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From: ladkin@kestrel.ARPA
Newsgroups: net.math
Subject: Re: Ok, I give up!
Message-ID: <4384@kestrel.ARPA>
Date: Wed, 29-Jan-86 22:30:41 EST
Article-I.D.: kestrel.4384
Posted: Wed Jan 29 22:30:41 1986
Date-Received: Sat, 1-Feb-86 03:44:14 EST
References: <11594@ucbvax.BERKELEY.EDU>
Organization: Kestrel Institute, Palo Alto, CA
Lines: 47

(smith on floating point arithmetic, speaking for many)

> >> .... [...] many people believe that such problems
> >> are in fact mathematical. Unfortunatly, these people are wrong. 

Jerry Coonen is getting a Ph. D. in MATH at Berkeley for
helping to write the IEEE standard for floating point arithmetic.
His advisor, William Kahan, is a mathematician, and has spent
much of his fruitful career dealing with the problem of how
to convey mathematical information via floating point arithmetic.
He designed the algorithms that are used in the HP34C, which
was the first calculator, I believe, to be able to give
accurate solutions to a general equation f(x)=0, where
f is in the closure of the rational functions, the
trig functions and the logarithmic functions (the same
class that Risch's algorithm can be used on).
Kahan also has shown that the tangent method is
equally good, in a precise sense, as Newton's method
for solving such equations.

(snyder)
> >A recent discussion on net.arch raised the problem of defining integer
> >division for negative numbers. 
> >[....]  I want to know mathematically if one is better than
> >the other.

(smith)
> 
>   Tim: Yes, of course one is better mathematically. The people who are t

(followed by some insults, and very little argument)

Gene, *mod* is mod, and integer division is not the mod function.
Some languages, like Pascal, have both.

There is extensive discussion by Kahan and students at Berkeley
about these issues. Anyone who is interested might attempt to
contact him for references.

I also can't resist noting:

(smith)
>   I really do give up. 

Thankyou. This may be the right solution.

Peter Ladkin