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116 lines
4.2 KiB
C
116 lines
4.2 KiB
C
/* Double-precision vector (SVE) erf function
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Copyright (C) 2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "sv_math.h"
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static const struct data
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{
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double third;
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double tenth, two_over_five, two_over_fifteen;
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double two_over_nine, two_over_fortyfive;
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double max, shift;
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} data = {
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.third = 0x1.5555555555556p-2, /* used to compute 2/3 and 1/6 too. */
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.two_over_fifteen = 0x1.1111111111111p-3,
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.tenth = -0x1.999999999999ap-4,
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.two_over_five = -0x1.999999999999ap-2,
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.two_over_nine = -0x1.c71c71c71c71cp-3,
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.two_over_fortyfive = 0x1.6c16c16c16c17p-5,
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.max = 5.9921875, /* 6 - 1/128. */
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.shift = 0x1p45,
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};
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#define SignMask (0x8000000000000000)
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/* Double-precision implementation of vector erf(x).
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Approximation based on series expansion near x rounded to
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nearest multiple of 1/128.
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Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
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erf(x) ~ erf(r) + scale * d * [
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+ 1
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- r d
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+ 1/3 (2 r^2 - 1) d^2
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- 1/6 (r (2 r^2 - 3)) d^3
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+ 1/30 (4 r^4 - 12 r^2 + 3) d^4
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- 1/90 (4 r^4 - 20 r^2 + 15) d^5
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]
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Maximum measure error: 2.29 ULP
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_ZGVsMxv_erf(-0x1.00003c924e5d1p-8) got -0x1.20dd59132ebadp-8
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want -0x1.20dd59132ebafp-8. */
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svfloat64_t SV_NAME_D1 (erf) (svfloat64_t x, const svbool_t pg)
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{
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const struct data *dat = ptr_barrier (&data);
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/* |x| >= 6.0 - 1/128. Opposite conditions except none of them catch NaNs so
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they can be used in lookup and BSLs to yield the expected results. */
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svbool_t a_ge_max = svacge (pg, x, dat->max);
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svbool_t a_lt_max = svaclt (pg, x, dat->max);
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/* Set r to multiple of 1/128 nearest to |x|. */
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svfloat64_t a = svabs_x (pg, x);
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svfloat64_t shift = sv_f64 (dat->shift);
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svfloat64_t z = svadd_x (pg, a, shift);
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svuint64_t i
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= svsub_x (pg, svreinterpret_u64 (z), svreinterpret_u64 (shift));
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/* Lookup without shortcut for small values but with predicate to avoid
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segfault for large values and NaNs. */
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svfloat64_t r = svsub_x (pg, z, shift);
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svfloat64_t erfr = svld1_gather_index (a_lt_max, __sv_erf_data.erf, i);
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svfloat64_t scale = svld1_gather_index (a_lt_max, __sv_erf_data.scale, i);
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/* erf(x) ~ erf(r) + scale * d * poly (r, d). */
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svfloat64_t d = svsub_x (pg, a, r);
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svfloat64_t d2 = svmul_x (pg, d, d);
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svfloat64_t r2 = svmul_x (pg, r, r);
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/* poly (d, r) = 1 + p1(r) * d + p2(r) * d^2 + ... + p5(r) * d^5. */
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svfloat64_t p1 = r;
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svfloat64_t third = sv_f64 (dat->third);
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svfloat64_t twothird = svmul_x (pg, third, 2.0);
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svfloat64_t sixth = svmul_x (pg, third, 0.5);
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svfloat64_t p2 = svmls_x (pg, third, r2, twothird);
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svfloat64_t p3 = svmad_x (pg, r2, third, -0.5);
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p3 = svmul_x (pg, r, p3);
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svfloat64_t p4
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= svmla_x (pg, sv_f64 (dat->two_over_five), r2, dat->two_over_fifteen);
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p4 = svmls_x (pg, sv_f64 (dat->tenth), r2, p4);
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svfloat64_t p5
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= svmla_x (pg, sv_f64 (dat->two_over_nine), r2, dat->two_over_fortyfive);
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p5 = svmla_x (pg, sixth, r2, p5);
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p5 = svmul_x (pg, r, p5);
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svfloat64_t p34 = svmla_x (pg, p3, d, p4);
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svfloat64_t p12 = svmla_x (pg, p1, d, p2);
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svfloat64_t y = svmla_x (pg, p34, d2, p5);
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y = svmla_x (pg, p12, d2, y);
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y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y));
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/* Solves the |x| = inf and NaN cases. */
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y = svsel (a_ge_max, sv_f64 (1.0), y);
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/* Copy sign. */
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svuint64_t ix = svreinterpret_u64 (x);
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svuint64_t iy = svreinterpret_u64 (y);
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svuint64_t sign = svand_x (pg, ix, SignMask);
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return svreinterpret_f64 (svorr_x (pg, sign, iy));
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}
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