Comments on: Variable Precision Arithmetic without the Symbolic Math Toolbox? http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/ <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadAuthor.do?objectId=1093599&objectType=author">Brett</a> & <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadAuthor.do?objectId=1094142&objectType=author">Jiro</a> share favorite user-contributed submissions from the File Exchange. Fri, 10 Feb 2012 16:12:39 +0000 hourly 1 http://wordpress.org/?v=3.2.1 By: Brett http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13085 Brett Fri, 13 Mar 2009 14:59:21 +0000 http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13085 I believe I downloaded this on 2/19/09, John, so if you posted an update since then, my blog post doesn't reflect it. Again, the 1 doesn't bother me, but the support for full arrays--nice! Sounds like I should get the new version. Brett I believe I downloaded this on 2/19/09, John, so if you posted an update since then, my blog post doesn’t reflect it. Again, the 1 doesn’t bother me, but the support for full arrays–nice! Sounds like I should get the new version.

Brett

]]> By: John DErrico http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13084 John DErrico Fri, 13 Mar 2009 14:41:51 +0000 http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13084 Actually, is it possible that you tested this with the previous release? I had a bug like that in an earlier release, but it does not seem to be there when I just tried your example. The new release allows full arrays of vpi numbers too. This was the main thing I added in the current release. >> factor(vpi(17)^17) ans = Columns 1 through 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 Columns 17 through 17 17 Actually, is it possible that you tested this with the previous release? I had a bug like that in an earlier release, but it does not seem to be there when I just tried your example. The new release allows full arrays of vpi numbers too. This was the main thing I added in the current release.

>> factor(vpi(17)^17)
ans =

Columns 1 through 16
17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17

Columns 17 through 17
17

]]> By: Brett http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13083 Brett Fri, 13 Mar 2009 14:27:27 +0000 http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13083 Thanks, John. The 1 doesn't really bother me--it's easily ignored. But then, "fixing" it would be trivial. Your code is impressive, and useful. Thanks again for sharing it. Brett Thanks, John. The 1 doesn’t really bother me–it’s easily ignored. But then, “fixing” it would be trivial.
Your code is impressive, and useful. Thanks again for sharing it.

Brett

]]> By: John DErrico http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13082 John DErrico Fri, 13 Mar 2009 14:23:26 +0000 http://blogs.mathworks.com/pick/2009/03/13/variable-precision-arithmetic-without-the-symbolic-toolbox/#comment-13082 Hi Brett. It looks like I need to put up a quick patch in my factor code. Somehow a factor of 1 slipped out of that code in your test case for factor. This last release was a fairly large one, so I'm not surprised that something minor slipped through. Regardless, factoring of large integers is one of the things I've been playing with in some depth lately. There are some very pretty results I've learned, as I wander through the depths of Pollard's rho, quadratic sieve algorithms, and beyond. It also points out how nicely these methods fit into a parallel processing scheme. They are very nicely distributable if you have multiple CPUs. Another very pretty area of mathematics lies in quadratic residues, solving quadratic congruential equations, Pell equations, etc. All very pretty stuff, at least for a long time numerical animalist like me. (If there are specific tools that someone needs, I'm always willing to add something, at least if I can figure out how to write the code.) What has amazed me as I've built these tools in only a relatively short time (at this point, I have about a man-month invested, but the tools have grown very substantially in that time) is how easily you can build a very serviceable suite of tools for such operations. Even more impressive is the fact that if one wanted to do so, similar tools for variable precision floating point arithmetic, or perhaps rational fractions, etc., would all be easy enough to build on top of such a basic tool. Matlab never ceases to surprise me in the sheer power of what you can do. John Hi Brett.

It looks like I need to put up a quick patch in my factor code. Somehow a factor of 1 slipped out of that code in your test case for factor. This last release was a fairly large one, so I’m not surprised that something minor slipped through.

Regardless, factoring of large integers is one of the things I’ve been playing with in some depth lately. There are some very pretty results I’ve learned, as I wander through the depths of Pollard’s rho, quadratic sieve algorithms, and beyond. It also points out how nicely these methods fit into a parallel processing scheme. They are very nicely distributable if you have multiple CPUs.

Another very pretty area of mathematics lies in quadratic residues, solving quadratic congruential equations, Pell equations, etc. All very pretty stuff, at least for a long time numerical animalist like me. (If there are specific tools that someone needs, I’m always willing to add something, at least if I can figure out how to write the code.)

What has amazed me as I’ve built these tools in only a relatively short time (at this point, I have about a man-month invested, but the tools have grown very substantially in that time) is how easily you can build a very serviceable suite of tools for such operations. Even more impressive is the fact that if one wanted to do so, similar tools for variable precision floating point arithmetic, or perhaps rational fractions, etc., would all be easy enough to build on top of such a basic tool.

Matlab never ceases to surprise me in the sheer power of what you can do.

John

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