HP Forum Archive 07

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Fractions on the HP-32SII Message #1 Posted by Joe Pasquale on 10 Dec 2001, 1:43 a.m. Does anyone know how fractions are implemented on the HP-32SII (and related HP calculators)? More specifically, given a 0 < z < 1, how do they determine the ratio x/y that is closest to z with a denominator between 1 and 4095 (the max settable on the 32SII)? For example, for z = 0.1763, x/y = 61/346, and for 1/PI, x/y = 113/355. I assume there is something more efficient than an exhaustive search. More generally, is there any reference that describes the numerical algorithms used in HP calculators? Thanks.

Re: Fractions on the HP-32SII Message #2 Posted by Rupert (Northern Italy, EU) on 10 Dec 2001, 5:29 p.m., in response to message #1 by Joe Pasquale >Does anyone know how fractions are implemented on the HP->32SII (and related HP calculators)? More specifically, [...] >exhaustive search. More generally, is there any reference >that describes the numerical algorithms used in HP >calculators? Thanks. I guess it is the Continued Fractions algorithm. For a quick reference you can check www.ulib.org\webRoot\Books\Numerical_Recipes\bookcpdf.html (Chapter 5 Evaluation of Functions, Paragraph 5.2 Evaluation of Continued Fractions 169). which explains the algorithm along whith many others...

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