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/* Double-precision vector (Advanced SIMD) 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 "v_math.h"
static const struct data
{
float64x2_t poly[7];
float64x2_t range_val, shift, inv_pi, half_pi, pi_1, pi_2, pi_3;
} data = {
/* Worst-case error is 3.3 ulp in [-pi/2, pi/2]. */
.poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7),
V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19),
V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33),
V2 (-0x1.9e9540300a1p-41) },
.inv_pi = V2 (0x1.45f306dc9c883p-2),
.half_pi = V2 (0x1.921fb54442d18p+0),
.pi_1 = V2 (0x1.921fb54442d18p+1),
.pi_2 = V2 (0x1.1a62633145c06p-53),
.pi_3 = V2 (0x1.c1cd129024e09p-106),
.shift = V2 (0x1.8p52),
.range_val = V2 (0x1p23)
};
#define C(i) d->poly[i]
static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
{
y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
return v_call_f64 (cos, x, y, cmp);
}
float64x2_t VPCS_ATTR V_NAME_D1 (cos) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
float64x2_t n, r, r2, r3, r4, t1, t2, t3, y;
uint64x2_t odd, cmp;
#if WANT_SIMD_EXCEPT
r = vabsq_f64 (x);
cmp = vcgeq_u64 (vreinterpretq_u64_f64 (r),
vreinterpretq_u64_f64 (d->range_val));
if (__glibc_unlikely (v_any_u64 (cmp)))
/* If fenv exceptions are to be triggered correctly, set any special lanes
to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by
special-case handler later. */
r = vbslq_f64 (cmp, v_f64 (1.0), r);
#else
cmp = vcageq_f64 (d->range_val, x);
cmp = vceqzq_u64 (cmp); /* cmp = ~cmp. */
r = x;
#endif
/* n = rint((|x|+pi/2)/pi) - 0.5. */
n = vfmaq_f64 (d->shift, d->inv_pi, vaddq_f64 (r, d->half_pi));
odd = vshlq_n_u64 (vreinterpretq_u64_f64 (n), 63);
n = vsubq_f64 (n, d->shift);
n = vsubq_f64 (n, v_f64 (0.5));
/* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
r = vfmsq_f64 (r, d->pi_1, n);
r = vfmsq_f64 (r, d->pi_2, n);
r = vfmsq_f64 (r, d->pi_3, n);
/* sin(r) poly approx. */
r2 = vmulq_f64 (r, r);
r3 = vmulq_f64 (r2, r);
r4 = vmulq_f64 (r2, r2);
t1 = vfmaq_f64 (C (4), C (5), r2);
t2 = vfmaq_f64 (C (2), C (3), r2);
t3 = vfmaq_f64 (C (0), C (1), r2);
y = vfmaq_f64 (t1, C (6), r4);
y = vfmaq_f64 (t2, y, r4);
y = vfmaq_f64 (t3, y, r4);
y = vfmaq_f64 (r, y, r3);
if (__glibc_unlikely (v_any_u64 (cmp)))
return special_case (x, y, odd, cmp);
return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
}
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