src/fdlibm/s_cbrt.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)s_cbrt.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 *
 */

#include "fdlibm.h"

/* cbrt(x)
 * Return cube root of x
 */
#ifdef __STDC__
static const unsigned 
#else
static unsigned 
#endif
        B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
        B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */

#ifdef __STDC__
static const double
#else
static double
#endif
C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */

#ifdef __STDC__
        double fd_cbrt(double x) 
#else
        double fd_cbrt(x) 
        double x;
#endif
{
        fd_twoints u;
        int     hx;
        double r,s,t=0.0,w;
        unsigned sign;

        u.d = x;
        hx = __HI(u);           /* high word of x */
        sign=hx&0x80000000;             /* sign= sign(x) */
        hx  ^=sign;
        if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
        if((hx|__LO(u))==0) {
            x = u.d;
            return(x);          /* cbrt(0) is itself */
        }
        u.d = x;
        __HI(u) = hx;   /* x <- |x| */
        x = u.d;
    /* rough cbrt to 5 bits */
        if(hx<0x00100000)               /* subnormal number */
          {u.d = t; __HI(u)=0x43500000; t=u.d;          /* set t= 2**54 */
           t*=x; __HI(u)=__HI(u)/3+B2;
          }
        else {
          u.d = t; __HI(u)=hx/3+B1; t = u.d;
        }


    /* new cbrt to 23 bits, may be implemented in single precision */
        r=t*t/x;
        s=C+r*t;
        t*=G+F/(s+E+D/s);       

    /* chopped to 20 bits and make it larger than cbrt(x) */ 
        u.d = t;
        __LO(u)=0; __HI(u)+=0x00000001;
        t = u.d;

    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
        s=t*t;          /* t*t is exact */
        r=x/s;
        w=t+t;
        r=(r-t)/(w+r);  /* r-s is exact */
        t=t+t*r;

    /* retore the sign bit */
        u.d = t;
        __HI(u) |= sign;
        t = u.d;
        return(t);
}
1	/* -- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 --
2	*
3	* *** BEGIN LICENSE BLOCK ***
4	* Version: MPL 1.1/GPL 2.0/LGPL 2.1
5	*
6	* The contents of this file are subject to the Mozilla Public License Version
7	* 1.1 (the "License"); you may not use this file except in compliance with
8	* the License. You may obtain a copy of the License at
9	* http://www.mozilla.org/MPL/
10	*
11	* Software distributed under the License is distributed on an "AS IS" basis,
12	* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13	* for the specific language governing rights and limitations under the
14	* License.
15	*
16	* The Original Code is Mozilla Communicator client code, released
17	* March 31, 1998.
18	*
19	* The Initial Developer of the Original Code is
20	* Sun Microsystems, Inc.
21	* Portions created by the Initial Developer are Copyright (C) 1998
22	* the Initial Developer. All Rights Reserved.
23	*
24	* Contributor(s):
25	*
26	* Alternatively, the contents of this file may be used under the terms of
27	* either of the GNU General Public License Version 2 or later (the "GPL"),
28	* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29	* in which case the provisions of the GPL or the LGPL are applicable instead
30	* of those above. If you wish to allow use of your version of this file only
31	* under the terms of either the GPL or the LGPL, and not to allow others to
32	* use your version of this file under the terms of the MPL, indicate your
33	* decision by deleting the provisions above and replace them with the notice
34	* and other provisions required by the GPL or the LGPL. If you do not delete
35	* the provisions above, a recipient may use your version of this file under
36	* the terms of any one of the MPL, the GPL or the LGPL.
37	*
38	* *** END LICENSE BLOCK *** */
39
40	/* @(#)s_cbrt.c 1.3 95/01/18 */
41	/*
42	* ====================================================
43	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44	*
45	* Developed at SunSoft, a Sun Microsystems, Inc. business.
46	* Permission to use, copy, modify, and distribute this
47	* software is freely granted, provided that this notice
48	* is preserved.
49	* ====================================================
50	*
51	*/
52
53	#include "fdlibm.h"
54
55	/* cbrt(x)
56	* Return cube root of x
57	*/
58	#ifdef __STDC__
59	static const unsigned
60	#else
61	static unsigned
62	#endif
63	B1 = 715094163, /* B1 = (682-0.03306235651)220 /
64	B2 = 696219795; /* B2 = (664-0.03306235651)220 /
65
66	#ifdef __STDC__
67	static const double
68	#else
69	static double
70	#endif
71	C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
72	D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
73	E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
74	F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
75	G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
76
77	#ifdef __STDC__
78	double fd_cbrt(double x)
79	#else
80	double fd_cbrt(x)
81	double x;
82	#endif
83	{
84	fd_twoints u;
85	int hx;
86	double r,s,t=0.0,w;
87	unsigned sign;
88
89	u.d = x;
90	hx = __HI(u); /* high word of x */
91	sign=hx&0x80000000; /* sign= sign(x) */
92	hx ^=sign;
93	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
94	if((hx\|__LO(u))==0) {
95	x = u.d;
96	return(x); /* cbrt(0) is itself */
97	}
98	u.d = x;
99	__HI(u) = hx; /* x <- \|x\| */
100	x = u.d;
101	/* rough cbrt to 5 bits */
102	if(hx<0x00100000) /* subnormal number */
103	{u.d = t; __HI(u)=0x43500000; t=u.d; /* set t= 2*54 /
104	t*=x; __HI(u)=__HI(u)/3+B2;
105	}
106	else {
107	u.d = t; __HI(u)=hx/3+B1; t = u.d;
108	}
109
110
111	/* new cbrt to 23 bits, may be implemented in single precision */
112	r=t*t/x;
113	s=C+r*t;
114	t*=G+F/(s+E+D/s);
115
116	/* chopped to 20 bits and make it larger than cbrt(x) */
117	u.d = t;
118	__LO(u)=0; __HI(u)+=0x00000001;
119	t = u.d;
120
121	/* one step newton iteration to 53 bits with error less than 0.667 ulps */
122	s=tt; / tt is exact /
123	r=x/s;
124	w=t+t;
125	r=(r-t)/(w+r); /* r-s is exact */
126	t=t+t*r;
127
128	/* retore the sign bit */
129	u.d = t;
130	__HI(u) \|= sign;
131	t = u.d;
132	return(t);
133	}