mirror of
https://github.com/boostorg/math.git
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Added refactored docs for existing Boost.Math libraries.
[SVN r39851]
This commit is contained in:
John Maddock
75
doc/gcd/Jamfile.v2
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75
doc/gcd/Jamfile.v2
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# Copyright John Maddock 2005. Use, modification, and distribution are
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# subject to the Boost Software License, Version 1.0. (See accompanying
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# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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using quickbook ;
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path-constant images_location : html ;
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xml math-gcd : math-gcd.qbk ;
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boostbook standalone
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:
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math-gcd
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:
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# Path for links to Boost:
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<xsl:param>boost.root=../../../../..
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# Path for libraries index:
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<xsl:param>boost.libraries=../../../../../libs/libraries.htm
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# Use the main Boost stylesheet:
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<xsl:param>html.stylesheet=../../../../../doc/html/boostbook.css
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# Some general style settings:
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<xsl:param>table.footnote.number.format=1
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<xsl:param>footnote.number.format=1
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# HTML options first:
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# Use graphics not text for navigation:
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<xsl:param>navig.graphics=1
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# How far down we chunk nested sections, basically all of them:
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<xsl:param>chunk.section.depth=10
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# Don't put the first section on the same page as the TOC:
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<xsl:param>chunk.first.sections=1
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# How far down sections get TOC's
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<xsl:param>toc.section.depth=10
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# Max depth in each TOC:
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<xsl:param>toc.max.depth=4
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# How far down we go with TOC's
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<xsl:param>generate.section.toc.level=10
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#<xsl:param>root.filename="sf_dist_and_tools"
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# PDF Options:
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# TOC Generation: this is needed for FOP-0.9 and later:
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# <xsl:param>fop1.extensions=1
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<format>pdf:<xsl:param>xep.extensions=1
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# TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9!
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<format>pdf:<xsl:param>fop.extensions=0
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# No indent on body text:
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<format>pdf:<xsl:param>body.start.indent=0pt
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# Margin size:
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<format>pdf:<xsl:param>page.margin.inner=0.5in
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# Margin size:
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<format>pdf:<xsl:param>page.margin.outer=0.5in
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# Paper type = A4
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<format>pdf:<xsl:param>paper.type=A4
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# Yes, we want graphics for admonishments:
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<xsl:param>admon.graphics=1
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# Set this one for PDF generation *only*:
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# default pnd graphics are awful in PDF form,
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# better use SVG's instead:
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<format>pdf:<xsl:param>admon.graphics.extension=".svg"
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<format>pdf:<xsl:param>use.role.for.mediaobject=1
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<format>pdf:<xsl:param>preferred.mediaobject.role=print
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<format>pdf:<xsl:param>img.src.path=$(images_location)/
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<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
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;
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57
doc/gcd/html/gcd_and_lcm/gcd_lcm.html
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57
doc/gcd/html/gcd_and_lcm/gcd_lcm.html
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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<title>Greatest Common Divisor and Least Common Multiple</title>
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<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../index.html" title="GCD and LCM">
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<link rel="up" href="../index.html" title="GCD and LCM">
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<link rel="prev" href="../index.html" title="GCD and LCM">
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<link rel="next" href="gcd_lcm/introduction.html" title="Introduction">
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</head>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
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<a accesskey="p" href="../index.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gcd_lcm/introduction.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
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<div class="section" lang="en">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
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<a name="gcd_and_lcm.gcd_lcm"></a><a href="gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple"> Greatest Common Divisor and Least
|
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Common Multiple</a>
|
||||
</h2></div></div></div>
|
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<div class="toc"><dl>
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<dt><span class="section"><a href="gcd_lcm/introduction.html">Introduction</a></span></dt>
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||||
<dt><span class="section"><a href="gcd_lcm/synopsis.html">Synopsis</a></span></dt>
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<dt><span class="section"><a href="gcd_lcm/gcd_function_object.html">GCD Function
|
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Object</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm/lcm_function_object.html">LCM Function
|
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Object</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm/run_time.html"> Run-time GCD & LCM
|
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Determination</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm/compile_time.html"> Compile time GCD and
|
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LCM determination</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm/header.html"> Header <boost/math/common_factor.hpp></a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm/demo.html"> Demonstration Program</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_lcm/rationale.html">Rationale</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_lcm/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_lcm/credits.html">Credits</a></span></dt>
|
||||
</dl></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
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<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
|
||||
</tr></table>
|
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<hr>
|
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<div class="spirit-nav">
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<a accesskey="p" href="../index.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gcd_lcm/introduction.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
|
||||
</body>
|
||||
</html>
|
||||
95
doc/gcd/html/gcd_and_lcm/gcd_lcm/compile_time.html
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95
doc/gcd/html/gcd_and_lcm/gcd_lcm/compile_time.html
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@@ -0,0 +1,95 @@
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<html>
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<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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<title>Compile time GCD and LCM determination</title>
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="start" href="../../index.html" title="GCD and LCM">
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<link rel="up" href="../gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple">
|
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<link rel="prev" href="run_time.html" title="Run-time GCD & LCM Determination">
|
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<link rel="next" href="header.html" title="Header <boost/math/common_factor.hpp>">
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</head>
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||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../../../index.htm">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="../../../../../../../people/people.htm">People</a></td>
|
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<td align="center"><a href="../../../../../../../more/faq.htm">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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</tr></table>
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||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="run_time.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../gcd_lcm.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
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||||
<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="gcd_and_lcm.gcd_lcm.compile_time"></a><a href="compile_time.html" title="Compile time GCD and LCM determination"> Compile time GCD and
|
||||
LCM determination</a>
|
||||
</h3></div></div></div>
|
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<p>
|
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<span class="bold"><strong>Header: </strong></span> <a href="../../../../../../../boost/math/common_factor_ct.hpp" target="_top"><boost/math/common_factor_ct.hpp></a>
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</p>
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<pre class="programlisting">
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<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value2</span> <span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_gcd</span>
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<span class="special">{</span>
|
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<span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">const</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">implementation_defined</span><span class="special">;</span>
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<span class="special">};</span>
|
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<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value2</span> <span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_lcm</span>
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<span class="special">{</span>
|
||||
<span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">const</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">implementation_defined</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
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</pre>
|
||||
<p>
|
||||
The boost::math::static_gcd and boost::math::static_lcm class templates take
|
||||
two value-based template parameters of the unsigned long type and have a
|
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single static constant data member, value, of that same type. The value of
|
||||
that member is the greatest common factor or least common multiple, respectively,
|
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of the template arguments. A compile-time error will occur if the least common
|
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multiple is beyond the range of an unsigned long.
|
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</p>
|
||||
<a name="gcd_and_lcm.gcd_lcm.compile_time.example"></a><h4>
|
||||
<a name="id490700"></a>
|
||||
<a href="compile_time.html#gcd_and_lcm.gcd_lcm.compile_time.example">Example</a>
|
||||
</h4>
|
||||
<pre class="programlisting">
|
||||
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">algorithm</span><span class="special">></span>
|
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iterator</span><span class="special">></span>
|
||||
|
||||
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<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span>
|
||||
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
|
||||
|
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<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The GCD and LCM of 6 and 15 are "</span>
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<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" and "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special"><<</span> <span class="string">", respectively."</span>
|
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<span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The GCD and LCM of 8 and 9 are "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_gcd</span><span class="special"><</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">>::</span><span class="identifier">value</span>
|
||||
<span class="special"><<</span> <span class="string">" and "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_lcm</span><span class="special"><</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">>::</span><span class="identifier">value</span>
|
||||
<span class="special"><<</span> <span class="string">", respectively."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">int</span> <span class="identifier">a</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">4</span><span class="special">,</span> <span class="number">5</span><span class="special">,</span> <span class="number">6</span> <span class="special">},</span> <span class="identifier">b</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">7</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">9</span> <span class="special">},</span> <span class="identifier">c</span><span class="special">[</span><span class="number">3</span><span class="special">];</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">transform</span><span class="special">(</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">c</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd_evaluator</span><span class="special"><</span><span class="keyword">int</span><span class="special">>()</span> <span class="special">);</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">copy</span><span class="special">(</span> <span class="identifier">c</span><span class="special">,</span> <span class="identifier">c</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream_iterator</span><span class="special"><</span><span class="keyword">int</span><span class="special">>(</span><span class="identifier">cout</span><span class="special">,</span> <span class="string">" "</span><span class="special">)</span> <span class="special">);</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
|
||||
</tr></table>
|
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="run_time.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../gcd_lcm.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</html>
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44
doc/gcd/html/gcd_and_lcm/gcd_lcm/credits.html
Normal file
44
doc/gcd/html/gcd_and_lcm/gcd_lcm/credits.html
Normal file
@@ -0,0 +1,44 @@
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>Credits</title>
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<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="prev" href="history.html" title="History">
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|
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|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The author of the Boost compilation of GCD and LCM computations is Daryle
|
||||
Walker. The code was prompted by existing code hiding in the implementations
|
||||
of Paul Moore's rational library and Steve Cleary's pool library. The code
|
||||
had updates by Helmut Zeisel.
|
||||
</p>
|
||||
</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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46
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|
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<a name="gcd_and_lcm.gcd_lcm.demo"></a><a href="demo.html" title="Demonstration Program"> Demonstration Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <a href="../../../../../../../libs/math/test/common_factor_test.cpp" target="_top">common_factor_test.cpp</a>
|
||||
is a demonstration of the results from instantiating various examples of
|
||||
the run-time GCD and LCM function templates and the compile-time GCD and
|
||||
LCM class templates. (The run-time GCD and LCM class templates are tested
|
||||
indirectly through the run-time function templates.)
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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71
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71
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<a name="gcd_and_lcm.gcd_lcm.gcd_function_object"></a><a href="gcd_function_object.html" title="GCD Function Object">GCD Function
|
||||
Object</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../../../boost/math/common_factor_rt.hpp" target="_top"><boost/math/common_factor_rt.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd_evaluator</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="comment">// Types
|
||||
</span> <span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">result_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">first_argument_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">second_argument_type</span><span class="special">;</span>
|
||||
|
||||
<span class="comment">// Function object interface
|
||||
</span> <span class="identifier">result_type</span> <span class="keyword">operator</span> <span class="special">()(</span> <span class="identifier">first_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span>
|
||||
<span class="identifier">second_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
The boost::math::gcd_evaluator class template defines a function object class
|
||||
to return the greatest common divisor of two integers. The template is parameterized
|
||||
by a single type, called IntegerType here. This type should be a numeric
|
||||
type that represents integers. The result of the function object is always
|
||||
nonnegative, even if either of the operator arguments is negative.
|
||||
</p>
|
||||
<p>
|
||||
This function object class template is used in the corresponding version
|
||||
of the GCD function template. If a numeric type wants to customize evaluations
|
||||
of its greatest common divisors, then the type should specialize on the gcd_evaluator
|
||||
class template.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
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48
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48
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||||
<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
This header simply includes the headers <a href="../../../../../../../boost/math/common_factor_ct.hpp" target="_top"><boost/math/common_factor_ct.hpp></a>
|
||||
and <a href="../../../../../../../boost/math/common_factor_rt.hpp" target="_top"><boost/math/common_factor_rt.hpp></a>.
|
||||
</p>
|
||||
<p>
|
||||
Note this is a legacy header: it used to contain the actual implementation,
|
||||
but the compile-time and run-time facilities were moved to separate headers
|
||||
(since they were independent of each other).
|
||||
</p>
|
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</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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|
||||
17 Dec 2005: Converted documentation to Quickbook Format.
|
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|
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|
||||
2 Jul 2002: Compile-time and run-time items separated to new headers.
|
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|
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|
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|
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|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The class and function templates in <boost/math/common_factor.hpp>
|
||||
provide run-time and compile-time evaluation of the greatest common divisor
|
||||
(GCD) or least common multiple (LCM) of two integers. These facilities are
|
||||
useful for many numeric-oriented generic programming problems.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
|
||||
</tr></table>
|
||||
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|
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|
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|
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|
||||
73
doc/gcd/html/gcd_and_lcm/gcd_lcm/lcm_function_object.html
Normal file
73
doc/gcd/html/gcd_and_lcm/gcd_lcm/lcm_function_object.html
Normal file
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|
||||
<a name="gcd_and_lcm.gcd_lcm.lcm_function_object"></a><a href="lcm_function_object.html" title="LCM Function Object">LCM Function
|
||||
Object</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../../../boost/math/common_factor_rt.hpp" target="_top"><boost/math/common_factor_rt.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm_evaluator</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="comment">// Types
|
||||
</span> <span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">result_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">first_argument_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">second_argument_type</span><span class="special">;</span>
|
||||
|
||||
<span class="comment">// Function object interface
|
||||
</span> <span class="identifier">result_type</span> <span class="keyword">operator</span> <span class="special">()(</span> <span class="identifier">first_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span>
|
||||
<span class="identifier">second_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
The boost::math::lcm_evaluator class template defines a function object class
|
||||
to return the least common multiple of two integers. The template is parameterized
|
||||
by a single type, called IntegerType here. This type should be a numeric
|
||||
type that represents integers. The result of the function object is always
|
||||
nonnegative, even if either of the operator arguments is negative. If the
|
||||
least common multiple is beyond the range of the integer type, the results
|
||||
are undefined.
|
||||
</p>
|
||||
<p>
|
||||
This function object class template is used in the corresponding version
|
||||
of the LCM function template. If a numeric type wants to customize evaluations
|
||||
of its least common multiples, then the type should specialize on the lcm_evaluator
|
||||
class template.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
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|
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|
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|
||||
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|
||||
</html>
|
||||
45
doc/gcd/html/gcd_and_lcm/gcd_lcm/rationale.html
Normal file
45
doc/gcd/html/gcd_and_lcm/gcd_lcm/rationale.html
Normal file
@@ -0,0 +1,45 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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||||
<title>Rationale</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
||||
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|
||||
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|
||||
<a name="gcd_and_lcm.gcd_lcm.rationale"></a><a href="rationale.html" title="Rationale">Rationale</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The greatest common divisor and least common multiple functions are greatly
|
||||
used in some numeric contexts, including some of the other Boost libraries.
|
||||
Centralizing these functions to one header improves code factoring and eases
|
||||
maintainence.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
|
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|
||||
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|
||||
</html>
|
||||
59
doc/gcd/html/gcd_and_lcm/gcd_lcm/run_time.html
Normal file
59
doc/gcd/html/gcd_and_lcm/gcd_lcm/run_time.html
Normal file
@@ -0,0 +1,59 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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|
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|
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<a name="gcd_and_lcm.gcd_lcm.run_time"></a><a href="run_time.html" title="Run-time GCD & LCM Determination"> Run-time GCD & LCM
|
||||
Determination</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../../../boost/math/common_factor_rt.hpp" target="_top"><boost/math/common_factor_rt.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
The boost::math::gcd function template returns the greatest common (nonnegative)
|
||||
divisor of the two integers passed to it. The boost::math::lcm function template
|
||||
returns the least common (nonnegative) multiple of the two integers passed
|
||||
to it. The function templates are parameterized on the function arguments'
|
||||
IntegerType, which is also the return type. Internally, these function templates
|
||||
use an object of the corresponding version of the gcd_evaluator and lcm_evaluator
|
||||
class templates, respectively.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
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|
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|
||||
</html>
|
||||
63
doc/gcd/html/gcd_and_lcm/gcd_lcm/synopsis.html
Normal file
63
doc/gcd/html/gcd_and_lcm/gcd_lcm/synopsis.html
Normal file
@@ -0,0 +1,63 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
|
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|
||||
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
|
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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|
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<link rel="prev" href="introduction.html" title="Introduction">
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<div class="section" lang="en">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="gcd_and_lcm.gcd_lcm.synopsis"></a><a href="synopsis.html" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting">
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">namespace</span> <span class="identifier">math</span>
|
||||
<span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">gcd_evaluator</span><span class="special">;</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">lcm_evaluator</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="identifier">IntegerType</span> <span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_gcd</span><span class="special">;</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_lcm</span><span class="special">;</span>
|
||||
|
||||
<span class="special">}</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><small>Copyright © 2001 -2002 Daryle Walker</small></td>
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<div>
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<div><h2 class="title">
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<a name="gcd_and_lcm"></a>GCD and LCM</h2></div>
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<div><div class="authorgroup"><div class="author"><h3 class="author">
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<span class="firstname">Daryle</span> <span class="surname">Walker</span>
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</h3></div></div></div>
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<div><p class="copyright">Copyright © 2001 -2002 Daryle Walker</p></div>
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<a name="id489770"></a><p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="toc">
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<p><b>Table of Contents</b></p>
|
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<dl>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm.html"> Greatest Common Divisor and Least
|
||||
Common Multiple</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/introduction.html">Introduction</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/synopsis.html">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/gcd_function_object.html">GCD Function
|
||||
Object</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/lcm_function_object.html">LCM Function
|
||||
Object</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/run_time.html"> Run-time GCD & LCM
|
||||
Determination</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/compile_time.html"> Compile time GCD and
|
||||
LCM determination</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/header.html"> Header <boost/math/common_factor.hpp></a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/demo.html"> Demonstration Program</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/rationale.html">Rationale</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="gcd_and_lcm/gcd_lcm/credits.html">Credits</a></span></dt>
|
||||
</dl></dd>
|
||||
</dl>
|
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</div>
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</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: December 29, 2006 at 11:08:32 +0000</small></p></td>
|
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<td align="right"><small></small></td>
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</tr></table>
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<hr>
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<div class="spirit-nav"><a accesskey="n" href="gcd_and_lcm/gcd_lcm.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a></div>
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243
doc/gcd/math-gcd.qbk
Normal file
243
doc/gcd/math-gcd.qbk
Normal file
@@ -0,0 +1,243 @@
|
||||
[article GCD and LCM
|
||||
[quickbook 1.3]
|
||||
[copyright 2001-2002 Daryle Walker]
|
||||
[license
|
||||
Distributed under the Boost Software License, Version 1.0.
|
||||
(See accompanying file LICENSE_1_0.txt or copy at
|
||||
[@http://www.boost.org/LICENSE_1_0.txt http://www.boost.org/LICENSE_1_0.txt])
|
||||
]
|
||||
[authors [Walker, Daryle]]
|
||||
[category math]
|
||||
[last-revision $Date: 2006-12-29 11:08:32 +0000 (Fri, 29 Dec 2006) $]
|
||||
]
|
||||
|
||||
|
||||
[section:gcd_lcm Greatest Common Divisor and Least Common Multiple]
|
||||
|
||||
[section Introduction]
|
||||
|
||||
The class and function templates in <boost/math/common_factor.hpp>
|
||||
provide run-time and compile-time evaluation of the greatest common divisor
|
||||
(GCD) or least common multiple (LCM) of two integers.
|
||||
These facilities are useful for many numeric-oriented generic
|
||||
programming problems.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Synopsis]
|
||||
|
||||
namespace boost
|
||||
{
|
||||
namespace math
|
||||
{
|
||||
|
||||
template < typename IntegerType >
|
||||
class gcd_evaluator;
|
||||
template < typename IntegerType >
|
||||
class lcm_evaluator;
|
||||
|
||||
template < typename IntegerType >
|
||||
IntegerType gcd( IntegerType const &a, IntegerType const &b );
|
||||
template < typename IntegerType >
|
||||
IntegerType lcm( IntegerType const &a, IntegerType const &b );
|
||||
|
||||
template < unsigned long Value1, unsigned long Value2 >
|
||||
struct static_gcd;
|
||||
template < unsigned long Value1, unsigned long Value2 >
|
||||
struct static_lcm;
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
[endsect]
|
||||
|
||||
[section GCD Function Object]
|
||||
|
||||
[*Header: ] [@../../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>]
|
||||
|
||||
template < typename IntegerType >
|
||||
class boost::math::gcd_evaluator
|
||||
{
|
||||
public:
|
||||
// Types
|
||||
typedef IntegerType result_type;
|
||||
typedef IntegerType first_argument_type;
|
||||
typedef IntegerType second_argument_type;
|
||||
|
||||
// Function object interface
|
||||
result_type operator ()( first_argument_type const &a,
|
||||
second_argument_type const &b ) const;
|
||||
};
|
||||
|
||||
The boost::math::gcd_evaluator class template defines a function object
|
||||
class to return the greatest common divisor of two integers.
|
||||
The template is parameterized by a single type, called IntegerType here.
|
||||
This type should be a numeric type that represents integers.
|
||||
The result of the function object is always nonnegative, even if either of
|
||||
the operator arguments is negative.
|
||||
|
||||
This function object class template is used in the corresponding version of
|
||||
the GCD function template. If a numeric type wants to customize evaluations
|
||||
of its greatest common divisors, then the type should specialize on the
|
||||
gcd_evaluator class template.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section LCM Function Object]
|
||||
|
||||
[*Header: ] [@../../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>]
|
||||
|
||||
template < typename IntegerType >
|
||||
class boost::math::lcm_evaluator
|
||||
{
|
||||
public:
|
||||
// Types
|
||||
typedef IntegerType result_type;
|
||||
typedef IntegerType first_argument_type;
|
||||
typedef IntegerType second_argument_type;
|
||||
|
||||
// Function object interface
|
||||
result_type operator ()( first_argument_type const &a,
|
||||
second_argument_type const &b ) const;
|
||||
};
|
||||
|
||||
The boost::math::lcm_evaluator class template defines a function object
|
||||
class to return the least common multiple of two integers. The template
|
||||
is parameterized by a single type, called IntegerType here. This type
|
||||
should be a numeric type that represents integers. The result of the
|
||||
function object is always nonnegative, even if either of the operator
|
||||
arguments is negative. If the least common multiple is beyond the range
|
||||
of the integer type, the results are undefined.
|
||||
|
||||
This function object class template is used in the corresponding version
|
||||
of the LCM function template. If a numeric type wants to customize
|
||||
evaluations of its least common multiples, then the type should
|
||||
specialize on the lcm_evaluator class template.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:run_time Run-time GCD & LCM Determination]
|
||||
|
||||
[*Header: ] [@../../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>]
|
||||
|
||||
template < typename IntegerType >
|
||||
IntegerType boost::math::gcd( IntegerType const &a, IntegerType const &b );
|
||||
|
||||
template < typename IntegerType >
|
||||
IntegerType boost::math::lcm( IntegerType const &a, IntegerType const &b );
|
||||
|
||||
The boost::math::gcd function template returns the greatest common
|
||||
(nonnegative) divisor of the two integers passed to it.
|
||||
The boost::math::lcm function template returns the least common
|
||||
(nonnegative) multiple of the two integers passed to it.
|
||||
The function templates are parameterized on the function arguments'
|
||||
IntegerType, which is also the return type. Internally, these function
|
||||
templates use an object of the corresponding version of the
|
||||
gcd_evaluator and lcm_evaluator class templates, respectively.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:compile_time Compile time GCD and LCM determination]
|
||||
|
||||
[*Header: ] [@../../../../../boost/math/common_factor_ct.hpp <boost/math/common_factor_ct.hpp>]
|
||||
|
||||
template < unsigned long Value1, unsigned long Value2 >
|
||||
struct boost::math::static_gcd
|
||||
{
|
||||
static unsigned long const value = implementation_defined;
|
||||
};
|
||||
|
||||
template < unsigned long Value1, unsigned long Value2 >
|
||||
struct boost::math::static_lcm
|
||||
{
|
||||
static unsigned long const value = implementation_defined;
|
||||
};
|
||||
|
||||
The boost::math::static_gcd and boost::math::static_lcm class templates
|
||||
take two value-based template parameters of the unsigned long type
|
||||
and have a single static constant data member, value, of that same type.
|
||||
The value of that member is the greatest common factor or least
|
||||
common multiple, respectively, of the template arguments.
|
||||
A compile-time error will occur if the least common multiple
|
||||
is beyond the range of an unsigned long.
|
||||
|
||||
[h3 Example]
|
||||
|
||||
#include <boost/math/common_factor.hpp>
|
||||
#include <algorithm>
|
||||
#include <iterator>
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
using std::cout;
|
||||
using std::endl;
|
||||
|
||||
cout << "The GCD and LCM of 6 and 15 are "
|
||||
<< boost::math::gcd(6, 15) << " and "
|
||||
<< boost::math::lcm(6, 15) << ", respectively."
|
||||
<< endl;
|
||||
|
||||
cout << "The GCD and LCM of 8 and 9 are "
|
||||
<< boost::math::static_gcd<8, 9>::value
|
||||
<< " and "
|
||||
<< boost::math::static_lcm<8, 9>::value
|
||||
<< ", respectively." << endl;
|
||||
|
||||
int a[] = { 4, 5, 6 }, b[] = { 7, 8, 9 }, c[3];
|
||||
std::transform( a, a + 3, b, c, boost::math::gcd_evaluator<int>() );
|
||||
std::copy( c, c + 3, std::ostream_iterator<int>(cout, " ") );
|
||||
}
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:header Header <boost/math/common_factor.hpp>]
|
||||
|
||||
This header simply includes the headers
|
||||
[@../../../../../boost/math/common_factor_ct.hpp <boost/math/common_factor_ct.hpp>]
|
||||
and [@../../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>].
|
||||
|
||||
Note this is a legacy header: it used to contain the actual implementation,
|
||||
but the compile-time and run-time facilities
|
||||
were moved to separate headers (since they were independent of each other).
|
||||
|
||||
[endsect]
|
||||
|
||||
[section:demo Demonstration Program]
|
||||
|
||||
The program [@../../../../../libs/math/test/common_factor_test.cpp common_factor_test.cpp] is a demonstration of the results from
|
||||
instantiating various examples of the run-time GCD and LCM function
|
||||
templates and the compile-time GCD and LCM class templates.
|
||||
(The run-time GCD and LCM class templates are tested indirectly through
|
||||
the run-time function templates.)
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Rationale]
|
||||
|
||||
The greatest common divisor and least common multiple functions are
|
||||
greatly used in some numeric contexts, including some of the other
|
||||
Boost libraries. Centralizing these functions to one header improves
|
||||
code factoring and eases maintainence.
|
||||
|
||||
[endsect]
|
||||
|
||||
[section History]
|
||||
|
||||
* 17 Dec 2005: Converted documentation to Quickbook Format.
|
||||
* 2 Jul 2002: Compile-time and run-time items separated to new headers.
|
||||
* 7 Nov 2001: Initial version
|
||||
|
||||
[endsect]
|
||||
|
||||
[section Credits]
|
||||
|
||||
The author of the Boost compilation of GCD and LCM computations is
|
||||
Daryle Walker. The code was prompted by existing code hiding in the
|
||||
implementations of Paul Moore's rational library and Steve Cleary's
|
||||
pool library. The code had updates by Helmut Zeisel.
|
||||
|
||||
[endsect]
|
||||
|
||||
[endsect]
|
||||
|
||||
Reference in New Issue
Block a user