1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
/* -*- 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);
}
|
