1
2/* @(#)s_cbrt.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, 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 "fdlibm.h"
16
17/* ieee_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 ieee_cbrt(double x)
41#else
42	double ieee_cbrt(x)
43	double x;
44#endif
45{
46	int	hx;
47	double r,s,t=0.0,w;
48	unsigned sign;
49
50
51	hx = __HI(x);		/* high word of x */
52	sign=hx&0x80000000; 		/* sign= sign(x) */
53	hx  ^=sign;
54	if(hx>=0x7ff00000) return(x+x); /* ieee_cbrt(NaN,INF) is itself */
55	if((hx|__LO(x))==0)
56	    return(x);		/* ieee_cbrt(0) is itself */
57
58	__HI(x) = hx;	/* x <- |x| */
59    /* rough cbrt to 5 bits */
60	if(hx<0x00100000) 		/* subnormal number */
61	  {__HI(t)=0x43500000; 		/* set t= 2**54 */
62	   t*=x; __HI(t)=__HI(t)/3+B2;
63	  }
64	else
65	  __HI(t)=hx/3+B1;
66
67
68    /* new cbrt to 23 bits, may be implemented in single precision */
69	r=t*t/x;
70	s=C+r*t;
71	t*=G+F/(s+E+D/s);
72
73    /* chopped to 20 bits and make it larger than ieee_cbrt(x) */
74	__LO(t)=0; __HI(t)+=0x00000001;
75
76
77    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
78	s=t*t;		/* t*t is exact */
79	r=x/s;
80	w=t+t;
81	r=(r-t)/(w+r);	/* r-s is exact */
82	t=t+t*r;
83
84    /* retore the sign bit */
85	__HI(t) |= sign;
86	return(t);
87}
88