diff options
author | Joe Ramsay <Joe.Ramsay@arm.com> | 2023-11-03 12:12:21 +0000 |
---|---|---|
committer | Szabolcs Nagy <szabolcs.nagy@arm.com> | 2023-11-10 17:07:42 +0000 |
commit | d30c39f80d19d62e8fd750c424ccb7eb06b617e5 (patch) | |
tree | 165524f2d3142341e753ca027db7addfc360157d /sysdeps/aarch64/fpu/atanf_sve.c | |
parent | b5d23367a8c1e92b26bd48cce984e790208cdac1 (diff) | |
download | glibc-d30c39f80d19d62e8fd750c424ccb7eb06b617e5.tar.gz glibc-d30c39f80d19d62e8fd750c424ccb7eb06b617e5.tar.xz glibc-d30c39f80d19d62e8fd750c424ccb7eb06b617e5.zip |
aarch64: Add vector implementations of atan routines
Diffstat (limited to 'sysdeps/aarch64/fpu/atanf_sve.c')
-rw-r--r-- | sysdeps/aarch64/fpu/atanf_sve.c | 79 |
1 files changed, 79 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atanf_sve.c b/sysdeps/aarch64/fpu/atanf_sve.c new file mode 100644 index 0000000000..9453e7aa29 --- /dev/null +++ b/sysdeps/aarch64/fpu/atanf_sve.c @@ -0,0 +1,79 @@ +/* Single-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_f32.h" + +static const struct data +{ + float32_t poly[8]; + float32_t pi_over_2; +} data = { + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on + [2**-128, 1.0]. */ + .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f, + -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f }, + .pi_over_2 = 0x1.921fb6p+0f, +}; + +#define SignMask (0x80000000) + +/* Fast implementation of SVE atanf 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 observed error is 2.9 ULP, close to +/-1.0: + _ZGVsMxv_atanf (0x1.0468f6p+0) got -0x1.967f06p-1 + want -0x1.967fp-1. */ +svfloat32_t SV_NAME_F1 (atan) (svfloat32_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. */ + svuint32_t ix = svreinterpret_u32 (x); + svuint32_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, 1.0f); + /* Avoid dependency in abs(x) in division (and comparison). */ + svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (1.0f), x), x); + /* Use absolute value only when needed (odd powers of z). */ + svfloat32_t az = svabs_x (pg, z); + az = svneg_m (az, red, az); + + /* Use split Estrin scheme for P(z^2) with deg(P)=7. */ + svfloat32_t z2 = svmul_x (pg, z, z); + svfloat32_t z4 = svmul_x (pg, z2, z2); + svfloat32_t z8 = svmul_x (pg, z4, z4); + + svfloat32_t y = sv_estrin_7_f32_x (pg, z2, z4, z8, d->poly); + + /* y = shift + z + z^3 * P(z^2). */ + svfloat32_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, sv_f32 (d->pi_over_2)); + + /* y = atan(x) if x>0, -atan(-x) otherwise. */ + return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign)); +} |