Path: utzoo!mnetor!uunet!seismo!sundc!pitstop!sun!quintus!ok
From: ok@quintus.UUCP (Richard A. O'Keefe)
Newsgroups: comp.lang.lisp
Subject: Re: Float/rational comparison
Message-ID: <891@cresswell.quintus.UUCP>
Date: 22 Apr 88 03:47:23 GMT
References: <888@cresswell.quintus.UUCP> <20062@think.UUCP>
Organization: Quintus Computer Systems, Mountain View, CA
Lines: 24

In article <20062@think.UUCP>, barmar@think.COM (Barry Margolin) writes:
> The reason for floating-point contagion is that floating point numbers
> are not considered exact, while rationals are.  It is therefore not
> proper to automatically convert floats to rationals, because you would
> be fooling yourself if you believe that the float actually represented
> that exact rational.

This is fair enough when one is talking about a computation delivering
numeric results, such as (+ float rational).  But a comparison doesn't
do that.  As I attempted to sketch in my first message on this topic,
it is possible to do an exact rational/float comparison without fully
converting the float to a rational.

If we argue that a float X represents the interval {X-somewhat,X+somewhat}
--I want to be vague about the boundaries--then converting a rational to
the nearest float and doing a float gives you a spurious "=" comparison
only if the rational is in that interval, so this result makes some sense.

But my interest is not so much in rational/float comparison as such,
but in having comparison functions which satisfy the axioms of a total
order.  It bothers me that there can be numbers X, Y, Z such that
	(= X Y) and (= Y Z) but (< X Z)
so that a sorting routine could be "provably correct" and nevertheless
deliver wrong answers.