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view libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/util/MathUtils.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| 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> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.util;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.math.BigDecimal;<a name="line.20"></a> <FONT color="green">021</FONT> import java.math.BigInteger;<a name="line.21"></a> <FONT color="green">022</FONT> import java.util.Arrays;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * Some useful additions to the built-in functions in {@link Math}.<a name="line.27"></a> <FONT color="green">028</FONT> * @version $Revision: 927249 $ $Date: 2010-03-24 21:06:51 -0400 (Wed, 24 Mar 2010) $<a name="line.28"></a> <FONT color="green">029</FONT> */<a name="line.29"></a> <FONT color="green">030</FONT> public final class MathUtils {<a name="line.30"></a> <FONT color="green">031</FONT> <a name="line.31"></a> <FONT color="green">032</FONT> /** Smallest positive number such that 1 - EPSILON is not numerically equal to 1. */<a name="line.32"></a> <FONT color="green">033</FONT> public static final double EPSILON = 0x1.0p-53;<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /** Safe minimum, such that 1 / SAFE_MIN does not overflow.<a name="line.35"></a> <FONT color="green">036</FONT> * <p>In IEEE 754 arithmetic, this is also the smallest normalized<a name="line.36"></a> <FONT color="green">037</FONT> * number 2<sup>-1022</sup>.</p><a name="line.37"></a> <FONT color="green">038</FONT> */<a name="line.38"></a> <FONT color="green">039</FONT> public static final double SAFE_MIN = 0x1.0p-1022;<a name="line.39"></a> <FONT color="green">040</FONT> <a name="line.40"></a> <FONT color="green">041</FONT> /**<a name="line.41"></a> <FONT color="green">042</FONT> * 2 &pi;.<a name="line.42"></a> <FONT color="green">043</FONT> * @since 2.1<a name="line.43"></a> <FONT color="green">044</FONT> */<a name="line.44"></a> <FONT color="green">045</FONT> public static final double TWO_PI = 2 * Math.PI;<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** -1.0 cast as a byte. */<a name="line.47"></a> <FONT color="green">048</FONT> private static final byte NB = (byte)-1;<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /** -1.0 cast as a short. */<a name="line.50"></a> <FONT color="green">051</FONT> private static final short NS = (short)-1;<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /** 1.0 cast as a byte. */<a name="line.53"></a> <FONT color="green">054</FONT> private static final byte PB = (byte)1;<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /** 1.0 cast as a short. */<a name="line.56"></a> <FONT color="green">057</FONT> private static final short PS = (short)1;<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** 0.0 cast as a byte. */<a name="line.59"></a> <FONT color="green">060</FONT> private static final byte ZB = (byte)0;<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> /** 0.0 cast as a short. */<a name="line.62"></a> <FONT color="green">063</FONT> private static final short ZS = (short)0;<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** Gap between NaN and regular numbers. */<a name="line.65"></a> <FONT color="green">066</FONT> private static final int NAN_GAP = 4 * 1024 * 1024;<a name="line.66"></a> <FONT color="green">067</FONT> <a name="line.67"></a> <FONT color="green">068</FONT> /** Offset to order signed double numbers lexicographically. */<a name="line.68"></a> <FONT color="green">069</FONT> private static final long SGN_MASK = 0x8000000000000000L;<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /** All long-representable factorials */<a name="line.71"></a> <FONT color="green">072</FONT> private static final long[] FACTORIALS = new long[] {<a name="line.72"></a> <FONT color="green">073</FONT> 1l, 1l, 2l,<a name="line.73"></a> <FONT color="green">074</FONT> 6l, 24l, 120l,<a name="line.74"></a> <FONT color="green">075</FONT> 720l, 5040l, 40320l,<a name="line.75"></a> <FONT color="green">076</FONT> 362880l, 3628800l, 39916800l,<a name="line.76"></a> <FONT color="green">077</FONT> 479001600l, 6227020800l, 87178291200l,<a name="line.77"></a> <FONT color="green">078</FONT> 1307674368000l, 20922789888000l, 355687428096000l,<a name="line.78"></a> <FONT color="green">079</FONT> 6402373705728000l, 121645100408832000l, 2432902008176640000l };<a name="line.79"></a> <FONT color="green">080</FONT> <a name="line.80"></a> <FONT color="green">081</FONT> /**<a name="line.81"></a> <FONT color="green">082</FONT> * Private Constructor<a name="line.82"></a> <FONT color="green">083</FONT> */<a name="line.83"></a> <FONT color="green">084</FONT> private MathUtils() {<a name="line.84"></a> <FONT color="green">085</FONT> super();<a name="line.85"></a> <FONT color="green">086</FONT> }<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> /**<a name="line.88"></a> <FONT color="green">089</FONT> * Add two integers, checking for overflow.<a name="line.89"></a> <FONT color="green">090</FONT> *<a name="line.90"></a> <FONT color="green">091</FONT> * @param x an addend<a name="line.91"></a> <FONT color="green">092</FONT> * @param y an addend<a name="line.92"></a> <FONT color="green">093</FONT> * @return the sum <code>x+y</code><a name="line.93"></a> <FONT color="green">094</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.94"></a> <FONT color="green">095</FONT> * int<a name="line.95"></a> <FONT color="green">096</FONT> * @since 1.1<a name="line.96"></a> <FONT color="green">097</FONT> */<a name="line.97"></a> <FONT color="green">098</FONT> public static int addAndCheck(int x, int y) {<a name="line.98"></a> <FONT color="green">099</FONT> long s = (long)x + (long)y;<a name="line.99"></a> <FONT color="green">100</FONT> if (s < Integer.MIN_VALUE || s > Integer.MAX_VALUE) {<a name="line.100"></a> <FONT color="green">101</FONT> throw new ArithmeticException("overflow: add");<a name="line.101"></a> <FONT color="green">102</FONT> }<a name="line.102"></a> <FONT color="green">103</FONT> return (int)s;<a name="line.103"></a> <FONT color="green">104</FONT> }<a name="line.104"></a> <FONT color="green">105</FONT> <a name="line.105"></a> <FONT color="green">106</FONT> /**<a name="line.106"></a> <FONT color="green">107</FONT> * Add two long integers, checking for overflow.<a name="line.107"></a> <FONT color="green">108</FONT> *<a name="line.108"></a> <FONT color="green">109</FONT> * @param a an addend<a name="line.109"></a> <FONT color="green">110</FONT> * @param b an addend<a name="line.110"></a> <FONT color="green">111</FONT> * @return the sum <code>a+b</code><a name="line.111"></a> <FONT color="green">112</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.112"></a> <FONT color="green">113</FONT> * long<a name="line.113"></a> <FONT color="green">114</FONT> * @since 1.2<a name="line.114"></a> <FONT color="green">115</FONT> */<a name="line.115"></a> <FONT color="green">116</FONT> public static long addAndCheck(long a, long b) {<a name="line.116"></a> <FONT color="green">117</FONT> return addAndCheck(a, b, "overflow: add");<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> <a name="line.119"></a> <FONT color="green">120</FONT> /**<a name="line.120"></a> <FONT color="green">121</FONT> * Add two long integers, checking for overflow.<a name="line.121"></a> <FONT color="green">122</FONT> *<a name="line.122"></a> <FONT color="green">123</FONT> * @param a an addend<a name="line.123"></a> <FONT color="green">124</FONT> * @param b an addend<a name="line.124"></a> <FONT color="green">125</FONT> * @param msg the message to use for any thrown exception.<a name="line.125"></a> <FONT color="green">126</FONT> * @return the sum <code>a+b</code><a name="line.126"></a> <FONT color="green">127</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.127"></a> <FONT color="green">128</FONT> * long<a name="line.128"></a> <FONT color="green">129</FONT> * @since 1.2<a name="line.129"></a> <FONT color="green">130</FONT> */<a name="line.130"></a> <FONT color="green">131</FONT> private static long addAndCheck(long a, long b, String msg) {<a name="line.131"></a> <FONT color="green">132</FONT> long ret;<a name="line.132"></a> <FONT color="green">133</FONT> if (a > b) {<a name="line.133"></a> <FONT color="green">134</FONT> // use symmetry to reduce boundary cases<a name="line.134"></a> <FONT color="green">135</FONT> ret = addAndCheck(b, a, msg);<a name="line.135"></a> <FONT color="green">136</FONT> } else {<a name="line.136"></a> <FONT color="green">137</FONT> // assert a <= b<a name="line.137"></a> <FONT color="green">138</FONT> <a name="line.138"></a> <FONT color="green">139</FONT> if (a < 0) {<a name="line.139"></a> <FONT color="green">140</FONT> if (b < 0) {<a name="line.140"></a> <FONT color="green">141</FONT> // check for negative overflow<a name="line.141"></a> <FONT color="green">142</FONT> if (Long.MIN_VALUE - b <= a) {<a name="line.142"></a> <FONT color="green">143</FONT> ret = a + b;<a name="line.143"></a> <FONT color="green">144</FONT> } else {<a name="line.144"></a> <FONT color="green">145</FONT> throw new ArithmeticException(msg);<a name="line.145"></a> <FONT color="green">146</FONT> }<a name="line.146"></a> <FONT color="green">147</FONT> } else {<a name="line.147"></a> <FONT color="green">148</FONT> // opposite sign addition is always safe<a name="line.148"></a> <FONT color="green">149</FONT> ret = a + b;<a name="line.149"></a> <FONT color="green">150</FONT> }<a name="line.150"></a> <FONT color="green">151</FONT> } else {<a name="line.151"></a> <FONT color="green">152</FONT> // assert a >= 0<a name="line.152"></a> <FONT color="green">153</FONT> // assert b >= 0<a name="line.153"></a> <FONT color="green">154</FONT> <a name="line.154"></a> <FONT color="green">155</FONT> // check for positive overflow<a name="line.155"></a> <FONT color="green">156</FONT> if (a <= Long.MAX_VALUE - b) {<a name="line.156"></a> <FONT color="green">157</FONT> ret = a + b;<a name="line.157"></a> <FONT color="green">158</FONT> } else {<a name="line.158"></a> <FONT color="green">159</FONT> throw new ArithmeticException(msg);<a name="line.159"></a> <FONT color="green">160</FONT> }<a name="line.160"></a> <FONT color="green">161</FONT> }<a name="line.161"></a> <FONT color="green">162</FONT> }<a name="line.162"></a> <FONT color="green">163</FONT> return ret;<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> /**<a name="line.166"></a> <FONT color="green">167</FONT> * Returns an exact representation of the <a<a name="line.167"></a> <FONT color="green">168</FONT> * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial<a name="line.168"></a> <FONT color="green">169</FONT> * Coefficient</a>, "<code>n choose k</code>", the number of<a name="line.169"></a> <FONT color="green">170</FONT> * <code>k</code>-element subsets that can be selected from an<a name="line.170"></a> <FONT color="green">171</FONT> * <code>n</code>-element set.<a name="line.171"></a> <FONT color="green">172</FONT> * <p><a name="line.172"></a> <FONT color="green">173</FONT> * <Strong>Preconditions</strong>:<a name="line.173"></a> <FONT color="green">174</FONT> * <ul><a name="line.174"></a> <FONT color="green">175</FONT> * <li> <code>0 <= k <= n </code> (otherwise<a name="line.175"></a> <FONT color="green">176</FONT> * <code>IllegalArgumentException</code> is thrown)</li><a name="line.176"></a> <FONT color="green">177</FONT> * <li> The result is small enough to fit into a <code>long</code>. The<a name="line.177"></a> <FONT color="green">178</FONT> * largest value of <code>n</code> for which all coefficients are<a name="line.178"></a> <FONT color="green">179</FONT> * <code> < Long.MAX_VALUE</code> is 66. If the computed value exceeds<a name="line.179"></a> <FONT color="green">180</FONT> * <code>Long.MAX_VALUE</code> an <code>ArithMeticException</code> is<a name="line.180"></a> <FONT color="green">181</FONT> * thrown.</li><a name="line.181"></a> <FONT color="green">182</FONT> * </ul></p><a name="line.182"></a> <FONT color="green">183</FONT> *<a name="line.183"></a> <FONT color="green">184</FONT> * @param n the size of the set<a name="line.184"></a> <FONT color="green">185</FONT> * @param k the size of the subsets to be counted<a name="line.185"></a> <FONT color="green">186</FONT> * @return <code>n choose k</code><a name="line.186"></a> <FONT color="green">187</FONT> * @throws IllegalArgumentException if preconditions are not met.<a name="line.187"></a> <FONT color="green">188</FONT> * @throws ArithmeticException if the result is too large to be represented<a name="line.188"></a> <FONT color="green">189</FONT> * by a long integer.<a name="line.189"></a> <FONT color="green">190</FONT> */<a name="line.190"></a> <FONT color="green">191</FONT> public static long binomialCoefficient(final int n, final int k) {<a name="line.191"></a> <FONT color="green">192</FONT> checkBinomial(n, k);<a name="line.192"></a> <FONT color="green">193</FONT> if ((n == k) || (k == 0)) {<a name="line.193"></a> <FONT color="green">194</FONT> return 1;<a name="line.194"></a> <FONT color="green">195</FONT> }<a name="line.195"></a> <FONT color="green">196</FONT> if ((k == 1) || (k == n - 1)) {<a name="line.196"></a> <FONT color="green">197</FONT> return n;<a name="line.197"></a> <FONT color="green">198</FONT> }<a name="line.198"></a> <FONT color="green">199</FONT> // Use symmetry for large k<a name="line.199"></a> <FONT color="green">200</FONT> if (k > n / 2)<a name="line.200"></a> <FONT color="green">201</FONT> return binomialCoefficient(n, n - k);<a name="line.201"></a> <FONT color="green">202</FONT> <a name="line.202"></a> <FONT color="green">203</FONT> // We use the formula<a name="line.203"></a> <FONT color="green">204</FONT> // (n choose k) = n! / (n-k)! / k!<a name="line.204"></a> <FONT color="green">205</FONT> // (n choose k) == ((n-k+1)*...*n) / (1*...*k)<a name="line.205"></a> <FONT color="green">206</FONT> // which could be written<a name="line.206"></a> <FONT color="green">207</FONT> // (n choose k) == (n-1 choose k-1) * n / k<a name="line.207"></a> <FONT color="green">208</FONT> long result = 1;<a name="line.208"></a> <FONT color="green">209</FONT> if (n <= 61) {<a name="line.209"></a> <FONT color="green">210</FONT> // For n <= 61, the naive implementation cannot overflow.<a name="line.210"></a> <FONT color="green">211</FONT> int i = n - k + 1;<a name="line.211"></a> <FONT color="green">212</FONT> for (int j = 1; j <= k; j++) {<a name="line.212"></a> <FONT color="green">213</FONT> result = result * i / j;<a name="line.213"></a> <FONT color="green">214</FONT> i++;<a name="line.214"></a> <FONT color="green">215</FONT> }<a name="line.215"></a> <FONT color="green">216</FONT> } else if (n <= 66) {<a name="line.216"></a> <FONT color="green">217</FONT> // For n > 61 but n <= 66, the result cannot overflow,<a name="line.217"></a> <FONT color="green">218</FONT> // but we must take care not to overflow intermediate values.<a name="line.218"></a> <FONT color="green">219</FONT> int i = n - k + 1;<a name="line.219"></a> <FONT color="green">220</FONT> for (int j = 1; j <= k; j++) {<a name="line.220"></a> <FONT color="green">221</FONT> // We know that (result * i) is divisible by j,<a name="line.221"></a> <FONT color="green">222</FONT> // but (result * i) may overflow, so we split j:<a name="line.222"></a> <FONT color="green">223</FONT> // Filter out the gcd, d, so j/d and i/d are integer.<a name="line.223"></a> <FONT color="green">224</FONT> // result is divisible by (j/d) because (j/d)<a name="line.224"></a> <FONT color="green">225</FONT> // is relative prime to (i/d) and is a divisor of<a name="line.225"></a> <FONT color="green">226</FONT> // result * (i/d).<a name="line.226"></a> <FONT color="green">227</FONT> final long d = gcd(i, j);<a name="line.227"></a> <FONT color="green">228</FONT> result = (result / (j / d)) * (i / d);<a name="line.228"></a> <FONT color="green">229</FONT> i++;<a name="line.229"></a> <FONT color="green">230</FONT> }<a name="line.230"></a> <FONT color="green">231</FONT> } else {<a name="line.231"></a> <FONT color="green">232</FONT> // For n > 66, a result overflow might occur, so we check<a name="line.232"></a> <FONT color="green">233</FONT> // the multiplication, taking care to not overflow<a name="line.233"></a> <FONT color="green">234</FONT> // unnecessary.<a name="line.234"></a> <FONT color="green">235</FONT> int i = n - k + 1;<a name="line.235"></a> <FONT color="green">236</FONT> for (int j = 1; j <= k; j++) {<a name="line.236"></a> <FONT color="green">237</FONT> final long d = gcd(i, j);<a name="line.237"></a> <FONT color="green">238</FONT> result = mulAndCheck(result / (j / d), i / d);<a name="line.238"></a> <FONT color="green">239</FONT> i++;<a name="line.239"></a> <FONT color="green">240</FONT> }<a name="line.240"></a> <FONT color="green">241</FONT> }<a name="line.241"></a> <FONT color="green">242</FONT> return result;<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> /**<a name="line.245"></a> <FONT color="green">246</FONT> * Returns a <code>double</code> representation of the <a<a name="line.246"></a> <FONT color="green">247</FONT> * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial<a name="line.247"></a> <FONT color="green">248</FONT> * Coefficient</a>, "<code>n choose k</code>", the number of<a name="line.248"></a> <FONT color="green">249</FONT> * <code>k</code>-element subsets that can be selected from an<a name="line.249"></a> <FONT color="green">250</FONT> * <code>n</code>-element set.<a name="line.250"></a> <FONT color="green">251</FONT> * <p><a name="line.251"></a> <FONT color="green">252</FONT> * <Strong>Preconditions</strong>:<a name="line.252"></a> <FONT color="green">253</FONT> * <ul><a name="line.253"></a> <FONT color="green">254</FONT> * <li> <code>0 <= k <= n </code> (otherwise<a name="line.254"></a> <FONT color="green">255</FONT> * <code>IllegalArgumentException</code> is thrown)</li><a name="line.255"></a> <FONT color="green">256</FONT> * <li> The result is small enough to fit into a <code>double</code>. The<a name="line.256"></a> <FONT color="green">257</FONT> * largest value of <code>n</code> for which all coefficients are <<a name="line.257"></a> <FONT color="green">258</FONT> * Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE,<a name="line.258"></a> <FONT color="green">259</FONT> * Double.POSITIVE_INFINITY is returned</li><a name="line.259"></a> <FONT color="green">260</FONT> * </ul></p><a name="line.260"></a> <FONT color="green">261</FONT> *<a name="line.261"></a> <FONT color="green">262</FONT> * @param n the size of the set<a name="line.262"></a> <FONT color="green">263</FONT> * @param k the size of the subsets to be counted<a name="line.263"></a> <FONT color="green">264</FONT> * @return <code>n choose k</code><a name="line.264"></a> <FONT color="green">265</FONT> * @throws IllegalArgumentException if preconditions are not met.<a name="line.265"></a> <FONT color="green">266</FONT> */<a name="line.266"></a> <FONT color="green">267</FONT> public static double binomialCoefficientDouble(final int n, final int k) {<a name="line.267"></a> <FONT color="green">268</FONT> checkBinomial(n, k);<a name="line.268"></a> <FONT color="green">269</FONT> if ((n == k) || (k == 0)) {<a name="line.269"></a> <FONT color="green">270</FONT> return 1d;<a name="line.270"></a> <FONT color="green">271</FONT> }<a name="line.271"></a> <FONT color="green">272</FONT> if ((k == 1) || (k == n - 1)) {<a name="line.272"></a> <FONT color="green">273</FONT> return n;<a name="line.273"></a> <FONT color="green">274</FONT> }<a name="line.274"></a> <FONT color="green">275</FONT> if (k > n/2) {<a name="line.275"></a> <FONT color="green">276</FONT> return binomialCoefficientDouble(n, n - k);<a name="line.276"></a> <FONT color="green">277</FONT> }<a name="line.277"></a> <FONT color="green">278</FONT> if (n < 67) {<a name="line.278"></a> <FONT color="green">279</FONT> return binomialCoefficient(n,k);<a name="line.279"></a> <FONT color="green">280</FONT> }<a name="line.280"></a> <FONT color="green">281</FONT> <a name="line.281"></a> <FONT color="green">282</FONT> double result = 1d;<a name="line.282"></a> <FONT color="green">283</FONT> for (int i = 1; i <= k; i++) {<a name="line.283"></a> <FONT color="green">284</FONT> result *= (double)(n - k + i) / (double)i;<a name="line.284"></a> <FONT color="green">285</FONT> }<a name="line.285"></a> <FONT color="green">286</FONT> <a name="line.286"></a> <FONT color="green">287</FONT> return Math.floor(result + 0.5);<a name="line.287"></a> <FONT color="green">288</FONT> }<a name="line.288"></a> <FONT color="green">289</FONT> <a name="line.289"></a> <FONT color="green">290</FONT> /**<a name="line.290"></a> <FONT color="green">291</FONT> * Returns the natural <code>log</code> of the <a<a name="line.291"></a> <FONT color="green">292</FONT> * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial<a name="line.292"></a> <FONT color="green">293</FONT> * Coefficient</a>, "<code>n choose k</code>", the number of<a name="line.293"></a> <FONT color="green">294</FONT> * <code>k</code>-element subsets that can be selected from an<a name="line.294"></a> <FONT color="green">295</FONT> * <code>n</code>-element set.<a name="line.295"></a> <FONT color="green">296</FONT> * <p><a name="line.296"></a> <FONT color="green">297</FONT> * <Strong>Preconditions</strong>:<a name="line.297"></a> <FONT color="green">298</FONT> * <ul><a name="line.298"></a> <FONT color="green">299</FONT> * <li> <code>0 <= k <= n </code> (otherwise<a name="line.299"></a> <FONT color="green">300</FONT> * <code>IllegalArgumentException</code> is thrown)</li><a name="line.300"></a> <FONT color="green">301</FONT> * </ul></p><a name="line.301"></a> <FONT color="green">302</FONT> *<a name="line.302"></a> <FONT color="green">303</FONT> * @param n the size of the set<a name="line.303"></a> <FONT color="green">304</FONT> * @param k the size of the subsets to be counted<a name="line.304"></a> <FONT color="green">305</FONT> * @return <code>n choose k</code><a name="line.305"></a> <FONT color="green">306</FONT> * @throws IllegalArgumentException if preconditions are not met.<a name="line.306"></a> <FONT color="green">307</FONT> */<a name="line.307"></a> <FONT color="green">308</FONT> public static double binomialCoefficientLog(final int n, final int k) {<a name="line.308"></a> <FONT color="green">309</FONT> checkBinomial(n, k);<a name="line.309"></a> <FONT color="green">310</FONT> if ((n == k) || (k == 0)) {<a name="line.310"></a> <FONT color="green">311</FONT> return 0;<a name="line.311"></a> <FONT color="green">312</FONT> }<a name="line.312"></a> <FONT color="green">313</FONT> if ((k == 1) || (k == n - 1)) {<a name="line.313"></a> <FONT color="green">314</FONT> return Math.log(n);<a name="line.314"></a> <FONT color="green">315</FONT> }<a name="line.315"></a> <FONT color="green">316</FONT> <a name="line.316"></a> <FONT color="green">317</FONT> /*<a name="line.317"></a> <FONT color="green">318</FONT> * For values small enough to do exact integer computation,<a name="line.318"></a> <FONT color="green">319</FONT> * return the log of the exact value<a name="line.319"></a> <FONT color="green">320</FONT> */<a name="line.320"></a> <FONT color="green">321</FONT> if (n < 67) {<a name="line.321"></a> <FONT color="green">322</FONT> return Math.log(binomialCoefficient(n,k));<a name="line.322"></a> <FONT color="green">323</FONT> }<a name="line.323"></a> <FONT color="green">324</FONT> <a name="line.324"></a> <FONT color="green">325</FONT> /*<a name="line.325"></a> <FONT color="green">326</FONT> * Return the log of binomialCoefficientDouble for values that will not<a name="line.326"></a> <FONT color="green">327</FONT> * overflow binomialCoefficientDouble<a name="line.327"></a> <FONT color="green">328</FONT> */<a name="line.328"></a> <FONT color="green">329</FONT> if (n < 1030) {<a name="line.329"></a> <FONT color="green">330</FONT> return Math.log(binomialCoefficientDouble(n, k));<a name="line.330"></a> <FONT color="green">331</FONT> }<a name="line.331"></a> <FONT color="green">332</FONT> <a name="line.332"></a> <FONT color="green">333</FONT> if (k > n / 2) {<a name="line.333"></a> <FONT color="green">334</FONT> return binomialCoefficientLog(n, n - k);<a name="line.334"></a> <FONT color="green">335</FONT> }<a name="line.335"></a> <FONT color="green">336</FONT> <a name="line.336"></a> <FONT color="green">337</FONT> /*<a name="line.337"></a> <FONT color="green">338</FONT> * Sum logs for values that could overflow<a name="line.338"></a> <FONT color="green">339</FONT> */<a name="line.339"></a> <FONT color="green">340</FONT> double logSum = 0;<a name="line.340"></a> <FONT color="green">341</FONT> <a name="line.341"></a> <FONT color="green">342</FONT> // n!/(n-k)!<a name="line.342"></a> <FONT color="green">343</FONT> for (int i = n - k + 1; i <= n; i++) {<a name="line.343"></a> <FONT color="green">344</FONT> logSum += Math.log(i);<a name="line.344"></a> <FONT color="green">345</FONT> }<a name="line.345"></a> <FONT color="green">346</FONT> <a name="line.346"></a> <FONT color="green">347</FONT> // divide by k!<a name="line.347"></a> <FONT color="green">348</FONT> for (int i = 2; i <= k; i++) {<a name="line.348"></a> <FONT color="green">349</FONT> logSum -= Math.log(i);<a name="line.349"></a> <FONT color="green">350</FONT> }<a name="line.350"></a> <FONT color="green">351</FONT> <a name="line.351"></a> <FONT color="green">352</FONT> return logSum;<a name="line.352"></a> <FONT color="green">353</FONT> }<a name="line.353"></a> <FONT color="green">354</FONT> <a name="line.354"></a> <FONT color="green">355</FONT> /**<a name="line.355"></a> <FONT color="green">356</FONT> * Check binomial preconditions.<a name="line.356"></a> <FONT color="green">357</FONT> * @param n the size of the set<a name="line.357"></a> <FONT color="green">358</FONT> * @param k the size of the subsets to be counted<a name="line.358"></a> <FONT color="green">359</FONT> * @exception IllegalArgumentException if preconditions are not met.<a name="line.359"></a> <FONT color="green">360</FONT> */<a name="line.360"></a> <FONT color="green">361</FONT> private static void checkBinomial(final int n, final int k)<a name="line.361"></a> <FONT color="green">362</FONT> throws IllegalArgumentException {<a name="line.362"></a> <FONT color="green">363</FONT> if (n < k) {<a name="line.363"></a> <FONT color="green">364</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.364"></a> <FONT color="green">365</FONT> "must have n >= k for binomial coefficient (n,k), got n = {0}, k = {1}",<a name="line.365"></a> <FONT color="green">366</FONT> n, k);<a name="line.366"></a> <FONT color="green">367</FONT> }<a name="line.367"></a> <FONT color="green">368</FONT> if (n < 0) {<a name="line.368"></a> <FONT color="green">369</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.369"></a> <FONT color="green">370</FONT> "must have n >= 0 for binomial coefficient (n,k), got n = {0}",<a name="line.370"></a> <FONT color="green">371</FONT> n);<a name="line.371"></a> <FONT color="green">372</FONT> }<a name="line.372"></a> <FONT color="green">373</FONT> }<a name="line.373"></a> <FONT color="green">374</FONT> <a name="line.374"></a> <FONT color="green">375</FONT> /**<a name="line.375"></a> <FONT color="green">376</FONT> * Compares two numbers given some amount of allowed error.<a name="line.376"></a> <FONT color="green">377</FONT> *<a name="line.377"></a> <FONT color="green">378</FONT> * @param x the first number<a name="line.378"></a> <FONT color="green">379</FONT> * @param y the second number<a name="line.379"></a> <FONT color="green">380</FONT> * @param eps the amount of error to allow when checking for equality<a name="line.380"></a> <FONT color="green">381</FONT> * @return <ul><li>0 if {@link #equals(double, double, double) equals(x, y, eps)}</li><a name="line.381"></a> <FONT color="green">382</FONT> * <li>&lt; 0 if !{@link #equals(double, double, double) equals(x, y, eps)} &amp;&amp; x &lt; y</li><a name="line.382"></a> <FONT color="green">383</FONT> * <li>> 0 if !{@link #equals(double, double, double) equals(x, y, eps)} &amp;&amp; x > y</li></ul><a name="line.383"></a> <FONT color="green">384</FONT> */<a name="line.384"></a> <FONT color="green">385</FONT> public static int compareTo(double x, double y, double eps) {<a name="line.385"></a> <FONT color="green">386</FONT> if (equals(x, y, eps)) {<a name="line.386"></a> <FONT color="green">387</FONT> return 0;<a name="line.387"></a> <FONT color="green">388</FONT> } else if (x < y) {<a name="line.388"></a> <FONT color="green">389</FONT> return -1;<a name="line.389"></a> <FONT color="green">390</FONT> }<a name="line.390"></a> <FONT color="green">391</FONT> return 1;<a name="line.391"></a> <FONT color="green">392</FONT> }<a name="line.392"></a> <FONT color="green">393</FONT> <a name="line.393"></a> <FONT color="green">394</FONT> /**<a name="line.394"></a> <FONT color="green">395</FONT> * Returns the <a href="http://mathworld.wolfram.com/HyperbolicCosine.html"><a name="line.395"></a> <FONT color="green">396</FONT> * hyperbolic cosine</a> of x.<a name="line.396"></a> <FONT color="green">397</FONT> *<a name="line.397"></a> <FONT color="green">398</FONT> * @param x double value for which to find the hyperbolic cosine<a name="line.398"></a> <FONT color="green">399</FONT> * @return hyperbolic cosine of x<a name="line.399"></a> <FONT color="green">400</FONT> */<a name="line.400"></a> <FONT color="green">401</FONT> public static double cosh(double x) {<a name="line.401"></a> <FONT color="green">402</FONT> return (Math.exp(x) + Math.exp(-x)) / 2.0;<a name="line.402"></a> <FONT color="green">403</FONT> }<a name="line.403"></a> <FONT color="green">404</FONT> <a name="line.404"></a> <FONT color="green">405</FONT> /**<a name="line.405"></a> <FONT color="green">406</FONT> * Returns true iff both arguments are NaN or neither is NaN and they are<a name="line.406"></a> <FONT color="green">407</FONT> * equal<a name="line.407"></a> <FONT color="green">408</FONT> *<a name="line.408"></a> <FONT color="green">409</FONT> * @param x first value<a name="line.409"></a> <FONT color="green">410</FONT> * @param y second value<a name="line.410"></a> <FONT color="green">411</FONT> * @return true if the values are equal or both are NaN<a name="line.411"></a> <FONT color="green">412</FONT> */<a name="line.412"></a> <FONT color="green">413</FONT> public static boolean equals(double x, double y) {<a name="line.413"></a> <FONT color="green">414</FONT> return (Double.isNaN(x) && Double.isNaN(y)) || x == y;<a name="line.414"></a> <FONT color="green">415</FONT> }<a name="line.415"></a> <FONT color="green">416</FONT> <a name="line.416"></a> <FONT color="green">417</FONT> /**<a name="line.417"></a> <FONT color="green">418</FONT> * Returns true iff both arguments are equal or within the range of allowed<a name="line.418"></a> <FONT color="green">419</FONT> * error (inclusive).<a name="line.419"></a> <FONT color="green">420</FONT> * <p><a name="line.420"></a> <FONT color="green">421</FONT> * Two NaNs are considered equals, as are two infinities with same sign.<a name="line.421"></a> <FONT color="green">422</FONT> * </p><a name="line.422"></a> <FONT color="green">423</FONT> *<a name="line.423"></a> <FONT color="green">424</FONT> * @param x first value<a name="line.424"></a> <FONT color="green">425</FONT> * @param y second value<a name="line.425"></a> <FONT color="green">426</FONT> * @param eps the amount of absolute error to allow<a name="line.426"></a> <FONT color="green">427</FONT> * @return true if the values are equal or within range of each other<a name="line.427"></a> <FONT color="green">428</FONT> */<a name="line.428"></a> <FONT color="green">429</FONT> public static boolean equals(double x, double y, double eps) {<a name="line.429"></a> <FONT color="green">430</FONT> return equals(x, y) || (Math.abs(y - x) <= eps);<a name="line.430"></a> <FONT color="green">431</FONT> }<a name="line.431"></a> <FONT color="green">432</FONT> <a name="line.432"></a> <FONT color="green">433</FONT> /**<a name="line.433"></a> <FONT color="green">434</FONT> * Returns true iff both arguments are equal or within the range of allowed<a name="line.434"></a> <FONT color="green">435</FONT> * error (inclusive).<a name="line.435"></a> <FONT color="green">436</FONT> * Adapted from <a<a name="line.436"></a> <FONT color="green">437</FONT> * href="http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"><a name="line.437"></a> <FONT color="green">438</FONT> * Bruce Dawson</a><a name="line.438"></a> <FONT color="green">439</FONT> *<a name="line.439"></a> <FONT color="green">440</FONT> * @param x first value<a name="line.440"></a> <FONT color="green">441</FONT> * @param y second value<a name="line.441"></a> <FONT color="green">442</FONT> * @param maxUlps {@code (maxUlps - 1)} is the number of floating point<a name="line.442"></a> <FONT color="green">443</FONT> * values between {@code x} and {@code y}.<a name="line.443"></a> <FONT color="green">444</FONT> * @return {@code true} if there are less than {@code maxUlps} floating<a name="line.444"></a> <FONT color="green">445</FONT> * point values between {@code x} and {@code y}<a name="line.445"></a> <FONT color="green">446</FONT> */<a name="line.446"></a> <FONT color="green">447</FONT> public static boolean equals(double x, double y, int maxUlps) {<a name="line.447"></a> <FONT color="green">448</FONT> // Check that "maxUlps" is non-negative and small enough so that the<a name="line.448"></a> <FONT color="green">449</FONT> // default NAN won't compare as equal to anything.<a name="line.449"></a> <FONT color="green">450</FONT> assert maxUlps > 0 && maxUlps < NAN_GAP;<a name="line.450"></a> <FONT color="green">451</FONT> <a name="line.451"></a> <FONT color="green">452</FONT> long xInt = Double.doubleToLongBits(x);<a name="line.452"></a> <FONT color="green">453</FONT> long yInt = Double.doubleToLongBits(y);<a name="line.453"></a> <FONT color="green">454</FONT> <a name="line.454"></a> <FONT color="green">455</FONT> // Make lexicographically ordered as a two's-complement integer.<a name="line.455"></a> <FONT color="green">456</FONT> if (xInt < 0) {<a name="line.456"></a> <FONT color="green">457</FONT> xInt = SGN_MASK - xInt;<a name="line.457"></a> <FONT color="green">458</FONT> }<a name="line.458"></a> <FONT color="green">459</FONT> if (yInt < 0) {<a name="line.459"></a> <FONT color="green">460</FONT> yInt = SGN_MASK - yInt;<a name="line.460"></a> <FONT color="green">461</FONT> }<a name="line.461"></a> <FONT color="green">462</FONT> <a name="line.462"></a> <FONT color="green">463</FONT> return Math.abs(xInt - yInt) <= maxUlps;<a name="line.463"></a> <FONT color="green">464</FONT> }<a name="line.464"></a> <FONT color="green">465</FONT> <a name="line.465"></a> <FONT color="green">466</FONT> /**<a name="line.466"></a> <FONT color="green">467</FONT> * Returns true iff both arguments are null or have same dimensions<a name="line.467"></a> <FONT color="green">468</FONT> * and all their elements are {@link #equals(double,double) equals}<a name="line.468"></a> <FONT color="green">469</FONT> *<a name="line.469"></a> <FONT color="green">470</FONT> * @param x first array<a name="line.470"></a> <FONT color="green">471</FONT> * @param y second array<a name="line.471"></a> <FONT color="green">472</FONT> * @return true if the values are both null or have same dimension<a name="line.472"></a> <FONT color="green">473</FONT> * and equal elements<a name="line.473"></a> <FONT color="green">474</FONT> * @since 1.2<a name="line.474"></a> <FONT color="green">475</FONT> */<a name="line.475"></a> <FONT color="green">476</FONT> public static boolean equals(double[] x, double[] y) {<a name="line.476"></a> <FONT color="green">477</FONT> if ((x == null) || (y == null)) {<a name="line.477"></a> <FONT color="green">478</FONT> return !((x == null) ^ (y == null));<a name="line.478"></a> <FONT color="green">479</FONT> }<a name="line.479"></a> <FONT color="green">480</FONT> if (x.length != y.length) {<a name="line.480"></a> <FONT color="green">481</FONT> return false;<a name="line.481"></a> <FONT color="green">482</FONT> }<a name="line.482"></a> <FONT color="green">483</FONT> for (int i = 0; i < x.length; ++i) {<a name="line.483"></a> <FONT color="green">484</FONT> if (!equals(x[i], y[i])) {<a name="line.484"></a> <FONT color="green">485</FONT> return false;<a name="line.485"></a> <FONT color="green">486</FONT> }<a name="line.486"></a> <FONT color="green">487</FONT> }<a name="line.487"></a> <FONT color="green">488</FONT> return true;<a name="line.488"></a> <FONT color="green">489</FONT> }<a name="line.489"></a> <FONT color="green">490</FONT> <a name="line.490"></a> <FONT color="green">491</FONT> /**<a name="line.491"></a> <FONT color="green">492</FONT> * Returns n!. Shorthand for <code>n</code> <a<a name="line.492"></a> <FONT color="green">493</FONT> * href="http://mathworld.wolfram.com/Factorial.html"> Factorial</a>, the<a name="line.493"></a> <FONT color="green">494</FONT> * product of the numbers <code>1,...,n</code>.<a name="line.494"></a> <FONT color="green">495</FONT> * <p><a name="line.495"></a> <FONT color="green">496</FONT> * <Strong>Preconditions</strong>:<a name="line.496"></a> <FONT color="green">497</FONT> * <ul><a name="line.497"></a> <FONT color="green">498</FONT> * <li> <code>n >= 0</code> (otherwise<a name="line.498"></a> <FONT color="green">499</FONT> * <code>IllegalArgumentException</code> is thrown)</li><a name="line.499"></a> <FONT color="green">500</FONT> * <li> The result is small enough to fit into a <code>long</code>. The<a name="line.500"></a> <FONT color="green">501</FONT> * largest value of <code>n</code> for which <code>n!</code> <<a name="line.501"></a> <FONT color="green">502</FONT> * Long.MAX_VALUE</code> is 20. If the computed value exceeds <code>Long.MAX_VALUE</code><a name="line.502"></a> <FONT color="green">503</FONT> * an <code>ArithMeticException </code> is thrown.</li><a name="line.503"></a> <FONT color="green">504</FONT> * </ul><a name="line.504"></a> <FONT color="green">505</FONT> * </p><a name="line.505"></a> <FONT color="green">506</FONT> *<a name="line.506"></a> <FONT color="green">507</FONT> * @param n argument<a name="line.507"></a> <FONT color="green">508</FONT> * @return <code>n!</code><a name="line.508"></a> <FONT color="green">509</FONT> * @throws ArithmeticException if the result is too large to be represented<a name="line.509"></a> <FONT color="green">510</FONT> * by a long integer.<a name="line.510"></a> <FONT color="green">511</FONT> * @throws IllegalArgumentException if n < 0<a name="line.511"></a> <FONT color="green">512</FONT> */<a name="line.512"></a> <FONT color="green">513</FONT> public static long factorial(final int n) {<a name="line.513"></a> <FONT color="green">514</FONT> if (n < 0) {<a name="line.514"></a> <FONT color="green">515</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.515"></a> <FONT color="green">516</FONT> "must have n >= 0 for n!, got n = {0}",<a name="line.516"></a> <FONT color="green">517</FONT> n);<a name="line.517"></a> <FONT color="green">518</FONT> }<a name="line.518"></a> <FONT color="green">519</FONT> if (n > 20) {<a name="line.519"></a> <FONT color="green">520</FONT> throw new ArithmeticException(<a name="line.520"></a> <FONT color="green">521</FONT> "factorial value is too large to fit in a long");<a name="line.521"></a> <FONT color="green">522</FONT> }<a name="line.522"></a> <FONT color="green">523</FONT> return FACTORIALS[n];<a name="line.523"></a> <FONT color="green">524</FONT> }<a name="line.524"></a> <FONT color="green">525</FONT> <a name="line.525"></a> <FONT color="green">526</FONT> /**<a name="line.526"></a> <FONT color="green">527</FONT> * Returns n!. Shorthand for <code>n</code> <a<a name="line.527"></a> <FONT color="green">528</FONT> * href="http://mathworld.wolfram.com/Factorial.html"> Factorial</a>, the<a name="line.528"></a> <FONT color="green">529</FONT> * product of the numbers <code>1,...,n</code> as a <code>double</code>.<a name="line.529"></a> <FONT color="green">530</FONT> * <p><a name="line.530"></a> <FONT color="green">531</FONT> * <Strong>Preconditions</strong>:<a name="line.531"></a> <FONT color="green">532</FONT> * <ul><a name="line.532"></a> <FONT color="green">533</FONT> * <li> <code>n >= 0</code> (otherwise<a name="line.533"></a> <FONT color="green">534</FONT> * <code>IllegalArgumentException</code> is thrown)</li><a name="line.534"></a> <FONT color="green">535</FONT> * <li> The result is small enough to fit into a <code>double</code>. The<a name="line.535"></a> <FONT color="green">536</FONT> * largest value of <code>n</code> for which <code>n!</code> <<a name="line.536"></a> <FONT color="green">537</FONT> * Double.MAX_VALUE</code> is 170. If the computed value exceeds<a name="line.537"></a> <FONT color="green">538</FONT> * Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned</li><a name="line.538"></a> <FONT color="green">539</FONT> * </ul><a name="line.539"></a> <FONT color="green">540</FONT> * </p><a name="line.540"></a> <FONT color="green">541</FONT> *<a name="line.541"></a> <FONT color="green">542</FONT> * @param n argument<a name="line.542"></a> <FONT color="green">543</FONT> * @return <code>n!</code><a name="line.543"></a> <FONT color="green">544</FONT> * @throws IllegalArgumentException if n < 0<a name="line.544"></a> <FONT color="green">545</FONT> */<a name="line.545"></a> <FONT color="green">546</FONT> public static double factorialDouble(final int n) {<a name="line.546"></a> <FONT color="green">547</FONT> if (n < 0) {<a name="line.547"></a> <FONT color="green">548</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.548"></a> <FONT color="green">549</FONT> "must have n >= 0 for n!, got n = {0}",<a name="line.549"></a> <FONT color="green">550</FONT> n);<a name="line.550"></a> <FONT color="green">551</FONT> }<a name="line.551"></a> <FONT color="green">552</FONT> if (n < 21) {<a name="line.552"></a> <FONT color="green">553</FONT> return factorial(n);<a name="line.553"></a> <FONT color="green">554</FONT> }<a name="line.554"></a> <FONT color="green">555</FONT> return Math.floor(Math.exp(factorialLog(n)) + 0.5);<a name="line.555"></a> <FONT color="green">556</FONT> }<a name="line.556"></a> <FONT color="green">557</FONT> <a name="line.557"></a> <FONT color="green">558</FONT> /**<a name="line.558"></a> <FONT color="green">559</FONT> * Returns the natural logarithm of n!.<a name="line.559"></a> <FONT color="green">560</FONT> * <p><a name="line.560"></a> <FONT color="green">561</FONT> * <Strong>Preconditions</strong>:<a name="line.561"></a> <FONT color="green">562</FONT> * <ul><a name="line.562"></a> <FONT color="green">563</FONT> * <li> <code>n >= 0</code> (otherwise<a name="line.563"></a> <FONT color="green">564</FONT> * <code>IllegalArgumentException</code> is thrown)</li><a name="line.564"></a> <FONT color="green">565</FONT> * </ul></p><a name="line.565"></a> <FONT color="green">566</FONT> *<a name="line.566"></a> <FONT color="green">567</FONT> * @param n argument<a name="line.567"></a> <FONT color="green">568</FONT> * @return <code>n!</code><a name="line.568"></a> <FONT color="green">569</FONT> * @throws IllegalArgumentException if preconditions are not met.<a name="line.569"></a> <FONT color="green">570</FONT> */<a name="line.570"></a> <FONT color="green">571</FONT> public static double factorialLog(final int n) {<a name="line.571"></a> <FONT color="green">572</FONT> if (n < 0) {<a name="line.572"></a> <FONT color="green">573</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.573"></a> <FONT color="green">574</FONT> "must have n >= 0 for n!, got n = {0}",<a name="line.574"></a> <FONT color="green">575</FONT> n);<a name="line.575"></a> <FONT color="green">576</FONT> }<a name="line.576"></a> <FONT color="green">577</FONT> if (n < 21) {<a name="line.577"></a> <FONT color="green">578</FONT> return Math.log(factorial(n));<a name="line.578"></a> <FONT color="green">579</FONT> }<a name="line.579"></a> <FONT color="green">580</FONT> double logSum = 0;<a name="line.580"></a> <FONT color="green">581</FONT> for (int i = 2; i <= n; i++) {<a name="line.581"></a> <FONT color="green">582</FONT> logSum += Math.log(i);<a name="line.582"></a> <FONT color="green">583</FONT> }<a name="line.583"></a> <FONT color="green">584</FONT> return logSum;<a name="line.584"></a> <FONT color="green">585</FONT> }<a name="line.585"></a> <FONT color="green">586</FONT> <a name="line.586"></a> <FONT color="green">587</FONT> /**<a name="line.587"></a> <FONT color="green">588</FONT> * <p><a name="line.588"></a> <FONT color="green">589</FONT> * Gets the greatest common divisor of the absolute value of two numbers,<a name="line.589"></a> <FONT color="green">590</FONT> * using the "binary gcd" method which avoids division and modulo<a name="line.590"></a> <FONT color="green">591</FONT> * operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef<a name="line.591"></a> <FONT color="green">592</FONT> * Stein (1961).<a name="line.592"></a> <FONT color="green">593</FONT> * </p><a name="line.593"></a> <FONT color="green">594</FONT> * Special cases:<a name="line.594"></a> <FONT color="green">595</FONT> * <ul><a name="line.595"></a> <FONT color="green">596</FONT> * <li>The invocations<a name="line.596"></a> <FONT color="green">597</FONT> * <code>gcd(Integer.MIN_VALUE, Integer.MIN_VALUE)</code>,<a name="line.597"></a> <FONT color="green">598</FONT> * <code>gcd(Integer.MIN_VALUE, 0)</code> and<a name="line.598"></a> <FONT color="green">599</FONT> * <code>gcd(0, Integer.MIN_VALUE)</code> throw an<a name="line.599"></a> <FONT color="green">600</FONT> * <code>ArithmeticException</code>, because the result would be 2^31, which<a name="line.600"></a> <FONT color="green">601</FONT> * is too large for an int value.</li><a name="line.601"></a> <FONT color="green">602</FONT> * <li>The result of <code>gcd(x, x)</code>, <code>gcd(0, x)</code> and<a name="line.602"></a> <FONT color="green">603</FONT> * <code>gcd(x, 0)</code> is the absolute value of <code>x</code>, except<a name="line.603"></a> <FONT color="green">604</FONT> * for the special cases above.<a name="line.604"></a> <FONT color="green">605</FONT> * <li>The invocation <code>gcd(0, 0)</code> is the only one which returns<a name="line.605"></a> <FONT color="green">606</FONT> * <code>0</code>.</li><a name="line.606"></a> <FONT color="green">607</FONT> * </ul><a name="line.607"></a> <FONT color="green">608</FONT> *<a name="line.608"></a> <FONT color="green">609</FONT> * @param p any number<a name="line.609"></a> <FONT color="green">610</FONT> * @param q any number<a name="line.610"></a> <FONT color="green">611</FONT> * @return the greatest common divisor, never negative<a name="line.611"></a> <FONT color="green">612</FONT> * @throws ArithmeticException if the result cannot be represented as a<a name="line.612"></a> <FONT color="green">613</FONT> * nonnegative int value<a name="line.613"></a> <FONT color="green">614</FONT> * @since 1.1<a name="line.614"></a> <FONT color="green">615</FONT> */<a name="line.615"></a> <FONT color="green">616</FONT> public static int gcd(final int p, final int q) {<a name="line.616"></a> <FONT color="green">617</FONT> int u = p;<a name="line.617"></a> <FONT color="green">618</FONT> int v = q;<a name="line.618"></a> <FONT color="green">619</FONT> if ((u == 0) || (v == 0)) {<a name="line.619"></a> <FONT color="green">620</FONT> if ((u == Integer.MIN_VALUE) || (v == Integer.MIN_VALUE)) {<a name="line.620"></a> <FONT color="green">621</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.621"></a> <FONT color="green">622</FONT> "overflow: gcd({0}, {1}) is 2^31",<a name="line.622"></a> <FONT color="green">623</FONT> p, q);<a name="line.623"></a> <FONT color="green">624</FONT> }<a name="line.624"></a> <FONT color="green">625</FONT> return Math.abs(u) + Math.abs(v);<a name="line.625"></a> <FONT color="green">626</FONT> }<a name="line.626"></a> <FONT color="green">627</FONT> // keep u and v negative, as negative integers range down to<a name="line.627"></a> <FONT color="green">628</FONT> // -2^31, while positive numbers can only be as large as 2^31-1<a name="line.628"></a> <FONT color="green">629</FONT> // (i.e. we can't necessarily negate a negative number without<a name="line.629"></a> <FONT color="green">630</FONT> // overflow)<a name="line.630"></a> <FONT color="green">631</FONT> /* assert u!=0 && v!=0; */<a name="line.631"></a> <FONT color="green">632</FONT> if (u > 0) {<a name="line.632"></a> <FONT color="green">633</FONT> u = -u;<a name="line.633"></a> <FONT color="green">634</FONT> } // make u negative<a name="line.634"></a> <FONT color="green">635</FONT> if (v > 0) {<a name="line.635"></a> <FONT color="green">636</FONT> v = -v;<a name="line.636"></a> <FONT color="green">637</FONT> } // make v negative<a name="line.637"></a> <FONT color="green">638</FONT> // B1. [Find power of 2]<a name="line.638"></a> <FONT color="green">639</FONT> int k = 0;<a name="line.639"></a> <FONT color="green">640</FONT> while ((u & 1) == 0 && (v & 1) == 0 && k < 31) { // while u and v are<a name="line.640"></a> <FONT color="green">641</FONT> // both even...<a name="line.641"></a> <FONT color="green">642</FONT> u /= 2;<a name="line.642"></a> <FONT color="green">643</FONT> v /= 2;<a name="line.643"></a> <FONT color="green">644</FONT> k++; // cast out twos.<a name="line.644"></a> <FONT color="green">645</FONT> }<a name="line.645"></a> <FONT color="green">646</FONT> if (k == 31) {<a name="line.646"></a> <FONT color="green">647</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.647"></a> <FONT color="green">648</FONT> "overflow: gcd({0}, {1}) is 2^31",<a name="line.648"></a> <FONT color="green">649</FONT> p, q);<a name="line.649"></a> <FONT color="green">650</FONT> }<a name="line.650"></a> <FONT color="green">651</FONT> // B2. Initialize: u and v have been divided by 2^k and at least<a name="line.651"></a> <FONT color="green">652</FONT> // one is odd.<a name="line.652"></a> <FONT color="green">653</FONT> int t = ((u & 1) == 1) ? v : -(u / 2)/* B3 */;<a name="line.653"></a> <FONT color="green">654</FONT> // t negative: u was odd, v may be even (t replaces v)<a name="line.654"></a> <FONT color="green">655</FONT> // t positive: u was even, v is odd (t replaces u)<a name="line.655"></a> <FONT color="green">656</FONT> do {<a name="line.656"></a> <FONT color="green">657</FONT> /* assert u<0 && v<0; */<a name="line.657"></a> <FONT color="green">658</FONT> // B4/B3: cast out twos from t.<a name="line.658"></a> <FONT color="green">659</FONT> while ((t & 1) == 0) { // while t is even..<a name="line.659"></a> <FONT color="green">660</FONT> t /= 2; // cast out twos<a name="line.660"></a> <FONT color="green">661</FONT> }<a name="line.661"></a> <FONT color="green">662</FONT> // B5 [reset max(u,v)]<a name="line.662"></a> <FONT color="green">663</FONT> if (t > 0) {<a name="line.663"></a> <FONT color="green">664</FONT> u = -t;<a name="line.664"></a> <FONT color="green">665</FONT> } else {<a name="line.665"></a> <FONT color="green">666</FONT> v = t;<a name="line.666"></a> <FONT color="green">667</FONT> }<a name="line.667"></a> <FONT color="green">668</FONT> // B6/B3. at this point both u and v should be odd.<a name="line.668"></a> <FONT color="green">669</FONT> t = (v - u) / 2;<a name="line.669"></a> <FONT color="green">670</FONT> // |u| larger: t positive (replace u)<a name="line.670"></a> <FONT color="green">671</FONT> // |v| larger: t negative (replace v)<a name="line.671"></a> <FONT color="green">672</FONT> } while (t != 0);<a name="line.672"></a> <FONT color="green">673</FONT> return -u * (1 << k); // gcd is u*2^k<a name="line.673"></a> <FONT color="green">674</FONT> }<a name="line.674"></a> <FONT color="green">675</FONT> <a name="line.675"></a> <FONT color="green">676</FONT> /**<a name="line.676"></a> <FONT color="green">677</FONT> * <p><a name="line.677"></a> <FONT color="green">678</FONT> * Gets the greatest common divisor of the absolute value of two numbers,<a name="line.678"></a> <FONT color="green">679</FONT> * using the "binary gcd" method which avoids division and modulo<a name="line.679"></a> <FONT color="green">680</FONT> * operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef<a name="line.680"></a> <FONT color="green">681</FONT> * Stein (1961).<a name="line.681"></a> <FONT color="green">682</FONT> * </p><a name="line.682"></a> <FONT color="green">683</FONT> * Special cases:<a name="line.683"></a> <FONT color="green">684</FONT> * <ul><a name="line.684"></a> <FONT color="green">685</FONT> * <li>The invocations<a name="line.685"></a> <FONT color="green">686</FONT> * <code>gcd(Long.MIN_VALUE, Long.MIN_VALUE)</code>,<a name="line.686"></a> <FONT color="green">687</FONT> * <code>gcd(Long.MIN_VALUE, 0L)</code> and<a name="line.687"></a> <FONT color="green">688</FONT> * <code>gcd(0L, Long.MIN_VALUE)</code> throw an<a name="line.688"></a> <FONT color="green">689</FONT> * <code>ArithmeticException</code>, because the result would be 2^63, which<a name="line.689"></a> <FONT color="green">690</FONT> * is too large for a long value.</li><a name="line.690"></a> <FONT color="green">691</FONT> * <li>The result of <code>gcd(x, x)</code>, <code>gcd(0L, x)</code> and<a name="line.691"></a> <FONT color="green">692</FONT> * <code>gcd(x, 0L)</code> is the absolute value of <code>x</code>, except<a name="line.692"></a> <FONT color="green">693</FONT> * for the special cases above.<a name="line.693"></a> <FONT color="green">694</FONT> * <li>The invocation <code>gcd(0L, 0L)</code> is the only one which returns<a name="line.694"></a> <FONT color="green">695</FONT> * <code>0L</code>.</li><a name="line.695"></a> <FONT color="green">696</FONT> * </ul><a name="line.696"></a> <FONT color="green">697</FONT> *<a name="line.697"></a> <FONT color="green">698</FONT> * @param p any number<a name="line.698"></a> <FONT color="green">699</FONT> * @param q any number<a name="line.699"></a> <FONT color="green">700</FONT> * @return the greatest common divisor, never negative<a name="line.700"></a> <FONT color="green">701</FONT> * @throws ArithmeticException if the result cannot be represented as a nonnegative long<a name="line.701"></a> <FONT color="green">702</FONT> * value<a name="line.702"></a> <FONT color="green">703</FONT> * @since 2.1<a name="line.703"></a> <FONT color="green">704</FONT> */<a name="line.704"></a> <FONT color="green">705</FONT> public static long gcd(final long p, final long q) {<a name="line.705"></a> <FONT color="green">706</FONT> long u = p;<a name="line.706"></a> <FONT color="green">707</FONT> long v = q;<a name="line.707"></a> <FONT color="green">708</FONT> if ((u == 0) || (v == 0)) {<a name="line.708"></a> <FONT color="green">709</FONT> if ((u == Long.MIN_VALUE) || (v == Long.MIN_VALUE)){<a name="line.709"></a> <FONT color="green">710</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.710"></a> <FONT color="green">711</FONT> "overflow: gcd({0}, {1}) is 2^63",<a name="line.711"></a> <FONT color="green">712</FONT> p, q);<a name="line.712"></a> <FONT color="green">713</FONT> }<a name="line.713"></a> <FONT color="green">714</FONT> return Math.abs(u) + Math.abs(v);<a name="line.714"></a> <FONT color="green">715</FONT> }<a name="line.715"></a> <FONT color="green">716</FONT> // keep u and v negative, as negative integers range down to<a name="line.716"></a> <FONT color="green">717</FONT> // -2^63, while positive numbers can only be as large as 2^63-1<a name="line.717"></a> <FONT color="green">718</FONT> // (i.e. we can't necessarily negate a negative number without<a name="line.718"></a> <FONT color="green">719</FONT> // overflow)<a name="line.719"></a> <FONT color="green">720</FONT> /* assert u!=0 && v!=0; */<a name="line.720"></a> <FONT color="green">721</FONT> if (u > 0) {<a name="line.721"></a> <FONT color="green">722</FONT> u = -u;<a name="line.722"></a> <FONT color="green">723</FONT> } // make u negative<a name="line.723"></a> <FONT color="green">724</FONT> if (v > 0) {<a name="line.724"></a> <FONT color="green">725</FONT> v = -v;<a name="line.725"></a> <FONT color="green">726</FONT> } // make v negative<a name="line.726"></a> <FONT color="green">727</FONT> // B1. [Find power of 2]<a name="line.727"></a> <FONT color="green">728</FONT> int k = 0;<a name="line.728"></a> <FONT color="green">729</FONT> while ((u & 1) == 0 && (v & 1) == 0 && k < 63) { // while u and v are<a name="line.729"></a> <FONT color="green">730</FONT> // both even...<a name="line.730"></a> <FONT color="green">731</FONT> u /= 2;<a name="line.731"></a> <FONT color="green">732</FONT> v /= 2;<a name="line.732"></a> <FONT color="green">733</FONT> k++; // cast out twos.<a name="line.733"></a> <FONT color="green">734</FONT> }<a name="line.734"></a> <FONT color="green">735</FONT> if (k == 63) {<a name="line.735"></a> <FONT color="green">736</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.736"></a> <FONT color="green">737</FONT> "overflow: gcd({0}, {1}) is 2^63",<a name="line.737"></a> <FONT color="green">738</FONT> p, q);<a name="line.738"></a> <FONT color="green">739</FONT> }<a name="line.739"></a> <FONT color="green">740</FONT> // B2. Initialize: u and v have been divided by 2^k and at least<a name="line.740"></a> <FONT color="green">741</FONT> // one is odd.<a name="line.741"></a> <FONT color="green">742</FONT> long t = ((u & 1) == 1) ? v : -(u / 2)/* B3 */;<a name="line.742"></a> <FONT color="green">743</FONT> // t negative: u was odd, v may be even (t replaces v)<a name="line.743"></a> <FONT color="green">744</FONT> // t positive: u was even, v is odd (t replaces u)<a name="line.744"></a> <FONT color="green">745</FONT> do {<a name="line.745"></a> <FONT color="green">746</FONT> /* assert u<0 && v<0; */<a name="line.746"></a> <FONT color="green">747</FONT> // B4/B3: cast out twos from t.<a name="line.747"></a> <FONT color="green">748</FONT> while ((t & 1) == 0) { // while t is even..<a name="line.748"></a> <FONT color="green">749</FONT> t /= 2; // cast out twos<a name="line.749"></a> <FONT color="green">750</FONT> }<a name="line.750"></a> <FONT color="green">751</FONT> // B5 [reset max(u,v)]<a name="line.751"></a> <FONT color="green">752</FONT> if (t > 0) {<a name="line.752"></a> <FONT color="green">753</FONT> u = -t;<a name="line.753"></a> <FONT color="green">754</FONT> } else {<a name="line.754"></a> <FONT color="green">755</FONT> v = t;<a name="line.755"></a> <FONT color="green">756</FONT> }<a name="line.756"></a> <FONT color="green">757</FONT> // B6/B3. at this point both u and v should be odd.<a name="line.757"></a> <FONT color="green">758</FONT> t = (v - u) / 2;<a name="line.758"></a> <FONT color="green">759</FONT> // |u| larger: t positive (replace u)<a name="line.759"></a> <FONT color="green">760</FONT> // |v| larger: t negative (replace v)<a name="line.760"></a> <FONT color="green">761</FONT> } while (t != 0);<a name="line.761"></a> <FONT color="green">762</FONT> return -u * (1L << k); // gcd is u*2^k<a name="line.762"></a> <FONT color="green">763</FONT> }<a name="line.763"></a> <FONT color="green">764</FONT> <a name="line.764"></a> <FONT color="green">765</FONT> /**<a name="line.765"></a> <FONT color="green">766</FONT> * Returns an integer hash code representing the given double value.<a name="line.766"></a> <FONT color="green">767</FONT> *<a name="line.767"></a> <FONT color="green">768</FONT> * @param value the value to be hashed<a name="line.768"></a> <FONT color="green">769</FONT> * @return the hash code<a name="line.769"></a> <FONT color="green">770</FONT> */<a name="line.770"></a> <FONT color="green">771</FONT> public static int hash(double value) {<a name="line.771"></a> <FONT color="green">772</FONT> return new Double(value).hashCode();<a name="line.772"></a> <FONT color="green">773</FONT> }<a name="line.773"></a> <FONT color="green">774</FONT> <a name="line.774"></a> <FONT color="green">775</FONT> /**<a name="line.775"></a> <FONT color="green">776</FONT> * Returns an integer hash code representing the given double array.<a name="line.776"></a> <FONT color="green">777</FONT> *<a name="line.777"></a> <FONT color="green">778</FONT> * @param value the value to be hashed (may be null)<a name="line.778"></a> <FONT color="green">779</FONT> * @return the hash code<a name="line.779"></a> <FONT color="green">780</FONT> * @since 1.2<a name="line.780"></a> <FONT color="green">781</FONT> */<a name="line.781"></a> <FONT color="green">782</FONT> public static int hash(double[] value) {<a name="line.782"></a> <FONT color="green">783</FONT> return Arrays.hashCode(value);<a name="line.783"></a> <FONT color="green">784</FONT> }<a name="line.784"></a> <FONT color="green">785</FONT> <a name="line.785"></a> <FONT color="green">786</FONT> /**<a name="line.786"></a> <FONT color="green">787</FONT> * For a byte value x, this method returns (byte)(+1) if x >= 0 and<a name="line.787"></a> <FONT color="green">788</FONT> * (byte)(-1) if x < 0.<a name="line.788"></a> <FONT color="green">789</FONT> *<a name="line.789"></a> <FONT color="green">790</FONT> * @param x the value, a byte<a name="line.790"></a> <FONT color="green">791</FONT> * @return (byte)(+1) or (byte)(-1), depending on the sign of x<a name="line.791"></a> <FONT color="green">792</FONT> */<a name="line.792"></a> <FONT color="green">793</FONT> public static byte indicator(final byte x) {<a name="line.793"></a> <FONT color="green">794</FONT> return (x >= ZB) ? PB : NB;<a name="line.794"></a> <FONT color="green">795</FONT> }<a name="line.795"></a> <FONT color="green">796</FONT> <a name="line.796"></a> <FONT color="green">797</FONT> /**<a name="line.797"></a> <FONT color="green">798</FONT> * For a double precision value x, this method returns +1.0 if x >= 0 and<a name="line.798"></a> <FONT color="green">799</FONT> * -1.0 if x < 0. Returns <code>NaN</code> if <code>x</code> is<a name="line.799"></a> <FONT color="green">800</FONT> * <code>NaN</code>.<a name="line.800"></a> <FONT color="green">801</FONT> *<a name="line.801"></a> <FONT color="green">802</FONT> * @param x the value, a double<a name="line.802"></a> <FONT color="green">803</FONT> * @return +1.0 or -1.0, depending on the sign of x<a name="line.803"></a> <FONT color="green">804</FONT> */<a name="line.804"></a> <FONT color="green">805</FONT> public static double indicator(final double x) {<a name="line.805"></a> <FONT color="green">806</FONT> if (Double.isNaN(x)) {<a name="line.806"></a> <FONT color="green">807</FONT> return Double.NaN;<a name="line.807"></a> <FONT color="green">808</FONT> }<a name="line.808"></a> <FONT color="green">809</FONT> return (x >= 0.0) ? 1.0 : -1.0;<a name="line.809"></a> <FONT color="green">810</FONT> }<a name="line.810"></a> <FONT color="green">811</FONT> <a name="line.811"></a> <FONT color="green">812</FONT> /**<a name="line.812"></a> <FONT color="green">813</FONT> * For a float value x, this method returns +1.0F if x >= 0 and -1.0F if x <<a name="line.813"></a> <FONT color="green">814</FONT> * 0. Returns <code>NaN</code> if <code>x</code> is <code>NaN</code>.<a name="line.814"></a> <FONT color="green">815</FONT> *<a name="line.815"></a> <FONT color="green">816</FONT> * @param x the value, a float<a name="line.816"></a> <FONT color="green">817</FONT> * @return +1.0F or -1.0F, depending on the sign of x<a name="line.817"></a> <FONT color="green">818</FONT> */<a name="line.818"></a> <FONT color="green">819</FONT> public static float indicator(final float x) {<a name="line.819"></a> <FONT color="green">820</FONT> if (Float.isNaN(x)) {<a name="line.820"></a> <FONT color="green">821</FONT> return Float.NaN;<a name="line.821"></a> <FONT color="green">822</FONT> }<a name="line.822"></a> <FONT color="green">823</FONT> return (x >= 0.0F) ? 1.0F : -1.0F;<a name="line.823"></a> <FONT color="green">824</FONT> }<a name="line.824"></a> <FONT color="green">825</FONT> <a name="line.825"></a> <FONT color="green">826</FONT> /**<a name="line.826"></a> <FONT color="green">827</FONT> * For an int value x, this method returns +1 if x >= 0 and -1 if x < 0.<a name="line.827"></a> <FONT color="green">828</FONT> *<a name="line.828"></a> <FONT color="green">829</FONT> * @param x the value, an int<a name="line.829"></a> <FONT color="green">830</FONT> * @return +1 or -1, depending on the sign of x<a name="line.830"></a> <FONT color="green">831</FONT> */<a name="line.831"></a> <FONT color="green">832</FONT> public static int indicator(final int x) {<a name="line.832"></a> <FONT color="green">833</FONT> return (x >= 0) ? 1 : -1;<a name="line.833"></a> <FONT color="green">834</FONT> }<a name="line.834"></a> <FONT color="green">835</FONT> <a name="line.835"></a> <FONT color="green">836</FONT> /**<a name="line.836"></a> <FONT color="green">837</FONT> * For a long value x, this method returns +1L if x >= 0 and -1L if x < 0.<a name="line.837"></a> <FONT color="green">838</FONT> *<a name="line.838"></a> <FONT color="green">839</FONT> * @param x the value, a long<a name="line.839"></a> <FONT color="green">840</FONT> * @return +1L or -1L, depending on the sign of x<a name="line.840"></a> <FONT color="green">841</FONT> */<a name="line.841"></a> <FONT color="green">842</FONT> public static long indicator(final long x) {<a name="line.842"></a> <FONT color="green">843</FONT> return (x >= 0L) ? 1L : -1L;<a name="line.843"></a> <FONT color="green">844</FONT> }<a name="line.844"></a> <FONT color="green">845</FONT> <a name="line.845"></a> <FONT color="green">846</FONT> /**<a name="line.846"></a> <FONT color="green">847</FONT> * For a short value x, this method returns (short)(+1) if x >= 0 and<a name="line.847"></a> <FONT color="green">848</FONT> * (short)(-1) if x < 0.<a name="line.848"></a> <FONT color="green">849</FONT> *<a name="line.849"></a> <FONT color="green">850</FONT> * @param x the value, a short<a name="line.850"></a> <FONT color="green">851</FONT> * @return (short)(+1) or (short)(-1), depending on the sign of x<a name="line.851"></a> <FONT color="green">852</FONT> */<a name="line.852"></a> <FONT color="green">853</FONT> public static short indicator(final short x) {<a name="line.853"></a> <FONT color="green">854</FONT> return (x >= ZS) ? PS : NS;<a name="line.854"></a> <FONT color="green">855</FONT> }<a name="line.855"></a> <FONT color="green">856</FONT> <a name="line.856"></a> <FONT color="green">857</FONT> /**<a name="line.857"></a> <FONT color="green">858</FONT> * <p><a name="line.858"></a> <FONT color="green">859</FONT> * Returns the least common multiple of the absolute value of two numbers,<a name="line.859"></a> <FONT color="green">860</FONT> * using the formula <code>lcm(a,b) = (a / gcd(a,b)) * b</code>.<a name="line.860"></a> <FONT color="green">861</FONT> * </p><a name="line.861"></a> <FONT color="green">862</FONT> * Special cases:<a name="line.862"></a> <FONT color="green">863</FONT> * <ul><a name="line.863"></a> <FONT color="green">864</FONT> * <li>The invocations <code>lcm(Integer.MIN_VALUE, n)</code> and<a name="line.864"></a> <FONT color="green">865</FONT> * <code>lcm(n, Integer.MIN_VALUE)</code>, where <code>abs(n)</code> is a<a name="line.865"></a> <FONT color="green">866</FONT> * power of 2, throw an <code>ArithmeticException</code>, because the result<a name="line.866"></a> <FONT color="green">867</FONT> * would be 2^31, which is too large for an int value.</li><a name="line.867"></a> <FONT color="green">868</FONT> * <li>The result of <code>lcm(0, x)</code> and <code>lcm(x, 0)</code> is<a name="line.868"></a> <FONT color="green">869</FONT> * <code>0</code> for any <code>x</code>.<a name="line.869"></a> <FONT color="green">870</FONT> * </ul><a name="line.870"></a> <FONT color="green">871</FONT> *<a name="line.871"></a> <FONT color="green">872</FONT> * @param a any number<a name="line.872"></a> <FONT color="green">873</FONT> * @param b any number<a name="line.873"></a> <FONT color="green">874</FONT> * @return the least common multiple, never negative<a name="line.874"></a> <FONT color="green">875</FONT> * @throws ArithmeticException<a name="line.875"></a> <FONT color="green">876</FONT> * if the result cannot be represented as a nonnegative int<a name="line.876"></a> <FONT color="green">877</FONT> * value<a name="line.877"></a> <FONT color="green">878</FONT> * @since 1.1<a name="line.878"></a> <FONT color="green">879</FONT> */<a name="line.879"></a> <FONT color="green">880</FONT> public static int lcm(int a, int b) {<a name="line.880"></a> <FONT color="green">881</FONT> if (a==0 || b==0){<a name="line.881"></a> <FONT color="green">882</FONT> return 0;<a name="line.882"></a> <FONT color="green">883</FONT> }<a name="line.883"></a> <FONT color="green">884</FONT> int lcm = Math.abs(mulAndCheck(a / gcd(a, b), b));<a name="line.884"></a> <FONT color="green">885</FONT> if (lcm == Integer.MIN_VALUE) {<a name="line.885"></a> <FONT color="green">886</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.886"></a> <FONT color="green">887</FONT> "overflow: lcm({0}, {1}) is 2^31",<a name="line.887"></a> <FONT color="green">888</FONT> a, b);<a name="line.888"></a> <FONT color="green">889</FONT> }<a name="line.889"></a> <FONT color="green">890</FONT> return lcm;<a name="line.890"></a> <FONT color="green">891</FONT> }<a name="line.891"></a> <FONT color="green">892</FONT> <a name="line.892"></a> <FONT color="green">893</FONT> /**<a name="line.893"></a> <FONT color="green">894</FONT> * <p><a name="line.894"></a> <FONT color="green">895</FONT> * Returns the least common multiple of the absolute value of two numbers,<a name="line.895"></a> <FONT color="green">896</FONT> * using the formula <code>lcm(a,b) = (a / gcd(a,b)) * b</code>.<a name="line.896"></a> <FONT color="green">897</FONT> * </p><a name="line.897"></a> <FONT color="green">898</FONT> * Special cases:<a name="line.898"></a> <FONT color="green">899</FONT> * <ul><a name="line.899"></a> <FONT color="green">900</FONT> * <li>The invocations <code>lcm(Long.MIN_VALUE, n)</code> and<a name="line.900"></a> <FONT color="green">901</FONT> * <code>lcm(n, Long.MIN_VALUE)</code>, where <code>abs(n)</code> is a<a name="line.901"></a> <FONT color="green">902</FONT> * power of 2, throw an <code>ArithmeticException</code>, because the result<a name="line.902"></a> <FONT color="green">903</FONT> * would be 2^63, which is too large for an int value.</li><a name="line.903"></a> <FONT color="green">904</FONT> * <li>The result of <code>lcm(0L, x)</code> and <code>lcm(x, 0L)</code> is<a name="line.904"></a> <FONT color="green">905</FONT> * <code>0L</code> for any <code>x</code>.<a name="line.905"></a> <FONT color="green">906</FONT> * </ul><a name="line.906"></a> <FONT color="green">907</FONT> *<a name="line.907"></a> <FONT color="green">908</FONT> * @param a any number<a name="line.908"></a> <FONT color="green">909</FONT> * @param b any number<a name="line.909"></a> <FONT color="green">910</FONT> * @return the least common multiple, never negative<a name="line.910"></a> <FONT color="green">911</FONT> * @throws ArithmeticException if the result cannot be represented as a nonnegative long<a name="line.911"></a> <FONT color="green">912</FONT> * value<a name="line.912"></a> <FONT color="green">913</FONT> * @since 2.1<a name="line.913"></a> <FONT color="green">914</FONT> */<a name="line.914"></a> <FONT color="green">915</FONT> public static long lcm(long a, long b) {<a name="line.915"></a> <FONT color="green">916</FONT> if (a==0 || b==0){<a name="line.916"></a> <FONT color="green">917</FONT> return 0;<a name="line.917"></a> <FONT color="green">918</FONT> }<a name="line.918"></a> <FONT color="green">919</FONT> long lcm = Math.abs(mulAndCheck(a / gcd(a, b), b));<a name="line.919"></a> <FONT color="green">920</FONT> if (lcm == Long.MIN_VALUE){<a name="line.920"></a> <FONT color="green">921</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.921"></a> <FONT color="green">922</FONT> "overflow: lcm({0}, {1}) is 2^63",<a name="line.922"></a> <FONT color="green">923</FONT> a, b);<a name="line.923"></a> <FONT color="green">924</FONT> }<a name="line.924"></a> <FONT color="green">925</FONT> return lcm;<a name="line.925"></a> <FONT color="green">926</FONT> }<a name="line.926"></a> <FONT color="green">927</FONT> <a name="line.927"></a> <FONT color="green">928</FONT> /**<a name="line.928"></a> <FONT color="green">929</FONT> * <p>Returns the<a name="line.929"></a> <FONT color="green">930</FONT> * <a href="http://mathworld.wolfram.com/Logarithm.html">logarithm</a><a name="line.930"></a> <FONT color="green">931</FONT> * for base <code>b</code> of <code>x</code>.<a name="line.931"></a> <FONT color="green">932</FONT> * </p><a name="line.932"></a> <FONT color="green">933</FONT> * <p>Returns <code>NaN<code> if either argument is negative. If<a name="line.933"></a> <FONT color="green">934</FONT> * <code>base</code> is 0 and <code>x</code> is positive, 0 is returned.<a name="line.934"></a> <FONT color="green">935</FONT> * If <code>base</code> is positive and <code>x</code> is 0,<a name="line.935"></a> <FONT color="green">936</FONT> * <code>Double.NEGATIVE_INFINITY</code> is returned. If both arguments<a name="line.936"></a> <FONT color="green">937</FONT> * are 0, the result is <code>NaN</code>.</p><a name="line.937"></a> <FONT color="green">938</FONT> *<a name="line.938"></a> <FONT color="green">939</FONT> * @param base the base of the logarithm, must be greater than 0<a name="line.939"></a> <FONT color="green">940</FONT> * @param x argument, must be greater than 0<a name="line.940"></a> <FONT color="green">941</FONT> * @return the value of the logarithm - the number y such that base^y = x.<a name="line.941"></a> <FONT color="green">942</FONT> * @since 1.2<a name="line.942"></a> <FONT color="green">943</FONT> */<a name="line.943"></a> <FONT color="green">944</FONT> public static double log(double base, double x) {<a name="line.944"></a> <FONT color="green">945</FONT> return Math.log(x)/Math.log(base);<a name="line.945"></a> <FONT color="green">946</FONT> }<a name="line.946"></a> <FONT color="green">947</FONT> <a name="line.947"></a> <FONT color="green">948</FONT> /**<a name="line.948"></a> <FONT color="green">949</FONT> * Multiply two integers, checking for overflow.<a name="line.949"></a> <FONT color="green">950</FONT> *<a name="line.950"></a> <FONT color="green">951</FONT> * @param x a factor<a name="line.951"></a> <FONT color="green">952</FONT> * @param y a factor<a name="line.952"></a> <FONT color="green">953</FONT> * @return the product <code>x*y</code><a name="line.953"></a> <FONT color="green">954</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.954"></a> <FONT color="green">955</FONT> * int<a name="line.955"></a> <FONT color="green">956</FONT> * @since 1.1<a name="line.956"></a> <FONT color="green">957</FONT> */<a name="line.957"></a> <FONT color="green">958</FONT> public static int mulAndCheck(int x, int y) {<a name="line.958"></a> <FONT color="green">959</FONT> long m = ((long)x) * ((long)y);<a name="line.959"></a> <FONT color="green">960</FONT> if (m < Integer.MIN_VALUE || m > Integer.MAX_VALUE) {<a name="line.960"></a> <FONT color="green">961</FONT> throw new ArithmeticException("overflow: mul");<a name="line.961"></a> <FONT color="green">962</FONT> }<a name="line.962"></a> <FONT color="green">963</FONT> return (int)m;<a name="line.963"></a> <FONT color="green">964</FONT> }<a name="line.964"></a> <FONT color="green">965</FONT> <a name="line.965"></a> <FONT color="green">966</FONT> /**<a name="line.966"></a> <FONT color="green">967</FONT> * Multiply two long integers, checking for overflow.<a name="line.967"></a> <FONT color="green">968</FONT> *<a name="line.968"></a> <FONT color="green">969</FONT> * @param a first value<a name="line.969"></a> <FONT color="green">970</FONT> * @param b second value<a name="line.970"></a> <FONT color="green">971</FONT> * @return the product <code>a * b</code><a name="line.971"></a> <FONT color="green">972</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.972"></a> <FONT color="green">973</FONT> * long<a name="line.973"></a> <FONT color="green">974</FONT> * @since 1.2<a name="line.974"></a> <FONT color="green">975</FONT> */<a name="line.975"></a> <FONT color="green">976</FONT> public static long mulAndCheck(long a, long b) {<a name="line.976"></a> <FONT color="green">977</FONT> long ret;<a name="line.977"></a> <FONT color="green">978</FONT> String msg = "overflow: multiply";<a name="line.978"></a> <FONT color="green">979</FONT> if (a > b) {<a name="line.979"></a> <FONT color="green">980</FONT> // use symmetry to reduce boundary cases<a name="line.980"></a> <FONT color="green">981</FONT> ret = mulAndCheck(b, a);<a name="line.981"></a> <FONT color="green">982</FONT> } else {<a name="line.982"></a> <FONT color="green">983</FONT> if (a < 0) {<a name="line.983"></a> <FONT color="green">984</FONT> if (b < 0) {<a name="line.984"></a> <FONT color="green">985</FONT> // check for positive overflow with negative a, negative b<a name="line.985"></a> <FONT color="green">986</FONT> if (a >= Long.MAX_VALUE / b) {<a name="line.986"></a> <FONT color="green">987</FONT> ret = a * b;<a name="line.987"></a> <FONT color="green">988</FONT> } else {<a name="line.988"></a> <FONT color="green">989</FONT> throw new ArithmeticException(msg);<a name="line.989"></a> <FONT color="green">990</FONT> }<a name="line.990"></a> <FONT color="green">991</FONT> } else if (b > 0) {<a name="line.991"></a> <FONT color="green">992</FONT> // check for negative overflow with negative a, positive b<a name="line.992"></a> <FONT color="green">993</FONT> if (Long.MIN_VALUE / b <= a) {<a name="line.993"></a> <FONT color="green">994</FONT> ret = a * b;<a name="line.994"></a> <FONT color="green">995</FONT> } else {<a name="line.995"></a> <FONT color="green">996</FONT> throw new ArithmeticException(msg);<a name="line.996"></a> <FONT color="green">997</FONT> <a name="line.997"></a> <FONT color="green">998</FONT> }<a name="line.998"></a> <FONT color="green">999</FONT> } else {<a name="line.999"></a> <FONT color="green">1000</FONT> // assert b == 0<a name="line.1000"></a> <FONT color="green">1001</FONT> ret = 0;<a name="line.1001"></a> <FONT color="green">1002</FONT> }<a name="line.1002"></a> <FONT color="green">1003</FONT> } else if (a > 0) {<a name="line.1003"></a> <FONT color="green">1004</FONT> // assert a > 0<a name="line.1004"></a> <FONT color="green">1005</FONT> // assert b > 0<a name="line.1005"></a> <FONT color="green">1006</FONT> <a name="line.1006"></a> <FONT color="green">1007</FONT> // check for positive overflow with positive a, positive b<a name="line.1007"></a> <FONT color="green">1008</FONT> if (a <= Long.MAX_VALUE / b) {<a name="line.1008"></a> <FONT color="green">1009</FONT> ret = a * b;<a name="line.1009"></a> <FONT color="green">1010</FONT> } else {<a name="line.1010"></a> <FONT color="green">1011</FONT> throw new ArithmeticException(msg);<a name="line.1011"></a> <FONT color="green">1012</FONT> }<a name="line.1012"></a> <FONT color="green">1013</FONT> } else {<a name="line.1013"></a> <FONT color="green">1014</FONT> // assert a == 0<a name="line.1014"></a> <FONT color="green">1015</FONT> ret = 0;<a name="line.1015"></a> <FONT color="green">1016</FONT> }<a name="line.1016"></a> <FONT color="green">1017</FONT> }<a name="line.1017"></a> <FONT color="green">1018</FONT> return ret;<a name="line.1018"></a> <FONT color="green">1019</FONT> }<a name="line.1019"></a> <FONT color="green">1020</FONT> <a name="line.1020"></a> <FONT color="green">1021</FONT> /**<a name="line.1021"></a> <FONT color="green">1022</FONT> * Get the next machine representable number after a number, moving<a name="line.1022"></a> <FONT color="green">1023</FONT> * in the direction of another number.<a name="line.1023"></a> <FONT color="green">1024</FONT> * <p><a name="line.1024"></a> <FONT color="green">1025</FONT> * If <code>direction</code> is greater than or equal to<code>d</code>,<a name="line.1025"></a> <FONT color="green">1026</FONT> * the smallest machine representable number strictly greater than<a name="line.1026"></a> <FONT color="green">1027</FONT> * <code>d</code> is returned; otherwise the largest representable number<a name="line.1027"></a> <FONT color="green">1028</FONT> * strictly less than <code>d</code> is returned.</p><a name="line.1028"></a> <FONT color="green">1029</FONT> * <p><a name="line.1029"></a> <FONT color="green">1030</FONT> * If <code>d</code> is NaN or Infinite, it is returned unchanged.</p><a name="line.1030"></a> <FONT color="green">1031</FONT> *<a name="line.1031"></a> <FONT color="green">1032</FONT> * @param d base number<a name="line.1032"></a> <FONT color="green">1033</FONT> * @param direction (the only important thing is whether<a name="line.1033"></a> <FONT color="green">1034</FONT> * direction is greater or smaller than d)<a name="line.1034"></a> <FONT color="green">1035</FONT> * @return the next machine representable number in the specified direction<a name="line.1035"></a> <FONT color="green">1036</FONT> * @since 1.2<a name="line.1036"></a> <FONT color="green">1037</FONT> */<a name="line.1037"></a> <FONT color="green">1038</FONT> public static double nextAfter(double d, double direction) {<a name="line.1038"></a> <FONT color="green">1039</FONT> <a name="line.1039"></a> <FONT color="green">1040</FONT> // handling of some important special cases<a name="line.1040"></a> <FONT color="green">1041</FONT> if (Double.isNaN(d) || Double.isInfinite(d)) {<a name="line.1041"></a> <FONT color="green">1042</FONT> return d;<a name="line.1042"></a> <FONT color="green">1043</FONT> } else if (d == 0) {<a name="line.1043"></a> <FONT color="green">1044</FONT> return (direction < 0) ? -Double.MIN_VALUE : Double.MIN_VALUE;<a name="line.1044"></a> <FONT color="green">1045</FONT> }<a name="line.1045"></a> <FONT color="green">1046</FONT> // special cases MAX_VALUE to infinity and MIN_VALUE to 0<a name="line.1046"></a> <FONT color="green">1047</FONT> // are handled just as normal numbers<a name="line.1047"></a> <FONT color="green">1048</FONT> <a name="line.1048"></a> <FONT color="green">1049</FONT> // split the double in raw components<a name="line.1049"></a> <FONT color="green">1050</FONT> long bits = Double.doubleToLongBits(d);<a name="line.1050"></a> <FONT color="green">1051</FONT> long sign = bits & 0x8000000000000000L;<a name="line.1051"></a> <FONT color="green">1052</FONT> long exponent = bits & 0x7ff0000000000000L;<a name="line.1052"></a> <FONT color="green">1053</FONT> long mantissa = bits & 0x000fffffffffffffL;<a name="line.1053"></a> <FONT color="green">1054</FONT> <a name="line.1054"></a> <FONT color="green">1055</FONT> if (d * (direction - d) >= 0) {<a name="line.1055"></a> <FONT color="green">1056</FONT> // we should increase the mantissa<a name="line.1056"></a> <FONT color="green">1057</FONT> if (mantissa == 0x000fffffffffffffL) {<a name="line.1057"></a> <FONT color="green">1058</FONT> return Double.longBitsToDouble(sign |<a name="line.1058"></a> <FONT color="green">1059</FONT> (exponent + 0x0010000000000000L));<a name="line.1059"></a> <FONT color="green">1060</FONT> } else {<a name="line.1060"></a> <FONT color="green">1061</FONT> return Double.longBitsToDouble(sign |<a name="line.1061"></a> <FONT color="green">1062</FONT> exponent | (mantissa + 1));<a name="line.1062"></a> <FONT color="green">1063</FONT> }<a name="line.1063"></a> <FONT color="green">1064</FONT> } else {<a name="line.1064"></a> <FONT color="green">1065</FONT> // we should decrease the mantissa<a name="line.1065"></a> <FONT color="green">1066</FONT> if (mantissa == 0L) {<a name="line.1066"></a> <FONT color="green">1067</FONT> return Double.longBitsToDouble(sign |<a name="line.1067"></a> <FONT color="green">1068</FONT> (exponent - 0x0010000000000000L) |<a name="line.1068"></a> <FONT color="green">1069</FONT> 0x000fffffffffffffL);<a name="line.1069"></a> <FONT color="green">1070</FONT> } else {<a name="line.1070"></a> <FONT color="green">1071</FONT> return Double.longBitsToDouble(sign |<a name="line.1071"></a> <FONT color="green">1072</FONT> exponent | (mantissa - 1));<a name="line.1072"></a> <FONT color="green">1073</FONT> }<a name="line.1073"></a> <FONT color="green">1074</FONT> }<a name="line.1074"></a> <FONT color="green">1075</FONT> <a name="line.1075"></a> <FONT color="green">1076</FONT> }<a name="line.1076"></a> <FONT color="green">1077</FONT> <a name="line.1077"></a> <FONT color="green">1078</FONT> /**<a name="line.1078"></a> <FONT color="green">1079</FONT> * Scale a number by 2<sup>scaleFactor</sup>.<a name="line.1079"></a> <FONT color="green">1080</FONT> * <p>If <code>d</code> is 0 or NaN or Infinite, it is returned unchanged.</p><a name="line.1080"></a> <FONT color="green">1081</FONT> *<a name="line.1081"></a> <FONT color="green">1082</FONT> * @param d base number<a name="line.1082"></a> <FONT color="green">1083</FONT> * @param scaleFactor power of two by which d sould be multiplied<a name="line.1083"></a> <FONT color="green">1084</FONT> * @return d &times; 2<sup>scaleFactor</sup><a name="line.1084"></a> <FONT color="green">1085</FONT> * @since 2.0<a name="line.1085"></a> <FONT color="green">1086</FONT> */<a name="line.1086"></a> <FONT color="green">1087</FONT> public static double scalb(final double d, final int scaleFactor) {<a name="line.1087"></a> <FONT color="green">1088</FONT> <a name="line.1088"></a> <FONT color="green">1089</FONT> // handling of some important special cases<a name="line.1089"></a> <FONT color="green">1090</FONT> if ((d == 0) || Double.isNaN(d) || Double.isInfinite(d)) {<a name="line.1090"></a> <FONT color="green">1091</FONT> return d;<a name="line.1091"></a> <FONT color="green">1092</FONT> }<a name="line.1092"></a> <FONT color="green">1093</FONT> <a name="line.1093"></a> <FONT color="green">1094</FONT> // split the double in raw components<a name="line.1094"></a> <FONT color="green">1095</FONT> final long bits = Double.doubleToLongBits(d);<a name="line.1095"></a> <FONT color="green">1096</FONT> final long exponent = bits & 0x7ff0000000000000L;<a name="line.1096"></a> <FONT color="green">1097</FONT> final long rest = bits & 0x800fffffffffffffL;<a name="line.1097"></a> <FONT color="green">1098</FONT> <a name="line.1098"></a> <FONT color="green">1099</FONT> // shift the exponent<a name="line.1099"></a> <FONT color="green">1100</FONT> final long newBits = rest | (exponent + (((long) scaleFactor) << 52));<a name="line.1100"></a> <FONT color="green">1101</FONT> return Double.longBitsToDouble(newBits);<a name="line.1101"></a> <FONT color="green">1102</FONT> <a name="line.1102"></a> <FONT color="green">1103</FONT> }<a name="line.1103"></a> <FONT color="green">1104</FONT> <a name="line.1104"></a> <FONT color="green">1105</FONT> /**<a name="line.1105"></a> <FONT color="green">1106</FONT> * Normalize an angle in a 2&pi wide interval around a center value.<a name="line.1106"></a> <FONT color="green">1107</FONT> * <p>This method has three main uses:</p><a name="line.1107"></a> <FONT color="green">1108</FONT> * <ul><a name="line.1108"></a> <FONT color="green">1109</FONT> * <li>normalize an angle between 0 and 2&pi;:<br/><a name="line.1109"></a> <FONT color="green">1110</FONT> * <code>a = MathUtils.normalizeAngle(a, Math.PI);</code></li><a name="line.1110"></a> <FONT color="green">1111</FONT> * <li>normalize an angle between -&pi; and +&pi;<br/><a name="line.1111"></a> <FONT color="green">1112</FONT> * <code>a = MathUtils.normalizeAngle(a, 0.0);</code></li><a name="line.1112"></a> <FONT color="green">1113</FONT> * <li>compute the angle between two defining angular positions:<br><a name="line.1113"></a> <FONT color="green">1114</FONT> * <code>angle = MathUtils.normalizeAngle(end, start) - start;</code></li><a name="line.1114"></a> <FONT color="green">1115</FONT> * </ul><a name="line.1115"></a> <FONT color="green">1116</FONT> * <p>Note that due to numerical accuracy and since &pi; cannot be represented<a name="line.1116"></a> <FONT color="green">1117</FONT> * exactly, the result interval is <em>closed</em>, it cannot be half-closed<a name="line.1117"></a> <FONT color="green">1118</FONT> * as would be more satisfactory in a purely mathematical view.</p><a name="line.1118"></a> <FONT color="green">1119</FONT> * @param a angle to normalize<a name="line.1119"></a> <FONT color="green">1120</FONT> * @param center center of the desired 2&pi; interval for the result<a name="line.1120"></a> <FONT color="green">1121</FONT> * @return a-2k&pi; with integer k and center-&pi; &lt;= a-2k&pi; &lt;= center+&pi;<a name="line.1121"></a> <FONT color="green">1122</FONT> * @since 1.2<a name="line.1122"></a> <FONT color="green">1123</FONT> */<a name="line.1123"></a> <FONT color="green">1124</FONT> public static double normalizeAngle(double a, double center) {<a name="line.1124"></a> <FONT color="green">1125</FONT> return a - TWO_PI * Math.floor((a + Math.PI - center) / TWO_PI);<a name="line.1125"></a> <FONT color="green">1126</FONT> }<a name="line.1126"></a> <FONT color="green">1127</FONT> <a name="line.1127"></a> <FONT color="green">1128</FONT> /**<a name="line.1128"></a> <FONT color="green">1129</FONT> * <p>Normalizes an array to make it sum to a specified value.<a name="line.1129"></a> <FONT color="green">1130</FONT> * Returns the result of the transformation <pre><a name="line.1130"></a> <FONT color="green">1131</FONT> * x |-> x * normalizedSum / sum<a name="line.1131"></a> <FONT color="green">1132</FONT> * </pre><a name="line.1132"></a> <FONT color="green">1133</FONT> * applied to each non-NaN element x of the input array, where sum is the<a name="line.1133"></a> <FONT color="green">1134</FONT> * sum of the non-NaN entries in the input array.</p><a name="line.1134"></a> <FONT color="green">1135</FONT> *<a name="line.1135"></a> <FONT color="green">1136</FONT> * <p>Throws IllegalArgumentException if <code>normalizedSum</code> is infinite<a name="line.1136"></a> <FONT color="green">1137</FONT> * or NaN and ArithmeticException if the input array contains any infinite elements<a name="line.1137"></a> <FONT color="green">1138</FONT> * or sums to 0</p><a name="line.1138"></a> <FONT color="green">1139</FONT> *<a name="line.1139"></a> <FONT color="green">1140</FONT> * <p>Ignores (i.e., copies unchanged to the output array) NaNs in the input array.</p><a name="line.1140"></a> <FONT color="green">1141</FONT> *<a name="line.1141"></a> <FONT color="green">1142</FONT> * @param values input array to be normalized<a name="line.1142"></a> <FONT color="green">1143</FONT> * @param normalizedSum target sum for the normalized array<a name="line.1143"></a> <FONT color="green">1144</FONT> * @return normalized array<a name="line.1144"></a> <FONT color="green">1145</FONT> * @throws ArithmeticException if the input array contains infinite elements or sums to zero<a name="line.1145"></a> <FONT color="green">1146</FONT> * @throws IllegalArgumentException if the target sum is infinite or NaN<a name="line.1146"></a> <FONT color="green">1147</FONT> * @since 2.1<a name="line.1147"></a> <FONT color="green">1148</FONT> */<a name="line.1148"></a> <FONT color="green">1149</FONT> public static double[] normalizeArray(double[] values, double normalizedSum)<a name="line.1149"></a> <FONT color="green">1150</FONT> throws ArithmeticException, IllegalArgumentException {<a name="line.1150"></a> <FONT color="green">1151</FONT> if (Double.isInfinite(normalizedSum)) {<a name="line.1151"></a> <FONT color="green">1152</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1152"></a> <FONT color="green">1153</FONT> "Cannot normalize to an infinite value");<a name="line.1153"></a> <FONT color="green">1154</FONT> }<a name="line.1154"></a> <FONT color="green">1155</FONT> if (Double.isNaN(normalizedSum)) {<a name="line.1155"></a> <FONT color="green">1156</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1156"></a> <FONT color="green">1157</FONT> "Cannot normalize to NaN");<a name="line.1157"></a> <FONT color="green">1158</FONT> }<a name="line.1158"></a> <FONT color="green">1159</FONT> double sum = 0d;<a name="line.1159"></a> <FONT color="green">1160</FONT> final int len = values.length;<a name="line.1160"></a> <FONT color="green">1161</FONT> double[] out = new double[len];<a name="line.1161"></a> <FONT color="green">1162</FONT> for (int i = 0; i < len; i++) {<a name="line.1162"></a> <FONT color="green">1163</FONT> if (Double.isInfinite(values[i])) {<a name="line.1163"></a> <FONT color="green">1164</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.1164"></a> <FONT color="green">1165</FONT> "Array contains an infinite element, {0} at index {1}", values[i], i);<a name="line.1165"></a> <FONT color="green">1166</FONT> }<a name="line.1166"></a> <FONT color="green">1167</FONT> if (!Double.isNaN(values[i])) {<a name="line.1167"></a> <FONT color="green">1168</FONT> sum += values[i];<a name="line.1168"></a> <FONT color="green">1169</FONT> }<a name="line.1169"></a> <FONT color="green">1170</FONT> }<a name="line.1170"></a> <FONT color="green">1171</FONT> if (sum == 0) {<a name="line.1171"></a> <FONT color="green">1172</FONT> throw MathRuntimeException.createArithmeticException(<a name="line.1172"></a> <FONT color="green">1173</FONT> "Array sums to zero");<a name="line.1173"></a> <FONT color="green">1174</FONT> }<a name="line.1174"></a> <FONT color="green">1175</FONT> for (int i = 0; i < len; i++) {<a name="line.1175"></a> <FONT color="green">1176</FONT> if (Double.isNaN(values[i])) {<a name="line.1176"></a> <FONT color="green">1177</FONT> out[i] = Double.NaN;<a name="line.1177"></a> <FONT color="green">1178</FONT> } else {<a name="line.1178"></a> <FONT color="green">1179</FONT> out[i] = values[i] * normalizedSum / sum;<a name="line.1179"></a> <FONT color="green">1180</FONT> }<a name="line.1180"></a> <FONT color="green">1181</FONT> }<a name="line.1181"></a> <FONT color="green">1182</FONT> return out;<a name="line.1182"></a> <FONT color="green">1183</FONT> }<a name="line.1183"></a> <FONT color="green">1184</FONT> <a name="line.1184"></a> <FONT color="green">1185</FONT> /**<a name="line.1185"></a> <FONT color="green">1186</FONT> * Round the given value to the specified number of decimal places. The<a name="line.1186"></a> <FONT color="green">1187</FONT> * value is rounded using the {@link BigDecimal#ROUND_HALF_UP} method.<a name="line.1187"></a> <FONT color="green">1188</FONT> *<a name="line.1188"></a> <FONT color="green">1189</FONT> * @param x the value to round.<a name="line.1189"></a> <FONT color="green">1190</FONT> * @param scale the number of digits to the right of the decimal point.<a name="line.1190"></a> <FONT color="green">1191</FONT> * @return the rounded value.<a name="line.1191"></a> <FONT color="green">1192</FONT> * @since 1.1<a name="line.1192"></a> <FONT color="green">1193</FONT> */<a name="line.1193"></a> <FONT color="green">1194</FONT> public static double round(double x, int scale) {<a name="line.1194"></a> <FONT color="green">1195</FONT> return round(x, scale, BigDecimal.ROUND_HALF_UP);<a name="line.1195"></a> <FONT color="green">1196</FONT> }<a name="line.1196"></a> <FONT color="green">1197</FONT> <a name="line.1197"></a> <FONT color="green">1198</FONT> /**<a name="line.1198"></a> <FONT color="green">1199</FONT> * Round the given value to the specified number of decimal places. The<a name="line.1199"></a> <FONT color="green">1200</FONT> * value is rounded using the given method which is any method defined in<a name="line.1200"></a> <FONT color="green">1201</FONT> * {@link BigDecimal}.<a name="line.1201"></a> <FONT color="green">1202</FONT> *<a name="line.1202"></a> <FONT color="green">1203</FONT> * @param x the value to round.<a name="line.1203"></a> <FONT color="green">1204</FONT> * @param scale the number of digits to the right of the decimal point.<a name="line.1204"></a> <FONT color="green">1205</FONT> * @param roundingMethod the rounding method as defined in<a name="line.1205"></a> <FONT color="green">1206</FONT> * {@link BigDecimal}.<a name="line.1206"></a> <FONT color="green">1207</FONT> * @return the rounded value.<a name="line.1207"></a> <FONT color="green">1208</FONT> * @since 1.1<a name="line.1208"></a> <FONT color="green">1209</FONT> */<a name="line.1209"></a> <FONT color="green">1210</FONT> public static double round(double x, int scale, int roundingMethod) {<a name="line.1210"></a> <FONT color="green">1211</FONT> try {<a name="line.1211"></a> <FONT color="green">1212</FONT> return (new BigDecimal<a name="line.1212"></a> <FONT color="green">1213</FONT> (Double.toString(x))<a name="line.1213"></a> <FONT color="green">1214</FONT> .setScale(scale, roundingMethod))<a name="line.1214"></a> <FONT color="green">1215</FONT> .doubleValue();<a name="line.1215"></a> <FONT color="green">1216</FONT> } catch (NumberFormatException ex) {<a name="line.1216"></a> <FONT color="green">1217</FONT> if (Double.isInfinite(x)) {<a name="line.1217"></a> <FONT color="green">1218</FONT> return x;<a name="line.1218"></a> <FONT color="green">1219</FONT> } else {<a name="line.1219"></a> <FONT color="green">1220</FONT> return Double.NaN;<a name="line.1220"></a> <FONT color="green">1221</FONT> }<a name="line.1221"></a> <FONT color="green">1222</FONT> }<a name="line.1222"></a> <FONT color="green">1223</FONT> }<a name="line.1223"></a> <FONT color="green">1224</FONT> <a name="line.1224"></a> <FONT color="green">1225</FONT> /**<a name="line.1225"></a> <FONT color="green">1226</FONT> * Round the given value to the specified number of decimal places. The<a name="line.1226"></a> <FONT color="green">1227</FONT> * value is rounding using the {@link BigDecimal#ROUND_HALF_UP} method.<a name="line.1227"></a> <FONT color="green">1228</FONT> *<a name="line.1228"></a> <FONT color="green">1229</FONT> * @param x the value to round.<a name="line.1229"></a> <FONT color="green">1230</FONT> * @param scale the number of digits to the right of the decimal point.<a name="line.1230"></a> <FONT color="green">1231</FONT> * @return the rounded value.<a name="line.1231"></a> <FONT color="green">1232</FONT> * @since 1.1<a name="line.1232"></a> <FONT color="green">1233</FONT> */<a name="line.1233"></a> <FONT color="green">1234</FONT> public static float round(float x, int scale) {<a name="line.1234"></a> <FONT color="green">1235</FONT> return round(x, scale, BigDecimal.ROUND_HALF_UP);<a name="line.1235"></a> <FONT color="green">1236</FONT> }<a name="line.1236"></a> <FONT color="green">1237</FONT> <a name="line.1237"></a> <FONT color="green">1238</FONT> /**<a name="line.1238"></a> <FONT color="green">1239</FONT> * Round the given value to the specified number of decimal places. The<a name="line.1239"></a> <FONT color="green">1240</FONT> * value is rounded using the given method which is any method defined in<a name="line.1240"></a> <FONT color="green">1241</FONT> * {@link BigDecimal}.<a name="line.1241"></a> <FONT color="green">1242</FONT> *<a name="line.1242"></a> <FONT color="green">1243</FONT> * @param x the value to round.<a name="line.1243"></a> <FONT color="green">1244</FONT> * @param scale the number of digits to the right of the decimal point.<a name="line.1244"></a> <FONT color="green">1245</FONT> * @param roundingMethod the rounding method as defined in<a name="line.1245"></a> <FONT color="green">1246</FONT> * {@link BigDecimal}.<a name="line.1246"></a> <FONT color="green">1247</FONT> * @return the rounded value.<a name="line.1247"></a> <FONT color="green">1248</FONT> * @since 1.1<a name="line.1248"></a> <FONT color="green">1249</FONT> */<a name="line.1249"></a> <FONT color="green">1250</FONT> public static float round(float x, int scale, int roundingMethod) {<a name="line.1250"></a> <FONT color="green">1251</FONT> float sign = indicator(x);<a name="line.1251"></a> <FONT color="green">1252</FONT> float factor = (float)Math.pow(10.0f, scale) * sign;<a name="line.1252"></a> <FONT color="green">1253</FONT> return (float)roundUnscaled(x * factor, sign, roundingMethod) / factor;<a name="line.1253"></a> <FONT color="green">1254</FONT> }<a name="line.1254"></a> <FONT color="green">1255</FONT> <a name="line.1255"></a> <FONT color="green">1256</FONT> /**<a name="line.1256"></a> <FONT color="green">1257</FONT> * Round the given non-negative, value to the "nearest" integer. Nearest is<a name="line.1257"></a> <FONT color="green">1258</FONT> * determined by the rounding method specified. Rounding methods are defined<a name="line.1258"></a> <FONT color="green">1259</FONT> * in {@link BigDecimal}.<a name="line.1259"></a> <FONT color="green">1260</FONT> *<a name="line.1260"></a> <FONT color="green">1261</FONT> * @param unscaled the value to round.<a name="line.1261"></a> <FONT color="green">1262</FONT> * @param sign the sign of the original, scaled value.<a name="line.1262"></a> <FONT color="green">1263</FONT> * @param roundingMethod the rounding method as defined in<a name="line.1263"></a> <FONT color="green">1264</FONT> * {@link BigDecimal}.<a name="line.1264"></a> <FONT color="green">1265</FONT> * @return the rounded value.<a name="line.1265"></a> <FONT color="green">1266</FONT> * @since 1.1<a name="line.1266"></a> <FONT color="green">1267</FONT> */<a name="line.1267"></a> <FONT color="green">1268</FONT> private static double roundUnscaled(double unscaled, double sign,<a name="line.1268"></a> <FONT color="green">1269</FONT> int roundingMethod) {<a name="line.1269"></a> <FONT color="green">1270</FONT> switch (roundingMethod) {<a name="line.1270"></a> <FONT color="green">1271</FONT> case BigDecimal.ROUND_CEILING :<a name="line.1271"></a> <FONT color="green">1272</FONT> if (sign == -1) {<a name="line.1272"></a> <FONT color="green">1273</FONT> unscaled = Math.floor(nextAfter(unscaled, Double.NEGATIVE_INFINITY));<a name="line.1273"></a> <FONT color="green">1274</FONT> } else {<a name="line.1274"></a> <FONT color="green">1275</FONT> unscaled = Math.ceil(nextAfter(unscaled, Double.POSITIVE_INFINITY));<a name="line.1275"></a> <FONT color="green">1276</FONT> }<a name="line.1276"></a> <FONT color="green">1277</FONT> break;<a name="line.1277"></a> <FONT color="green">1278</FONT> case BigDecimal.ROUND_DOWN :<a name="line.1278"></a> <FONT color="green">1279</FONT> unscaled = Math.floor(nextAfter(unscaled, Double.NEGATIVE_INFINITY));<a name="line.1279"></a> <FONT color="green">1280</FONT> break;<a name="line.1280"></a> <FONT color="green">1281</FONT> case BigDecimal.ROUND_FLOOR :<a name="line.1281"></a> <FONT color="green">1282</FONT> if (sign == -1) {<a name="line.1282"></a> <FONT color="green">1283</FONT> unscaled = Math.ceil(nextAfter(unscaled, Double.POSITIVE_INFINITY));<a name="line.1283"></a> <FONT color="green">1284</FONT> } else {<a name="line.1284"></a> <FONT color="green">1285</FONT> unscaled = Math.floor(nextAfter(unscaled, Double.NEGATIVE_INFINITY));<a name="line.1285"></a> <FONT color="green">1286</FONT> }<a name="line.1286"></a> <FONT color="green">1287</FONT> break;<a name="line.1287"></a> <FONT color="green">1288</FONT> case BigDecimal.ROUND_HALF_DOWN : {<a name="line.1288"></a> <FONT color="green">1289</FONT> unscaled = nextAfter(unscaled, Double.NEGATIVE_INFINITY);<a name="line.1289"></a> <FONT color="green">1290</FONT> double fraction = unscaled - Math.floor(unscaled);<a name="line.1290"></a> <FONT color="green">1291</FONT> if (fraction > 0.5) {<a name="line.1291"></a> <FONT color="green">1292</FONT> unscaled = Math.ceil(unscaled);<a name="line.1292"></a> <FONT color="green">1293</FONT> } else {<a name="line.1293"></a> <FONT color="green">1294</FONT> unscaled = Math.floor(unscaled);<a name="line.1294"></a> <FONT color="green">1295</FONT> }<a name="line.1295"></a> <FONT color="green">1296</FONT> break;<a name="line.1296"></a> <FONT color="green">1297</FONT> }<a name="line.1297"></a> <FONT color="green">1298</FONT> case BigDecimal.ROUND_HALF_EVEN : {<a name="line.1298"></a> <FONT color="green">1299</FONT> double fraction = unscaled - Math.floor(unscaled);<a name="line.1299"></a> <FONT color="green">1300</FONT> if (fraction > 0.5) {<a name="line.1300"></a> <FONT color="green">1301</FONT> unscaled = Math.ceil(unscaled);<a name="line.1301"></a> <FONT color="green">1302</FONT> } else if (fraction < 0.5) {<a name="line.1302"></a> <FONT color="green">1303</FONT> unscaled = Math.floor(unscaled);<a name="line.1303"></a> <FONT color="green">1304</FONT> } else {<a name="line.1304"></a> <FONT color="green">1305</FONT> // The following equality test is intentional and needed for rounding purposes<a name="line.1305"></a> <FONT color="green">1306</FONT> if (Math.floor(unscaled) / 2.0 == Math.floor(Math<a name="line.1306"></a> <FONT color="green">1307</FONT> .floor(unscaled) / 2.0)) { // even<a name="line.1307"></a> <FONT color="green">1308</FONT> unscaled = Math.floor(unscaled);<a name="line.1308"></a> <FONT color="green">1309</FONT> } else { // odd<a name="line.1309"></a> <FONT color="green">1310</FONT> unscaled = Math.ceil(unscaled);<a name="line.1310"></a> <FONT color="green">1311</FONT> }<a name="line.1311"></a> <FONT color="green">1312</FONT> }<a name="line.1312"></a> <FONT color="green">1313</FONT> break;<a name="line.1313"></a> <FONT color="green">1314</FONT> }<a name="line.1314"></a> <FONT color="green">1315</FONT> case BigDecimal.ROUND_HALF_UP : {<a name="line.1315"></a> <FONT color="green">1316</FONT> unscaled = nextAfter(unscaled, Double.POSITIVE_INFINITY);<a name="line.1316"></a> <FONT color="green">1317</FONT> double fraction = unscaled - Math.floor(unscaled);<a name="line.1317"></a> <FONT color="green">1318</FONT> if (fraction >= 0.5) {<a name="line.1318"></a> <FONT color="green">1319</FONT> unscaled = Math.ceil(unscaled);<a name="line.1319"></a> <FONT color="green">1320</FONT> } else {<a name="line.1320"></a> <FONT color="green">1321</FONT> unscaled = Math.floor(unscaled);<a name="line.1321"></a> <FONT color="green">1322</FONT> }<a name="line.1322"></a> <FONT color="green">1323</FONT> break;<a name="line.1323"></a> <FONT color="green">1324</FONT> }<a name="line.1324"></a> <FONT color="green">1325</FONT> case BigDecimal.ROUND_UNNECESSARY :<a name="line.1325"></a> <FONT color="green">1326</FONT> if (unscaled != Math.floor(unscaled)) {<a name="line.1326"></a> <FONT color="green">1327</FONT> throw new ArithmeticException("Inexact result from rounding");<a name="line.1327"></a> <FONT color="green">1328</FONT> }<a name="line.1328"></a> <FONT color="green">1329</FONT> break;<a name="line.1329"></a> <FONT color="green">1330</FONT> case BigDecimal.ROUND_UP :<a name="line.1330"></a> <FONT color="green">1331</FONT> unscaled = Math.ceil(nextAfter(unscaled, Double.POSITIVE_INFINITY));<a name="line.1331"></a> <FONT color="green">1332</FONT> break;<a name="line.1332"></a> <FONT color="green">1333</FONT> default :<a name="line.1333"></a> <FONT color="green">1334</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1334"></a> <FONT color="green">1335</FONT> "invalid rounding method {0}, valid methods: {1} ({2}), {3} ({4})," +<a name="line.1335"></a> <FONT color="green">1336</FONT> " {5} ({6}), {7} ({8}), {9} ({10}), {11} ({12}), {13} ({14}), {15} ({16})",<a name="line.1336"></a> <FONT color="green">1337</FONT> roundingMethod,<a name="line.1337"></a> <FONT color="green">1338</FONT> "ROUND_CEILING", BigDecimal.ROUND_CEILING,<a name="line.1338"></a> <FONT color="green">1339</FONT> "ROUND_DOWN", BigDecimal.ROUND_DOWN,<a name="line.1339"></a> <FONT color="green">1340</FONT> "ROUND_FLOOR", BigDecimal.ROUND_FLOOR,<a name="line.1340"></a> <FONT color="green">1341</FONT> "ROUND_HALF_DOWN", BigDecimal.ROUND_HALF_DOWN,<a name="line.1341"></a> <FONT color="green">1342</FONT> "ROUND_HALF_EVEN", BigDecimal.ROUND_HALF_EVEN,<a name="line.1342"></a> <FONT color="green">1343</FONT> "ROUND_HALF_UP", BigDecimal.ROUND_HALF_UP,<a name="line.1343"></a> <FONT color="green">1344</FONT> "ROUND_UNNECESSARY", BigDecimal.ROUND_UNNECESSARY,<a name="line.1344"></a> <FONT color="green">1345</FONT> "ROUND_UP", BigDecimal.ROUND_UP);<a name="line.1345"></a> <FONT color="green">1346</FONT> }<a name="line.1346"></a> <FONT color="green">1347</FONT> return unscaled;<a name="line.1347"></a> <FONT color="green">1348</FONT> }<a name="line.1348"></a> <FONT color="green">1349</FONT> <a name="line.1349"></a> <FONT color="green">1350</FONT> /**<a name="line.1350"></a> <FONT color="green">1351</FONT> * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a><a name="line.1351"></a> <FONT color="green">1352</FONT> * for byte value <code>x</code>.<a name="line.1352"></a> <FONT color="green">1353</FONT> * <p><a name="line.1353"></a> <FONT color="green">1354</FONT> * For a byte value x, this method returns (byte)(+1) if x > 0, (byte)(0) if<a name="line.1354"></a> <FONT color="green">1355</FONT> * x = 0, and (byte)(-1) if x < 0.</p><a name="line.1355"></a> <FONT color="green">1356</FONT> *<a name="line.1356"></a> <FONT color="green">1357</FONT> * @param x the value, a byte<a name="line.1357"></a> <FONT color="green">1358</FONT> * @return (byte)(+1), (byte)(0), or (byte)(-1), depending on the sign of x<a name="line.1358"></a> <FONT color="green">1359</FONT> */<a name="line.1359"></a> <FONT color="green">1360</FONT> public static byte sign(final byte x) {<a name="line.1360"></a> <FONT color="green">1361</FONT> return (x == ZB) ? ZB : (x > ZB) ? PB : NB;<a name="line.1361"></a> <FONT color="green">1362</FONT> }<a name="line.1362"></a> <FONT color="green">1363</FONT> <a name="line.1363"></a> <FONT color="green">1364</FONT> /**<a name="line.1364"></a> <FONT color="green">1365</FONT> * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a><a name="line.1365"></a> <FONT color="green">1366</FONT> * for double precision <code>x</code>.<a name="line.1366"></a> <FONT color="green">1367</FONT> * <p><a name="line.1367"></a> <FONT color="green">1368</FONT> * For a double value <code>x</code>, this method returns<a name="line.1368"></a> <FONT color="green">1369</FONT> * <code>+1.0</code> if <code>x > 0</code>, <code>0.0</code> if<a name="line.1369"></a> <FONT color="green">1370</FONT> * <code>x = 0.0</code>, and <code>-1.0</code> if <code>x < 0</code>.<a name="line.1370"></a> <FONT color="green">1371</FONT> * Returns <code>NaN</code> if <code>x</code> is <code>NaN</code>.</p><a name="line.1371"></a> <FONT color="green">1372</FONT> *<a name="line.1372"></a> <FONT color="green">1373</FONT> * @param x the value, a double<a name="line.1373"></a> <FONT color="green">1374</FONT> * @return +1.0, 0.0, or -1.0, depending on the sign of x<a name="line.1374"></a> <FONT color="green">1375</FONT> */<a name="line.1375"></a> <FONT color="green">1376</FONT> public static double sign(final double x) {<a name="line.1376"></a> <FONT color="green">1377</FONT> if (Double.isNaN(x)) {<a name="line.1377"></a> <FONT color="green">1378</FONT> return Double.NaN;<a name="line.1378"></a> <FONT color="green">1379</FONT> }<a name="line.1379"></a> <FONT color="green">1380</FONT> return (x == 0.0) ? 0.0 : (x > 0.0) ? 1.0 : -1.0;<a name="line.1380"></a> <FONT color="green">1381</FONT> }<a name="line.1381"></a> <FONT color="green">1382</FONT> <a name="line.1382"></a> <FONT color="green">1383</FONT> /**<a name="line.1383"></a> <FONT color="green">1384</FONT> * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a><a name="line.1384"></a> <FONT color="green">1385</FONT> * for float value <code>x</code>.<a name="line.1385"></a> <FONT color="green">1386</FONT> * <p><a name="line.1386"></a> <FONT color="green">1387</FONT> * For a float value x, this method returns +1.0F if x > 0, 0.0F if x =<a name="line.1387"></a> <FONT color="green">1388</FONT> * 0.0F, and -1.0F if x < 0. Returns <code>NaN</code> if <code>x</code><a name="line.1388"></a> <FONT color="green">1389</FONT> * is <code>NaN</code>.</p><a name="line.1389"></a> <FONT color="green">1390</FONT> *<a name="line.1390"></a> <FONT color="green">1391</FONT> * @param x the value, a float<a name="line.1391"></a> <FONT color="green">1392</FONT> * @return +1.0F, 0.0F, or -1.0F, depending on the sign of x<a name="line.1392"></a> <FONT color="green">1393</FONT> */<a name="line.1393"></a> <FONT color="green">1394</FONT> public static float sign(final float x) {<a name="line.1394"></a> <FONT color="green">1395</FONT> if (Float.isNaN(x)) {<a name="line.1395"></a> <FONT color="green">1396</FONT> return Float.NaN;<a name="line.1396"></a> <FONT color="green">1397</FONT> }<a name="line.1397"></a> <FONT color="green">1398</FONT> return (x == 0.0F) ? 0.0F : (x > 0.0F) ? 1.0F : -1.0F;<a name="line.1398"></a> <FONT color="green">1399</FONT> }<a name="line.1399"></a> <FONT color="green">1400</FONT> <a name="line.1400"></a> <FONT color="green">1401</FONT> /**<a name="line.1401"></a> <FONT color="green">1402</FONT> * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a><a name="line.1402"></a> <FONT color="green">1403</FONT> * for int value <code>x</code>.<a name="line.1403"></a> <FONT color="green">1404</FONT> * <p><a name="line.1404"></a> <FONT color="green">1405</FONT> * For an int value x, this method returns +1 if x > 0, 0 if x = 0, and -1<a name="line.1405"></a> <FONT color="green">1406</FONT> * if x < 0.</p><a name="line.1406"></a> <FONT color="green">1407</FONT> *<a name="line.1407"></a> <FONT color="green">1408</FONT> * @param x the value, an int<a name="line.1408"></a> <FONT color="green">1409</FONT> * @return +1, 0, or -1, depending on the sign of x<a name="line.1409"></a> <FONT color="green">1410</FONT> */<a name="line.1410"></a> <FONT color="green">1411</FONT> public static int sign(final int x) {<a name="line.1411"></a> <FONT color="green">1412</FONT> return (x == 0) ? 0 : (x > 0) ? 1 : -1;<a name="line.1412"></a> <FONT color="green">1413</FONT> }<a name="line.1413"></a> <FONT color="green">1414</FONT> <a name="line.1414"></a> <FONT color="green">1415</FONT> /**<a name="line.1415"></a> <FONT color="green">1416</FONT> * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a><a name="line.1416"></a> <FONT color="green">1417</FONT> * for long value <code>x</code>.<a name="line.1417"></a> <FONT color="green">1418</FONT> * <p><a name="line.1418"></a> <FONT color="green">1419</FONT> * For a long value x, this method returns +1L if x > 0, 0L if x = 0, and<a name="line.1419"></a> <FONT color="green">1420</FONT> * -1L if x < 0.</p><a name="line.1420"></a> <FONT color="green">1421</FONT> *<a name="line.1421"></a> <FONT color="green">1422</FONT> * @param x the value, a long<a name="line.1422"></a> <FONT color="green">1423</FONT> * @return +1L, 0L, or -1L, depending on the sign of x<a name="line.1423"></a> <FONT color="green">1424</FONT> */<a name="line.1424"></a> <FONT color="green">1425</FONT> public static long sign(final long x) {<a name="line.1425"></a> <FONT color="green">1426</FONT> return (x == 0L) ? 0L : (x > 0L) ? 1L : -1L;<a name="line.1426"></a> <FONT color="green">1427</FONT> }<a name="line.1427"></a> <FONT color="green">1428</FONT> <a name="line.1428"></a> <FONT color="green">1429</FONT> /**<a name="line.1429"></a> <FONT color="green">1430</FONT> * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a><a name="line.1430"></a> <FONT color="green">1431</FONT> * for short value <code>x</code>.<a name="line.1431"></a> <FONT color="green">1432</FONT> * <p><a name="line.1432"></a> <FONT color="green">1433</FONT> * For a short value x, this method returns (short)(+1) if x > 0, (short)(0)<a name="line.1433"></a> <FONT color="green">1434</FONT> * if x = 0, and (short)(-1) if x < 0.</p><a name="line.1434"></a> <FONT color="green">1435</FONT> *<a name="line.1435"></a> <FONT color="green">1436</FONT> * @param x the value, a short<a name="line.1436"></a> <FONT color="green">1437</FONT> * @return (short)(+1), (short)(0), or (short)(-1), depending on the sign of<a name="line.1437"></a> <FONT color="green">1438</FONT> * x<a name="line.1438"></a> <FONT color="green">1439</FONT> */<a name="line.1439"></a> <FONT color="green">1440</FONT> public static short sign(final short x) {<a name="line.1440"></a> <FONT color="green">1441</FONT> return (x == ZS) ? ZS : (x > ZS) ? PS : NS;<a name="line.1441"></a> <FONT color="green">1442</FONT> }<a name="line.1442"></a> <FONT color="green">1443</FONT> <a name="line.1443"></a> <FONT color="green">1444</FONT> /**<a name="line.1444"></a> <FONT color="green">1445</FONT> * Returns the <a href="http://mathworld.wolfram.com/HyperbolicSine.html"><a name="line.1445"></a> <FONT color="green">1446</FONT> * hyperbolic sine</a> of x.<a name="line.1446"></a> <FONT color="green">1447</FONT> *<a name="line.1447"></a> <FONT color="green">1448</FONT> * @param x double value for which to find the hyperbolic sine<a name="line.1448"></a> <FONT color="green">1449</FONT> * @return hyperbolic sine of x<a name="line.1449"></a> <FONT color="green">1450</FONT> */<a name="line.1450"></a> <FONT color="green">1451</FONT> public static double sinh(double x) {<a name="line.1451"></a> <FONT color="green">1452</FONT> return (Math.exp(x) - Math.exp(-x)) / 2.0;<a name="line.1452"></a> <FONT color="green">1453</FONT> }<a name="line.1453"></a> <FONT color="green">1454</FONT> <a name="line.1454"></a> <FONT color="green">1455</FONT> /**<a name="line.1455"></a> <FONT color="green">1456</FONT> * Subtract two integers, checking for overflow.<a name="line.1456"></a> <FONT color="green">1457</FONT> *<a name="line.1457"></a> <FONT color="green">1458</FONT> * @param x the minuend<a name="line.1458"></a> <FONT color="green">1459</FONT> * @param y the subtrahend<a name="line.1459"></a> <FONT color="green">1460</FONT> * @return the difference <code>x-y</code><a name="line.1460"></a> <FONT color="green">1461</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.1461"></a> <FONT color="green">1462</FONT> * int<a name="line.1462"></a> <FONT color="green">1463</FONT> * @since 1.1<a name="line.1463"></a> <FONT color="green">1464</FONT> */<a name="line.1464"></a> <FONT color="green">1465</FONT> public static int subAndCheck(int x, int y) {<a name="line.1465"></a> <FONT color="green">1466</FONT> long s = (long)x - (long)y;<a name="line.1466"></a> <FONT color="green">1467</FONT> if (s < Integer.MIN_VALUE || s > Integer.MAX_VALUE) {<a name="line.1467"></a> <FONT color="green">1468</FONT> throw new ArithmeticException("overflow: subtract");<a name="line.1468"></a> <FONT color="green">1469</FONT> }<a name="line.1469"></a> <FONT color="green">1470</FONT> return (int)s;<a name="line.1470"></a> <FONT color="green">1471</FONT> }<a name="line.1471"></a> <FONT color="green">1472</FONT> <a name="line.1472"></a> <FONT color="green">1473</FONT> /**<a name="line.1473"></a> <FONT color="green">1474</FONT> * Subtract two long integers, checking for overflow.<a name="line.1474"></a> <FONT color="green">1475</FONT> *<a name="line.1475"></a> <FONT color="green">1476</FONT> * @param a first value<a name="line.1476"></a> <FONT color="green">1477</FONT> * @param b second value<a name="line.1477"></a> <FONT color="green">1478</FONT> * @return the difference <code>a-b</code><a name="line.1478"></a> <FONT color="green">1479</FONT> * @throws ArithmeticException if the result can not be represented as an<a name="line.1479"></a> <FONT color="green">1480</FONT> * long<a name="line.1480"></a> <FONT color="green">1481</FONT> * @since 1.2<a name="line.1481"></a> <FONT color="green">1482</FONT> */<a name="line.1482"></a> <FONT color="green">1483</FONT> public static long subAndCheck(long a, long b) {<a name="line.1483"></a> <FONT color="green">1484</FONT> long ret;<a name="line.1484"></a> <FONT color="green">1485</FONT> String msg = "overflow: subtract";<a name="line.1485"></a> <FONT color="green">1486</FONT> if (b == Long.MIN_VALUE) {<a name="line.1486"></a> <FONT color="green">1487</FONT> if (a < 0) {<a name="line.1487"></a> <FONT color="green">1488</FONT> ret = a - b;<a name="line.1488"></a> <FONT color="green">1489</FONT> } else {<a name="line.1489"></a> <FONT color="green">1490</FONT> throw new ArithmeticException(msg);<a name="line.1490"></a> <FONT color="green">1491</FONT> }<a name="line.1491"></a> <FONT color="green">1492</FONT> } else {<a name="line.1492"></a> <FONT color="green">1493</FONT> // use additive inverse<a name="line.1493"></a> <FONT color="green">1494</FONT> ret = addAndCheck(a, -b, msg);<a name="line.1494"></a> <FONT color="green">1495</FONT> }<a name="line.1495"></a> <FONT color="green">1496</FONT> return ret;<a name="line.1496"></a> <FONT color="green">1497</FONT> }<a name="line.1497"></a> <FONT color="green">1498</FONT> <a name="line.1498"></a> <FONT color="green">1499</FONT> /**<a name="line.1499"></a> <FONT color="green">1500</FONT> * Raise an int to an int power.<a name="line.1500"></a> <FONT color="green">1501</FONT> * @param k number to raise<a name="line.1501"></a> <FONT color="green">1502</FONT> * @param e exponent (must be positive or null)<a name="line.1502"></a> <FONT color="green">1503</FONT> * @return k<sup>e</sup><a name="line.1503"></a> <FONT color="green">1504</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1504"></a> <FONT color="green">1505</FONT> */<a name="line.1505"></a> <FONT color="green">1506</FONT> public static int pow(final int k, int e)<a name="line.1506"></a> <FONT color="green">1507</FONT> throws IllegalArgumentException {<a name="line.1507"></a> <FONT color="green">1508</FONT> <a name="line.1508"></a> <FONT color="green">1509</FONT> if (e < 0) {<a name="line.1509"></a> <FONT color="green">1510</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1510"></a> <FONT color="green">1511</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1511"></a> <FONT color="green">1512</FONT> k, e);<a name="line.1512"></a> <FONT color="green">1513</FONT> }<a name="line.1513"></a> <FONT color="green">1514</FONT> <a name="line.1514"></a> <FONT color="green">1515</FONT> int result = 1;<a name="line.1515"></a> <FONT color="green">1516</FONT> int k2p = k;<a name="line.1516"></a> <FONT color="green">1517</FONT> while (e != 0) {<a name="line.1517"></a> <FONT color="green">1518</FONT> if ((e & 0x1) != 0) {<a name="line.1518"></a> <FONT color="green">1519</FONT> result *= k2p;<a name="line.1519"></a> <FONT color="green">1520</FONT> }<a name="line.1520"></a> <FONT color="green">1521</FONT> k2p *= k2p;<a name="line.1521"></a> <FONT color="green">1522</FONT> e = e >> 1;<a name="line.1522"></a> <FONT color="green">1523</FONT> }<a name="line.1523"></a> <FONT color="green">1524</FONT> <a name="line.1524"></a> <FONT color="green">1525</FONT> return result;<a name="line.1525"></a> <FONT color="green">1526</FONT> <a name="line.1526"></a> <FONT color="green">1527</FONT> }<a name="line.1527"></a> <FONT color="green">1528</FONT> <a name="line.1528"></a> <FONT color="green">1529</FONT> /**<a name="line.1529"></a> <FONT color="green">1530</FONT> * Raise an int to a long power.<a name="line.1530"></a> <FONT color="green">1531</FONT> * @param k number to raise<a name="line.1531"></a> <FONT color="green">1532</FONT> * @param e exponent (must be positive or null)<a name="line.1532"></a> <FONT color="green">1533</FONT> * @return k<sup>e</sup><a name="line.1533"></a> <FONT color="green">1534</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1534"></a> <FONT color="green">1535</FONT> */<a name="line.1535"></a> <FONT color="green">1536</FONT> public static int pow(final int k, long e)<a name="line.1536"></a> <FONT color="green">1537</FONT> throws IllegalArgumentException {<a name="line.1537"></a> <FONT color="green">1538</FONT> <a name="line.1538"></a> <FONT color="green">1539</FONT> if (e < 0) {<a name="line.1539"></a> <FONT color="green">1540</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1540"></a> <FONT color="green">1541</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1541"></a> <FONT color="green">1542</FONT> k, e);<a name="line.1542"></a> <FONT color="green">1543</FONT> }<a name="line.1543"></a> <FONT color="green">1544</FONT> <a name="line.1544"></a> <FONT color="green">1545</FONT> int result = 1;<a name="line.1545"></a> <FONT color="green">1546</FONT> int k2p = k;<a name="line.1546"></a> <FONT color="green">1547</FONT> while (e != 0) {<a name="line.1547"></a> <FONT color="green">1548</FONT> if ((e & 0x1) != 0) {<a name="line.1548"></a> <FONT color="green">1549</FONT> result *= k2p;<a name="line.1549"></a> <FONT color="green">1550</FONT> }<a name="line.1550"></a> <FONT color="green">1551</FONT> k2p *= k2p;<a name="line.1551"></a> <FONT color="green">1552</FONT> e = e >> 1;<a name="line.1552"></a> <FONT color="green">1553</FONT> }<a name="line.1553"></a> <FONT color="green">1554</FONT> <a name="line.1554"></a> <FONT color="green">1555</FONT> return result;<a name="line.1555"></a> <FONT color="green">1556</FONT> <a name="line.1556"></a> <FONT color="green">1557</FONT> }<a name="line.1557"></a> <FONT color="green">1558</FONT> <a name="line.1558"></a> <FONT color="green">1559</FONT> /**<a name="line.1559"></a> <FONT color="green">1560</FONT> * Raise a long to an int power.<a name="line.1560"></a> <FONT color="green">1561</FONT> * @param k number to raise<a name="line.1561"></a> <FONT color="green">1562</FONT> * @param e exponent (must be positive or null)<a name="line.1562"></a> <FONT color="green">1563</FONT> * @return k<sup>e</sup><a name="line.1563"></a> <FONT color="green">1564</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1564"></a> <FONT color="green">1565</FONT> */<a name="line.1565"></a> <FONT color="green">1566</FONT> public static long pow(final long k, int e)<a name="line.1566"></a> <FONT color="green">1567</FONT> throws IllegalArgumentException {<a name="line.1567"></a> <FONT color="green">1568</FONT> <a name="line.1568"></a> <FONT color="green">1569</FONT> if (e < 0) {<a name="line.1569"></a> <FONT color="green">1570</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1570"></a> <FONT color="green">1571</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1571"></a> <FONT color="green">1572</FONT> k, e);<a name="line.1572"></a> <FONT color="green">1573</FONT> }<a name="line.1573"></a> <FONT color="green">1574</FONT> <a name="line.1574"></a> <FONT color="green">1575</FONT> long result = 1l;<a name="line.1575"></a> <FONT color="green">1576</FONT> long k2p = k;<a name="line.1576"></a> <FONT color="green">1577</FONT> while (e != 0) {<a name="line.1577"></a> <FONT color="green">1578</FONT> if ((e & 0x1) != 0) {<a name="line.1578"></a> <FONT color="green">1579</FONT> result *= k2p;<a name="line.1579"></a> <FONT color="green">1580</FONT> }<a name="line.1580"></a> <FONT color="green">1581</FONT> k2p *= k2p;<a name="line.1581"></a> <FONT color="green">1582</FONT> e = e >> 1;<a name="line.1582"></a> <FONT color="green">1583</FONT> }<a name="line.1583"></a> <FONT color="green">1584</FONT> <a name="line.1584"></a> <FONT color="green">1585</FONT> return result;<a name="line.1585"></a> <FONT color="green">1586</FONT> <a name="line.1586"></a> <FONT color="green">1587</FONT> }<a name="line.1587"></a> <FONT color="green">1588</FONT> <a name="line.1588"></a> <FONT color="green">1589</FONT> /**<a name="line.1589"></a> <FONT color="green">1590</FONT> * Raise a long to a long power.<a name="line.1590"></a> <FONT color="green">1591</FONT> * @param k number to raise<a name="line.1591"></a> <FONT color="green">1592</FONT> * @param e exponent (must be positive or null)<a name="line.1592"></a> <FONT color="green">1593</FONT> * @return k<sup>e</sup><a name="line.1593"></a> <FONT color="green">1594</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1594"></a> <FONT color="green">1595</FONT> */<a name="line.1595"></a> <FONT color="green">1596</FONT> public static long pow(final long k, long e)<a name="line.1596"></a> <FONT color="green">1597</FONT> throws IllegalArgumentException {<a name="line.1597"></a> <FONT color="green">1598</FONT> <a name="line.1598"></a> <FONT color="green">1599</FONT> if (e < 0) {<a name="line.1599"></a> <FONT color="green">1600</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1600"></a> <FONT color="green">1601</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1601"></a> <FONT color="green">1602</FONT> k, e);<a name="line.1602"></a> <FONT color="green">1603</FONT> }<a name="line.1603"></a> <FONT color="green">1604</FONT> <a name="line.1604"></a> <FONT color="green">1605</FONT> long result = 1l;<a name="line.1605"></a> <FONT color="green">1606</FONT> long k2p = k;<a name="line.1606"></a> <FONT color="green">1607</FONT> while (e != 0) {<a name="line.1607"></a> <FONT color="green">1608</FONT> if ((e & 0x1) != 0) {<a name="line.1608"></a> <FONT color="green">1609</FONT> result *= k2p;<a name="line.1609"></a> <FONT color="green">1610</FONT> }<a name="line.1610"></a> <FONT color="green">1611</FONT> k2p *= k2p;<a name="line.1611"></a> <FONT color="green">1612</FONT> e = e >> 1;<a name="line.1612"></a> <FONT color="green">1613</FONT> }<a name="line.1613"></a> <FONT color="green">1614</FONT> <a name="line.1614"></a> <FONT color="green">1615</FONT> return result;<a name="line.1615"></a> <FONT color="green">1616</FONT> <a name="line.1616"></a> <FONT color="green">1617</FONT> }<a name="line.1617"></a> <FONT color="green">1618</FONT> <a name="line.1618"></a> <FONT color="green">1619</FONT> /**<a name="line.1619"></a> <FONT color="green">1620</FONT> * Raise a BigInteger to an int power.<a name="line.1620"></a> <FONT color="green">1621</FONT> * @param k number to raise<a name="line.1621"></a> <FONT color="green">1622</FONT> * @param e exponent (must be positive or null)<a name="line.1622"></a> <FONT color="green">1623</FONT> * @return k<sup>e</sup><a name="line.1623"></a> <FONT color="green">1624</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1624"></a> <FONT color="green">1625</FONT> */<a name="line.1625"></a> <FONT color="green">1626</FONT> public static BigInteger pow(final BigInteger k, int e)<a name="line.1626"></a> <FONT color="green">1627</FONT> throws IllegalArgumentException {<a name="line.1627"></a> <FONT color="green">1628</FONT> <a name="line.1628"></a> <FONT color="green">1629</FONT> if (e < 0) {<a name="line.1629"></a> <FONT color="green">1630</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1630"></a> <FONT color="green">1631</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1631"></a> <FONT color="green">1632</FONT> k, e);<a name="line.1632"></a> <FONT color="green">1633</FONT> }<a name="line.1633"></a> <FONT color="green">1634</FONT> <a name="line.1634"></a> <FONT color="green">1635</FONT> return k.pow(e);<a name="line.1635"></a> <FONT color="green">1636</FONT> <a name="line.1636"></a> <FONT color="green">1637</FONT> }<a name="line.1637"></a> <FONT color="green">1638</FONT> <a name="line.1638"></a> <FONT color="green">1639</FONT> /**<a name="line.1639"></a> <FONT color="green">1640</FONT> * Raise a BigInteger to a long power.<a name="line.1640"></a> <FONT color="green">1641</FONT> * @param k number to raise<a name="line.1641"></a> <FONT color="green">1642</FONT> * @param e exponent (must be positive or null)<a name="line.1642"></a> <FONT color="green">1643</FONT> * @return k<sup>e</sup><a name="line.1643"></a> <FONT color="green">1644</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1644"></a> <FONT color="green">1645</FONT> */<a name="line.1645"></a> <FONT color="green">1646</FONT> public static BigInteger pow(final BigInteger k, long e)<a name="line.1646"></a> <FONT color="green">1647</FONT> throws IllegalArgumentException {<a name="line.1647"></a> <FONT color="green">1648</FONT> <a name="line.1648"></a> <FONT color="green">1649</FONT> if (e < 0) {<a name="line.1649"></a> <FONT color="green">1650</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1650"></a> <FONT color="green">1651</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1651"></a> <FONT color="green">1652</FONT> k, e);<a name="line.1652"></a> <FONT color="green">1653</FONT> }<a name="line.1653"></a> <FONT color="green">1654</FONT> <a name="line.1654"></a> <FONT color="green">1655</FONT> BigInteger result = BigInteger.ONE;<a name="line.1655"></a> <FONT color="green">1656</FONT> BigInteger k2p = k;<a name="line.1656"></a> <FONT color="green">1657</FONT> while (e != 0) {<a name="line.1657"></a> <FONT color="green">1658</FONT> if ((e & 0x1) != 0) {<a name="line.1658"></a> <FONT color="green">1659</FONT> result = result.multiply(k2p);<a name="line.1659"></a> <FONT color="green">1660</FONT> }<a name="line.1660"></a> <FONT color="green">1661</FONT> k2p = k2p.multiply(k2p);<a name="line.1661"></a> <FONT color="green">1662</FONT> e = e >> 1;<a name="line.1662"></a> <FONT color="green">1663</FONT> }<a name="line.1663"></a> <FONT color="green">1664</FONT> <a name="line.1664"></a> <FONT color="green">1665</FONT> return result;<a name="line.1665"></a> <FONT color="green">1666</FONT> <a name="line.1666"></a> <FONT color="green">1667</FONT> }<a name="line.1667"></a> <FONT color="green">1668</FONT> <a name="line.1668"></a> <FONT color="green">1669</FONT> /**<a name="line.1669"></a> <FONT color="green">1670</FONT> * Raise a BigInteger to a BigInteger power.<a name="line.1670"></a> <FONT color="green">1671</FONT> * @param k number to raise<a name="line.1671"></a> <FONT color="green">1672</FONT> * @param e exponent (must be positive or null)<a name="line.1672"></a> <FONT color="green">1673</FONT> * @return k<sup>e</sup><a name="line.1673"></a> <FONT color="green">1674</FONT> * @exception IllegalArgumentException if e is negative<a name="line.1674"></a> <FONT color="green">1675</FONT> */<a name="line.1675"></a> <FONT color="green">1676</FONT> public static BigInteger pow(final BigInteger k, BigInteger e)<a name="line.1676"></a> <FONT color="green">1677</FONT> throws IllegalArgumentException {<a name="line.1677"></a> <FONT color="green">1678</FONT> <a name="line.1678"></a> <FONT color="green">1679</FONT> if (e.compareTo(BigInteger.ZERO) < 0) {<a name="line.1679"></a> <FONT color="green">1680</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.1680"></a> <FONT color="green">1681</FONT> "cannot raise an integral value to a negative power ({0}^{1})",<a name="line.1681"></a> <FONT color="green">1682</FONT> k, e);<a name="line.1682"></a> <FONT color="green">1683</FONT> }<a name="line.1683"></a> <FONT color="green">1684</FONT> <a name="line.1684"></a> <FONT color="green">1685</FONT> BigInteger result = BigInteger.ONE;<a name="line.1685"></a> <FONT color="green">1686</FONT> BigInteger k2p = k;<a name="line.1686"></a> <FONT color="green">1687</FONT> while (!BigInteger.ZERO.equals(e)) {<a name="line.1687"></a> <FONT color="green">1688</FONT> if (e.testBit(0)) {<a name="line.1688"></a> <FONT color="green">1689</FONT> result = result.multiply(k2p);<a name="line.1689"></a> <FONT color="green">1690</FONT> }<a name="line.1690"></a> <FONT color="green">1691</FONT> k2p = k2p.multiply(k2p);<a name="line.1691"></a> <FONT color="green">1692</FONT> e = e.shiftRight(1);<a name="line.1692"></a> <FONT color="green">1693</FONT> }<a name="line.1693"></a> <FONT color="green">1694</FONT> <a name="line.1694"></a> <FONT color="green">1695</FONT> return result;<a name="line.1695"></a> <FONT color="green">1696</FONT> <a name="line.1696"></a> <FONT color="green">1697</FONT> }<a name="line.1697"></a> <FONT color="green">1698</FONT> <a name="line.1698"></a> <FONT color="green">1699</FONT> /**<a name="line.1699"></a> <FONT color="green">1700</FONT> * Calculates the L<sub>1</sub> (sum of abs) distance between two points.<a name="line.1700"></a> <FONT color="green">1701</FONT> *<a name="line.1701"></a> <FONT color="green">1702</FONT> * @param p1 the first point<a name="line.1702"></a> <FONT color="green">1703</FONT> * @param p2 the second point<a name="line.1703"></a> <FONT color="green">1704</FONT> * @return the L<sub>1</sub> distance between the two points<a name="line.1704"></a> <FONT color="green">1705</FONT> */<a name="line.1705"></a> <FONT color="green">1706</FONT> public static double distance1(double[] p1, double[] p2) {<a name="line.1706"></a> <FONT color="green">1707</FONT> double sum = 0;<a name="line.1707"></a> <FONT color="green">1708</FONT> for (int i = 0; i < p1.length; i++) {<a name="line.1708"></a> <FONT color="green">1709</FONT> sum += Math.abs(p1[i] - p2[i]);<a name="line.1709"></a> <FONT color="green">1710</FONT> }<a name="line.1710"></a> <FONT color="green">1711</FONT> return sum;<a name="line.1711"></a> <FONT color="green">1712</FONT> }<a name="line.1712"></a> <FONT color="green">1713</FONT> <a name="line.1713"></a> <FONT color="green">1714</FONT> /**<a name="line.1714"></a> <FONT color="green">1715</FONT> * Calculates the L<sub>1</sub> (sum of abs) distance between two points.<a name="line.1715"></a> <FONT color="green">1716</FONT> *<a name="line.1716"></a> <FONT color="green">1717</FONT> * @param p1 the first point<a name="line.1717"></a> <FONT color="green">1718</FONT> * @param p2 the second point<a name="line.1718"></a> <FONT color="green">1719</FONT> * @return the L<sub>1</sub> distance between the two points<a name="line.1719"></a> <FONT color="green">1720</FONT> */<a name="line.1720"></a> <FONT color="green">1721</FONT> public static int distance1(int[] p1, int[] p2) {<a name="line.1721"></a> <FONT color="green">1722</FONT> int sum = 0;<a name="line.1722"></a> <FONT color="green">1723</FONT> for (int i = 0; i < p1.length; i++) {<a name="line.1723"></a> <FONT color="green">1724</FONT> sum += Math.abs(p1[i] - p2[i]);<a name="line.1724"></a> <FONT color="green">1725</FONT> }<a name="line.1725"></a> <FONT color="green">1726</FONT> return sum;<a name="line.1726"></a> <FONT color="green">1727</FONT> }<a name="line.1727"></a> <FONT color="green">1728</FONT> <a name="line.1728"></a> <FONT color="green">1729</FONT> /**<a name="line.1729"></a> <FONT color="green">1730</FONT> * Calculates the L<sub>2</sub> (Euclidean) distance between two points.<a name="line.1730"></a> <FONT color="green">1731</FONT> *<a name="line.1731"></a> <FONT color="green">1732</FONT> * @param p1 the first point<a name="line.1732"></a> <FONT color="green">1733</FONT> * @param p2 the second point<a name="line.1733"></a> <FONT color="green">1734</FONT> * @return the L<sub>2</sub> distance between the two points<a name="line.1734"></a> <FONT color="green">1735</FONT> */<a name="line.1735"></a> <FONT color="green">1736</FONT> public static double distance(double[] p1, double[] p2) {<a name="line.1736"></a> <FONT color="green">1737</FONT> double sum = 0;<a name="line.1737"></a> <FONT color="green">1738</FONT> for (int i = 0; i < p1.length; i++) {<a name="line.1738"></a> <FONT color="green">1739</FONT> final double dp = p1[i] - p2[i];<a name="line.1739"></a> <FONT color="green">1740</FONT> sum += dp * dp;<a name="line.1740"></a> <FONT color="green">1741</FONT> }<a name="line.1741"></a> <FONT color="green">1742</FONT> return Math.sqrt(sum);<a name="line.1742"></a> <FONT color="green">1743</FONT> }<a name="line.1743"></a> <FONT color="green">1744</FONT> <a name="line.1744"></a> <FONT color="green">1745</FONT> /**<a name="line.1745"></a> <FONT color="green">1746</FONT> * Calculates the L<sub>2</sub> (Euclidean) distance between two points.<a name="line.1746"></a> <FONT color="green">1747</FONT> *<a name="line.1747"></a> <FONT color="green">1748</FONT> * @param p1 the first point<a name="line.1748"></a> <FONT color="green">1749</FONT> * @param p2 the second point<a name="line.1749"></a> <FONT color="green">1750</FONT> * @return the L<sub>2</sub> distance between the two points<a name="line.1750"></a> <FONT color="green">1751</FONT> */<a name="line.1751"></a> <FONT color="green">1752</FONT> public static double distance(int[] p1, int[] p2) {<a name="line.1752"></a> <FONT color="green">1753</FONT> double sum = 0;<a name="line.1753"></a> <FONT color="green">1754</FONT> for (int i = 0; i < p1.length; i++) {<a name="line.1754"></a> <FONT color="green">1755</FONT> final double dp = p1[i] - p2[i];<a name="line.1755"></a> <FONT color="green">1756</FONT> sum += dp * dp;<a name="line.1756"></a> <FONT color="green">1757</FONT> }<a name="line.1757"></a> <FONT color="green">1758</FONT> return Math.sqrt(sum);<a name="line.1758"></a> <FONT color="green">1759</FONT> }<a name="line.1759"></a> <FONT color="green">1760</FONT> <a name="line.1760"></a> <FONT color="green">1761</FONT> /**<a name="line.1761"></a> <FONT color="green">1762</FONT> * Calculates the L<sub>&infin;</sub> (max of abs) distance between two points.<a name="line.1762"></a> <FONT color="green">1763</FONT> *<a name="line.1763"></a> <FONT color="green">1764</FONT> * @param p1 the first point<a name="line.1764"></a> <FONT color="green">1765</FONT> * @param p2 the second point<a name="line.1765"></a> <FONT color="green">1766</FONT> * @return the L<sub>&infin;</sub> distance between the two points<a name="line.1766"></a> <FONT color="green">1767</FONT> */<a name="line.1767"></a> <FONT color="green">1768</FONT> public static double distanceInf(double[] p1, double[] p2) {<a name="line.1768"></a> <FONT color="green">1769</FONT> double max = 0;<a name="line.1769"></a> <FONT color="green">1770</FONT> for (int i = 0; i < p1.length; i++) {<a name="line.1770"></a> <FONT color="green">1771</FONT> max = Math.max(max, Math.abs(p1[i] - p2[i]));<a name="line.1771"></a> <FONT color="green">1772</FONT> }<a name="line.1772"></a> <FONT color="green">1773</FONT> return max;<a name="line.1773"></a> <FONT color="green">1774</FONT> }<a name="line.1774"></a> <FONT color="green">1775</FONT> <a name="line.1775"></a> <FONT color="green">1776</FONT> /**<a name="line.1776"></a> <FONT color="green">1777</FONT> * Calculates the L<sub>&infin;</sub> (max of abs) distance between two points.<a name="line.1777"></a> <FONT color="green">1778</FONT> *<a name="line.1778"></a> <FONT color="green">1779</FONT> * @param p1 the first point<a name="line.1779"></a> <FONT color="green">1780</FONT> * @param p2 the second point<a name="line.1780"></a> <FONT color="green">1781</FONT> * @return the L<sub>&infin;</sub> distance between the two points<a name="line.1781"></a> <FONT color="green">1782</FONT> */<a name="line.1782"></a> <FONT color="green">1783</FONT> public static int distanceInf(int[] p1, int[] p2) {<a name="line.1783"></a> <FONT color="green">1784</FONT> int max = 0;<a name="line.1784"></a> <FONT color="green">1785</FONT> for (int i = 0; i < p1.length; i++) {<a name="line.1785"></a> <FONT color="green">1786</FONT> max = Math.max(max, Math.abs(p1[i] - p2[i]));<a name="line.1786"></a> <FONT color="green">1787</FONT> }<a name="line.1787"></a> <FONT color="green">1788</FONT> return max;<a name="line.1788"></a> <FONT color="green">1789</FONT> }<a name="line.1789"></a> <FONT color="green">1790</FONT> <a name="line.1790"></a> <FONT color="green">1791</FONT> /**<a name="line.1791"></a> <FONT color="green">1792</FONT> * Checks that the given array is sorted.<a name="line.1792"></a> <FONT color="green">1793</FONT> *<a name="line.1793"></a> <FONT color="green">1794</FONT> * @param val Values<a name="line.1794"></a> <FONT color="green">1795</FONT> * @param dir Order direction (-1 for decreasing, 1 for increasing)<a name="line.1795"></a> <FONT color="green">1796</FONT> * @param strict Whether the order should be strict<a name="line.1796"></a> <FONT color="green">1797</FONT> * @throws IllegalArgumentException if the array is not sorted.<a name="line.1797"></a> <FONT color="green">1798</FONT> */<a name="line.1798"></a> <FONT color="green">1799</FONT> public static void checkOrder(double[] val, int dir, boolean strict) {<a name="line.1799"></a> <FONT color="green">1800</FONT> double previous = val[0];<a name="line.1800"></a> <FONT color="green">1801</FONT> <a name="line.1801"></a> <FONT color="green">1802</FONT> int max = val.length;<a name="line.1802"></a> <FONT color="green">1803</FONT> for (int i = 1; i < max; i++) {<a name="line.1803"></a> <FONT color="green">1804</FONT> if (dir > 0) {<a name="line.1804"></a> <FONT color="green">1805</FONT> if (strict) {<a name="line.1805"></a> <FONT color="green">1806</FONT> if (val[i] <= previous) {<a name="line.1806"></a> <FONT color="green">1807</FONT> throw MathRuntimeException.createIllegalArgumentException("points {0} and {1} are not strictly increasing ({2} >= {3})",<a name="line.1807"></a> <FONT color="green">1808</FONT> i - 1, i, previous, val[i]);<a name="line.1808"></a> <FONT color="green">1809</FONT> }<a name="line.1809"></a> <FONT color="green">1810</FONT> } else {<a name="line.1810"></a> <FONT color="green">1811</FONT> if (val[i] < previous) {<a name="line.1811"></a> <FONT color="green">1812</FONT> throw MathRuntimeException.createIllegalArgumentException("points {0} and {1} are not increasing ({2} > {3})",<a name="line.1812"></a> <FONT color="green">1813</FONT> i - 1, i, previous, val[i]);<a name="line.1813"></a> <FONT color="green">1814</FONT> }<a name="line.1814"></a> <FONT color="green">1815</FONT> }<a name="line.1815"></a> <FONT color="green">1816</FONT> } else {<a name="line.1816"></a> <FONT color="green">1817</FONT> if (strict) {<a name="line.1817"></a> <FONT color="green">1818</FONT> if (val[i] >= previous) {<a name="line.1818"></a> <FONT color="green">1819</FONT> throw MathRuntimeException.createIllegalArgumentException("points {0} and {1} are not strictly decreasing ({2} <= {3})",<a name="line.1819"></a> <FONT color="green">1820</FONT> i - 1, i, previous, val[i]);<a name="line.1820"></a> <FONT color="green">1821</FONT> }<a name="line.1821"></a> <FONT color="green">1822</FONT> } else {<a name="line.1822"></a> <FONT color="green">1823</FONT> if (val[i] > previous) {<a name="line.1823"></a> <FONT color="green">1824</FONT> throw MathRuntimeException.createIllegalArgumentException("points {0} and {1} are not decreasing ({2} < {3})",<a name="line.1824"></a> <FONT color="green">1825</FONT> i - 1, i, previous, val[i]);<a name="line.1825"></a> <FONT color="green">1826</FONT> }<a name="line.1826"></a> <FONT color="green">1827</FONT> }<a name="line.1827"></a> <FONT color="green">1828</FONT> }<a name="line.1828"></a> <FONT color="green">1829</FONT> <a name="line.1829"></a> <FONT color="green">1830</FONT> previous = val[i];<a name="line.1830"></a> <FONT color="green">1831</FONT> }<a name="line.1831"></a> <FONT color="green">1832</FONT> }<a name="line.1832"></a> <FONT color="green">1833</FONT> }<a name="line.1833"></a> </PRE> </BODY> </HTML>