Precision and CD's
Richard J. Fateman
fateman at cs.berkeley.edu
Tue Jul 20 00:30:37 CEST 1999
I think that the rational numbers (ratios of arbitrary precision
integers) solve the problem that you seem to be addressing
(how to represent 1/7, etc.)
Basically I think of the floats as a selection of rational
representatives from the REAL numbers, so a completion in the
rationals is not interesting.
Other considerations:
The major advantage of floats/ bigfloats is that the cost of
operations is mostly a function of the desired precision, and
not (usually) the value. The usual
operations include sqrt, exp, log, sin, cos etc. as well as +-*/.
Closing the floats exactly under + is already a bad idea because
1+1*10^1000 requires 1000 decimal digits in the fraction.
Closing the floats under division (except division by zero) just to
make them a field has some esthetic mathematical appeal, but in my
opinion it is not worth the complexity and cost of handling repeated
decimals or unknown expansion size.
RJF
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