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Diffstat (limited to 'sysdeps/aarch64/fpu/acospi_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/acospi_sve.c | 112 |
1 files changed, 112 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/acospi_sve.c b/sysdeps/aarch64/fpu/acospi_sve.c new file mode 100644 index 0000000..e41eaad --- /dev/null +++ b/sysdeps/aarch64/fpu/acospi_sve.c @@ -0,0 +1,112 @@ +/* Double-Precision vector (SVE) inverse cospi function + + Copyright (C) 2025 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 +{ + float64_t c1, c3, c5, c7, c9, c11; + float64_t c0, c2, c4, c6, c8, c10; + float64_t inv_pi, half; +} data = { + /* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2) + on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using + iterative approach for minimisation of relative error in asinpif Sollya + file. */ + .c0 = 0x1.b2995e7b7b5fbp-5, .c1 = 0x1.8723a1d58d83p-6, + .c2 = 0x1.d1a452eacf2fep-7, .c3 = 0x1.3ce52c4d75582p-7, + .c4 = 0x1.d2b2a0aea27d5p-8, .c5 = 0x1.6a0b9b92cad8bp-8, + .c6 = 0x1.2290c84438caep-8, .c7 = 0x1.efba896580d02p-9, + .c8 = 0x1.44446707af38p-9, .c9 = 0x1.5070b3e7aa03ep-8, + .c10 = -0x1.c70015d0ebdafp-9, .c11 = 0x1.27029c383fed9p-7, + .inv_pi = 0x1.45f306dc9c883p-2, .half = 0.5, +}; + +/* Double-precision SVE implementation of vector acospi(x). + + For |x| in [0, 0.5], use order 11 polynomial P to approximate asinpi + such that the final approximation of acospi is: + + acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)). + + The largest observed error in this region is 1.35 ulp: + _ZGVsMxv_acospi (0x1.fb014996aea18p-2) got 0x1.572a91755bbf6p-2 + want 0x1.572a91755bbf7p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.55 ulp: + _ZGVsMxv_acospi(0x1.d90d50357410cp-1) got 0x1.ffd43d5dd3a9ep-4 + want 0x1.ffd43d5dd3a9bp-4. */ +svfloat64_t SV_NAME_D1 (acospi) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + svbool_t ptrue = svptrue_b64 (); + + svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000); + svfloat64_t ax = svabs_x (pg, x); + svbool_t a_gt_half = svacgt (pg, x, 0.5f); + + /* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with + z2 = x ^ 2 and z = |x| , if |x| < 0.5 + z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */ + svfloat64_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5), + svmul_x (ptrue, x, x)); + svfloat64_t z = svsqrt_m (ax, a_gt_half, z2); + + /* Order-11 Estrin. */ + svfloat64_t z4 = svmul_x (ptrue, z2, z2); + svfloat64_t z8 = svmul_x (ptrue, z4, z4); + + svfloat64_t c13 = svld1rq (ptrue, &d->c1); + svfloat64_t c57 = svld1rq (ptrue, &d->c5); + svfloat64_t c911 = svld1rq (ptrue, &d->c9); + + svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0); + svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1); + svfloat64_t p03 = svmla_x (pg, p01, z4, p23); + + svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0); + svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1); + svfloat64_t p47 = svmla_x (pg, p45, z4, p67); + + svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0); + svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1); + svfloat64_t p811 = svmla_x (pg, p89, z4, p1011); + + svfloat64_t p411 = svmla_x (pg, p47, z8, p811); + svfloat64_t p = svmla_x (pg, p03, z8, p411); + + p = svmla_x (pg, sv_f64 (d->inv_pi), z2, p); + p = svmul_x (ptrue, p, z); + + /* acospi(|x|) = 1/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */ + svfloat64_t mul = svreinterpret_f64 ( + svlsl_m (a_gt_half, svreinterpret_u64 (sv_f64 (1.0)), 10)); + mul = svreinterpret_f64 (sveor_x (ptrue, svreinterpret_u64 (mul), sign)); + svfloat64_t add = svreinterpret_f64 ( + svorr_x (ptrue, sign, svreinterpret_u64 (sv_f64 (d->half)))); + add = svsub_m (a_gt_half, sv_f64 (d->half), add); + + return svmsb_x (pg, p, mul, add); +} |