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
cbrtl(double x)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
main()83 main ()
84 {
85 if ((int) (cbrtl (27.0) + 0.5) != 3)
86 abort ();
87
88 exit (0);
89 }
90 #else
main()91 main () { exit (0); }
92 #endif
93