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*To*: hplabs!common-lisp@sail.stanford.edu@hplabs.HP.COM*Subject*: Re: Bognumosity*From*: David Bein <pyramid!bein@hplabs.HP.COM>*Date*: Thu, 16 Apr 1987 18:44:00 -0000

Stan: I agree with the spirit of essentially unlimited size bignums. On most of the systems I know of, most-positive-fixnum is 27 bits or more, implying that a bignum that long would take at least 16 megabytes to represent unless one is willing to introduce a notion like floating point where low order bits are not represented beyond some limit, at which point why not use floating point to begin with. My system in fact adheres roughly to your suggestion, where technically a bignum 134217702 bits long can be allocated (most-positive-fixnum is 134217727 in my system). I think you'll find that doing anything with a bignum that long is next to impossible since other resources like scratch stack space may not accomodate multiple copies of something that large (which of course is not very interesting when it happens). I would almost suggest that if there is a limit, it be tied to notions like the largest float since a larger bignum can't be converted properly unless we introduce notions like floating-infinities into the language. If we do that however, we end up needing a definition for rational infinity. I don't have a good handle on what infinity means from an operational point of view. Maybe getting out of digit computers for a while would help -- :-) I too am uncomfortable with the idea that rational numbers overflow, but don't have any practical ideas about what do besides treat the problem as simply a resource problem which is what I am already doing. --David

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