s_cbrt.c revision 21673 
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[] = "$FreeBSD: head/lib/msun/src/s_cbrt.c 21673 1997-01-14 07:20:47Z jkh $";
15#endif
16
17#include "math.h"
18#include "math_private.h"
19
20/* cbrt(x)
21 * Return cube root of x
22 */
23#ifdef __STDC__
24static const u_int32_t
25#else
26static u_int32_t
27#endif
28	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
29	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
30
31#ifdef __STDC__
32static const double
33#else
34static double
35#endif
36C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
37D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
38E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
39F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
40G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
41
42#ifdef __STDC__
43	double cbrt(double x)
44#else
45	double cbrt(x)
46	double x;
47#endif
48{
49	int32_t	hx;
50	double r,s,t=0.0,w;
51	u_int32_t sign;
52	u_int32_t high,low;
53
54	GET_HIGH_WORD(hx,x);
55	sign=hx&0x80000000; 		/* sign= sign(x) */
56	hx  ^=sign;
57	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
58	GET_LOW_WORD(low,x);
59	if((hx|low)==0)
60	    return(x);		/* cbrt(0) is itself */
61
62	SET_HIGH_WORD(x,hx);	/* x <- |x| */
63    /* rough cbrt to 5 bits */
64	if(hx<0x00100000) 		/* subnormal number */
65	  {SET_HIGH_WORD(t,0x43500000);	/* set t= 2**54 */
66	   t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
67	  }
68	else
69	  SET_HIGH_WORD(t,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	GET_HIGH_WORD(high,t);
79	INSERT_WORDS(t,high+0x00000001,0);
80
81
82    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
83	s=t*t;		/* t*t is exact */
84	r=x/s;
85	w=t+t;
86	r=(r-t)/(w+r);	/* r-s is exact */
87	t=t+t*r;
88
89    /* retore the sign bit */
90	GET_HIGH_WORD(high,t);
91	SET_HIGH_WORD(t,high|sign);
92	return(t);
93}
94