Path: utzoo!attcan!uunet!samsung!usc!trwind!gumby!wiley!scott
From: scott@wiley.uucp (Scott Simpson)
Newsgroups: comp.lang.lisp
Subject: Re: Virtues of Lisp syntax
Summary: Real programmers don't use real numbers.
Keywords: floating point numbers, representations, precision
Message-ID: <26F4D816.45FF@wilbur.coyote.trw.com>
Date: 17 Sep 90 14:05:10 GMT
References: <33709@cup.portal.com> <1990Sep10.091911.20877@hellgate.utah.edu> <PCG.90Sep13135243@odin.cs.aber.ac.uk> <3758@goanna.cs.rmit.oz.au> <PCG.90Sep15203024@odin.cs.aber.ac.uk>
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Reply-To: scott@wiley.UUCP (Scott Simpson)
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In article <PCG.90Sep15203024@odin.cs.aber.ac.uk> pcg@cs.aber.ac.uk (Piercarlo Grandi) writes:
>Anyone doing floating point arithmetic on *any* machine, IEEE standard
>or Cray, has to be very very wary of assuming it is the same as
>arithmetic on reals, and yet a lot of people do (and then complain that
>two computers with different floating representations print utterly
>different results to their programs!).

Real programmers don't use real numbers. Donald Knuth did all the
arithmetic in TeX in fixed point numbers he called FIXes, which are
numbers raised to 2^20th (i.e., he uses the lower 20 bits for the
fractional part). This gives the same results on all (32 bit or
greater) machines but you still must be wary with your arithmetic.
(Come to think of it, maybe he did it in scaled points (which are
2^16th). I don't have the source here. I'll have to check. My point is
the same though.)
Scott Simpson    		TRW 			scott@coyote.trw.com