1  /*
       2   * ====================================================
       3   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       4   *
       5   * Developed at SunPro, a Sun Microsystems, Inc. business.
       6   * Permission to use, copy, modify, and distribute this
       7   * software is freely granted, provided that this notice
       8   * is preserved.
       9   * ====================================================
      10  */
      11  
      12  #ifndef __vax__
      13  static const unsigned long
      14  	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
      15  	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
      16  
      17  static const double
      18  	C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
      19  	D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
      20  	E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
      21  	F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
      22  	G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
      23  
      24  double
      25  cbrtl (double x)
      26  {
      27    long hx;
      28    double r,s,w;
      29    double lt;
      30    unsigned sign;
      31    typedef unsigned unsigned32 __attribute__((mode(SI)));
      32    union {
      33      double t;
      34      unsigned32 pt[2];
      35    } ut, ux;
      36    int n0;
      37  
      38    ut.t = 1.0;
      39    n0 = (ut.pt[0] == 0);
      40  
      41    ut.t = 0.0;
      42    ux.t = x;
      43  
      44    hx = ux.pt[n0];			/* high word of x */
      45    sign=hx&0x80000000;			/* sign= sign(x) */
      46    hx  ^=sign;
      47    if(hx>=0x7ff00000) return(x+x);	/* cbrt(NaN,INF) is itself */
      48    if((hx| ux.pt[1-n0])==0)
      49      return(ux.t);			/* cbrt(0) is itself */
      50  
      51    ux.pt[n0] = hx;
      52    /* rough cbrt to 5 bits */
      53    if(hx<0x00100000)			/* subnormal number */
      54      {ut.pt[n0]=0x43500000;		/* set t= 2**54 */
      55       ut.t*=x; ut.pt[n0]=ut.pt[n0]/3+B2;
      56     }
      57    else
      58      ut.pt[n0]=hx/3+B1;
      59  
      60    /* new cbrt to 23 bits, may be implemented in single precision */
      61    r=ut.t*ut.t/ux.t;
      62    s=C+r*ut.t;
      63    ut.t*=G+F/(s+E+D/s);
      64  
      65    /* chopped to 20 bits and make it larger than cbrt(x) */
      66    ut.pt[1-n0]=0; ut.pt[n0]+=0x00000001;
      67  
      68    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
      69    s=ut.t*ut.t;				/* t*t is exact */
      70    r=ux.t/s;
      71    w=ut.t+ut.t;
      72    r=(r-ut.t)/(w+r);			/* r-s is exact */
      73    ut.t=ut.t+ut.t*r;
      74  
      75    /* restore the sign bit */
      76    ut.pt[n0] |= sign;
      77  
      78    lt = ut.t;
      79    lt -= (lt - (x/(lt*lt))) * 0.333333333333333333333;
      80    return lt;
      81  }
      82  
      83  main ()
      84  {
      85    if ((int) (cbrtl (27.0) + 0.5) != 3)
      86      abort ();
      87  
      88    exit (0);
      89  }
      90  #else
      91  main () { exit (0); }
      92  #endif