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/* Double-precision vector (SVE) cos function.
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"
static const struct data
{
double inv_pio2, pio2_1, pio2_2, pio2_3, shift;
} data = {
/* Polynomial coefficients are hardwired in FTMAD instructions. */
.inv_pio2 = 0x1.45f306dc9c882p-1,
.pio2_1 = 0x1.921fb50000000p+0,
.pio2_2 = 0x1.110b460000000p-26,
.pio2_3 = 0x1.1a62633145c07p-54,
/* Original shift used in AdvSIMD cos,
plus a contribution to set the bit #0 of q
as expected by trigonometric instructions. */
.shift = 0x1.8000000000001p52
};
#define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */
static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t out_of_bounds)
{
return sv_call_f64 (cos, x, y, out_of_bounds);
}
/* A fast SVE implementation of cos based on trigonometric
instructions (FTMAD, FTSSEL, FTSMUL).
Maximum measured error: 2.108 ULPs.
SV_NAME_D1 (cos)(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3
want -0x1.fddd4c65c7f05p-3. */
svfloat64_t SV_NAME_D1 (cos) (svfloat64_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svfloat64_t r = svabs_f64_x (pg, x);
svbool_t out_of_bounds
= svcmpge_n_u64 (pg, svreinterpret_u64_f64 (r), RangeVal);
/* Load some constants in quad-word chunks to minimise memory access. */
svbool_t ptrue = svptrue_b64 ();
svfloat64_t invpio2_and_pio2_1 = svld1rq_f64 (ptrue, &d->inv_pio2);
svfloat64_t pio2_23 = svld1rq_f64 (ptrue, &d->pio2_2);
/* n = rint(|x|/(pi/2)). */
svfloat64_t q = svmla_lane_f64 (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0);
svfloat64_t n = svsub_n_f64_x (pg, q, d->shift);
/* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
r = svmls_lane_f64 (r, n, invpio2_and_pio2_1, 1);
r = svmls_lane_f64 (r, n, pio2_23, 0);
r = svmls_lane_f64 (r, n, pio2_23, 1);
/* cos(r) poly approx. */
svfloat64_t r2 = svtsmul_f64 (r, svreinterpret_u64_f64 (q));
svfloat64_t y = sv_f64 (0.0);
y = svtmad_f64 (y, r2, 7);
y = svtmad_f64 (y, r2, 6);
y = svtmad_f64 (y, r2, 5);
y = svtmad_f64 (y, r2, 4);
y = svtmad_f64 (y, r2, 3);
y = svtmad_f64 (y, r2, 2);
y = svtmad_f64 (y, r2, 1);
y = svtmad_f64 (y, r2, 0);
/* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
svfloat64_t f = svtssel_f64 (r, svreinterpret_u64_f64 (q));
/* Apply factor. */
y = svmul_f64_x (pg, f, y);
if (__glibc_unlikely (svptest_any (pg, out_of_bounds)))
return special_case (x, y, out_of_bounds);
return y;
}
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