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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<div class="subTitle">org.apache.commons.math3.dfp</div>
<h2 title="Class DfpMath" class="title">Class DfpMath</h2>
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<pre>public class <span class="strong">DfpMath</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Mathematical routines for use with <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a>.
The constants are defined in <a href="../../../../../org/apache/commons/math3/dfp/DfpField.html" title="class in org.apache.commons.math3.dfp"><code>DfpField</code></a></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<h3>Method Summary</h3>
<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"> </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 <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#acos(org.apache.commons.math3.dfp.Dfp)">acos</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the arc-cosine of the argument.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#asin(org.apache.commons.math3.dfp.Dfp)">asin</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the arc-sine of the argument.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#atan(org.apache.commons.math3.dfp.Dfp)">atan</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the arc tangent of the argument
Uses the typical taylor series
but may reduce arguments using the following identity
tan(x+y) = (tan(x) + tan(y)) / (1 - tan(x)*tan(y))
since tan(PI/8) = sqrt(2)-1,
atan(x) = atan( (x - sqrt(2) + 1) / (1+x*sqrt(2) - x) + PI/8.0</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#atanInternal(org.apache.commons.math3.dfp.Dfp)">atanInternal</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the arc-tangent of the argument.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#cos(org.apache.commons.math3.dfp.Dfp)">cos</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the cosine of the argument.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#cosInternal(org.apache.commons.math3.dfp.Dfp[])">cosInternal</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a)</code>
<div class="block">Computes cos(a) Used when 0 < a < pi/4.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#exp(org.apache.commons.math3.dfp.Dfp)">exp</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">Computes e to the given power.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#expInternal(org.apache.commons.math3.dfp.Dfp)">expInternal</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">Computes e to the given power.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#log(org.apache.commons.math3.dfp.Dfp)">log</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">Returns the natural logarithm of a.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#logInternal(org.apache.commons.math3.dfp.Dfp[])">logInternal</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a)</code>
<div class="block">Computes the natural log of a number between 0 and 2.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#pow(org.apache.commons.math3.dfp.Dfp,%20org.apache.commons.math3.dfp.Dfp)">pow</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> x,
<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> y)</code>
<div class="block">Computes x to the y power.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#pow(org.apache.commons.math3.dfp.Dfp,%20int)">pow</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> base,
int a)</code>
<div class="block">Raises base to the power a by successive squaring.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#sin(org.apache.commons.math3.dfp.Dfp)">sin</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the sine of the argument.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#sinInternal(org.apache.commons.math3.dfp.Dfp[])">sinInternal</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a)</code>
<div class="block">Computes sin(a) Used when 0 < a < pi/4.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#split(org.apache.commons.math3.dfp.Dfp)">split</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">Splits a <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a> into 2 <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a>'s such that their sum is equal to the input <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#split(org.apache.commons.math3.dfp.DfpField,%20java.lang.String)">split</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/DfpField.html" title="class in org.apache.commons.math3.dfp">DfpField</a> field,
<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> a)</code>
<div class="block">Breaks a string representation up into two dfp's.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#splitDiv(org.apache.commons.math3.dfp.Dfp[],%20org.apache.commons.math3.dfp.Dfp[])">splitDiv</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a,
<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] b)</code>
<div class="block">Divide two numbers that are split in to two pieces that are meant to be added together.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#splitMult(org.apache.commons.math3.dfp.Dfp[],%20org.apache.commons.math3.dfp.Dfp[])">splitMult</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a,
<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] b)</code>
<div class="block">Multiply two numbers that are split in to two pieces that are
meant to be added together.</div>
</td>
</tr>
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<td class="colFirst"><code>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#splitPow(org.apache.commons.math3.dfp.Dfp[],%20int)">splitPow</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] base,
int a)</code>
<div class="block">Raise a split base to the a power.</div>
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<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html#tan(org.apache.commons.math3.dfp.Dfp)">tan</a></strong>(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</code>
<div class="block">computes the tangent of the argument.</div>
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<code><a href="http://docs.oracle.com/javase/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] split(<a href="../../../../../org/apache/commons/math3/dfp/DfpField.html" title="class in org.apache.commons.math3.dfp">DfpField</a> field,
<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> a)</pre>
<div class="block">Breaks a string representation up into two dfp's.
<p>The two dfp are such that the sum of them is equivalent
to the input string, but has higher precision than using a
single dfp. This is useful for improving accuracy of
exponentiation and critical multiplies.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>field</code> - field to which the Dfp must belong</dd><dd><code>a</code> - string representation to split</dd>
<dt><span class="strong">Returns:</span></dt><dd>an array of two <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a> which sum is a</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] split(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">Splits a <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a> into 2 <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a>'s such that their sum is equal to the input <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number to split</dd>
<dt><span class="strong">Returns:</span></dt><dd>two elements array containing the split number</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] splitMult(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a,
<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] b)</pre>
<div class="block">Multiply two numbers that are split in to two pieces that are
meant to be added together.
Use binomial multiplication so ab = a0 b0 + a0 b1 + a1 b0 + a1 b1
Store the first term in result0, the rest in result1</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first factor of the multiplication, in split form</dd><dd><code>b</code> - second factor of the multiplication, in split form</dd>
<dt><span class="strong">Returns:</span></dt><dd>a × b, in split form</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] splitDiv(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a,
<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] b)</pre>
<div class="block">Divide two numbers that are split in to two pieces that are meant to be added together.
Inverse of split multiply above:
(a+b) / (c+d) = (a/c) + ( (bc-ad)/(c**2+cd) )</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - dividend, in split form</dd><dd><code>b</code> - divisor, in split form</dd>
<dt><span class="strong">Returns:</span></dt><dd>a / b, in split form</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> splitPow(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] base,
int a)</pre>
<div class="block">Raise a split base to the a power.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>base</code> - number to raise</dd><dd><code>a</code> - power</dd>
<dt><span class="strong">Returns:</span></dt><dd>base<sup>a</sup></dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> pow(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> base,
int a)</pre>
<div class="block">Raises base to the power a by successive squaring.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>base</code> - number to raise</dd><dd><code>a</code> - power</dd>
<dt><span class="strong">Returns:</span></dt><dd>base<sup>a</sup></dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> exp(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">Computes e to the given power.
a is broken into two parts, such that a = n+m where n is an integer.
We use pow() to compute e<sup>n</sup> and a Taylor series to compute
e<sup>m</sup>. We return e*<sup>n</sup> × e<sup>m</sup></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - power at which e should be raised</dd>
<dt><span class="strong">Returns:</span></dt><dd>e<sup>a</sup></dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> expInternal(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">Computes e to the given power.
Where -1 < a < 1. Use the classic Taylor series. 1 + x**2/2! + x**3/3! + x**4/4! ...</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - power at which e should be raised</dd>
<dt><span class="strong">Returns:</span></dt><dd>e<sup>a</sup></dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> log(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">Returns the natural logarithm of a.
a is first split into three parts such that a = (10000^h)(2^j)k.
ln(a) is computed by ln(a) = ln(5)*h + ln(2)*(h+j) + ln(k)
k is in the range 2/3 < k <4/3 and is passed on to a series expansion.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which logarithm is requested</dd>
<dt><span class="strong">Returns:</span></dt><dd>log(a)</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] logInternal(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a)</pre>
<div class="block">Computes the natural log of a number between 0 and 2.
Let f(x) = ln(x),
We know that f'(x) = 1/x, thus from Taylor's theorum we have:
----- n+1 n
f(x) = \ (-1) (x - 1)
/ ---------------- for 1 <= n <= infinity
----- n
or
2 3 4
(x-1) (x-1) (x-1)
ln(x) = (x-1) - ----- + ------ - ------ + ...
2 3 4
alternatively,
2 3 4
x x x
ln(x+1) = x - - + - - - + ...
2 3 4
This series can be used to compute ln(x), but it converges too slowly.
If we substitute -x for x above, we get
2 3 4
x x x
ln(1-x) = -x - - - - - - + ...
2 3 4
Note that all terms are now negative. Because the even powered ones
absorbed the sign. Now, subtract the series above from the previous
one to get ln(x+1) - ln(1-x). Note the even terms cancel out leaving
only the odd ones
3 5 7
2x 2x 2x
ln(x+1) - ln(x-1) = 2x + --- + --- + ---- + ...
3 5 7
By the property of logarithms that ln(a) - ln(b) = ln (a/b) we have:
3 5 7
x+1 / x x x \
ln ----- = 2 * | x + ---- + ---- + ---- + ... |
x-1 \ 3 5 7 /
But now we want to find ln(a), so we need to find the value of x
such that a = (x+1)/(x-1). This is easily solved to find that
x = (a-1)/(a+1).</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which logarithm is requested, in split form</dd>
<dt><span class="strong">Returns:</span></dt><dd>log(a)</dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> pow(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> x,
<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> y)</pre>
<div class="block">Computes x to the y power.<p>
Uses the following method:<p>
<ol>
<li> Set u = rint(y), v = y-u
<li> Compute a = v * ln(x)
<li> Compute b = rint( a/ln(2) )
<li> Compute c = a - b*ln(2)
<li> x<sup>y</sup> = x<sup>u</sup> * 2<sup>b</sup> * e<sup>c</sup>
</ol>
if |y| > 1e8, then we compute by exp(y*ln(x)) <p>
<b>Special Cases</b><p>
<ul>
<li> if y is 0.0 or -0.0 then result is 1.0
<li> if y is 1.0 then result is x
<li> if y is NaN then result is NaN
<li> if x is NaN and y is not zero then result is NaN
<li> if |x| > 1.0 and y is +Infinity then result is +Infinity
<li> if |x| < 1.0 and y is -Infinity then result is +Infinity
<li> if |x| > 1.0 and y is -Infinity then result is +0
<li> if |x| < 1.0 and y is +Infinity then result is +0
<li> if |x| = 1.0 and y is +/-Infinity then result is NaN
<li> if x = +0 and y > 0 then result is +0
<li> if x = +Inf and y < 0 then result is +0
<li> if x = +0 and y < 0 then result is +Inf
<li> if x = +Inf and y > 0 then result is +Inf
<li> if x = -0 and y > 0, finite, not odd integer then result is +0
<li> if x = -0 and y < 0, finite, and odd integer then result is -Inf
<li> if x = -Inf and y > 0, finite, and odd integer then result is -Inf
<li> if x = -0 and y < 0, not finite odd integer then result is +Inf
<li> if x = -Inf and y > 0, not finite odd integer then result is +Inf
<li> if x < 0 and y > 0, finite, and odd integer then result is -(|x|<sup>y</sup>)
<li> if x < 0 and y > 0, finite, and not integer then result is NaN
</ul></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - base to be raised</dd><dd><code>y</code> - power to which base should be raised</dd>
<dt><span class="strong">Returns:</span></dt><dd>x<sup>y</sup></dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> sinInternal(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a)</pre>
<div class="block">Computes sin(a) Used when 0 < a < pi/4.
Uses the classic Taylor series. x - x**3/3! + x**5/5! ...</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which sine is desired, in split form</dd>
<dt><span class="strong">Returns:</span></dt><dd>sin(a)</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> cosInternal(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a>[] a)</pre>
<div class="block">Computes cos(a) Used when 0 < a < pi/4.
Uses the classic Taylor series for cosine. 1 - x**2/2! + x**4/4! ...</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which cosine is desired, in split form</dd>
<dt><span class="strong">Returns:</span></dt><dd>cos(a)</dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> sin(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the sine of the argument.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which sine is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>sin(a)</dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> cos(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the cosine of the argument.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which cosine is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>cos(a)</dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> tan(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the tangent of the argument.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which tangent is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>tan(a)</dd></dl>
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<pre>protected static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> atanInternal(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the arc-tangent of the argument.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which arc-tangent is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>atan(a)</dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> atan(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the arc tangent of the argument
Uses the typical taylor series
but may reduce arguments using the following identity
tan(x+y) = (tan(x) + tan(y)) / (1 - tan(x)*tan(y))
since tan(PI/8) = sqrt(2)-1,
atan(x) = atan( (x - sqrt(2) + 1) / (1+x*sqrt(2) - x) + PI/8.0</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which arc-tangent is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>atan(a)</dd></dl>
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<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> asin(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the arc-sine of the argument.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which arc-sine is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>asin(a)</dd></dl>
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<h4>acos</h4>
<pre>public static <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> acos(<a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a> a)</pre>
<div class="block">computes the arc-cosine of the argument.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - number from which arc-cosine is desired</dd>
<dt><span class="strong">Returns:</span></dt><dd>acos(a)</dd></dl>
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