1  /* Double-precision vector (Advanced SIMD) sin function.
       2  
       3     Copyright (C) 2023 Free Software Foundation, Inc.
       4     This file is part of the GNU C Library.
       5  
       6     The GNU C Library is free software; you can redistribute it and/or
       7     modify it under the terms of the GNU Lesser General Public
       8     License as published by the Free Software Foundation; either
       9     version 2.1 of the License, or (at your option) any later version.
      10  
      11     The GNU C Library is distributed in the hope that it will be useful,
      12     but WITHOUT ANY WARRANTY; without even the implied warranty of
      13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      14     Lesser General Public License for more details.
      15  
      16     You should have received a copy of the GNU Lesser General Public
      17     License along with the GNU C Library; if not, see
      18     <https://www.gnu.org/licenses/>.  */
      19  
      20  #include "v_math.h"
      21  
      22  static const struct data
      23  {
      24    float64x2_t poly[7];
      25    float64x2_t range_val, inv_pi, shift, pi_1, pi_2, pi_3;
      26  } data = {
      27    /* Worst-case error is 2.8 ulp in [-pi/2, pi/2].  */
      28    .poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7),
      29  	    V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19),
      30  	    V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33),
      31  	    V2 (-0x1.9e9540300a1p-41) },
      32  
      33    .range_val = V2 (0x1p23),
      34    .inv_pi = V2 (0x1.45f306dc9c883p-2),
      35    .pi_1 = V2 (0x1.921fb54442d18p+1),
      36    .pi_2 = V2 (0x1.1a62633145c06p-53),
      37    .pi_3 = V2 (0x1.c1cd129024e09p-106),
      38    .shift = V2 (0x1.8p52),
      39  };
      40  
      41  #if WANT_SIMD_EXCEPT
      42  # define TinyBound v_u64 (0x3000000000000000) /* asuint64 (0x1p-255).  */
      43  # define Thresh v_u64 (0x1160000000000000)    /* RangeVal - TinyBound.  */
      44  #endif
      45  
      46  #define C(i) d->poly[i]
      47  
      48  static float64x2_t VPCS_ATTR NOINLINE
      49  special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
      50  {
      51    y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
      52    return v_call_f64 (sin, x, y, cmp);
      53  }
      54  
      55  float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x)
      56  {
      57    const struct data *d = ptr_barrier (&data);
      58    float64x2_t n, r, r2, r3, r4, y, t1, t2, t3;
      59    uint64x2_t odd, cmp, eqz;
      60  
      61  #if WANT_SIMD_EXCEPT
      62    /* Detect |x| <= TinyBound or |x| >= RangeVal. If fenv exceptions are to be
      63       triggered correctly, set any special lanes to 1 (which is neutral w.r.t.
      64       fenv). These lanes will be fixed by special-case handler later.  */
      65    uint64x2_t ir = vreinterpretq_u64_f64 (vabsq_f64 (x));
      66    cmp = vcgeq_u64 (vsubq_u64 (ir, TinyBound), Thresh);
      67    r = vbslq_f64 (cmp, vreinterpretq_f64_u64 (cmp), x);
      68  #else
      69    r = x;
      70    cmp = vcageq_f64 (d->range_val, x);
      71    cmp = vceqzq_u64 (cmp); /* cmp = ~cmp.  */
      72  #endif
      73    eqz = vceqzq_f64 (x);
      74  
      75    /* n = rint(|x|/pi).  */
      76    n = vfmaq_f64 (d->shift, d->inv_pi, r);
      77    odd = vshlq_n_u64 (vreinterpretq_u64_f64 (n), 63);
      78    n = vsubq_f64 (n, d->shift);
      79  
      80    /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2).  */
      81    r = vfmsq_f64 (r, d->pi_1, n);
      82    r = vfmsq_f64 (r, d->pi_2, n);
      83    r = vfmsq_f64 (r, d->pi_3, n);
      84  
      85    /* sin(r) poly approx.  */
      86    r2 = vmulq_f64 (r, r);
      87    r3 = vmulq_f64 (r2, r);
      88    r4 = vmulq_f64 (r2, r2);
      89  
      90    t1 = vfmaq_f64 (C (4), C (5), r2);
      91    t2 = vfmaq_f64 (C (2), C (3), r2);
      92    t3 = vfmaq_f64 (C (0), C (1), r2);
      93  
      94    y = vfmaq_f64 (t1, C (6), r4);
      95    y = vfmaq_f64 (t2, y, r4);
      96    y = vfmaq_f64 (t3, y, r4);
      97    y = vfmaq_f64 (r, y, r3);
      98  
      99    /* Sign of 0 is discarded by polynomial, so copy it back here.  */
     100    if (__glibc_unlikely (v_any_u64 (eqz)))
     101      y = vbslq_f64 (eqz, x, y);
     102  
     103    if (__glibc_unlikely (v_any_u64 (cmp)))
     104      return special_case (x, y, odd, cmp);
     105    return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
     106  }