diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/erfc_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/erfc_sve.c | 167 |
1 files changed, 167 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/erfc_sve.c b/sysdeps/aarch64/fpu/erfc_sve.c new file mode 100644 index 0000000000..c17d3e4484 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfc_sve.c @@ -0,0 +1,167 @@ +/* Double-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" +#include "vecmath_config.h" + +static const struct data +{ + uint64_t off_idx, off_arr; + double max, shift; + double p20, p40, p41, p42; + double p51, p52; + double q5, r5; + double q6, r6; + double q7, r7; + double q8, r8; + double q9, r9; + uint64_t table_scale; +} data = { + /* Set an offset so the range of the index used for lookup is 3487, and it + can be clamped using a saturated add on an offset index. + Index offset is 0xffffffffffffffff - asuint64(shift) - 3487. */ + .off_idx = 0xbd3ffffffffff260, + .off_arr = 0xfffffffffffff260, /* 0xffffffffffffffff - 3487. */ + .max = 0x1.b3ep+4, /* 3487/128. */ + .shift = 0x1p45, + .table_scale = 0x37f0000000000000, /* asuint64(0x1p-128). */ + .p20 = 0x1.5555555555555p-2, /* 1/3, used to compute 2/3 and 1/6. */ + .p40 = -0x1.999999999999ap-4, /* 1/10. */ + .p41 = -0x1.999999999999ap-2, /* 2/5. */ + .p42 = 0x1.1111111111111p-3, /* 2/15. */ + .p51 = -0x1.c71c71c71c71cp-3, /* 2/9. */ + .p52 = 0x1.6c16c16c16c17p-5, /* 2/45. */ + /* Qi = (i+1) / i, for i = 5, ..., 9. */ + .q5 = 0x1.3333333333333p0, + .q6 = 0x1.2aaaaaaaaaaabp0, + .q7 = 0x1.2492492492492p0, + .q8 = 0x1.2p0, + .q9 = 0x1.1c71c71c71c72p0, + /* Ri = -2 * i / ((i+1)*(i+2)), for i = 5, ..., 9. */ + .r5 = -0x1.e79e79e79e79ep-3, + .r6 = -0x1.b6db6db6db6dbp-3, + .r7 = -0x1.8e38e38e38e39p-3, + .r8 = -0x1.6c16c16c16c17p-3, + .r9 = -0x1.4f2094f2094f2p-3, +}; + +/* Optimized double-precision vector erfc(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, + + 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 + - r * (2/45 r^4 - 2/9 r^2 + 1/6) d^5 + + p6(r) d^6 + ... + p10(r) d^10 + + Polynomials p6(r) to p10(r) are computed using recurrence relation + + 2(i+1)p_i + 2r(i+2)p_{i+1} + (i+2)(i+3)p_{i+2} = 0, + with p0 = 1, and p1(r) = -r. + + 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 measured error: 1.71 ULP + _ZGVsMxv_erfc(0x1.46cfe976733p+4) got 0x1.e15fcbea3e7afp-608 + want 0x1.e15fcbea3e7adp-608. */ +svfloat64_t SV_NAME_D1 (erfc) (svfloat64_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + svfloat64_t a = svabs_x (pg, x); + + /* Clamp input at |x| <= 3487/128. */ + a = svmin_x (pg, a, dat->max); + + /* Reduce x to the nearest multiple of 1/128. */ + svfloat64_t shift = sv_f64 (dat->shift); + svfloat64_t z = svadd_x (pg, a, shift); + + /* Saturate index for the NaN case. */ + svuint64_t i = svqadd (svreinterpret_u64 (z), dat->off_idx); + + /* Lookup erfc(r) and 2/sqrt(pi)*exp(-r^2) in tables. */ + i = svadd_x (pg, i, i); + const float64_t *p = &__erfc_data.tab[0].erfc - 2 * dat->off_arr; + svfloat64_t erfcr = svld1_gather_index (pg, p, i); + svfloat64_t scale = svld1_gather_index (pg, p + 1, i); + + /* erfc(x) ~ erfc(r) - scale * d * poly(r, d). */ + svfloat64_t r = svsub_x (pg, z, shift); + 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 + ... + p9(r) * d^9. */ + svfloat64_t p1 = r; + svfloat64_t third = sv_f64 (dat->p20); + 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->p41), r2, dat->p42); + p4 = svmls_x (pg, sv_f64 (dat->p40), r2, p4); + svfloat64_t p5 = svmla_x (pg, sv_f64 (dat->p51), r2, dat->p52); + p5 = svmla_x (pg, sixth, r2, p5); + p5 = svmul_x (pg, r, p5); + /* Compute p_i using recurrence relation: + p_{i+2} = (p_i + r * Q_{i+1} * p_{i+1}) * R_{i+1}. */ + svfloat64_t qr5 = svld1rq (svptrue_b64 (), &dat->q5); + svfloat64_t qr6 = svld1rq (svptrue_b64 (), &dat->q6); + svfloat64_t qr7 = svld1rq (svptrue_b64 (), &dat->q7); + svfloat64_t qr8 = svld1rq (svptrue_b64 (), &dat->q8); + svfloat64_t qr9 = svld1rq (svptrue_b64 (), &dat->q9); + svfloat64_t p6 = svmla_x (pg, p4, p5, svmul_lane (r, qr5, 0)); + p6 = svmul_lane (p6, qr5, 1); + svfloat64_t p7 = svmla_x (pg, p5, p6, svmul_lane (r, qr6, 0)); + p7 = svmul_lane (p7, qr6, 1); + svfloat64_t p8 = svmla_x (pg, p6, p7, svmul_lane (r, qr7, 0)); + p8 = svmul_lane (p8, qr7, 1); + svfloat64_t p9 = svmla_x (pg, p7, p8, svmul_lane (r, qr8, 0)); + p9 = svmul_lane (p9, qr8, 1); + svfloat64_t p10 = svmla_x (pg, p8, p9, svmul_lane (r, qr9, 0)); + p10 = svmul_lane (p10, qr9, 1); + /* Compute polynomial in d using pairwise Horner scheme. */ + svfloat64_t p90 = svmla_x (pg, p9, d, p10); + svfloat64_t p78 = svmla_x (pg, p7, d, p8); + svfloat64_t p56 = svmla_x (pg, p5, d, p6); + svfloat64_t p34 = svmla_x (pg, p3, d, p4); + svfloat64_t p12 = svmla_x (pg, p1, d, p2); + svfloat64_t y = svmla_x (pg, p78, d2, p90); + y = svmla_x (pg, p56, d2, y); + y = svmla_x (pg, p34, d2, y); + y = svmla_x (pg, p12, d2, y); + + y = svmls_x (pg, erfcr, scale, svmls_x (pg, d, d2, y)); + + /* Offset equals 2.0 if sign, else 0.0. */ + svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000); + svfloat64_t off = svreinterpret_f64 (svlsr_x (pg, sign, 1)); + /* Handle sign and scale back in a single fma. */ + svfloat64_t fac = svreinterpret_f64 (svorr_x (pg, sign, dat->table_scale)); + + return svmla_x (pg, off, fac, y); +} |