
static const struct data
{
uint32_t off_idx, off_arr;
float max, shift;
float third, two_thirds, two_over_fifteen, two_over_five, tenth;
} data = {
/* Set an offset so the range of the index used for lookup is 644, and it can
be clamped using a saturated add. */
.off_idx = 0xb7fffd7b, /* 0xffffffff - asuint(shift) - 644. */
.off_arr = 0xfffffd7b, /* 0xffffffff - 644. */
.max = 10.0625f, /* 644/64. */
.shift = 0x1p17f,
.third = 0x1.555556p-2f,
.two_thirds = 0x1.555556p-1f,
.two_over_fifteen = 0x1.111112p-3f,
.two_over_five = -0x1.99999ap-2f,
.tenth = -0x1.99999ap-4f,
};
#define SignMask 0x80000000
#define TableScale 0x28000000 /* 0x1p-47. */
/* Optimized single-precision vector erfcf(x).
Approximation based on series expansion near x rounded to
nearest multiple of 1/64.
Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
erfc(x) ~ erfc(r) - scale * d * poly(r, d), with
poly(r, d) = 1 - r d + (2/3 r^2 - 1/3) d^2 - r (1/3 r^2 - 1/2) d^3
+ (2/15 r^4 - 2/5 r^2 + 1/10) d^4
Values of erfc(r) and scale are read from lookup tables. Stored values
are scaled to avoid hitting the subnormal range.
Note that for x < 0, erfc(x) = 2.0 - erfc(-x).
Maximum error: 1.63 ULP (~1.0 ULP for x < 0.0).
_ZGVsMxv_erfcf(0x1.1dbf7ap+3) got 0x1.f51212p-120
want 0x1.f51216p-120. */
svfloat32_t SV_NAME_F1 (erfc) (svfloat32_t x, const svbool_t pg)
{
const struct data *dat = ptr_barrier (&data);
svfloat32_t a = svabs_x (pg, x);
/* Clamp input at |x| <= 10.0 + 4/64. */
a = svmin_x (pg, a, dat->max);
/* Reduce x to the nearest multiple of 1/64. */
svfloat32_t shift = sv_f32 (dat->shift);
svfloat32_t z = svadd_x (pg, a, shift);
/* Saturate index for the NaN case. */
svuint32_t i = svqadd (svreinterpret_u32 (z), dat->off_idx);
/* Lookup erfc(r) and 2/sqrt(pi)*exp(-r^2) in tables. */
i = svmul_x (pg, i, 2);
const float32_t *p = &__erfcf_data.tab[0].erfc - 2 * dat->off_arr;
svfloat32_t erfcr = svld1_gather_index (pg, p, i);
svfloat32_t scale = svld1_gather_index (pg, p + 1, i);
/* erfc(x) ~ erfc(r) - scale * d * poly(r, d). */
svfloat32_t r = svsub_x (pg, z, shift);
svfloat32_t d = svsub_x (pg, a, r);
svfloat32_t d2 = svmul_x (pg, d, d);
svfloat32_t r2 = svmul_x (pg, r, r);
svfloat32_t coeffs = svld1rq (svptrue_b32 (), &dat->third);
svfloat32_t third = svdup_lane (coeffs, 0);
svfloat32_t p1 = r;
svfloat32_t p2 = svmls_lane (third, r2, coeffs, 1);
svfloat32_t p3 = svmul_x (pg, r, svmla_lane (sv_f32 (-0.5), r2, coeffs, 0));
svfloat32_t p4 = svmla_lane (sv_f32 (dat->two_over_five), r2, coeffs, 2);
p4 = svmls_x (pg, sv_f32 (dat->tenth), r2, p4);
svfloat32_t y = svmla_x (pg, p3, d, p4);
y = svmla_x (pg, p2, d, y);
y = svmla_x (pg, p1, d, y);
/* Solves the |x| = inf/nan case. */
y = svmls_x (pg, erfcr, scale, svmls_x (pg, d, d2, y));
/* Offset equals 2.0f if sign, else 0.0f. */
svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), SignMask);
svfloat32_t off = svreinterpret_f32 (svlsr_x (pg, sign, 1));
/* Handle sign and scale back in a single fma. */
svfloat32_t fac = svreinterpret_f32 (svorr_x (pg, sign, TableScale));
return svmla_x (pg, off, fac, y);
}
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