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

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Wed Aug 1 13:51:53 2007 UTC (14 years, 9 months ago) by siliconforks
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Initial import.

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 /* @(#)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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