Is .2 irrational?
Gary M. Samuelson
garys at bunker.UUCP
Fri Jan 9 04:59:12 AEST 1987
In article <568 at brl-sem.ARPA> ron at brl-sem.ARPA (Ron Natalie <ron>) writes:
>In article <1384 at bunker.UUCP>, garys at bunker.UUCP (Gary M. Samuelson) writes:
>> A floating point format could
>> be designed which allowed exact representation of all decimal fractions,
>> up to some number of places precision.
>
>Gee, how do you deal with 1/3? I'm not sure how I do that even on
>a decimal computer. Perhaps you meant that can handle an exact represntation
>of all fractions of the form INTEGER/(Power of 10)
I did say "up to some number of places precision," which I think covers
your objection to my imprecise wording.
But if you really want: Define a floating point number as a triple of
integers (Numerator, Denominator, Exponent). Let this represent the
number (N/D) * B ** E, where B is a constant (e.g., 10). In normalized
form, N and D have no common factors, and neither N nor D is divisible by B.
As a special case, define (0, 0, 0) to represent zero.
Formal analysis of this scheme, including proofs that each representable
number would have a unique normalized form, or that its arithmetic
would be well defined, is left as an exercise to the reader. (However,
if someone wants to pay my living expenses while I pursue this line of
research, let me know :-).
Gary Samuelson
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