1  /* Double-precision vector (Advanced SIMD) cos 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, shift, inv_pi, half_pi, pi_1, pi_2, pi_3;
      26  } data = {
      27    /* Worst-case error is 3.3 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    .inv_pi = V2 (0x1.45f306dc9c883p-2),
      33    .half_pi = V2 (0x1.921fb54442d18p+0),
      34    .pi_1 = V2 (0x1.921fb54442d18p+1),
      35    .pi_2 = V2 (0x1.1a62633145c06p-53),
      36    .pi_3 = V2 (0x1.c1cd129024e09p-106),
      37    .shift = V2 (0x1.8p52),
      38    .range_val = V2 (0x1p23)
      39  };
      40  
      41  #define C(i) d->poly[i]
      42  
      43  static float64x2_t VPCS_ATTR NOINLINE
      44  special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
      45  {
      46    y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
      47    return v_call_f64 (cos, x, y, cmp);
      48  }
      49  
      50  float64x2_t VPCS_ATTR V_NAME_D1 (cos) (float64x2_t x)
      51  {
      52    const struct data *d = ptr_barrier (&data);
      53    float64x2_t n, r, r2, r3, r4, t1, t2, t3, y;
      54    uint64x2_t odd, cmp;
      55  
      56  #if WANT_SIMD_EXCEPT
      57    r = vabsq_f64 (x);
      58    cmp = vcgeq_u64 (vreinterpretq_u64_f64 (r),
      59  		   vreinterpretq_u64_f64 (d->range_val));
      60    if (__glibc_unlikely (v_any_u64 (cmp)))
      61      /* If fenv exceptions are to be triggered correctly, set any special lanes
      62         to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by
      63         special-case handler later.  */
      64      r = vbslq_f64 (cmp, v_f64 (1.0), r);
      65  #else
      66    cmp = vcageq_f64 (d->range_val, x);
      67    cmp = vceqzq_u64 (cmp); /* cmp = ~cmp.  */
      68    r = x;
      69  #endif
      70  
      71    /* n = rint((|x|+pi/2)/pi) - 0.5.  */
      72    n = vfmaq_f64 (d->shift, d->inv_pi, vaddq_f64 (r, d->half_pi));
      73    odd = vshlq_n_u64 (vreinterpretq_u64_f64 (n), 63);
      74    n = vsubq_f64 (n, d->shift);
      75    n = vsubq_f64 (n, v_f64 (0.5));
      76  
      77    /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2).  */
      78    r = vfmsq_f64 (r, d->pi_1, n);
      79    r = vfmsq_f64 (r, d->pi_2, n);
      80    r = vfmsq_f64 (r, d->pi_3, n);
      81  
      82    /* sin(r) poly approx.  */
      83    r2 = vmulq_f64 (r, r);
      84    r3 = vmulq_f64 (r2, r);
      85    r4 = vmulq_f64 (r2, r2);
      86  
      87    t1 = vfmaq_f64 (C (4), C (5), r2);
      88    t2 = vfmaq_f64 (C (2), C (3), r2);
      89    t3 = vfmaq_f64 (C (0), C (1), r2);
      90  
      91    y = vfmaq_f64 (t1, C (6), r4);
      92    y = vfmaq_f64 (t2, y, r4);
      93    y = vfmaq_f64 (t3, y, r4);
      94    y = vfmaq_f64 (r, y, r3);
      95  
      96    if (__glibc_unlikely (v_any_u64 (cmp)))
      97      return special_case (x, y, odd, cmp);
      98    return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
      99  }