diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/erff_sve.c')
-rw-r--r-- | sysdeps/aarch64/fpu/erff_sve.c | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/erff_sve.c b/sysdeps/aarch64/fpu/erff_sve.c new file mode 100644 index 0000000000..38f00db9be --- /dev/null +++ b/sysdeps/aarch64/fpu/erff_sve.c @@ -0,0 +1,93 @@ +/* Single-precision vector (SVE) 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 "sv_math.h" + +static const struct data +{ + float min, max, scale, shift, third; +} data = { + .min = 0x1.cp-7f, /* 1/64 - 1/512. */ + .max = 3.9375, /* 4 - 8/128. */ + .scale = 0x1.20dd76p+0f, /* 2/sqrt(pi). */ + .shift = 0x1p16f, + .third = 0x1.555556p-2f, /* 1/3. */ +}; + +#define SignMask (0x80000000) + +/* 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| < 0x1.cp-7, the algorithm sets r = 0, erf(r) = 0, and scale = 2 / + sqrt(pi), so it simply boils down to a Taylor series expansion near 0. For + |x| > 3.9375, erf(|x|) rounds to 1.0f. + + Maximum error on each interval: + - [0, 0x1.cp-7]: 1.93 ULP + _ZGVsMxv_erff(0x1.c373e6p-9) got 0x1.fd686cp-9 want 0x1.fd6868p-9 + - [0x1.cp-7, 4.0]: 1.26 ULP + _ZGVsMxv_erff(0x1.1d002ep+0) got 0x1.c4eb9ap-1 want 0x1.c4eb98p-1. */ +svfloat32_t SV_NAME_F1 (erf) (svfloat32_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + /* |x| > 1/64 - 1/512. */ + svbool_t a_gt_min = svacgt (pg, x, dat->min); + + /* |x| >= 4.0 - 8/128. */ + svbool_t a_ge_max = svacge (pg, x, dat->max); + svfloat32_t a = svabs_x (pg, x); + + svfloat32_t shift = sv_f32 (dat->shift); + svfloat32_t z = svadd_x (pg, a, shift); + svuint32_t i + = svsub_x (pg, svreinterpret_u32 (z), svreinterpret_u32 (shift)); + + /* Saturate lookup index. */ + i = svsel (a_ge_max, sv_u32 (512), i); + + /* r and erf(r) set to 0 for |x| below min. */ + svfloat32_t r = svsub_z (a_gt_min, z, shift); + svfloat32_t erfr = svld1_gather_index (a_gt_min, __sv_erff_data.erf, i); + + /* scale set to 2/sqrt(pi) for |x| below min. */ + svfloat32_t scale = svld1_gather_index (a_gt_min, __sv_erff_data.scale, i); + scale = svsel (a_gt_min, scale, sv_f32 (dat->scale)); + + /* erf(x) ~ erf(r) + scale * d * (1 - r * d + 1/3 * d^2). */ + svfloat32_t d = svsub_x (pg, a, r); + svfloat32_t d2 = svmul_x (pg, d, d); + svfloat32_t y = svmla_x (pg, r, d, dat->third); + y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y)); + + /* Solves the |x| = inf case. */ + y = svsel (a_ge_max, sv_f32 (1.0f), y); + + /* Copy sign. */ + svuint32_t ix = svreinterpret_u32 (x); + svuint32_t iy = svreinterpret_u32 (y); + svuint32_t sign = svand_x (pg, ix, SignMask); + return svreinterpret_f32 (svorr_x (pg, sign, iy)); +} |