1  /* Single-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    float32x4_t poly[4];
      25    float32x4_t range_val, inv_pi, shift, pi_1, pi_2, pi_3;
      26  } data = {
      27    /* 1.886 ulp error.  */
      28    .poly = { V4 (-0x1.555548p-3f), V4 (0x1.110df4p-7f), V4 (-0x1.9f42eap-13f),
      29  	    V4 (0x1.5b2e76p-19f) },
      30  
      31    .pi_1 = V4 (0x1.921fb6p+1f),
      32    .pi_2 = V4 (-0x1.777a5cp-24f),
      33    .pi_3 = V4 (-0x1.ee59dap-49f),
      34  
      35    .inv_pi = V4 (0x1.45f306p-2f),
      36    .shift = V4 (0x1.8p+23f),
      37    .range_val = V4 (0x1p20f)
      38  };
      39  
      40  #if WANT_SIMD_EXCEPT
      41  # define TinyBound v_u32 (0x21000000) /* asuint32(0x1p-61f).  */
      42  # define Thresh v_u32 (0x28800000)    /* RangeVal - TinyBound.  */
      43  #endif
      44  
      45  #define C(i) d->poly[i]
      46  
      47  static float32x4_t VPCS_ATTR NOINLINE
      48  special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
      49  {
      50    /* Fall back to scalar code.  */
      51    y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
      52    return v_call_f32 (sinf, x, y, cmp);
      53  }
      54  
      55  float32x4_t VPCS_ATTR V_NAME_F1 (sin) (float32x4_t x)
      56  {
      57    const struct data *d = ptr_barrier (&data);
      58    float32x4_t n, r, r2, y;
      59    uint32x4_t odd, cmp, eqz;
      60  
      61  #if WANT_SIMD_EXCEPT
      62    uint32x4_t ir = vreinterpretq_u32_f32 (vabsq_f32 (x));
      63    cmp = vcgeq_u32 (vsubq_u32 (ir, TinyBound), Thresh);
      64    /* If fenv exceptions are to be triggered correctly, set any special lanes
      65       to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by
      66       special-case handler later.  */
      67    r = vbslq_f32 (cmp, vreinterpretq_f32_u32 (cmp), x);
      68  #else
      69    r = x;
      70    cmp = vcageq_f32 (d->range_val, x);
      71    cmp = vceqzq_u32 (cmp); /* cmp = ~cmp.  */
      72  #endif
      73    eqz = vceqzq_f32 (x);
      74  
      75    /* n = rint(|x|/pi) */
      76    n = vfmaq_f32 (d->shift, d->inv_pi, r);
      77    odd = vshlq_n_u32 (vreinterpretq_u32_f32 (n), 31);
      78    n = vsubq_f32 (n, d->shift);
      79  
      80    /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2) */
      81    r = vfmsq_f32 (r, d->pi_1, n);
      82    r = vfmsq_f32 (r, d->pi_2, n);
      83    r = vfmsq_f32 (r, d->pi_3, n);
      84  
      85    /* y = sin(r) */
      86    r2 = vmulq_f32 (r, r);
      87    y = vfmaq_f32 (C (2), C (3), r2);
      88    y = vfmaq_f32 (C (1), y, r2);
      89    y = vfmaq_f32 (C (0), y, r2);
      90    y = vfmaq_f32 (r, vmulq_f32 (y, r2), r);
      91  
      92    /* Sign of 0 is discarded by polynomial, so copy it back here.  */
      93    if (__glibc_unlikely (v_any_u32 (eqz)))
      94      y = vbslq_f32 (eqz, x, y);
      95  
      96    if (__glibc_unlikely (v_any_u32 (cmp)))
      97      return special_case (x, y, odd, cmp);
      98    return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
      99  }