Re: rational to floating point

Thant Tessman <thant@acm.org> writes:
|>
|> I've been writing an interpreter for a functional programming language
|> in C++. One of the datatypes it supports is an arbitrary-precision
|> rational number type. Currently the interpreter displays rational
|> numbers as the ratio of two integers. I'd like it to display rational
|> numbers as floating-point numbers whenever the conversion to floating
|> point won't produce an infinite (repeating) stream of digits.
|>
|> The question is: Under what conditions will a rational number produce
|> an infinite stream of digits for a given base? What I've come up with
|> is this:


Assuming that the number has been reduced to its simplest terms
(i.e. with all common factors removed), then it will be whenever
the denominator contains any prime factor other than 2 and 5.


But you may not find this a good idea, even for numbers that do
expand directly, because of their resulting length. Expand out
1/1024, for example.




Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email: nmm1@cam.ac.uk
Tel.: +44 1223 334761 Fax: +44 1223 334679

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