/[jscoverage]/trunk/js/src/fdlibm/e_hypot.c
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Annotation of /trunk/js/src/fdlibm/e_hypot.c

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Wed Aug 1 13:51:53 2007 UTC (14 years, 11 months ago) by siliconforks
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1 siliconforks 2 /* -*- 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     /* @(#)e_hypot.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     /* __ieee754_hypot(x,y)
53     *
54     * Method :
55     * If (assume round-to-nearest) z=x*x+y*y
56     * has error less than sqrt(2)/2 ulp, than
57     * sqrt(z) has error less than 1 ulp (exercise).
58     *
59     * So, compute sqrt(x*x+y*y) with some care as
60     * follows to get the error below 1 ulp:
61     *
62     * Assume x>y>0;
63     * (if possible, set rounding to round-to-nearest)
64     * 1. if x > 2y use
65     * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
66     * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
67     * 2. if x <= 2y use
68     * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
69     * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
70     * y1= y with lower 32 bits chopped, y2 = y-y1.
71     *
72     * NOTE: scaling may be necessary if some argument is too
73     * large or too tiny
74     *
75     * Special cases:
76     * hypot(x,y) is INF if x or y is +INF or -INF; else
77     * hypot(x,y) is NAN if x or y is NAN.
78     *
79     * Accuracy:
80     * hypot(x,y) returns sqrt(x^2+y^2) with error less
81     * than 1 ulps (units in the last place)
82     */
83    
84     #include "fdlibm.h"
85    
86     #ifdef __STDC__
87     double __ieee754_hypot(double x, double y)
88     #else
89     double __ieee754_hypot(x,y)
90     double x, y;
91     #endif
92     {
93     fd_twoints ux, uy;
94     double a=x,b=y,t1,t2,y1,y2,w;
95     int j,k,ha,hb;
96    
97     ux.d = x; uy.d = y;
98     ha = __HI(ux)&0x7fffffff; /* high word of x */
99     hb = __HI(uy)&0x7fffffff; /* high word of y */
100     if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
101     ux.d = a; uy.d = b;
102     __HI(ux) = ha; /* a <- |a| */
103     __HI(uy) = hb; /* b <- |b| */
104     a = ux.d; b = uy.d;
105     if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
106     k=0;
107     if(ha > 0x5f300000) { /* a>2**500 */
108     if(ha >= 0x7ff00000) { /* Inf or NaN */
109     w = a+b; /* for sNaN */
110     ux.d = a; uy.d = b;
111     if(((ha&0xfffff)|__LO(ux))==0) w = a;
112     if(((hb^0x7ff00000)|__LO(uy))==0) w = b;
113     return w;
114     }
115     /* scale a and b by 2**-600 */
116     ha -= 0x25800000; hb -= 0x25800000; k += 600;
117     ux.d = a; uy.d = b;
118     __HI(ux) = ha;
119     __HI(uy) = hb;
120     a = ux.d; b = uy.d;
121     }
122     if(hb < 0x20b00000) { /* b < 2**-500 */
123     if(hb <= 0x000fffff) { /* subnormal b or 0 */
124     uy.d = b;
125     if((hb|(__LO(uy)))==0) return a;
126     t1=0;
127     ux.d = t1;
128     __HI(ux) = 0x7fd00000; /* t1=2^1022 */
129     t1 = ux.d;
130     b *= t1;
131     a *= t1;
132     k -= 1022;
133     } else { /* scale a and b by 2^600 */
134     ha += 0x25800000; /* a *= 2^600 */
135     hb += 0x25800000; /* b *= 2^600 */
136     k -= 600;
137     ux.d = a; uy.d = b;
138     __HI(ux) = ha;
139     __HI(uy) = hb;
140     a = ux.d; b = uy.d;
141     }
142     }
143     /* medium size a and b */
144     w = a-b;
145     if (w>b) {
146     t1 = 0;
147     ux.d = t1;
148     __HI(ux) = ha;
149     t1 = ux.d;
150     t2 = a-t1;
151     w = fd_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
152     } else {
153     a = a+a;
154     y1 = 0;
155     ux.d = y1;
156     __HI(ux) = hb;
157     y1 = ux.d;
158     y2 = b - y1;
159     t1 = 0;
160     ux.d = t1;
161     __HI(ux) = ha+0x00100000;
162     t1 = ux.d;
163     t2 = a - t1;
164     w = fd_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
165     }
166     if(k!=0) {
167     t1 = 1.0;
168     ux.d = t1;
169     __HI(ux) += (k<<20);
170     t1 = ux.d;
171     return t1*w;
172     } else return w;
173     }

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