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  Class java.lang.Math
</title>
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<pre>
<a href="packages.html">All Packages</a>  <a href="tree.html">Class Hierarchy</a>  <a href="Package-java.lang.html">This Package</a>  <a href="java.lang.Long.html#_top_">Previous</a>  <a href="java.lang.Number.html#_top_">Next</a>  <a href="AllNames.html">Index</a></pre>
<hr>
<h1>
  Class java.lang.Math
</h1>
<pre>
<a href="java.lang.Object.html#_top_">java.lang.Object</a>
   |
   +----java.lang.Math
</pre>
<hr>
<dl>
  <dt> public final class <b>Math</b>
  <dt> extends <a href="java.lang.Object.html#_top_">Object</a>
</dl>
The class <code>Math</code> contains methods for performing basic 
 numeric operations such as the elementary exponential, logarithm, 
 square root, and trigonometric functions. 
 <p>
 To help ensure portability of Java programs, the definitions of 
 many of the numeric functions in this package require that they 
 produce the same results as certain published algorithms. These 
 algorithms are available from the well-known network library 
 <code>netlib</code> as the package "Freely Distributable 
 Math Library" (<code>fdlibm</code>). These algorithms, which 
 are written in the C programming language, are then to be 
 understood as executed with all floating-point operations 
 following the rules of Java floating-point arithmetic. 
 <p>
 The network library may be found on the World Wide Web at 
 <ul><code>
   http://netlib.att.com/
 </code></ul>
 <p>
 then perform a keyword search for "<code>fdlibm</code>".
 <p>
 The Java math library is defined with respect to the version of 
 <code>fdlibm</code> dated January 4, 1995. Where 
 <code>fdlibm</code> provides more than one definition for a 
 function (such as <code>acos</code>), use the "IEEE 754 core 
 function" version (residing in a file whose name begins with 
 the letter <code>e</code>).
<p>
<hr>
<a name="index"></a>
<h2>
  <img src="images/variable-index.gif" width=207 height=38 alt="Variable Index">
</h2>
<dl>
  <dt> <img src="images/blue-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#E"><b>E</b></a>
  <dd>  The <code>double</code> value that is closer than any other to 
 <code>e</code>, the base of the natural logarithms.
  <dt> <img src="images/blue-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#PI"><b>PI</b></a>
  <dd>  The <code>double</code> value that is closer than any other to 
 <i>pi</i>, the ratio of the circumference of a circle to its diameter.
</dl>
<h2>
  <img src="images/method-index.gif" width=207 height=38 alt="Method Index">
</h2>
<dl>
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#abs(double)"><b>abs</b></a>(double)
  <dd>  Returns the absolute value of a <code>double</code> value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#abs(float)"><b>abs</b></a>(float)
  <dd>  Returns the absolute value of a <code>float</code> value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#abs(int)"><b>abs</b></a>(int)
  <dd>  Returns the absolute value of an <code>int</code> value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#abs(long)"><b>abs</b></a>(long)
  <dd>  Returns the absolute value of a <code>long</code> value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#acos(double)"><b>acos</b></a>(double)
  <dd>  Returns the arc cosine of an angle, in the range of 0.0 through
 <i>pi</i>.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#asin(double)"><b>asin</b></a>(double)
  <dd>  Returns the arc sine of an angle, in the range of -<i>pi</i>/2 through
 <i>pi</i>/2.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#atan(double)"><b>atan</b></a>(double)
  <dd>  Returns the arc tangent of an angle, in the range of -<i>pi</i>/2
 through <i>pi</i>/2.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#atan2(double, double)"><b>atan2</b></a>(double, double)
  <dd>  Converts rectangular coordinates (<code>b</code>,&nbsp;<code>a</code>)
 to polar (r,&nbsp;<i>theta</i>).
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#ceil(double)"><b>ceil</b></a>(double)
  <dd>  Returns the smallest (closest to negative infinity) 
 <code>double</code> value that is not less than the argument and is 
 equal to a mathematical integer.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#cos(double)"><b>cos</b></a>(double)
  <dd>  Returns the trigonometric cosine of an angle.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#exp(double)"><b>exp</b></a>(double)
  <dd>  Returns the exponential number <i>e</i> (i.e., 2.718...) raised to
 the power of a <code>double</code> value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#floor(double)"><b>floor</b></a>(double)
  <dd>  Returns the largest (closest to positive infinity) 
 <code>double</code> value that is not greater than the argument and 
 is equal to a mathematical integer.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#IEEEremainder(double, double)"><b>IEEEremainder</b></a>(double, double)
  <dd>  Computes the remainder operation on two arguments as prescribed 
 by the IEEE 754 standard.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#log(double)"><b>log</b></a>(double)
  <dd>  Returns the natural logarithm (base <i>e</i>) of a <code>double</code>
 value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#max(double, double)"><b>max</b></a>(double, double)
  <dd>  Returns the greater of two <code>double</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#max(float, float)"><b>max</b></a>(float, float)
  <dd>  Returns the greater of two <code>float</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#max(int, int)"><b>max</b></a>(int, int)
  <dd>  Returns the greater of two <code>int</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#max(long, long)"><b>max</b></a>(long, long)
  <dd>  Returns the greater of two <code>long</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#min(double, double)"><b>min</b></a>(double, double)
  <dd>  Returns the smaller of two <code>double</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#min(float, float)"><b>min</b></a>(float, float)
  <dd>  Returns the smaller of two <code>float</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#min(int, int)"><b>min</b></a>(int, int)
  <dd>  Returns the smaller of two <code>int</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#min(long, long)"><b>min</b></a>(long, long)
  <dd>  Returns the smaller of two <code>long</code> values.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#pow(double, double)"><b>pow</b></a>(double, double)
  <dd>  Returns of value of the first argument raised to the power of the
 second argument.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#random()"><b>random</b></a>()
  <dd>  Returns a random number between <code>0.0</code> and <code>1.0</code>.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#rint(double)"><b>rint</b></a>(double)
  <dd>  returns the closest integer to the argument.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#round(double)"><b>round</b></a>(double)
  <dd>  Returns the closest <code>long</code> to the argument.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#round(float)"><b>round</b></a>(float)
  <dd>  Returns the closest <code>int</code> to the argument.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#sin(double)"><b>sin</b></a>(double)
  <dd>  Returns the trigonometric sine of an angle.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#sqrt(double)"><b>sqrt</b></a>(double)
  <dd>  Returns the square root of a <code>double</code> value.
  <dt> <img src="images/green-ball-small.gif" width=6 height=6 alt=" o ">
	<a href="#tan(double)"><b>tan</b></a>(double)
  <dd>  Returns the trigonometric tangent of an angle.
</dl>
<a name="variables"></a>
<h2>
  <img src="images/variables.gif" width=153 height=38 alt="Variables">
</h2>
<a name="E"><img src="images/blue-ball.gif" width=12 height=12 alt=" o "></a>
<b>E</b>
<pre>
 public static final double E
</pre>
<dl>
  <dd> The <code>double</code> value that is closer than any other to 
 <code>e</code>, the base of the natural logarithms.<p>
</dl>
<a name="PI"><img src="images/blue-ball.gif" width=12 height=12 alt=" o "></a>
<b>PI</b>
<pre>
 public static final double PI
</pre>
<dl>
  <dd> The <code>double</code> value that is closer than any other to 
 <i>pi</i>, the ratio of the circumference of a circle to its diameter.<p>
</dl>
<a name="methods"></a>
<h2>
  <img src="images/methods.gif" width=151 height=38 alt="Methods">
</h2>
<a name="sin(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="sin"><b>sin</b></a>
<pre>
 public static native double sin(double a)
</pre>
<dl>
  <dd> Returns the trigonometric sine of an angle.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an angle, in radians.
    <dt> <b>Returns:</b>
    <dd> the sine of the argument.
  </dl></dd>
</dl>
<a name="cos(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="cos"><b>cos</b></a>
<pre>
 public static native double cos(double a)
</pre>
<dl>
  <dd> Returns the trigonometric cosine of an angle.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an angle, in radians.
    <dt> <b>Returns:</b>
    <dd> the cosine of the argument.
  </dl></dd>
</dl>
<a name="tan(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="tan"><b>tan</b></a>
<pre>
 public static native double tan(double a)
</pre>
<dl>
  <dd> Returns the trigonometric tangent of an angle.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an angle, in radians.
    <dt> <b>Returns:</b>
    <dd> the tangent of the argument.
  </dl></dd>
</dl>
<a name="asin(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="asin"><b>asin</b></a>
<pre>
 public static native double asin(double a)
</pre>
<dl>
  <dd> Returns the arc sine of an angle, in the range of -<i>pi</i>/2 through
 <i>pi</i>/2.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an angle, in radians.
    <dt> <b>Returns:</b>
    <dd> the arc sine of the argument.
  </dl></dd>
</dl>
<a name="acos(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="acos"><b>acos</b></a>
<pre>
 public static native double acos(double a)
</pre>
<dl>
  <dd> Returns the arc cosine of an angle, in the range of 0.0 through
 <i>pi</i>.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an angle, in radians.
    <dt> <b>Returns:</b>
    <dd> the arc cosine of the argument.
  </dl></dd>
</dl>
<a name="atan(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="atan"><b>atan</b></a>
<pre>
 public static native double atan(double a)
</pre>
<dl>
  <dd> Returns the arc tangent of an angle, in the range of -<i>pi</i>/2
 through <i>pi</i>/2.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an angle, in radians.
    <dt> <b>Returns:</b>
    <dd> the arc tangent of the argument.
  </dl></dd>
</dl>
<a name="exp(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="exp"><b>exp</b></a>
<pre>
 public static native double exp(double a)
</pre>
<dl>
  <dd> Returns the exponential number <i>e</i> (i.e., 2.718...) raised to
 the power of a <code>double</code> value.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the value <i>e</i><sup>a</sup>, where <i>e</i> is the base of
          the natural logarithms.
  </dl></dd>
</dl>
<a name="log(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="log"><b>log</b></a>
<pre>
 public static native double log(double a)
</pre>
<dl>
  <dd> Returns the natural logarithm (base <i>e</i>) of a <code>double</code>
 value.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a number greater than <code>0.0</code>.
    <dt> <b>Returns:</b>
    <dd> the value ln&nbsp;<code>a</code>, the natural logarithm of
          <code>a</code>.
  </dl></dd>
</dl>
<a name="sqrt(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="sqrt"><b>sqrt</b></a>
<pre>
 public static native double sqrt(double a)
</pre>
<dl>
  <dd> Returns the square root of a <code>double</code> value.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
 <!--@return  the value of &radic;&nbsp;<code>a</code>.-->
    <dt> <b>Returns:</b>
    <dd> the square root of <code>a</code>.
          If the argument is NaN or less than zero, the result is NaN.
  </dl></dd>
</dl>
<a name="IEEEremainder(double, double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="IEEEremainder"><b>IEEEremainder</b></a>
<pre>
 public static native double IEEEremainder(double f1,
                                           double f2)
</pre>
<dl>
  <dd> Computes the remainder operation on two arguments as prescribed 
 by the IEEE 754 standard.
 The remainder value is mathematically equal to 
 <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
 where <i>n</i> is the mathematical integer closest to the exact 
 mathematical value of the quotient <code>f1/f2</code>, and if two 
 mathematical integers are equally close to <code>f1/f2</code>, 
 then <i>n</i> is the integer that is even. If the remainder is 
 zero, its sign is the same as the sign of the first argument.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> f1 - the dividend.
    <dd> f2 - the divisor.
    <dt> <b>Returns:</b>
    <dd> the remainder when <code>f1</code> is divided by
          <code>f2</code>.
  </dl></dd>
</dl>
<a name="ceil(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="ceil"><b>ceil</b></a>
<pre>
 public static native double ceil(double a)
</pre>
<dl>
  <dd> Returns the smallest (closest to negative infinity) 
 <code>double</code> value that is not less than the argument and is 
 equal to a mathematical integer.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
 <!--@return  the value &lceil;&nbsp;<code>a</code>&nbsp;&rceil;.-->
    <dt> <b>Returns:</b>
    <dd> the smallest (closest to negative infinity)
          <code>double</code> value that is not less than the argument
          and is equal to a mathematical integer.
  </dl></dd>
</dl>
<a name="floor(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="floor"><b>floor</b></a>
<pre>
 public static native double floor(double a)
</pre>
<dl>
  <dd> Returns the largest (closest to positive infinity) 
 <code>double</code> value that is not greater than the argument and 
 is equal to a mathematical integer.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dd> a - an assigned value.
 <!--@return  the value &lfloor;&nbsp;<code>a</code>&nbsp;&rfloor;.-->
    <dt> <b>Returns:</b>
    <dd> the largest (closest to positive infinity)
          <code>double</code> value that is not greater than the argument
          and is equal to a mathematical integer.
  </dl></dd>
</dl>
<a name="rint(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="rint"><b>rint</b></a>
<pre>
 public static native double rint(double a)
</pre>
<dl>
  <dd> returns the closest integer to the argument.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the closest <code>double</code> value to <code>a</code> that is
          equal to a mathematical integer. If two <code>double</code>
          values that are mathematical integers are equally close to the
          value of the argument, the result is the integer value that
          is even.
  </dl></dd>
</dl>
<a name="atan2(double, double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="atan2"><b>atan2</b></a>
<pre>
 public static native double atan2(double a,
                                   double b)
</pre>
<dl>
  <dd> Converts rectangular coordinates (<code>b</code>,&nbsp;<code>a</code>)
 to polar (r,&nbsp;<i>theta</i>).
 This method computes the phase <i>theta</i> by computing an arc tangent
 of <code>b/a</code> in the range of -<i>pi</i> to <i>pi</i>.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dd> b - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the <i>theta</i> component of the point
          (<i>r</i>,&nbsp;<i>theta</i>)
          in polar coordinates that corresponds to the point
          (<i>b</i>,&nbsp;<i>a</i>) in Cartesian coordinates.
  </dl></dd>
</dl>
<a name="pow(double, double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="pow"><b>pow</b></a>
<pre>
 public static native double pow(double a,
                                 double b)
</pre>
<dl>
  <dd> Returns of value of the first argument raised to the power of the
 second argument.
 <p>
 If (<code>a&nbsp;==&nbsp;0.0</code>), then <code>b</code> must be
 greater than <code>0.0</code>; otherwise an exception is thrown. 
 An exception also will occur if (<code>a&nbsp;&lt;=&nbsp;0.0</code>)
 and <code>b</code> is not equal to a whole number.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dd> b - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the value <code>a<sup>b</sup></code>.
    <dt> <b>Throws:</b> <a href="java.lang.ArithmeticException.html#_top_">ArithmeticException</a>
    <dd> if (<code>a&nbsp;==&nbsp;0.0</code>) and
              (<code>b&nbsp;&lt;=&nbsp0.0</code>), or
              if (<code>a&nbsp;&lt;=&nbsp;0.0</code>) and <code>b</code>
              is not equal to a whole number.
  </dl></dd>
</dl>
<a name="round(float)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="round"><b>round</b></a>
<pre>
 public static int round(float a)
</pre>
<dl>
  <dd> Returns the closest <code>int</code> to the argument. 
 <p>
 If the argument is negative infinity or any value less than or 
 equal to the value of <code>Integer.MIN_VALUE</code>, the result is 
 equal to the value of <code>Integer.MIN_VALUE</code>. 
 <p>
 If the argument is positive infinity or any value greater than or 
 equal to the value of <code>Integer.MAX_VALUE</code>, the result is 
 equal to the value of <code>Integer.MAX_VALUE</code>.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>float</code> value.
    <dt> <b>Returns:</b>
    <dd> the value of the argument rounded to the nearest
          <code>int</code> value.
    <dt> <b>See Also:</b>
    <dd> <a href="java.lang.Integer.html#MAX_VALUE">MAX_VALUE</a>, <a href="java.lang.Integer.html#MIN_VALUE">MIN_VALUE</a>
  </dl></dd>
</dl>
<a name="round(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="round"><b>round</b></a>
<pre>
 public static long round(double a)
</pre>
<dl>
  <dd> Returns the closest <code>long</code> to the argument. 
 <p>
 If the argument is negative infinity or any value less than or 
 equal to the value of <code>Long.MIN_VALUE</code>, the result is 
 equal to the value of <code>Long.MIN_VALUE</code>. 
 <p>
 If the argument is positive infinity or any value greater than or 
 equal to the value of <code>Long.MAX_VALUE</code>, the result is 
 equal to the value of <code>Long.MAX_VALUE</code>.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the value of the argument rounded to the nearest
          <code>long</code> value.
    <dt> <b>See Also:</b>
    <dd> <a href="java.lang.Long.html#MAX_VALUE">MAX_VALUE</a>, <a href="java.lang.Long.html#MIN_VALUE">MIN_VALUE</a>
  </dl></dd>
</dl>
<a name="random()"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="random"><b>random</b></a>
<pre>
 public static synchronized double random()
</pre>
<dl>
  <dd> Returns a random number between <code>0.0</code> and <code>1.0</code>.
 Random number generators are often referred to as pseudorandom number 
 generators because the numbers produced tend to repeat themselves after
 a period of time.
<p>
  <dd><dl>
    <dt> <b>Returns:</b>
    <dd> a pseudorandom <code>double</code> between <code>0.0</code>
          and <code>1.0</code>.
    <dt> <b>See Also:</b>
    <dd> <a href="java.util.Random.html#nextDouble()">nextDouble</a>
  </dl></dd>
</dl>
<a name="abs(int)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="abs"><b>abs</b></a>
<pre>
 public static int abs(int a)
</pre>
<dl>
  <dd> Returns the absolute value of an <code>int</code> value.
 If the argument is not negative, the argument is returned.
 If the argument is negative, the negation of the argument is returned. 
 <p>
 Note that if the argument is equal to the value of 
 <code>Integer.MIN_VALUE</code>, the most negative representable 
 <code>int</code> value, the result is that same value, which is 
 negative.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an <code>int</code> value.
    <dt> <b>Returns:</b>
    <dd> the absolute value of the argument.
    <dt> <b>See Also:</b>
    <dd> <a href="java.lang.Integer.html#MIN_VALUE">MIN_VALUE</a>
  </dl></dd>
</dl>
<a name="abs(long)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="abs"><b>abs</b></a>
<pre>
 public static long abs(long a)
</pre>
<dl>
  <dd> Returns the absolute value of a <code>long</code> value.
 If the argument is not negative, the argument is returned.
 If the argument is negative, the negation of the argument is returned. 
 <p>
 Note that if the argument is equal to the value of 
 <code>Long.MIN_VALUE</code>, the most negative representable 
 <code>long</code> value, the result is that same value, which is 
 negative.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>long</code> value.
    <dt> <b>Returns:</b>
    <dd> the absolute value of the argument.
    <dt> <b>See Also:</b>
    <dd> <a href="java.lang.Long.html#MIN_VALUE">MIN_VALUE</a>
  </dl></dd>
</dl>
<a name="abs(float)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="abs"><b>abs</b></a>
<pre>
 public static float abs(float a)
</pre>
<dl>
  <dd> Returns the absolute value of a <code>float</code> value.
 If the argument is not negative, the argument is returned.
 If the argument is negative, the negation of the argument is returned.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>float</code> value.
    <dt> <b>Returns:</b>
    <dd> the absolute value of the argument.
  </dl></dd>
</dl>
<a name="abs(double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="abs"><b>abs</b></a>
<pre>
 public static double abs(double a)
</pre>
<dl>
  <dd> Returns the absolute value of a <code>double</code> value.
 If the argument is not negative, the argument is returned.
 If the argument is negative, the negation of the argument is returned.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the absolute value of the argument.
  </dl></dd>
</dl>
<a name="max(int, int)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="max"><b>max</b></a>
<pre>
 public static int max(int a,
                       int b)
</pre>
<dl>
  <dd> Returns the greater of two <code>int</code> values.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an <code>int</code> value.
    <dd> b - an <code>int</code> value.
    <dt> <b>Returns:</b>
    <dd> the larger of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<a name="max(long, long)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="max"><b>max</b></a>
<pre>
 public static long max(long a,
                        long b)
</pre>
<dl>
  <dd> Returns the greater of two <code>long</code> values.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>long</code> value.
    <dd> b - a <code>long</code> value.
    <dt> <b>Returns:</b>
    <dd> the larger of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<a name="max(float, float)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="max"><b>max</b></a>
<pre>
 public static float max(float a,
                         float b)
</pre>
<dl>
  <dd> Returns the greater of two <code>float</code> values.  If either value
 is <code>NaN</code>, then the result is <code>NaN</code>.  Unlike the
 the numerical comparison operators, this method considers negative zero
 to be strictly smaller than positive zero.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>float</code> value.
    <dd> b - a <code>float</code> value.
    <dt> <b>Returns:</b>
    <dd> the larger of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<a name="max(double, double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="max"><b>max</b></a>
<pre>
 public static double max(double a,
                          double b)
</pre>
<dl>
  <dd> Returns the greater of two <code>double</code> values.  If either value
 is <code>NaN</code>, then the result is <code>NaN</code>.  Unlike the
 the numerical comparison operators, this method considers negative zero
 to be strictly smaller than positive zero.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dd> b - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the larger of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<a name="min(int, int)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="min"><b>min</b></a>
<pre>
 public static int min(int a,
                       int b)
</pre>
<dl>
  <dd> Returns the smaller of two <code>int</code> values.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - an <code>int</code> value.
    <dd> b - an <code>int</code> value.
    <dt> <b>Returns:</b>
    <dd> the smaller of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<a name="min(long, long)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="min"><b>min</b></a>
<pre>
 public static long min(long a,
                        long b)
</pre>
<dl>
  <dd> Returns the smaller of two <code>long</code> values.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>long</code> value.
    <dd> b - a <code>long</code> value.
    <dt> <b>Returns:</b>
    <dd> the smaller of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<a name="min(float, float)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="min"><b>min</b></a>
<pre>
 public static float min(float a,
                         float b)
</pre>
<dl>
  <dd> Returns the smaller of two <code>float</code> values.  If either value
 is <code>NaN</code>, then the result is <code>NaN</code>.  Unlike the
 the numerical comparison operators, this method considers negative zero
 to be strictly smaller than positive zero.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>float</code> value.
    <dd> b - a <code>float</code> value.
    <dt> <b>Returns:</b>
    <dd> the smaller of <code>a</code> and <code>b.</code>
  </dl></dd>
</dl>
<a name="min(double, double)"><img src="images/green-ball.gif" width=12 height=12 alt=" o "></a>
<a name="min"><b>min</b></a>
<pre>
 public static double min(double a,
                          double b)
</pre>
<dl>
  <dd> Returns the smaller of two <code>double</code> values.  If either value
 is <code>NaN</code>, then the result is <code>NaN</code>.  Unlike the
 the numerical comparison operators, this method considers negative zero
 to be strictly smaller than positive zero.
<p>
  <dd><dl>
    <dt> <b>Parameters:</b>
    <dd> a - a <code>double</code> value.
    <dd> b - a <code>double</code> value.
    <dt> <b>Returns:</b>
    <dd> the smaller of <code>a</code> and <code>b</code>.
  </dl></dd>
</dl>
<hr>
<pre>
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