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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.random;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> /** This class implements a powerful pseudo-random number generator<a name="line.22"></a> <FONT color="green">023</FONT> * developed by Makoto Matsumoto and Takuji Nishimura during<a name="line.23"></a> <FONT color="green">024</FONT> * 1996-1997.<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> * <p>This generator features an extremely long period<a name="line.26"></a> <FONT color="green">027</FONT> * (2<sup>19937</sup>-1) and 623-dimensional equidistribution up to 32<a name="line.27"></a> <FONT color="green">028</FONT> * bits accuracy. The home page for this generator is located at <a<a name="line.28"></a> <FONT color="green">029</FONT> * href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html"><a name="line.29"></a> <FONT color="green">030</FONT> * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html</a>.</p><a name="line.30"></a> <FONT color="green">031</FONT> <a name="line.31"></a> <FONT color="green">032</FONT> * <p>This generator is described in a paper by Makoto Matsumoto and<a name="line.32"></a> <FONT color="green">033</FONT> * Takuji Nishimura in 1998: <a<a name="line.33"></a> <FONT color="green">034</FONT> * href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf">Mersenne<a name="line.34"></a> <FONT color="green">035</FONT> * Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random<a name="line.35"></a> <FONT color="green">036</FONT> * Number Generator</a>, ACM Transactions on Modeling and Computer<a name="line.36"></a> <FONT color="green">037</FONT> * Simulation, Vol. 8, No. 1, January 1998, pp 3--30</p><a name="line.37"></a> <FONT color="green">038</FONT> <a name="line.38"></a> <FONT color="green">039</FONT> * <p>This class is mainly a Java port of the 2002-01-26 version of<a name="line.39"></a> <FONT color="green">040</FONT> * the generator written in C by Makoto Matsumoto and Takuji<a name="line.40"></a> <FONT color="green">041</FONT> * Nishimura. Here is their original copyright:</p><a name="line.41"></a> <FONT color="green">042</FONT> <a name="line.42"></a> <FONT color="green">043</FONT> * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"><a name="line.43"></a> <FONT color="green">044</FONT> * <tr><td>Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,<a name="line.44"></a> <FONT color="green">045</FONT> * All rights reserved.</td></tr><a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> * <tr><td>Redistribution and use in source and binary forms, with or without<a name="line.47"></a> <FONT color="green">048</FONT> * modification, are permitted provided that the following conditions<a name="line.48"></a> <FONT color="green">049</FONT> * are met:<a name="line.49"></a> <FONT color="green">050</FONT> * <ol><a name="line.50"></a> <FONT color="green">051</FONT> * <li>Redistributions of source code must retain the above copyright<a name="line.51"></a> <FONT color="green">052</FONT> * notice, this list of conditions and the following disclaimer.</li><a name="line.52"></a> <FONT color="green">053</FONT> * <li>Redistributions in binary form must reproduce the above copyright<a name="line.53"></a> <FONT color="green">054</FONT> * notice, this list of conditions and the following disclaimer in the<a name="line.54"></a> <FONT color="green">055</FONT> * documentation and/or other materials provided with the distribution.</li><a name="line.55"></a> <FONT color="green">056</FONT> * <li>The names of its contributors may not be used to endorse or promote<a name="line.56"></a> <FONT color="green">057</FONT> * products derived from this software without specific prior written<a name="line.57"></a> <FONT color="green">058</FONT> * permission.</li><a name="line.58"></a> <FONT color="green">059</FONT> * </ol></td></tr><a name="line.59"></a> <FONT color="green">060</FONT> <a name="line.60"></a> <FONT color="green">061</FONT> * <tr><td><strong>THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND<a name="line.61"></a> <FONT color="green">062</FONT> * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,<a name="line.62"></a> <FONT color="green">063</FONT> * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF<a name="line.63"></a> <FONT color="green">064</FONT> * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE<a name="line.64"></a> <FONT color="green">065</FONT> * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS<a name="line.65"></a> <FONT color="green">066</FONT> * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,<a name="line.66"></a> <FONT color="green">067</FONT> * OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,<a name="line.67"></a> <FONT color="green">068</FONT> * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR<a name="line.68"></a> <FONT color="green">069</FONT> * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY<a name="line.69"></a> <FONT color="green">070</FONT> * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT<a name="line.70"></a> <FONT color="green">071</FONT> * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE<a name="line.71"></a> <FONT color="green">072</FONT> * USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH<a name="line.72"></a> <FONT color="green">073</FONT> * DAMAGE.</strong></td></tr><a name="line.73"></a> <FONT color="green">074</FONT> * </table><a name="line.74"></a> <FONT color="green">075</FONT> <a name="line.75"></a> <FONT color="green">076</FONT> * @version $Revision: 902203 $ $Date: 2010-01-22 13:27:41 -0500 (Fri, 22 Jan 2010) $<a name="line.76"></a> <FONT color="green">077</FONT> * @since 2.0<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> */<a name="line.79"></a> <FONT color="green">080</FONT> public class MersenneTwister extends BitsStreamGenerator implements Serializable {<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> /** Serializable version identifier. */<a name="line.82"></a> <FONT color="green">083</FONT> private static final long serialVersionUID = 8661194735290153518L;<a name="line.83"></a> <FONT color="green">084</FONT> <a name="line.84"></a> <FONT color="green">085</FONT> /** Size of the bytes pool. */<a name="line.85"></a> <FONT color="green">086</FONT> private static final int N = 624;<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> /** Period second parameter. */<a name="line.88"></a> <FONT color="green">089</FONT> private static final int M = 397;<a name="line.89"></a> <FONT color="green">090</FONT> <a name="line.90"></a> <FONT color="green">091</FONT> /** X * MATRIX_A for X = {0, 1}. */<a name="line.91"></a> <FONT color="green">092</FONT> private static final int[] MAG01 = { 0x0, 0x9908b0df };<a name="line.92"></a> <FONT color="green">093</FONT> <a name="line.93"></a> <FONT color="green">094</FONT> /** Bytes pool. */<a name="line.94"></a> <FONT color="green">095</FONT> private int[] mt;<a name="line.95"></a> <FONT color="green">096</FONT> <a name="line.96"></a> <FONT color="green">097</FONT> /** Current index in the bytes pool. */<a name="line.97"></a> <FONT color="green">098</FONT> private int mti;<a name="line.98"></a> <FONT color="green">099</FONT> <a name="line.99"></a> <FONT color="green">100</FONT> /** Creates a new random number generator.<a name="line.100"></a> <FONT color="green">101</FONT> * <p>The instance is initialized using the current time as the<a name="line.101"></a> <FONT color="green">102</FONT> * seed.</p><a name="line.102"></a> <FONT color="green">103</FONT> */<a name="line.103"></a> <FONT color="green">104</FONT> public MersenneTwister() {<a name="line.104"></a> <FONT color="green">105</FONT> mt = new int[N];<a name="line.105"></a> <FONT color="green">106</FONT> setSeed(System.currentTimeMillis());<a name="line.106"></a> <FONT color="green">107</FONT> }<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> /** Creates a new random number generator using a single int seed.<a name="line.109"></a> <FONT color="green">110</FONT> * @param seed the initial seed (32 bits integer)<a name="line.110"></a> <FONT color="green">111</FONT> */<a name="line.111"></a> <FONT color="green">112</FONT> public MersenneTwister(int seed) {<a name="line.112"></a> <FONT color="green">113</FONT> mt = new int[N];<a name="line.113"></a> <FONT color="green">114</FONT> setSeed(seed);<a name="line.114"></a> <FONT color="green">115</FONT> }<a name="line.115"></a> <FONT color="green">116</FONT> <a name="line.116"></a> <FONT color="green">117</FONT> /** Creates a new random number generator using an int array seed.<a name="line.117"></a> <FONT color="green">118</FONT> * @param seed the initial seed (32 bits integers array), if null<a name="line.118"></a> <FONT color="green">119</FONT> * the seed of the generator will be related to the current time<a name="line.119"></a> <FONT color="green">120</FONT> */<a name="line.120"></a> <FONT color="green">121</FONT> public MersenneTwister(int[] seed) {<a name="line.121"></a> <FONT color="green">122</FONT> mt = new int[N];<a name="line.122"></a> <FONT color="green">123</FONT> setSeed(seed);<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> <a name="line.125"></a> <FONT color="green">126</FONT> /** Creates a new random number generator using a single long seed.<a name="line.126"></a> <FONT color="green">127</FONT> * @param seed the initial seed (64 bits integer)<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> public MersenneTwister(long seed) {<a name="line.129"></a> <FONT color="green">130</FONT> mt = new int[N];<a name="line.130"></a> <FONT color="green">131</FONT> setSeed(seed);<a name="line.131"></a> <FONT color="green">132</FONT> }<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> /** Reinitialize the generator as if just built with the given int seed.<a name="line.134"></a> <FONT color="green">135</FONT> * <p>The state of the generator is exactly the same as a new<a name="line.135"></a> <FONT color="green">136</FONT> * generator built with the same seed.</p><a name="line.136"></a> <FONT color="green">137</FONT> * @param seed the initial seed (32 bits integer)<a name="line.137"></a> <FONT color="green">138</FONT> */<a name="line.138"></a> <FONT color="green">139</FONT> @Override<a name="line.139"></a> <FONT color="green">140</FONT> public void setSeed(int seed) {<a name="line.140"></a> <FONT color="green">141</FONT> // we use a long masked by 0xffffffffL as a poor man unsigned int<a name="line.141"></a> <FONT color="green">142</FONT> long longMT = seed;<a name="line.142"></a> <FONT color="green">143</FONT> mt[0]= (int) longMT;<a name="line.143"></a> <FONT color="green">144</FONT> for (mti = 1; mti < N; ++mti) {<a name="line.144"></a> <FONT color="green">145</FONT> // See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier.<a name="line.145"></a> <FONT color="green">146</FONT> // initializer from the 2002-01-09 C version by Makoto Matsumoto<a name="line.146"></a> <FONT color="green">147</FONT> longMT = (1812433253l * (longMT ^ (longMT >> 30)) + mti) & 0xffffffffL;<a name="line.147"></a> <FONT color="green">148</FONT> mt[mti]= (int) longMT;<a name="line.148"></a> <FONT color="green">149</FONT> }<a name="line.149"></a> <FONT color="green">150</FONT> }<a name="line.150"></a> <FONT color="green">151</FONT> <a name="line.151"></a> <FONT color="green">152</FONT> /** Reinitialize the generator as if just built with the given int array seed.<a name="line.152"></a> <FONT color="green">153</FONT> * <p>The state of the generator is exactly the same as a new<a name="line.153"></a> <FONT color="green">154</FONT> * generator built with the same seed.</p><a name="line.154"></a> <FONT color="green">155</FONT> * @param seed the initial seed (32 bits integers array), if null<a name="line.155"></a> <FONT color="green">156</FONT> * the seed of the generator will be related to the current time<a name="line.156"></a> <FONT color="green">157</FONT> */<a name="line.157"></a> <FONT color="green">158</FONT> @Override<a name="line.158"></a> <FONT color="green">159</FONT> public void setSeed(int[] seed) {<a name="line.159"></a> <FONT color="green">160</FONT> <a name="line.160"></a> <FONT color="green">161</FONT> if (seed == null) {<a name="line.161"></a> <FONT color="green">162</FONT> setSeed(System.currentTimeMillis());<a name="line.162"></a> <FONT color="green">163</FONT> return;<a name="line.163"></a> <FONT color="green">164</FONT> }<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> setSeed(19650218);<a name="line.166"></a> <FONT color="green">167</FONT> int i = 1;<a name="line.167"></a> <FONT color="green">168</FONT> int j = 0;<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> for (int k = Math.max(N, seed.length); k != 0; k--) {<a name="line.170"></a> <FONT color="green">171</FONT> long l0 = (mt[i] & 0x7fffffffl) | ((mt[i] < 0) ? 0x80000000l : 0x0l);<a name="line.171"></a> <FONT color="green">172</FONT> long l1 = (mt[i-1] & 0x7fffffffl) | ((mt[i-1] < 0) ? 0x80000000l : 0x0l);<a name="line.172"></a> <FONT color="green">173</FONT> long l = (l0 ^ ((l1 ^ (l1 >> 30)) * 1664525l)) + seed[j] + j; // non linear<a name="line.173"></a> <FONT color="green">174</FONT> mt[i] = (int) (l & 0xffffffffl);<a name="line.174"></a> <FONT color="green">175</FONT> i++; j++;<a name="line.175"></a> <FONT color="green">176</FONT> if (i >= N) {<a name="line.176"></a> <FONT color="green">177</FONT> mt[0] = mt[N - 1];<a name="line.177"></a> <FONT color="green">178</FONT> i = 1;<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> if (j >= seed.length) {<a name="line.180"></a> <FONT color="green">181</FONT> j = 0;<a name="line.181"></a> <FONT color="green">182</FONT> }<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> <a name="line.184"></a> <FONT color="green">185</FONT> for (int k = N - 1; k != 0; k--) {<a name="line.185"></a> <FONT color="green">186</FONT> long l0 = (mt[i] & 0x7fffffffl) | ((mt[i] < 0) ? 0x80000000l : 0x0l);<a name="line.186"></a> <FONT color="green">187</FONT> long l1 = (mt[i-1] & 0x7fffffffl) | ((mt[i-1] < 0) ? 0x80000000l : 0x0l);<a name="line.187"></a> <FONT color="green">188</FONT> long l = (l0 ^ ((l1 ^ (l1 >> 30)) * 1566083941l)) - i; // non linear<a name="line.188"></a> <FONT color="green">189</FONT> mt[i] = (int) (l & 0xffffffffL);<a name="line.189"></a> <FONT color="green">190</FONT> i++;<a name="line.190"></a> <FONT color="green">191</FONT> if (i >= N) {<a name="line.191"></a> <FONT color="green">192</FONT> mt[0] = mt[N - 1];<a name="line.192"></a> <FONT color="green">193</FONT> i = 1;<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> }<a name="line.195"></a> <FONT color="green">196</FONT> <a name="line.196"></a> <FONT color="green">197</FONT> mt[0] = 0x80000000; // MSB is 1; assuring non-zero initial array<a name="line.197"></a> <FONT color="green">198</FONT> <a name="line.198"></a> <FONT color="green">199</FONT> }<a name="line.199"></a> <FONT color="green">200</FONT> <a name="line.200"></a> <FONT color="green">201</FONT> /** Reinitialize the generator as if just built with the given long seed.<a name="line.201"></a> <FONT color="green">202</FONT> * <p>The state of the generator is exactly the same as a new<a name="line.202"></a> <FONT color="green">203</FONT> * generator built with the same seed.</p><a name="line.203"></a> <FONT color="green">204</FONT> * @param seed the initial seed (64 bits integer)<a name="line.204"></a> <FONT color="green">205</FONT> */<a name="line.205"></a> <FONT color="green">206</FONT> @Override<a name="line.206"></a> <FONT color="green">207</FONT> public void setSeed(long seed) {<a name="line.207"></a> <FONT color="green">208</FONT> setSeed(new int[] { (int) (seed >>> 32), (int) (seed & 0xffffffffl) });<a name="line.208"></a> <FONT color="green">209</FONT> }<a name="line.209"></a> <FONT color="green">210</FONT> <a name="line.210"></a> <FONT color="green">211</FONT> /** Generate next pseudorandom number.<a name="line.211"></a> <FONT color="green">212</FONT> * <p>This method is the core generation algorithm. It is used by all the<a name="line.212"></a> <FONT color="green">213</FONT> * public generation methods for the various primitive types {@link<a name="line.213"></a> <FONT color="green">214</FONT> * #nextBoolean()}, {@link #nextBytes(byte[])}, {@link #nextDouble()},<a name="line.214"></a> <FONT color="green">215</FONT> * {@link #nextFloat()}, {@link #nextGaussian()}, {@link #nextInt()},<a name="line.215"></a> <FONT color="green">216</FONT> * {@link #next(int)} and {@link #nextLong()}.</p><a name="line.216"></a> <FONT color="green">217</FONT> * @param bits number of random bits to produce<a name="line.217"></a> <FONT color="green">218</FONT> * @return random bits generated<a name="line.218"></a> <FONT color="green">219</FONT> */<a name="line.219"></a> <FONT color="green">220</FONT> @Override<a name="line.220"></a> <FONT color="green">221</FONT> protected int next(int bits) {<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> int y;<a name="line.223"></a> <FONT color="green">224</FONT> <a name="line.224"></a> <FONT color="green">225</FONT> if (mti >= N) { // generate N words at one time<a name="line.225"></a> <FONT color="green">226</FONT> int mtNext = mt[0];<a name="line.226"></a> <FONT color="green">227</FONT> for (int k = 0; k < N - M; ++k) {<a name="line.227"></a> <FONT color="green">228</FONT> int mtCurr = mtNext;<a name="line.228"></a> <FONT color="green">229</FONT> mtNext = mt[k + 1];<a name="line.229"></a> <FONT color="green">230</FONT> y = (mtCurr & 0x80000000) | (mtNext & 0x7fffffff);<a name="line.230"></a> <FONT color="green">231</FONT> mt[k] = mt[k + M] ^ (y >>> 1) ^ MAG01[y & 0x1];<a name="line.231"></a> <FONT color="green">232</FONT> }<a name="line.232"></a> <FONT color="green">233</FONT> for (int k = N - M; k < N - 1; ++k) {<a name="line.233"></a> <FONT color="green">234</FONT> int mtCurr = mtNext;<a name="line.234"></a> <FONT color="green">235</FONT> mtNext = mt[k + 1];<a name="line.235"></a> <FONT color="green">236</FONT> y = (mtCurr & 0x80000000) | (mtNext & 0x7fffffff);<a name="line.236"></a> <FONT color="green">237</FONT> mt[k] = mt[k + (M - N)] ^ (y >>> 1) ^ MAG01[y & 0x1];<a name="line.237"></a> <FONT color="green">238</FONT> }<a name="line.238"></a> <FONT color="green">239</FONT> y = (mtNext & 0x80000000) | (mt[0] & 0x7fffffff);<a name="line.239"></a> <FONT color="green">240</FONT> mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ MAG01[y & 0x1];<a name="line.240"></a> <FONT color="green">241</FONT> <a name="line.241"></a> <FONT color="green">242</FONT> mti = 0;<a name="line.242"></a> <FONT color="green">243</FONT> }<a name="line.243"></a> <FONT color="green">244</FONT> <a name="line.244"></a> <FONT color="green">245</FONT> y = mt[mti++];<a name="line.245"></a> <FONT color="green">246</FONT> <a name="line.246"></a> <FONT color="green">247</FONT> // tempering<a name="line.247"></a> <FONT color="green">248</FONT> y ^= y >>> 11;<a name="line.248"></a> <FONT color="green">249</FONT> y ^= (y << 7) & 0x9d2c5680;<a name="line.249"></a> <FONT color="green">250</FONT> y ^= (y << 15) & 0xefc60000;<a name="line.250"></a> <FONT color="green">251</FONT> y ^= y >>> 18;<a name="line.251"></a> <FONT color="green">252</FONT> <a name="line.252"></a> <FONT color="green">253</FONT> return y >>> (32 - bits);<a name="line.253"></a> <FONT color="green">254</FONT> <a name="line.254"></a> <FONT color="green">255</FONT> }<a name="line.255"></a> <FONT color="green">256</FONT> <a name="line.256"></a> <FONT color="green">257</FONT> }<a name="line.257"></a> </PRE> </BODY> </HTML>