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/* Double-precision vector (Advanced SIMD) sin function.
Copyright (C) 2023-2024 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, inv_pi, pi_1, pi_2, pi_3;
} data = {
.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) },
.range_val = V2 (0x1p23),
.inv_pi = V2 (0x1.45f306dc9c883p-2),
.pi_1 = V2 (0x1.921fb54442d18p+1),
.pi_2 = V2 (0x1.1a62633145c06p-53),
.pi_3 = V2 (0x1.c1cd129024e09p-106),
};
#if WANT_SIMD_EXCEPT
/* asuint64(0x1p-253)), below which multiply by inv_pi underflows. */
# define TinyBound v_u64 (0x3020000000000000)
/* RangeVal - TinyBound. */
# define Thresh v_u64 (0x1160000000000000)
#endif
#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 (sin, x, y, cmp);
}
/* Vector (AdvSIMD) sin approximation.
Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
is 2.87 ULP:
_ZGVnN2v_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
want 0x1.fffffffa7dc05p-1
Maximum observed error in the entire non-special domain ([-2^23, 2^23])
is 3.22 ULP:
_ZGVnN2v_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
want 0x1.ffdcd125c84f8p-3. */
float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
float64x2_t n, r, r2, r3, r4, y, t1, t2, t3;
uint64x2_t odd, cmp;
#if WANT_SIMD_EXCEPT
/* Detect |x| <= TinyBound or |x| >= RangeVal. 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. */
uint64x2_t ir = vreinterpretq_u64_f64 (vabsq_f64 (x));
cmp = vcgeq_u64 (vsubq_u64 (ir, TinyBound), Thresh);
r = vreinterpretq_f64_u64 (vbicq_u64 (vreinterpretq_u64_f64 (x), cmp));
#else
r = x;
cmp = vcageq_f64 (x, d->range_val);
#endif
/* n = rint(|x|/pi). */
n = vrndaq_f64 (vmulq_f64 (r, d->inv_pi));
odd = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtq_s64_f64 (n)), 63);
/* 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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