diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/asinpi_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/asinpi_advsimd.c | 109 |
1 files changed, 109 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/asinpi_advsimd.c b/sysdeps/aarch64/fpu/asinpi_advsimd.c new file mode 100644 index 0000000..b11f98b --- /dev/null +++ b/sysdeps/aarch64/fpu/asinpi_advsimd.c @@ -0,0 +1,109 @@ +/* Double-Precision vector (Advanced SIMD) inverse sinpi 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 "v_math.h" + +static const struct data +{ + float64x2_t c0, c2, c4, c6, c8, c10; + float64x2_t pi_over_2, inv_pi; + uint64x2_t abs_mask; + double c1, c3, c5, c7, c9, c11; +} data = { + /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) + on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */ + .c0 = V2 (0x1.555555555554ep-3), .c1 = 0x1.3333333337233p-4, + .c2 = V2 (0x1.6db6db67f6d9fp-5), .c3 = 0x1.f1c71fbd29fbbp-6, + .c4 = V2 (0x1.6e8b264d467d6p-6), .c5 = 0x1.1c5997c357e9dp-6, + .c6 = V2 (0x1.c86a22cd9389dp-7), .c7 = 0x1.856073c22ebbep-7, + .c8 = V2 (0x1.fd1151acb6bedp-8), .c9 = 0x1.087182f799c1dp-6, + .c10 = V2 (-0x1.6602748120927p-7), .c11 = 0x1.cfa0dd1f9478p-6, + .pi_over_2 = V2 (0x1.921fb54442d18p+0), .abs_mask = V2 (0x7fffffffffffffff), + .inv_pi = V2 (0x1.45f306dc9c883p-2), +}; + +/* Double-precision implementation of vector asinpi(x). + + For |x| in [0, 0.5], use an order 11 polynomial P such that the final + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). + asinpi(x) = asin(x) * 1/pi. + + The largest observed error in this region is 1.63 ulps, + _ZGVnN2v_asinpi (0x1.9125919fa617p-19) got 0x1.fec183497ea53p-21 + want 0x1.fec183497ea51p-21. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 3.04 ulps, + _ZGVnN2v_asinpi (0x1.0479b7bd98553p-1) got 0x1.5beebec797326p-3 + want 0x1.5beebec797329p-3. */ + +float64x2_t VPCS_ATTR V_NAME_D1 (asinpi) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + float64x2_t ax = vabsq_f64 (x); + + uint64x2_t a_lt_half = vcaltq_f64 (x, v_f64 (0.5)); + + /* Evaluate polynomial Q(x) = y + y * z * P(z) with + z = x ^ 2 and y = |x| , if |x| < 0.5 + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ + float64x2_t z2 = vbslq_f64 (a_lt_half, vmulq_f64 (x, x), + vfmsq_n_f64 (v_f64 (0.5), ax, 0.5)); + float64x2_t z = vbslq_f64 (a_lt_half, ax, vsqrtq_f64 (z2)); + + /* Use a single polynomial approximation P for both intervals. */ + float64x2_t z4 = vmulq_f64 (z2, z2); + float64x2_t z8 = vmulq_f64 (z4, z4); + float64x2_t z16 = vmulq_f64 (z8, z8); + + /* order-11 Estrin. */ + float64x2_t c13 = vld1q_f64 (&d->c1); + float64x2_t c57 = vld1q_f64 (&d->c5); + float64x2_t c911 = vld1q_f64 (&d->c9); + + float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0); + float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1); + float64x2_t p03 = vfmaq_f64 (p01, z4, p23); + + float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0); + float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1); + float64x2_t p47 = vfmaq_f64 (p45, z4, p67); + + float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0); + float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1); + float64x2_t p811 = vfmaq_f64 (p89, z4, p1011); + + float64x2_t p07 = vfmaq_f64 (p03, z8, p47); + float64x2_t p = vfmaq_f64 (p07, z16, p811); + + /* Finalize polynomial: z + z * z2 * P(z2). */ + p = vfmaq_f64 (z, vmulq_f64 (z, z2), p); + + /* asin(|x|) = Q(|x|) , for |x| < 0.5 + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ + float64x2_t y = vbslq_f64 (a_lt_half, p, vfmsq_n_f64 (d->pi_over_2, p, 2.0)); + /* asinpi(|x|) = asin(|x|) /pi. */ + y = vmulq_f64 (y, d->inv_pi); + + /* Copy sign. */ + return vbslq_f64 (d->abs_mask, y, x); +} |