Re: Bognumosity

[David Bein <pyramid!bein@hplabs.HP.COM>]

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