mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-29 16:21:07 +00:00
91 lines
3.4 KiB
C
91 lines
3.4 KiB
C
/* 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;
|
|
}
|