Best Rational Approximation Calculation Utility For Windows


A common request is for a utility to calculate best rational approximations (this can be done using a continued fraction algorithm explained in the materials linked to from this page).  Best rational approximations of this type are sometimes useful in microcontroller work.

The console-mode utility supplied on this page was created using Microsoft Visual C++ 6.0, and has no external dependencies (no .DLL dependencies, for example).  It should run on any Windows 95 or later system.

The screen snapshot below shows the utility being used to find the best rational approximation to p (or actually, to 3.14159265359 since p is irrational) with numerator not exceeding 65,535 and denominator not exceeding 32,767.  The screen snapshot shows that this best rational approximation is 65,298/20,785.

The underlying algorithms are O(log N) and an arbitrary-precision integer library is used, so they should work for any practical case.

This standalone utility and other supporting documents can be downloaded from the links in the table below.

Download Link Description File Size And MD5
cfbrapab.exe Windows utility to calculate best rational approximations. Size:
81,920
MD-5
02c8738054c23445a69bd0d675ceca0a
paper_brap_detailed.pdf Detailed paper explaining the mathematical basis of best rational approximation.  (Note:  this paper was never published, and copyrights do not apply.) Size:
273,133
MD-5:
fea545ffe55e1c1ef639f93eb844e0bb
paper_brap_reduced.pdf Less detailed paper explaining how to calculate best rational approximations.  (Note:  this paper was never published, and copyrights do not apply.) Size:
152,959
MD-5:
cdd7b25e94c4c304315002eb858a125d
book_c4_c5.pdf Chapters 4 (Farey Series) and 5 (Continued Fractions) of book, under construction.  This document gives much more detail about the mathematical basis of best rational approximation.  (Note:  the copyright status of the book is uncertain.  For the present time, no copyrights apply.) Size:
631,559
MD-5:
87e410eb524ad5dd0e8011f5567f9e30

Other notes:


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