Path: utzoo!mnetor!uunet!mcrware!jejones
From: jejones@mcrware.UUCP (James Jones)
Newsgroups: comp.arch
Subject: Re: Round-off
Message-ID: <589@mcrware.UUCP>
Date: 11 Jan 88 08:05:16 GMT
References: <189@mithras> <614@PT.CS.CMU.EDU> <4404@ecsvax.UUCP>
Organization: Microware Systems Corp., Des Moines, Ia.
Lines: 16
Keywords: IBM HEX ???
Summary: numerical bummers of hex exponents

In article <4404@ecsvax.UUCP>, hes@ecsvax.UUCP (Henry Schaffer) writes:
> Why not?  Why can't [numerical analysts] just treat it as hex roundoff -
> without worrying that the first bit in hex 1-7 is a 0?

It turns out that there are some proofs of convergence that count on the
property

			(x * 2) / 2 = x

(aside from over/underflow), and using base 16 violates that property.
In fact, I recall that the ITF BASIC and PL/I exp() function once had
a bug that caused exp(1 +/- epsilon) to be zero for 0 < epsilon < some
(small) value x, and I believe that the cause of the bug was the 360/370's
use of base 16 floating-point arithmetic.

		James Jones