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	<title>Sputsoft &#187; multiple-precision</title>
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	<description>Mathematics and Computer Programming</description>
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		<title>Bitwise Operators and Negative Numbers</title>
		<link>http://sputsoft.com/blog/2010/07/bitwise-operators-and-negative-numbers.html</link>
		<comments>http://sputsoft.com/blog/2010/07/bitwise-operators-and-negative-numbers.html#comments</comments>
		<pubDate>Sat, 24 Jul 2010 17:55:05 +0000</pubDate>
		<dc:creator>sput</dc:creator>
				<category><![CDATA[mathematics]]></category>
		<category><![CDATA[bitwise operators]]></category>
		<category><![CDATA[multiple-precision]]></category>
		<category><![CDATA[number representation]]></category>
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		<guid isPermaLink="false">http://sputsoft.com/?p=1471</guid>
		<description><![CDATA[When representing integers using a fixed number of bits, negative numbers are typically represented using two&#8217;s complement. If using n bit numbers, the two&#8217;s complement of a number x with 0 &#8804; x &#60; 2n is (-x) mod 2n = 2n - x. But what do you do if you want to work with unbounded/multiple-precision [...]]]></description>
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		<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>
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		<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>
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		<category><![CDATA[multiple-precision]]></category>
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		<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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