s_cbrt.c revision 1.4 
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 1.4 1994/03/03 17:04:28 jtc Exp $";
15#endif
16
17#include <math.h>
18#include <machine/endian.h>
19
20#if BYTE_ORDER == LITTLE_ENDIAN
21#define n0	1
22#else
23#define n0	0
24#endif
25
26/* cbrt(x)
27 * Return cube root of x
28 */
29#ifdef __STDC__
30static const unsigned
31#else
32static unsigned
33#endif
34	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
35	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
36
37#ifdef __STDC__
38static const double
39#else
40static double
41#endif
42C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
43D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
44E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
45F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
46G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
47
48#ifdef __STDC__
49	double cbrt(double x)
50#else
51	double cbrt(x)
52	double x;
53#endif
54{
55	int	hx;
56	double r,s,t=0.0,w;
57	unsigned *pt = (unsigned *) &t, sign;
58
59	hx = *( n0 + (int*)&x);		/* high word of x */
60	sign=hx&0x80000000; 		/* sign= sign(x) */
61	hx  ^=sign;
62	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
63	if((hx|*(1-n0+(int*)&x))==0)
64	    return(x);		/* cbrt(0) is itself */
65
66	*(n0+(int*)&x) = hx;	/* x <- |x| */
67    /* rough cbrt to 5 bits */
68	if(hx<0x00100000) 		/* subnormal number */
69	  {pt[n0]=0x43500000; 		/* set t= 2**54 */
70	   t*=x; pt[n0]=pt[n0]/3+B2;
71	  }
72	else
73	  pt[n0]=hx/3+B1;
74
75
76    /* new cbrt to 23 bits, may be implemented in single precision */
77	r=t*t/x;
78	s=C+r*t;
79	t*=G+F/(s+E+D/s);
80
81    /* chopped to 20 bits and make it larger than cbrt(x) */
82	pt[1-n0]=0; pt[n0]+=0x00000001;
83
84
85    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
86	s=t*t;		/* t*t is exact */
87	r=x/s;
88	w=t+t;
89	r=(r-t)/(w+r);	/* r-s is exact */
90	t=t+t*r;
91
92    /* retore the sign bit */
93	pt[n0] |= sign;
94	return(t);
95}
96