s_cbrt.c revision 1.11 
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#include <sys/cdefs.h>
14#if defined(LIBM_SCCS) && !defined(lint)
15__RCSID("$NetBSD: s_cbrt.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
16#endif
17
18#include "math.h"
19#include "math_private.h"
20
21/* cbrt(x)
22 * Return cube root of x
23 */
24static const u_int32_t
25	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
26	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
27
28static const double
29C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
30D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
31E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
32F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
33G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
34
35double
36cbrt(double x)
37{
38	int32_t	hx;
39	double r,s,t=0.0,w;
40	u_int32_t sign;
41	u_int32_t high,low;
42
43	GET_HIGH_WORD(hx,x);
44	sign=hx&0x80000000; 		/* sign= sign(x) */
45	hx  ^=sign;
46	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
47	GET_LOW_WORD(low,x);
48	if((hx|low)==0)
49	    return(x);		/* cbrt(0) is itself */
50
51	SET_HIGH_WORD(x,hx);	/* x <- |x| */
52    /* rough cbrt to 5 bits */
53	if(hx<0x00100000) 		/* subnormal number */
54	  {SET_HIGH_WORD(t,0x43500000);	/* set t= 2**54 */
55	   t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
56	  }
57	else
58	  SET_HIGH_WORD(t,hx/3+B1);
59
60
61    /* new cbrt to 23 bits, may be implemented in single precision */
62	r=t*t/x;
63	s=C+r*t;
64	t*=G+F/(s+E+D/s);
65
66    /* chopped to 20 bits and make it larger than cbrt(x) */
67	GET_HIGH_WORD(high,t);
68	INSERT_WORDS(t,high+0x00000001,0);
69
70
71    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
72	s=t*t;		/* t*t is exact */
73	r=x/s;
74	w=t+t;
75	r=(r-t)/(w+r);	/* r-s is exact */
76	t=t+t*r;
77
78    /* retore the sign bit */
79	GET_HIGH_WORD(high,t);
80	SET_HIGH_WORD(t,high|sign);
81	return(t);
82}
83