text: /* @(#)s_sincos.c 5.1 13/07/15 */
  /*
   * ====================================================
   * Copyright (C) 2013 Elliot Saba. All rights reserved.
   *
   * Developed at the University of Washington.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
   #include "cdefs-compat.h"
  
  /* sincos(x, s, c)
   * Several applications need sine and cosine of the same
   * angle x. This function computes both at the same time,
   * and stores the results in *sin and *cos.
   *
   * kernel function:
   *	__kernel_sin		... sine function on [-pi/4,pi/4]
   *	__kernel_cos		... cose function on [-pi/4,pi/4]
   *	__ieee754_rem_pio2	... argument reduction routine
   *
   * Method.
   *      Borrow liberally from s_sin.c and s_cos.c, merging
   *  efforts where applicable and returning their values in
   * appropriate variables, thereby slightly reducing the
   * amount of work relative to just calling sin/cos(x) 
   * separately
   *
   * Special cases:
   *      Let trig be any of sin, cos, or tan.
   *      sincos(+-INF, s, c)  is NaN, with signals;
   *      sincos(NaN, s, c)    is that NaN;
   */
  
  #include <float.h>
  #include <openlibm_math.h>
  
  //#define INLINE_REM_PIO2
  #include "math_private.h"
  //#include "e_rem_pio2.c"
  
  /* Constants used in polynomial approximation of sin/cos */
  static const double
  one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
  S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
  S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
  S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
  S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
  S6  =  1.58969099521155010221e-10, /* 0x3DE5D93A, 0x5ACFD57C */
  C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
  C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
  C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
  C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
  C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
  C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
  
  static void
  __kernel_sincos( double x, double y, int iy, double * k_s, double * k_c )
  {
      /* Inline calculation of sin/cos, as we can save
      some work, and we will always need to calculate
      both values, no matter the result of switch */
      double z, w, r, v, hz;
      z   = x*x;
      w   = z*z;
  
      /* cos-specific computation; equivalent to calling
       __kernel_cos(x,y) and storing in k_c*/
      r   = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6));
      hz  = 0.5*z;
      v   = one-hz;
  
      *k_c = v + (((one-v)-hz) + (z*r-x*y));
  
      /* sin-specific computation; equivalent to calling
      __kernel_sin(x,y,1) and storing in k_s*/
      r   = S2+z*(S3+z*S4) + z*w*(S5+z*S6);
      v   = z*x;
      if(iy == 0)
          *k_s = x+v*(S1+z*r);
      else
          *k_s = x-((z*(half*y-v*r)-y)-v*S1);
  }
  
  OLM_DLLEXPORT void
  sincos(double x, double * s, double * c)
  {
      double y[2];
      int32_t ix;
  
      /* Store high word of x in ix */
      GET_HIGH_WORD(ix,x);
  
      /* |x| ~< pi/4 */
      ix &= 0x7fffffff;
      if(ix <= 0x3fe921fb) {
          /* Check for small x for sin and cos */
          if(ix<0x3e46a09e) {
              /* Check for exact zero */
              if( (int)x==0 ) {
                  *s = x;
                  *c = 1.0;
                  return;
              }
          }
          /* Call kernel function with 0 extra */
          __kernel_sincos(x,0.0,0, s, c);
      } else if( ix >= 0x7ff00000 ) {
          /* sincos(Inf or NaN) is NaN */
          *s = x-x;
          *c = x-x;
      }
  
      /*argument reduction needed*/
      else {
          double k_c, k_s;
  
          /* Calculate remainer, then sub out to kernel */
          int32_t n = __ieee754_rem_pio2(x,y);
          __kernel_sincos( y[0], y[1], 1, &k_s, &k_c );
  
          /* Figure out permutation of sin/cos outputs to true outputs */
          switch(n&3) {
              case 0:
                  *c =  k_c;
                  *s =  k_s;
                  break;
              case 1:
                  *c = -k_s;
                  *s =  k_c;
                  break;
              case 2:
                  *c = -k_c;
                  *s = -k_s;
                  break;
              default:
                  *c =  k_s;
                  *s = -k_c;
                  break;
          }
      }
  }
  
  #if (LDBL_MANT_DIG == 53)
  openlibm_weak_reference(sincos, sincosl);
  #endif
  