1  /* Single-precision vector (SVE) 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 "sv_math.h"
      21  
      22  static const struct data
      23  {
      24    float neg_pio2_1, neg_pio2_2, neg_pio2_3, inv_pio2, shift;
      25  } data = {
      26    /* Polynomial coefficients are hard-wired in FTMAD instructions.  */
      27    .neg_pio2_1 = -0x1.921fb6p+0f,
      28    .neg_pio2_2 = 0x1.777a5cp-25f,
      29    .neg_pio2_3 = 0x1.ee59dap-50f,
      30    .inv_pio2 = 0x1.45f306p-1f,
      31    /* Original shift used in AdvSIMD cosf,
      32       plus a contribution to set the bit #0 of q
      33       as expected by trigonometric instructions.  */
      34    .shift = 0x1.800002p+23f
      35  };
      36  
      37  #define RangeVal 0x49800000 /* asuint32(0x1p20f).  */
      38  
      39  static svfloat32_t NOINLINE
      40  special_case (svfloat32_t x, svfloat32_t y, svbool_t out_of_bounds)
      41  {
      42    return sv_call_f32 (cosf, x, y, out_of_bounds);
      43  }
      44  
      45  /* A fast SVE implementation of cosf based on trigonometric
      46     instructions (FTMAD, FTSSEL, FTSMUL).
      47     Maximum measured error: 2.06 ULPs.
      48     SV_NAME_F1 (cos)(0x1.dea2f2p+19) got 0x1.fffe7ap-6
      49  				   want 0x1.fffe76p-6.  */
      50  svfloat32_t SV_NAME_F1 (cos) (svfloat32_t x, const svbool_t pg)
      51  {
      52    const struct data *d = ptr_barrier (&data);
      53  
      54    svfloat32_t r = svabs_f32_x (pg, x);
      55    svbool_t out_of_bounds
      56      = svcmpge_n_u32 (pg, svreinterpret_u32_f32 (r), RangeVal);
      57  
      58    /* Load some constants in quad-word chunks to minimise memory access.  */
      59    svfloat32_t negpio2_and_invpio2
      60        = svld1rq_f32 (svptrue_b32 (), &d->neg_pio2_1);
      61  
      62    /* n = rint(|x|/(pi/2)).  */
      63    svfloat32_t q
      64        = svmla_lane_f32 (sv_f32 (d->shift), r, negpio2_and_invpio2, 3);
      65    svfloat32_t n = svsub_n_f32_x (pg, q, d->shift);
      66  
      67    /* r = |x| - n*(pi/2)  (range reduction into -pi/4 .. pi/4).  */
      68    r = svmla_lane_f32 (r, n, negpio2_and_invpio2, 0);
      69    r = svmla_lane_f32 (r, n, negpio2_and_invpio2, 1);
      70    r = svmla_lane_f32 (r, n, negpio2_and_invpio2, 2);
      71  
      72    /* Final multiplicative factor: 1.0 or x depending on bit #0 of q.  */
      73    svfloat32_t f = svtssel_f32 (r, svreinterpret_u32_f32 (q));
      74  
      75    /* cos(r) poly approx.  */
      76    svfloat32_t r2 = svtsmul_f32 (r, svreinterpret_u32_f32 (q));
      77    svfloat32_t y = sv_f32 (0.0f);
      78    y = svtmad_f32 (y, r2, 4);
      79    y = svtmad_f32 (y, r2, 3);
      80    y = svtmad_f32 (y, r2, 2);
      81    y = svtmad_f32 (y, r2, 1);
      82    y = svtmad_f32 (y, r2, 0);
      83  
      84    /* Apply factor.  */
      85    y = svmul_f32_x (pg, f, y);
      86  
      87    if (__glibc_unlikely (svptest_any (pg, out_of_bounds)))
      88      return special_case (x, y, out_of_bounds);
      89    return y;
      90  }