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
93