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	<title>Sputsoft &#187; C++</title>
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	<description>Mathematics and Computer Programming</description>
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		<title>Continued Fractions and Continuants</title>
		<link>http://sputsoft.com/blog/2009/11/continued-fractions-and-continuants.html</link>
		<comments>http://sputsoft.com/blog/2009/11/continued-fractions-and-continuants.html#comments</comments>
		<pubDate>Tue, 10 Nov 2009 15:27:42 +0000</pubDate>
		<dc:creator>sput</dc:creator>
				<category><![CDATA[mathematics]]></category>
		<category><![CDATA[programming]]></category>
		<category><![CDATA[algorithms]]></category>
		<category><![CDATA[C++]]></category>
		<category><![CDATA[continuant]]></category>
		<category><![CDATA[continued fraction]]></category>
		<category><![CDATA[Fibonacci number]]></category>
		<category><![CDATA[quadratic irrationality]]></category>

		<guid isPermaLink="false">http://sputsoft.com/?p=904</guid>
		<description><![CDATA[We will be considering continued fractions of the form

<div class="math">
a_0 + \displaystyle\frac{1}{a_1 + \displaystyle\frac{1}{\ddots + \displaystyle\frac{1}{a_{n-1} + \displaystyle\frac{1}{a_n}}}}
</div>

where the <span class="math">a_k</span>'s are real numbers called the partial quotients [...]]]></description>
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		<slash:comments>4</slash:comments>
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		<title>Computing the Greatest Common Divisor</title>
		<link>http://sputsoft.com/blog/2009/10/computing-the-greatest-common-divisor.html</link>
		<comments>http://sputsoft.com/blog/2009/10/computing-the-greatest-common-divisor.html#comments</comments>
		<pubDate>Thu, 29 Oct 2009 17:18:49 +0000</pubDate>
		<dc:creator>sput</dc:creator>
				<category><![CDATA[programming]]></category>
		<category><![CDATA[algorithms]]></category>
		<category><![CDATA[C++]]></category>
		<category><![CDATA[gcd]]></category>
		<category><![CDATA[generic programming]]></category>
		<category><![CDATA[number theory]]></category>
		<category><![CDATA[numbers project]]></category>

		<guid isPermaLink="false">http://sputsoft.com/?p=845</guid>
		<description><![CDATA[The greatest common divisor of two integers is the largest positive integer that divides them both. This article considers two algorithms for computing gcd(u,v), the greatest common divisor of u and v [...]]]></description>
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		<slash:comments>4</slash:comments>
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		<item>
		<title>Implementing Multiple-Precision Arithmetic, Part 2</title>
		<link>http://sputsoft.com/blog/2009/08/implementing-multiple-precision-arithmetic-part-2.html</link>
		<comments>http://sputsoft.com/blog/2009/08/implementing-multiple-precision-arithmetic-part-2.html#comments</comments>
		<pubDate>Thu, 20 Aug 2009 08:31:30 +0000</pubDate>
		<dc:creator>sput</dc:creator>
				<category><![CDATA[programming]]></category>
		<category><![CDATA[algorithms]]></category>
		<category><![CDATA[arithmetic]]></category>
		<category><![CDATA[C++]]></category>
		<category><![CDATA[multiple-precision]]></category>
		<category><![CDATA[numbers project]]></category>

		<guid isPermaLink="false">http://sputsoft.com/?p=573</guid>
		<description><![CDATA[Introduction This article is a follow-up to part 1 where multiple-precision addition, subtraction, and multiplication for non-negative integers was discussed. This article deals with division. Again, the theoretic foundation is based on Section&#160;4.3.1, The Classical Algorithms, of The Art of Computer Programming, Volume&#160;2, by Donald E. Knuth. Fundamentals With u = (u_{m-1} \ldots u_1 u_0)_b [...]]]></description>
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		<slash:comments>5</slash:comments>
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		<title>Implementing Multiple-Precision Arithmetic, Part 1</title>
		<link>http://sputsoft.com/blog/2009/07/implementing-multiple-precision-arithmetic-part-1.html</link>
		<comments>http://sputsoft.com/blog/2009/07/implementing-multiple-precision-arithmetic-part-1.html#comments</comments>
		<pubDate>Thu, 23 Jul 2009 08:58:04 +0000</pubDate>
		<dc:creator>sput</dc:creator>
				<category><![CDATA[programming]]></category>
		<category><![CDATA[algorithms]]></category>
		<category><![CDATA[arithmetic]]></category>
		<category><![CDATA[C++]]></category>
		<category><![CDATA[multiple-precision]]></category>
		<category><![CDATA[numbers project]]></category>

		<guid isPermaLink="false">http://sputsoft.com/?p=495</guid>
		<description><![CDATA[This article is the first in a series dealing with algorithms for multiple-precision arithmetic. The goal is to present both a theoretical foundation with high-level algorithm descriptions (based on Section 4.3.1, <em>The Classical Algorithms</em>, of <a href="http://www-cs-faculty.stanford.edu/~knuth/taocp.html">The Art of Computer Programming</a>, Volume 2, by <a href="http://www-cs-faculty.stanford.edu/~knuth/">Donald E. Knuth</a>) and a portable C++ implementation of the algorithms. The theory and high-level algorithms will be quite universal and generic, whereas the presented code will be just one way to implement the algorithms in a specific programming language.]]></description>
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		<slash:comments>7</slash:comments>
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