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110 lines
3.7 KiB
C
110 lines
3.7 KiB
C
/* Double-precision vector (Advanced SIMD) sin function.
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Copyright (C) 2023-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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static const struct data
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{
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float64x2_t poly[7];
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float64x2_t range_val, inv_pi, shift, pi_1, pi_2, pi_3;
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} data = {
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.poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7),
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V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19),
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V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33),
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V2 (-0x1.9e9540300a1p-41) },
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.range_val = V2 (0x1p23),
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.inv_pi = V2 (0x1.45f306dc9c883p-2),
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.pi_1 = V2 (0x1.921fb54442d18p+1),
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.pi_2 = V2 (0x1.1a62633145c06p-53),
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.pi_3 = V2 (0x1.c1cd129024e09p-106),
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.shift = V2 (0x1.8p52),
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};
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#if WANT_SIMD_EXCEPT
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# define TinyBound v_u64 (0x3000000000000000) /* asuint64 (0x1p-255). */
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# define Thresh v_u64 (0x1160000000000000) /* RangeVal - TinyBound. */
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#endif
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#define C(i) d->poly[i]
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
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{
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y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
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return v_call_f64 (sin, x, y, cmp);
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}
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/* Vector (AdvSIMD) sin approximation.
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Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
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is 2.87 ULP:
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_ZGVnN2v_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
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want 0x1.fffffffa7dc05p-1
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Maximum observed error in the entire non-special domain ([-2^23, 2^23])
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is 3.22 ULP:
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_ZGVnN2v_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
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want 0x1.ffdcd125c84f8p-3. */
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float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float64x2_t n, r, r2, r3, r4, y, t1, t2, t3;
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uint64x2_t odd, cmp;
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#if WANT_SIMD_EXCEPT
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/* Detect |x| <= TinyBound or |x| >= RangeVal. If fenv exceptions are to be
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triggered correctly, set any special lanes to 1 (which is neutral w.r.t.
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fenv). These lanes will be fixed by special-case handler later. */
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uint64x2_t ir = vreinterpretq_u64_f64 (vabsq_f64 (x));
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cmp = vcgeq_u64 (vsubq_u64 (ir, TinyBound), Thresh);
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r = vbslq_f64 (cmp, vreinterpretq_f64_u64 (cmp), x);
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#else
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r = x;
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cmp = vcageq_f64 (d->range_val, x);
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cmp = vceqzq_u64 (cmp); /* cmp = ~cmp. */
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#endif
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/* n = rint(|x|/pi). */
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n = vfmaq_f64 (d->shift, d->inv_pi, r);
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odd = vshlq_n_u64 (vreinterpretq_u64_f64 (n), 63);
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n = vsubq_f64 (n, d->shift);
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/* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
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r = vfmsq_f64 (r, d->pi_1, n);
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r = vfmsq_f64 (r, d->pi_2, n);
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r = vfmsq_f64 (r, d->pi_3, n);
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/* sin(r) poly approx. */
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r2 = vmulq_f64 (r, r);
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r3 = vmulq_f64 (r2, r);
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r4 = vmulq_f64 (r2, r2);
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t1 = vfmaq_f64 (C (4), C (5), r2);
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t2 = vfmaq_f64 (C (2), C (3), r2);
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t3 = vfmaq_f64 (C (0), C (1), r2);
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y = vfmaq_f64 (t1, C (6), r4);
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y = vfmaq_f64 (t2, y, r4);
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y = vfmaq_f64 (t3, y, r4);
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y = vfmaq_f64 (r, y, r3);
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if (__glibc_unlikely (v_any_u64 (cmp)))
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return special_case (x, y, odd, cmp);
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return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
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}
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