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<div class="subTitle">org.apache.commons.math3.util</div>
<h2 title="Class FastMath" class="title">Class FastMath</h2>
</div>
<div class="contentContainer">
<ul class="inheritance">
<li><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
<li>
<ul class="inheritance">
<li>org.apache.commons.math3.util.FastMath</li>
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<pre>public class <span class="strong">FastMath</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Faster, more accurate, portable alternative to <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true" title="class or interface in java.lang"><code>Math</code></a> and
<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/StrictMath.html?is-external=true" title="class or interface in java.lang"><code>StrictMath</code></a> for large scale computation.
<p>
FastMath is a drop-in replacement for both Math and StrictMath. This
means that for any method in Math (say <code>Math.sin(x)</code> or
<code>Math.cbrt(y)</code>), user can directly change the class and use the
methods as is (using <code>FastMath.sin(x)</code> or <code>FastMath.cbrt(y)</code>
in the previous example).
</p>
<p>
FastMath speed is achieved by relying heavily on optimizing compilers
to native code present in many JVMs today and use of large tables.
The larger tables are lazily initialised on first use, so that the setup
time does not penalise methods that don't need them.
</p>
<p>
Note that FastMath is
extensively used inside Apache Commons Math, so by calling some algorithms,
the overhead when the the tables need to be intialised will occur
regardless of the end-user calling FastMath methods directly or not.
Performance figures for a specific JVM and hardware can be evaluated by
running the FastMathTestPerformance tests in the test directory of the source
distribution.
</p>
<p>
FastMath accuracy should be mostly independent of the JVM as it relies only
on IEEE-754 basic operations and on embedded tables. Almost all operations
are accurate to about 0.5 ulp throughout the domain range. This statement,
of course is only a rough global observed behavior, it is <em>not</em> a
guarantee for <em>every</em> double numbers input (see William Kahan's <a
href="http://en.wikipedia.org/wiki/Rounding#The_table-maker.27s_dilemma">Table
Maker's Dilemma</a>).
</p>
<p>
FastMath additionally implements the following methods not found in Math/StrictMath:
<ul>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#asinh(double)"><code>asinh(double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#acosh(double)"><code>acosh(double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#atanh(double)"><code>atanh(double)</code></a></li>
</ul>
The following methods are found in Math/StrictMath since 1.6 only, they are provided
by FastMath even in 1.5 Java virtual machines
<ul>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#copySign(double, double)"><code>copySign(double, double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#getExponent(double)"><code>getExponent(double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextAfter(double, double)"><code>nextAfter(double,double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextUp(double)"><code>nextUp(double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#scalb(double, int)"><code>scalb(double, int)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#copySign(float, float)"><code>copySign(float, float)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#getExponent(float)"><code>getExponent(float)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextAfter(float, double)"><code>nextAfter(float,double)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextUp(float)"><code>nextUp(float)</code></a></li>
<li><a href="../../../../../org/apache/commons/math3/util/FastMath.html#scalb(float, int)"><code>scalb(float, int)</code></a></li>
</ul>
</p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: FastMath.java 1591835 2014-05-02 09:04:01Z tn $</dd></dl>
</li>
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<caption><span>Fields</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#E">E</a></strong></code>
<div class="block">Napier's constant e, base of the natural logarithm.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#PI">PI</a></strong></code>
<div class="block">Archimede's constant PI, ratio of circle circumference to diameter.</div>
</td>
</tr>
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</li>
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<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#abs(double)">abs</a></strong>(double&nbsp;x)</code>
<div class="block">Absolute value.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#abs(float)">abs</a></strong>(float&nbsp;x)</code>
<div class="block">Absolute value.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#abs(int)">abs</a></strong>(int&nbsp;x)</code>
<div class="block">Absolute value.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#abs(long)">abs</a></strong>(long&nbsp;x)</code>
<div class="block">Absolute value.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#acos(double)">acos</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the arc cosine of a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#acosh(double)">acosh</a></strong>(double&nbsp;a)</code>
<div class="block">Compute the inverse hyperbolic cosine of a number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#asin(double)">asin</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the arc sine of a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#asinh(double)">asinh</a></strong>(double&nbsp;a)</code>
<div class="block">Compute the inverse hyperbolic sine of a number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#atan(double)">atan</a></strong>(double&nbsp;x)</code>
<div class="block">Arctangent function</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#atan2(double, double)">atan2</a></strong>(double&nbsp;y,
double&nbsp;x)</code>
<div class="block">Two arguments arctangent function</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#atanh(double)">atanh</a></strong>(double&nbsp;a)</code>
<div class="block">Compute the inverse hyperbolic tangent of a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#cbrt(double)">cbrt</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the cubic root of a number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#ceil(double)">ceil</a></strong>(double&nbsp;x)</code>
<div class="block">Get the smallest whole number larger than x.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#copySign(double, double)">copySign</a></strong>(double&nbsp;magnitude,
double&nbsp;sign)</code>
<div class="block">Returns the first argument with the sign of the second argument.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#copySign(float, float)">copySign</a></strong>(float&nbsp;magnitude,
float&nbsp;sign)</code>
<div class="block">Returns the first argument with the sign of the second argument.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#cos(double)">cos</a></strong>(double&nbsp;x)</code>
<div class="block">Cosine function.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)">cosh</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the hyperbolic cosine of a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#exp(double)">exp</a></strong>(double&nbsp;x)</code>
<div class="block">Exponential function.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#expm1(double)">expm1</a></strong>(double&nbsp;x)</code>
<div class="block">Compute exp(x) - 1</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#floor(double)">floor</a></strong>(double&nbsp;x)</code>
<div class="block">Get the largest whole number smaller than x.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#getExponent(double)">getExponent</a></strong>(double&nbsp;d)</code>
<div class="block">Return the exponent of a double number, removing the bias.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#getExponent(float)">getExponent</a></strong>(float&nbsp;f)</code>
<div class="block">Return the exponent of a float number, removing the bias.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#hypot(double, double)">hypot</a></strong>(double&nbsp;x,
double&nbsp;y)</code>
<div class="block">Returns the hypotenuse of a triangle with sides <code>x</code> and <code>y</code>
- sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)<br/>
avoiding intermediate overflow or underflow.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#IEEEremainder(double, double)">IEEEremainder</a></strong>(double&nbsp;dividend,
double&nbsp;divisor)</code>
<div class="block">Computes the remainder as prescribed by the IEEE 754 standard.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#log(double)">log</a></strong>(double&nbsp;x)</code>
<div class="block">Natural logarithm.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#log(double, double)">log</a></strong>(double&nbsp;base,
double&nbsp;x)</code>
<div class="block">Computes the <a href="http://mathworld.wolfram.com/Logarithm.html">
logarithm</a> in a given base.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#log10(double)">log10</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the base 10 logarithm.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#log1p(double)">log1p</a></strong>(double&nbsp;x)</code>
<div class="block">Computes log(1 + x).</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#main(java.lang.String[])">main</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>[]&nbsp;a)</code>
<div class="block">Print out contents of arrays, and check the length.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#max(double, double)">max</a></strong>(double&nbsp;a,
double&nbsp;b)</code>
<div class="block">Compute the maximum of two values</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#max(float, float)">max</a></strong>(float&nbsp;a,
float&nbsp;b)</code>
<div class="block">Compute the maximum of two values</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#max(int, int)">max</a></strong>(int&nbsp;a,
int&nbsp;b)</code>
<div class="block">Compute the maximum of two values</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#max(long, long)">max</a></strong>(long&nbsp;a,
long&nbsp;b)</code>
<div class="block">Compute the maximum of two values</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#min(double, double)">min</a></strong>(double&nbsp;a,
double&nbsp;b)</code>
<div class="block">Compute the minimum of two values</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#min(float, float)">min</a></strong>(float&nbsp;a,
float&nbsp;b)</code>
<div class="block">Compute the minimum of two values</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#min(int, int)">min</a></strong>(int&nbsp;a,
int&nbsp;b)</code>
<div class="block">Compute the minimum of two values</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#min(long, long)">min</a></strong>(long&nbsp;a,
long&nbsp;b)</code>
<div class="block">Compute the minimum of two values</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextAfter(double, double)">nextAfter</a></strong>(double&nbsp;d,
double&nbsp;direction)</code>
<div class="block">Get the next machine representable number after a number, moving
in the direction of another number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextAfter(float, double)">nextAfter</a></strong>(float&nbsp;f,
double&nbsp;direction)</code>
<div class="block">Get the next machine representable number after a number, moving
in the direction of another number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextUp(double)">nextUp</a></strong>(double&nbsp;a)</code>
<div class="block">Compute next number towards positive infinity.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#nextUp(float)">nextUp</a></strong>(float&nbsp;a)</code>
<div class="block">Compute next number towards positive infinity.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#pow(double, double)">pow</a></strong>(double&nbsp;x,
double&nbsp;y)</code>
<div class="block">Power function.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#pow(double, int)">pow</a></strong>(double&nbsp;d,
int&nbsp;e)</code>
<div class="block">Raise a double to an int power.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#random()">random</a></strong>()</code>
<div class="block">Returns a pseudo-random number between 0.0 and 1.0.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#rint(double)">rint</a></strong>(double&nbsp;x)</code>
<div class="block">Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static long</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#round(double)">round</a></strong>(double&nbsp;x)</code>
<div class="block">Get the closest long to x.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#round(float)">round</a></strong>(float&nbsp;x)</code>
<div class="block">Get the closest int to x.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#scalb(double, int)">scalb</a></strong>(double&nbsp;d,
int&nbsp;n)</code>
<div class="block">Multiply a double number by a power of 2.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#scalb(float, int)">scalb</a></strong>(float&nbsp;f,
int&nbsp;n)</code>
<div class="block">Multiply a float number by a power of 2.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#signum(double)">signum</a></strong>(double&nbsp;a)</code>
<div class="block">Compute the signum of a number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#signum(float)">signum</a></strong>(float&nbsp;a)</code>
<div class="block">Compute the signum of a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#sin(double)">sin</a></strong>(double&nbsp;x)</code>
<div class="block">Sine function.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)">sinh</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the hyperbolic sine of a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#sqrt(double)">sqrt</a></strong>(double&nbsp;a)</code>
<div class="block">Compute the square root of a number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#tan(double)">tan</a></strong>(double&nbsp;x)</code>
<div class="block">Tangent function.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#tanh(double)">tanh</a></strong>(double&nbsp;x)</code>
<div class="block">Compute the hyperbolic tangent of a number.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#toDegrees(double)">toDegrees</a></strong>(double&nbsp;x)</code>
<div class="block">Convert radians to degrees, with error of less than 0.5 ULP</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#toRadians(double)">toRadians</a></strong>(double&nbsp;x)</code>
<div class="block">Convert degrees to radians, with error of less than 0.5 ULP</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#ulp(double)">ulp</a></strong>(double&nbsp;x)</code>
<div class="block">Compute least significant bit (Unit in Last Position) for a number.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static float</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/FastMath.html#ulp(float)">ulp</a></strong>(float&nbsp;x)</code>
<div class="block">Compute least significant bit (Unit in Last Position) for a number.</div>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<a name="PI">
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<h4>PI</h4>
<pre>public static final&nbsp;double PI</pre>
<div class="block">Archimede's constant PI, ratio of circle circumference to diameter.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.util.FastMath.PI">Constant Field Values</a></dd></dl>
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<pre>public static final&nbsp;double E</pre>
<div class="block">Napier's constant e, base of the natural logarithm.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.util.FastMath.E">Constant Field Values</a></dd></dl>
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<pre>public static&nbsp;double&nbsp;sqrt(double&nbsp;a)</pre>
<div class="block">Compute the square root of a number.
<p><b>Note:</b> this implementation currently delegates to <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#sqrt(double)" title="class or interface in java.lang"><code>Math.sqrt(double)</code></a></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>square root of a</dd></dl>
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<pre>public static&nbsp;double&nbsp;cosh(double&nbsp;x)</pre>
<div class="block">Compute the hyperbolic cosine of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>hyperbolic cosine of x</dd></dl>
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<pre>public static&nbsp;double&nbsp;sinh(double&nbsp;x)</pre>
<div class="block">Compute the hyperbolic sine of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>hyperbolic sine of x</dd></dl>
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<pre>public static&nbsp;double&nbsp;tanh(double&nbsp;x)</pre>
<div class="block">Compute the hyperbolic tangent of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>hyperbolic tangent of x</dd></dl>
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<pre>public static&nbsp;double&nbsp;acosh(double&nbsp;a)</pre>
<div class="block">Compute the inverse hyperbolic cosine of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>inverse hyperbolic cosine of a</dd></dl>
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<pre>public static&nbsp;double&nbsp;asinh(double&nbsp;a)</pre>
<div class="block">Compute the inverse hyperbolic sine of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>inverse hyperbolic sine of a</dd></dl>
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<pre>public static&nbsp;double&nbsp;atanh(double&nbsp;a)</pre>
<div class="block">Compute the inverse hyperbolic tangent of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>inverse hyperbolic tangent of a</dd></dl>
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<pre>public static&nbsp;double&nbsp;signum(double&nbsp;a)</pre>
<div class="block">Compute the signum of a number.
The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a</dd></dl>
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<pre>public static&nbsp;float&nbsp;signum(float&nbsp;a)</pre>
<div class="block">Compute the signum of a number.
The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a</dd></dl>
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<pre>public static&nbsp;double&nbsp;nextUp(double&nbsp;a)</pre>
<div class="block">Compute next number towards positive infinity.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number to which neighbor should be computed</dd>
<dt><span class="strong">Returns:</span></dt><dd>neighbor of a towards positive infinity</dd></dl>
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<pre>public static&nbsp;float&nbsp;nextUp(float&nbsp;a)</pre>
<div class="block">Compute next number towards positive infinity.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number to which neighbor should be computed</dd>
<dt><span class="strong">Returns:</span></dt><dd>neighbor of a towards positive infinity</dd></dl>
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<pre>public static&nbsp;double&nbsp;random()</pre>
<div class="block">Returns a pseudo-random number between 0.0 and 1.0.
<p><b>Note:</b> this implementation currently delegates to <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#random()" title="class or interface in java.lang"><code>Math.random()</code></a></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a random number between 0.0 and 1.0</dd></dl>
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<pre>public static&nbsp;double&nbsp;exp(double&nbsp;x)</pre>
<div class="block">Exponential function.
Computes exp(x), function result is nearly rounded. It will be correctly
rounded to the theoretical value for 99.9% of input values, otherwise it will
have a 1 UPL error.
Method:
Lookup intVal = exp(int(x))
Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 );
Compute z as the exponential of the remaining bits by a polynomial minus one
exp(x) = intVal * fracVal * (1 + z)
Accuracy:
Calculation is done with 63 bits of precision, so result should be correctly
rounded for 99.9% of input values, with less than 1 ULP error otherwise.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - a double</dd>
<dt><span class="strong">Returns:</span></dt><dd>double e<sup>x</sup></dd></dl>
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<pre>public static&nbsp;double&nbsp;expm1(double&nbsp;x)</pre>
<div class="block">Compute exp(x) - 1</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number to compute shifted exponential</dd>
<dt><span class="strong">Returns:</span></dt><dd>exp(x) - 1</dd></dl>
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<pre>public static&nbsp;double&nbsp;log(double&nbsp;x)</pre>
<div class="block">Natural logarithm.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - a double</dd>
<dt><span class="strong">Returns:</span></dt><dd>log(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;log1p(double&nbsp;x)</pre>
<div class="block">Computes log(1 + x).</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Number.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>log(1 + x)</code>.</dd></dl>
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<pre>public static&nbsp;double&nbsp;log10(double&nbsp;x)</pre>
<div class="block">Compute the base 10 logarithm.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - a number</dd>
<dt><span class="strong">Returns:</span></dt><dd>log10(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;log(double&nbsp;base,
double&nbsp;x)</pre>
<div class="block">Computes the <a href="http://mathworld.wolfram.com/Logarithm.html">
logarithm</a> in a given base.
Returns <code>NaN</code> if either argument is negative.
If <code>base</code> is 0 and <code>x</code> is positive, 0 is returned.
If <code>base</code> is positive and <code>x</code> is 0,
<code>Double.NEGATIVE_INFINITY</code> is returned.
If both arguments are 0, the result is <code>NaN</code>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>base</code> - Base of the logarithm, must be greater than 0.</dd><dd><code>x</code> - Argument, must be greater than 0.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the value of the logarithm, i.e. the number <code>y</code> such that
<code>base<sup>y</sup> = x</code>.</dd><dt><span class="strong">Since:</span></dt>
<dd>1.2 (previously in <code>MathUtils</code>, moved as of version 3.0)</dd></dl>
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<pre>public static&nbsp;double&nbsp;pow(double&nbsp;x,
double&nbsp;y)</pre>
<div class="block">Power function. Compute x^y.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - a double</dd><dd><code>y</code> - a double</dd>
<dt><span class="strong">Returns:</span></dt><dd>double</dd></dl>
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<pre>public static&nbsp;double&nbsp;pow(double&nbsp;d,
int&nbsp;e)</pre>
<div class="block">Raise a double to an int power.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - Number to raise.</dd><dd><code>e</code> - Exponent.</dd>
<dt><span class="strong">Returns:</span></dt><dd>d<sup>e</sup></dd><dt><span class="strong">Since:</span></dt>
<dd>3.1</dd></dl>
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<pre>public static&nbsp;double&nbsp;sin(double&nbsp;x)</pre>
<div class="block">Sine function.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Argument.</dd>
<dt><span class="strong">Returns:</span></dt><dd>sin(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;cos(double&nbsp;x)</pre>
<div class="block">Cosine function.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Argument.</dd>
<dt><span class="strong">Returns:</span></dt><dd>cos(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;tan(double&nbsp;x)</pre>
<div class="block">Tangent function.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Argument.</dd>
<dt><span class="strong">Returns:</span></dt><dd>tan(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;atan(double&nbsp;x)</pre>
<div class="block">Arctangent function</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - a number</dd>
<dt><span class="strong">Returns:</span></dt><dd>atan(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;atan2(double&nbsp;y,
double&nbsp;x)</pre>
<div class="block">Two arguments arctangent function</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>y</code> - ordinate</dd><dd><code>x</code> - abscissa</dd>
<dt><span class="strong">Returns:</span></dt><dd>phase angle of point (x,y) between <code>-PI</code> and <code>PI</code></dd></dl>
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<pre>public static&nbsp;double&nbsp;asin(double&nbsp;x)</pre>
<div class="block">Compute the arc sine of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>arc sine of x</dd></dl>
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<pre>public static&nbsp;double&nbsp;acos(double&nbsp;x)</pre>
<div class="block">Compute the arc cosine of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>arc cosine of x</dd></dl>
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<pre>public static&nbsp;double&nbsp;cbrt(double&nbsp;x)</pre>
<div class="block">Compute the cubic root of a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number on which evaluation is done</dd>
<dt><span class="strong">Returns:</span></dt><dd>cubic root of x</dd></dl>
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<pre>public static&nbsp;double&nbsp;toRadians(double&nbsp;x)</pre>
<div class="block">Convert degrees to radians, with error of less than 0.5 ULP</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - angle in degrees</dd>
<dt><span class="strong">Returns:</span></dt><dd>x converted into radians</dd></dl>
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<pre>public static&nbsp;double&nbsp;toDegrees(double&nbsp;x)</pre>
<div class="block">Convert radians to degrees, with error of less than 0.5 ULP</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - angle in radians</dd>
<dt><span class="strong">Returns:</span></dt><dd>x converted into degrees</dd></dl>
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<pre>public static&nbsp;int&nbsp;abs(int&nbsp;x)</pre>
<div class="block">Absolute value.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which absolute value is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>abs(x)</dd></dl>
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<pre>public static&nbsp;long&nbsp;abs(long&nbsp;x)</pre>
<div class="block">Absolute value.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which absolute value is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>abs(x)</dd></dl>
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<pre>public static&nbsp;float&nbsp;abs(float&nbsp;x)</pre>
<div class="block">Absolute value.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which absolute value is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>abs(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;abs(double&nbsp;x)</pre>
<div class="block">Absolute value.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which absolute value is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>abs(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;ulp(double&nbsp;x)</pre>
<div class="block">Compute least significant bit (Unit in Last Position) for a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which ulp is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>ulp(x)</dd></dl>
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<pre>public static&nbsp;float&nbsp;ulp(float&nbsp;x)</pre>
<div class="block">Compute least significant bit (Unit in Last Position) for a number.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which ulp is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>ulp(x)</dd></dl>
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<pre>public static&nbsp;double&nbsp;scalb(double&nbsp;d,
int&nbsp;n)</pre>
<div class="block">Multiply a double number by a power of 2.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - number to multiply</dd><dd><code>n</code> - power of 2</dd>
<dt><span class="strong">Returns:</span></dt><dd>d &times; 2<sup>n</sup></dd></dl>
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<pre>public static&nbsp;float&nbsp;scalb(float&nbsp;f,
int&nbsp;n)</pre>
<div class="block">Multiply a float number by a power of 2.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>f</code> - number to multiply</dd><dd><code>n</code> - power of 2</dd>
<dt><span class="strong">Returns:</span></dt><dd>f &times; 2<sup>n</sup></dd></dl>
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<pre>public static&nbsp;double&nbsp;nextAfter(double&nbsp;d,
double&nbsp;direction)</pre>
<div class="block">Get the next machine representable number after a number, moving
in the direction of another number.
<p>
The ordering is as follows (increasing):
<ul>
<li>-INFINITY</li>
<li>-MAX_VALUE</li>
<li>-MIN_VALUE</li>
<li>-0.0</li>
<li>+0.0</li>
<li>+MIN_VALUE</li>
<li>+MAX_VALUE</li>
<li>+INFINITY</li>
<li></li>
<p>
If arguments compare equal, then the second argument is returned.
<p>
If <code>direction</code> is greater than <code>d</code>,
the smallest machine representable number strictly greater than
<code>d</code> is returned; if less, then the largest representable number
strictly less than <code>d</code> is returned.</p>
<p>
If <code>d</code> is infinite and direction does not
bring it back to finite numbers, it is returned unchanged.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - base number</dd><dd><code>direction</code> - (the only important thing is whether
<code>direction</code> is greater or smaller than <code>d</code>)</dd>
<dt><span class="strong">Returns:</span></dt><dd>the next machine representable number in the specified direction</dd></dl>
</li>
</ul>
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<pre>public static&nbsp;float&nbsp;nextAfter(float&nbsp;f,
double&nbsp;direction)</pre>
<div class="block">Get the next machine representable number after a number, moving
in the direction of another number.
<p>
The ordering is as follows (increasing):
<ul>
<li>-INFINITY</li>
<li>-MAX_VALUE</li>
<li>-MIN_VALUE</li>
<li>-0.0</li>
<li>+0.0</li>
<li>+MIN_VALUE</li>
<li>+MAX_VALUE</li>
<li>+INFINITY</li>
<li></li>
<p>
If arguments compare equal, then the second argument is returned.
<p>
If <code>direction</code> is greater than <code>f</code>,
the smallest machine representable number strictly greater than
<code>f</code> is returned; if less, then the largest representable number
strictly less than <code>f</code> is returned.</p>
<p>
If <code>f</code> is infinite and direction does not
bring it back to finite numbers, it is returned unchanged.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>f</code> - base number</dd><dd><code>direction</code> - (the only important thing is whether
<code>direction</code> is greater or smaller than <code>f</code>)</dd>
<dt><span class="strong">Returns:</span></dt><dd>the next machine representable number in the specified direction</dd></dl>
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<pre>public static&nbsp;double&nbsp;floor(double&nbsp;x)</pre>
<div class="block">Get the largest whole number smaller than x.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which floor is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>a double number f such that f is an integer f <= x < f + 1.0</dd></dl>
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<pre>public static&nbsp;double&nbsp;ceil(double&nbsp;x)</pre>
<div class="block">Get the smallest whole number larger than x.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which ceil is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>a double number c such that c is an integer c - 1.0 < x <= c</dd></dl>
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<pre>public static&nbsp;double&nbsp;rint(double&nbsp;x)</pre>
<div class="block">Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which nearest whole number is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>a double number r such that r is an integer r - 0.5 <= x <= r + 0.5</dd></dl>
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<pre>public static&nbsp;long&nbsp;round(double&nbsp;x)</pre>
<div class="block">Get the closest long to x.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which closest long is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>closest long to x</dd></dl>
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<pre>public static&nbsp;int&nbsp;round(float&nbsp;x)</pre>
<div class="block">Get the closest int to x.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - number from which closest int is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>closest int to x</dd></dl>
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<pre>public static&nbsp;int&nbsp;min(int&nbsp;a,
int&nbsp;b)</pre>
<div class="block">Compute the minimum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>a if a is lesser or equal to b, b otherwise</dd></dl>
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<pre>public static&nbsp;long&nbsp;min(long&nbsp;a,
long&nbsp;b)</pre>
<div class="block">Compute the minimum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>a if a is lesser or equal to b, b otherwise</dd></dl>
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<pre>public static&nbsp;float&nbsp;min(float&nbsp;a,
float&nbsp;b)</pre>
<div class="block">Compute the minimum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>a if a is lesser or equal to b, b otherwise</dd></dl>
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<pre>public static&nbsp;double&nbsp;min(double&nbsp;a,
double&nbsp;b)</pre>
<div class="block">Compute the minimum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>a if a is lesser or equal to b, b otherwise</dd></dl>
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<pre>public static&nbsp;int&nbsp;max(int&nbsp;a,
int&nbsp;b)</pre>
<div class="block">Compute the maximum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>b if a is lesser or equal to b, a otherwise</dd></dl>
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<pre>public static&nbsp;long&nbsp;max(long&nbsp;a,
long&nbsp;b)</pre>
<div class="block">Compute the maximum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>b if a is lesser or equal to b, a otherwise</dd></dl>
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<pre>public static&nbsp;float&nbsp;max(float&nbsp;a,
float&nbsp;b)</pre>
<div class="block">Compute the maximum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>b if a is lesser or equal to b, a otherwise</dd></dl>
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<pre>public static&nbsp;double&nbsp;max(double&nbsp;a,
double&nbsp;b)</pre>
<div class="block">Compute the maximum of two values</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value</dd><dd><code>b</code> - second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>b if a is lesser or equal to b, a otherwise</dd></dl>
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<pre>public static&nbsp;double&nbsp;hypot(double&nbsp;x,
double&nbsp;y)</pre>
<div class="block">Returns the hypotenuse of a triangle with sides <code>x</code> and <code>y</code>
- sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)<br/>
avoiding intermediate overflow or underflow.
<ul>
<li> If either argument is infinite, then the result is positive infinity.</li>
<li> else, if either argument is NaN then the result is NaN.</li>
</ul></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - a value</dd><dd><code>y</code> - a value</dd>
<dt><span class="strong">Returns:</span></dt><dd>sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)</dd></dl>
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<pre>public static&nbsp;double&nbsp;IEEEremainder(double&nbsp;dividend,
double&nbsp;divisor)</pre>
<div class="block">Computes the remainder as prescribed by the IEEE 754 standard.
The remainder value is mathematically equal to <code>x - y*n</code>
where <code>n</code> is the mathematical integer closest to the exact mathematical value
of the quotient <code>x/y</code>.
If two mathematical integers are equally close to <code>x/y</code> then
<code>n</code> is the integer that is even.
<p>
<ul>
<li>If either operand is NaN, the result is NaN.</li>
<li>If the result is not NaN, the sign of the result equals the sign of the dividend.</li>
<li>If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.</li>
<li>If the dividend is finite and the divisor is an infinity, the result equals the dividend.</li>
<li>If the dividend is a zero and the divisor is finite, the result equals the dividend.</li>
</ul>
<p><b>Note:</b> this implementation currently delegates to <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/StrictMath.html?is-external=true#IEEEremainder(double, double)" title="class or interface in java.lang"><code>StrictMath.IEEEremainder(double, double)</code></a></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>dividend</code> - the number to be divided</dd><dd><code>divisor</code> - the number by which to divide</dd>
<dt><span class="strong">Returns:</span></dt><dd>the remainder, rounded</dd></dl>
</li>
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<pre>public static&nbsp;double&nbsp;copySign(double&nbsp;magnitude,
double&nbsp;sign)</pre>
<div class="block">Returns the first argument with the sign of the second argument.
A NaN <code>sign</code> argument is treated as positive.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>magnitude</code> - the value to return</dd><dd><code>sign</code> - the sign for the returned value</dd>
<dt><span class="strong">Returns:</span></dt><dd>the magnitude with the same sign as the <code>sign</code> argument</dd></dl>
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<pre>public static&nbsp;float&nbsp;copySign(float&nbsp;magnitude,
float&nbsp;sign)</pre>
<div class="block">Returns the first argument with the sign of the second argument.
A NaN <code>sign</code> argument is treated as positive.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>magnitude</code> - the value to return</dd><dd><code>sign</code> - the sign for the returned value</dd>
<dt><span class="strong">Returns:</span></dt><dd>the magnitude with the same sign as the <code>sign</code> argument</dd></dl>
</li>
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<a name="getExponent(double)">
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<pre>public static&nbsp;int&nbsp;getExponent(double&nbsp;d)</pre>
<div class="block">Return the exponent of a double number, removing the bias.
<p>
For double numbers of the form 2<sup>x</sup>, the unbiased
exponent is exactly x.
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - number from which exponent is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>exponent for d in IEEE754 representation, without bias</dd></dl>
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<pre>public static&nbsp;int&nbsp;getExponent(float&nbsp;f)</pre>
<div class="block">Return the exponent of a float number, removing the bias.
<p>
For float numbers of the form 2<sup>x</sup>, the unbiased
exponent is exactly x.
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>f</code> - number from which exponent is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>exponent for d in IEEE754 representation, without bias</dd></dl>
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<h4>main</h4>
<pre>public static&nbsp;void&nbsp;main(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>[]&nbsp;a)</pre>
<div class="block">Print out contents of arrays, and check the length.
<p>used to generate the preset arrays originally.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - unused</dd></dl>
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