s_cbrt.c revision 1.2 
1
2/* @(#)s_cbrt.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15#include <math.h>
16
17/* cbrt(x)
18 * Return cube root of x
19 */
20#ifdef __STDC__
21static const unsigned
22#else
23static unsigned
24#endif
25	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
26	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
27
28#ifdef __STDC__
29static const double
30#else
31static double
32#endif
33C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
34D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
35E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
36F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
37G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
38
39#ifdef __STDC__
40	double cbrt(double x)
41#else
42	double cbrt(x)
43	double x;
44#endif
45{
46	double	one	= 1.0;
47	int	n0,hx;
48	double r,s,t=0.0,w;
49	unsigned *pt = (unsigned *) &t, sign;
50
51
52	n0 = ((*(int*)&one)>>29)^1;	/* index of high word */
53	hx = *( n0 + (int*)&x);		/* high word of x */
54	sign=hx&0x80000000; 		/* sign= sign(x) */
55	hx  ^=sign;
56	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
57	if((hx|*(1-n0+(int*)&x))==0)
58	    return(x);		/* cbrt(0) is itself */
59
60	*(n0+(int*)&x) = hx;	/* x <- |x| */
61    /* rough cbrt to 5 bits */
62	if(hx<0x00100000) 		/* subnormal number */
63	  {pt[n0]=0x43500000; 		/* set t= 2**54 */
64	   t*=x; pt[n0]=pt[n0]/3+B2;
65	  }
66	else
67	  pt[n0]=hx/3+B1;
68
69
70    /* new cbrt to 23 bits, may be implemented in single precision */
71	r=t*t/x;
72	s=C+r*t;
73	t*=G+F/(s+E+D/s);
74
75    /* chopped to 20 bits and make it larger than cbrt(x) */
76	pt[1-n0]=0; pt[n0]+=0x00000001;
77
78
79    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
80	s=t*t;		/* t*t is exact */
81	r=x/s;
82	w=t+t;
83	r=(r-t)/(w+r);	/* r-s is exact */
84	t=t+t*r;
85
86    /* retore the sign bit */
87	pt[n0] |= sign;
88	return(t);
89}
90