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Weird numeric predicates?
Date: Fri, 17 Mar 89 11:26:05 -0500
From: jinx@chamartin.AI.MIT.EDU (Guillermo J. Rozas)
I haven't thought about it carefully, but it may not be reasonable
(unless it is defined that way) to implement n-ary < and friends as
the "AND accumulation" of binary <. Comparisons between exact and
inexact numbers should coerce the exact numbers to inexact, and this
value may have to be used consistently afterwards.
If <= is to behave transitively, even on inexact arguments, then you have
to coerce inexact number to exact numbers in order to perform comparisons.
(Or you must behave as if you did.) To see why, consider the following
(DEFINE A (- (EXPT 10 38) 1))
(DEFINE B 1E38)
(DEFINE C (+ (EXPT 10 38) 1))
Assuming your implementation has an exact representation for A and C
(probably as a BIGNUM) and the inexact B is represented in a floating point
format with less (probably far less!) that 38 digits of precision, then
coercing either A or C to inexact will most likely return B. If comparison
predicates coerce EXACT->INEXACT, then the following will be true:
(<= C B) ==> #T
(<= B A) ==> #T
(<= C A) ==> #F
(= C B) ==> #T
(= B A) ==> #T
(= C A) ==> #F
If instead comparison predicates coerce INEXACT->EXACT then consistently
transitive answers will be obtained.