diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/erf_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/erf_sve.c | 115 |
1 files changed, 115 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/erf_sve.c b/sysdeps/aarch64/fpu/erf_sve.c new file mode 100644 index 0000000000..7d51417406 --- /dev/null +++ b/sysdeps/aarch64/fpu/erf_sve.c @@ -0,0 +1,115 @@ +/* Double-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 +{ + double third; + double tenth, two_over_five, two_over_fifteen; + double two_over_nine, two_over_fortyfive; + double max, shift; +} data = { + .third = 0x1.5555555555556p-2, /* used to compute 2/3 and 1/6 too. */ + .two_over_fifteen = 0x1.1111111111111p-3, + .tenth = -0x1.999999999999ap-4, + .two_over_five = -0x1.999999999999ap-2, + .two_over_nine = -0x1.c71c71c71c71cp-3, + .two_over_fortyfive = 0x1.6c16c16c16c17p-5, + .max = 5.9921875, /* 6 - 1/128. */ + .shift = 0x1p45, +}; + +#define SignMask (0x8000000000000000) + +/* Double-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 (2 r^2 - 1) d^2 + - 1/6 (r (2 r^2 - 3)) d^3 + + 1/30 (4 r^4 - 12 r^2 + 3) d^4 + - 1/90 (4 r^4 - 20 r^2 + 15) d^5 + ] + + Maximum measure error: 2.29 ULP + _ZGVsMxv_erf(-0x1.00003c924e5d1p-8) got -0x1.20dd59132ebadp-8 + want -0x1.20dd59132ebafp-8. */ +svfloat64_t SV_NAME_D1 (erf) (svfloat64_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + /* |x| >= 6.0 - 1/128. Opposite conditions except none of them catch NaNs so + they can be used in lookup and BSLs to yield the expected results. */ + svbool_t a_ge_max = svacge (pg, x, dat->max); + svbool_t a_lt_max = svaclt (pg, x, dat->max); + + /* Set r to multiple of 1/128 nearest to |x|. */ + svfloat64_t a = svabs_x (pg, x); + svfloat64_t shift = sv_f64 (dat->shift); + svfloat64_t z = svadd_x (pg, a, shift); + svuint64_t i + = svsub_x (pg, svreinterpret_u64 (z), svreinterpret_u64 (shift)); + + /* Lookup without shortcut for small values but with predicate to avoid + segfault for large values and NaNs. */ + svfloat64_t r = svsub_x (pg, z, shift); + svfloat64_t erfr = svld1_gather_index (a_lt_max, __sv_erf_data.erf, i); + svfloat64_t scale = svld1_gather_index (a_lt_max, __sv_erf_data.scale, i); + + /* erf(x) ~ erf(r) + scale * d * poly (r, d). */ + svfloat64_t d = svsub_x (pg, a, r); + svfloat64_t d2 = svmul_x (pg, d, d); + svfloat64_t r2 = svmul_x (pg, r, r); + + /* poly (d, r) = 1 + p1(r) * d + p2(r) * d^2 + ... + p5(r) * d^5. */ + svfloat64_t p1 = r; + svfloat64_t third = sv_f64 (dat->third); + svfloat64_t twothird = svmul_x (pg, third, 2.0); + svfloat64_t sixth = svmul_x (pg, third, 0.5); + svfloat64_t p2 = svmls_x (pg, third, r2, twothird); + svfloat64_t p3 = svmad_x (pg, r2, third, -0.5); + p3 = svmul_x (pg, r, p3); + svfloat64_t p4 + = svmla_x (pg, sv_f64 (dat->two_over_five), r2, dat->two_over_fifteen); + p4 = svmls_x (pg, sv_f64 (dat->tenth), r2, p4); + svfloat64_t p5 + = svmla_x (pg, sv_f64 (dat->two_over_nine), r2, dat->two_over_fortyfive); + p5 = svmla_x (pg, sixth, r2, p5); + p5 = svmul_x (pg, r, p5); + + svfloat64_t p34 = svmla_x (pg, p3, d, p4); + svfloat64_t p12 = svmla_x (pg, p1, d, p2); + svfloat64_t y = svmla_x (pg, p34, d2, p5); + y = svmla_x (pg, p12, d2, y); + + y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y)); + + /* Solves the |x| = inf and NaN cases. */ + y = svsel (a_ge_max, sv_f64 (1.0), y); + + /* Copy sign. */ + svuint64_t ix = svreinterpret_u64 (x); + svuint64_t iy = svreinterpret_u64 (y); + svuint64_t sign = svand_x (pg, ix, SignMask); + return svreinterpret_f64 (svorr_x (pg, sign, iy)); +} |