diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/acospif_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/acospif_sve.c | 91 |
1 files changed, 91 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/acospif_sve.c b/sysdeps/aarch64/fpu/acospif_sve.c new file mode 100644 index 0000000..ea4fc4a --- /dev/null +++ b/sysdeps/aarch64/fpu/acospif_sve.c @@ -0,0 +1,91 @@ +/* Single-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 +{ + float32_t c0, c1, c2, c3, c4, 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. */ + .c0 = 0x1.b29968p-5f, .c1 = 0x1.871424p-6f, .c2 = 0x1.d56e44p-7f, + .c3 = 0x1.149bb8p-7f, .c4 = 0x1.8e07fep-7f, .inv_pi = 0x1.45f306p-2f, + .half = 0.5f, +}; + +/* Single-precision SVE implementation of vector acospi(x). + + For |x| in [0, 0.5], use order 5 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 1.3 ulps, + _ZGVsMxv_acospif(0x1.ffa9d2p-2) got 0x1.557504p-2 + want 0x1.557502p-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 2.61 ulps, + _ZGVsMxv_acospif (0x1.6b232ep-1) got 0x1.fe04bap-3 + want 0x1.fe04cp-3. */ +svfloat32_t SV_NAME_F1 (acospi) (svfloat32_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svbool_t ptrue = svptrue_b32 (); + + svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000); + svfloat32_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. */ + svfloat32_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f32 (0.5f), ax, 0.5f), + svmul_x (ptrue, x, x)); + svfloat32_t z = svsqrt_m (ax, a_gt_half, z2); + + /* Use a single polynomial approximation P for both intervals. */ + svfloat32_t p = svmla_x (pg, sv_f32 (d->c3), z2, d->c4); + p = svmad_x (pg, z2, p, d->c2); + p = svmad_x (pg, z2, p, d->c1); + p = svmad_x (pg, z2, p, d->c0); + /* Add 1/pi as final coeff. */ + p = svmla_x (pg, sv_f32 (d->inv_pi), z2, p); + /* Finalize polynomial: z * P(z^2). */ + p = svmul_x (ptrue, z, p); + + /* 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. */ + svfloat32_t y + = svreinterpret_f32 (svorr_x (ptrue, svreinterpret_u32 (p), sign)); + svfloat32_t mul = svsel (a_gt_half, sv_f32 (2.0f), sv_f32 (-1.0f)); + svfloat32_t add = svreinterpret_f32 ( + svorr_x (ptrue, sign, svreinterpret_u32 (sv_f32 (d->half)))); + add = svsub_m (a_gt_half, sv_f32 (d->half), add); + + return svmad_x (pg, y, mul, add); +} |