diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan_sve.c | 90 |
1 files changed, 90 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atan_sve.c b/sysdeps/aarch64/fpu/atan_sve.c new file mode 100644 index 0000000000..35587ef212 --- /dev/null +++ b/sysdeps/aarch64/fpu/atan_sve.c @@ -0,0 +1,90 @@ +/* Double-precision SVE inverse tan + + Copyright (C) 2023 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 "poly_sve_f64.h" + +static const struct data +{ + float64_t poly[20]; + float64_t pi_over_2; +} data = { + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on + [2**-1022, 1.0]. */ + .poly = { -0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3, + 0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4, + -0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5, + 0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5, + -0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6, + 0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10, + -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, }, + .pi_over_2 = 0x1.921fb54442d18p+0, +}; + +/* Useful constants. */ +#define SignMask (0x8000000000000000) + +/* Fast implementation of SVE atan. + Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using + z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed + error is 2.27 ulps: + _ZGVsMxv_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 + want 0x1.9225645bdd7c3p-1. */ +svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + /* No need to trigger special case. Small cases, infs and nans + are supported by our approximation technique. */ + svuint64_t ix = svreinterpret_u64 (x); + svuint64_t sign = svand_x (pg, ix, SignMask); + + /* Argument reduction: + y := arctan(x) for x < 1 + y := pi/2 + arctan(-1/x) for x > 1 + Hence, use z=-1/a if x>=1, otherwise z=a. */ + svbool_t red = svacgt (pg, x, 1.0); + /* Avoid dependency in abs(x) in division (and comparison). */ + svfloat64_t z = svsel (red, svdivr_x (pg, x, 1.0), x); + /* Use absolute value only when needed (odd powers of z). */ + svfloat64_t az = svabs_x (pg, z); + az = svneg_m (az, red, az); + + /* Use split Estrin scheme for P(z^2) with deg(P)=19. */ + svfloat64_t z2 = svmul_x (pg, z, z); + svfloat64_t x2 = svmul_x (pg, z2, z2); + svfloat64_t x4 = svmul_x (pg, x2, x2); + svfloat64_t x8 = svmul_x (pg, x4, x4); + + svfloat64_t y + = svmla_x (pg, sv_estrin_7_f64_x (pg, z2, x2, x4, d->poly), + sv_estrin_11_f64_x (pg, z2, x2, x4, x8, d->poly + 8), x8); + + /* y = shift + z + z^3 * P(z^2). */ + svfloat64_t z3 = svmul_x (pg, z2, az); + y = svmla_x (pg, az, z3, y); + + /* Apply shift as indicated by `red` predicate. */ + y = svadd_m (red, y, d->pi_over_2); + + /* y = atan(x) if x>0, -atan(-x) otherwise. */ + y = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)); + + return y; +} |