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__
13static const unsigned long
14	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
15	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
16
17static 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
24double
25cbrtl (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
83main ()
84{
85  if ((int) (cbrtl (27.0) + 0.5) != 3)
86    abort ();
87
88  exit (0);
89}
90#else
91main () { exit (0); }
92#endif
93