s_cbrt.c revision 1.3 
1/* @(#)s_cbrt.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#ifndef lint
14static char rcsid[] = "$Id: s_cbrt.c,v 1.3 1994/02/18 02:26:15 jtc Exp $";
15#endif
16
17#include <math.h>
18
19/* cbrt(x)
20 * Return cube root of x
21 */
22#ifdef __STDC__
23static const unsigned
24#else
25static unsigned
26#endif
27	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
28	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
29
30#ifdef __STDC__
31static const double
32#else
33static double
34#endif
35C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
36D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
37E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
38F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
39G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
40
41#ifdef __STDC__
42	double cbrt(double x)
43#else
44	double cbrt(x)
45	double x;
46#endif
47{
48	double	one	= 1.0;
49	int	n0,hx;
50	double r,s,t=0.0,w;
51	unsigned *pt = (unsigned *) &t, sign;
52
53
54	n0 = ((*(int*)&one)>>29)^1;	/* index of high word */
55	hx = *( n0 + (int*)&x);		/* high word of x */
56	sign=hx&0x80000000; 		/* sign= sign(x) */
57	hx  ^=sign;
58	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
59	if((hx|*(1-n0+(int*)&x))==0)
60	    return(x);		/* cbrt(0) is itself */
61
62	*(n0+(int*)&x) = hx;	/* x <- |x| */
63    /* rough cbrt to 5 bits */
64	if(hx<0x00100000) 		/* subnormal number */
65	  {pt[n0]=0x43500000; 		/* set t= 2**54 */
66	   t*=x; pt[n0]=pt[n0]/3+B2;
67	  }
68	else
69	  pt[n0]=hx/3+B1;
70
71
72    /* new cbrt to 23 bits, may be implemented in single precision */
73	r=t*t/x;
74	s=C+r*t;
75	t*=G+F/(s+E+D/s);
76
77    /* chopped to 20 bits and make it larger than cbrt(x) */
78	pt[1-n0]=0; pt[n0]+=0x00000001;
79
80
81    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
82	s=t*t;		/* t*t is exact */
83	r=x/s;
84	w=t+t;
85	r=(r-t)/(w+r);	/* r-s is exact */
86	t=t+t*r;
87
88    /* retore the sign bit */
89	pt[n0] |= sign;
90	return(t);
91}
92