1  /* Used by sinf, cosf and sincosf functions.  X86-64 version.
       2     Copyright (C) 2018-2023 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4  
       5     The GNU C Library is free software; you can redistribute it and/or
       6     modify it under the terms of the GNU Lesser General Public
       7     License as published by the Free Software Foundation; either
       8     version 2.1 of the License, or (at your option) any later version.
       9  
      10     The GNU C Library is distributed in the hope that it will be useful,
      11     but WITHOUT ANY WARRANTY; without even the implied warranty of
      12     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      13     Lesser General Public License for more details.
      14  
      15     You should have received a copy of the GNU Lesser General Public
      16     License along with the GNU C Library; if not, see
      17     <https://www.gnu.org/licenses/>.  */
      18  
      19  typedef double v2df_t __attribute__ ((vector_size (2 * sizeof (double))));
      20  
      21  #ifdef __SSE2_MATH__
      22  typedef float v4sf_t __attribute__ ((vector_size (4 * sizeof (float))));
      23  
      24  static inline void
      25  v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
      26  {
      27    v4sf_t v4sf = __builtin_ia32_cvtpd2ps (v2df);
      28    *f0p = v4sf[0];
      29    *f1p = v4sf[1];
      30  }
      31  #else
      32  static inline void
      33  v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
      34  {
      35    *f0p = (float) v2df[0];
      36    *f1p = (float) v2df[1];
      37  }
      38  #endif
      39  
      40  /* The constants and polynomials for sine and cosine.  */
      41  typedef struct
      42  {
      43    double sign[4];		/* Sign of sine in quadrants 0..3.  */
      44    double hpi_inv;		/* 2 / PI ( * 2^24 if !TOINT_INTRINSICS).  */
      45    double hpi;			/* PI / 2.  */
      46    /* Cosine polynomial: c0, c1, c2, c3, c4.
      47       Sine polynomial: s1, s2, s3.  */
      48    double c0, c1;
      49    v2df_t s1c2, s2c3, s3c4;
      50  } sincos_t;
      51  
      52  /* Compute the sine and cosine of inputs X and X2 (X squared), using the
      53     polynomial P and store the results in SINP and COSP.  N is the quadrant,
      54     if odd the cosine and sine polynomials are swapped.  */
      55  static inline void
      56  sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
      57  	      float *cosp)
      58  {
      59    v2df_t vx2x2 = { x2, x2 };
      60    v2df_t vxx2 = { x, x2 };
      61    v2df_t vx3x4, vs1c2;
      62  
      63    vx3x4 = vx2x2 * vxx2;
      64    vs1c2 = p->s2c3 + vx2x2 * p->s3c4;
      65  
      66    /* Swap sin/cos result based on quadrant.  */
      67    if (n & 1)
      68      {
      69        float *tmp = cosp;
      70        cosp = sinp;
      71        sinp = tmp;
      72      }
      73  
      74    double c1 = p->c0 + x2 * p->c1;
      75    v2df_t vxc1 = { x, c1 };
      76    v2df_t vx5x6 = vx3x4 * vx2x2;
      77  
      78    v2df_t vsincos = vxc1 + vx3x4 * p->s1c2;
      79    vsincos = vsincos + vx5x6 * vs1c2;
      80    v2df_to_sf (vsincos, sinp, cosp);
      81  }
      82  
      83  /* Return the sine of inputs X and X2 (X squared) using the polynomial P.
      84     N is the quadrant, and if odd the cosine polynomial is used.  */
      85  static inline float
      86  sinf_poly (double x, double x2, const sincos_t *p, int n)
      87  {
      88    double x3, x4, x6, x7, s, c, c1, c2, s1;
      89  
      90    if ((n & 1) == 0)
      91      {
      92        x3 = x * x2;
      93        s1 = p->s2c3[0] + x2 * p->s3c4[0];
      94  
      95        x7 = x3 * x2;
      96        s = x + x3 * p->s1c2[0];
      97  
      98        return s + x7 * s1;
      99      }
     100    else
     101      {
     102        x4 = x2 * x2;
     103        c2 = p->s2c3[1] + x2 * p->s3c4[1];
     104        c1 = p->c0 + x2 * p->c1;
     105  
     106        x6 = x4 * x2;
     107        c = c1 + x4 * p->s1c2[1];
     108  
     109        return c + x6 * c2;
     110      }
     111  }