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*To*: info-mcl@cambridge.apple.com*Subject*: real to rational*From*: bright@ENH.NIST.GOV*Date*: 07 Jan 1993 08:46:57 -0500

Does anyone have an algorithm that returns a rational approximation for a real number? Many years ago, I saw a very simple iterative algorithm that ran on a HP desktop calculator. For example, with an input of pi, the first iteration might have given a numerator of 22 and a denominator of 7. The next iteration might give 157/50, etc. Each iteration gave a more accurate approximation of the real, with larger and larger numerators and denominators. The approximations were better than just chopping off digits: 3/1, 31/10, 314/100 etc. My use for the algorithm would be to avoid floats in repetitive calculations. For coordinate transformations, for example, it is convenient to calculate the rotation matrix using trig functions. But then, I would like to convert the results to rationals (with the numerator and denominator separated) so that many points can be scaled and plotted quickly using integer arithmetic. {A good example of the integer arithmetic is the muldiv function (a*b/c) in thermometer.lisp, MCL2 examples folder. - Thanks to Bill St. Clair.} Thanks --Dave David S. Bright bright@enh.nist.gov Microanalysis Research Group National Institute of Standards & Technology (NIST, formerly NBS) Gaithersburg, MD 20899 USA 301-975-3911

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