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From: tim@ism780c.UUCP (Tim Smith)
Newsgroups: net.math
Subject: Integer division
Message-ID: <332@ism780c.UUCP>
Date: Mon, 27-Jan-86 22:48:14 EST
Article-I.D.: ism780c.332
Posted: Mon Jan 27 22:48:14 1986
Date-Received: Thu, 30-Jan-86 04:44:29 EST
Distribution: net
Organization: Interactive Systems Corp., Santa Monica, CA
Lines: 31

A recent discussion on net.arch raised the problem of defining integer
division for negative numbers.  Most computers seem to say that -3/2 is
-1, and -3%2 is -1.  Many people thought this was fine, but some of us
think that -3/2 should be -2, and -3%2 should be 1.  Both sides agree
that integer division on computers must be defined to satisfy

	(1) (a/b)*b + a%b = a.

Everyone agreed that for positive a and b, a/b should round toward zero.
The people who want -3/2 to be -1 argue that the following should hold:

	(2) (-a)/b = -(a/b).

Those of us who want -3/2 to be -2 want the following to hold:

	(3) a%b for positve b has a range of [0,b-1], not [-b+1,b-1], and
	(4) (a+b)/b = a/b + 1.

Are there any good mathematical grounds for choosing one alternative over
the other here?  Note that I am not asking from a hardware point of view
which is better.  I want to know mathematically if one is better than
the other.

My opinion is that (3) and (4) are more important properties than (2),
but when I was a math major my major interest was number theory, where
(3) and (4) are more useful than (2).

[ I have been havig trouble with my mailer, so please respond to net.math ]

-- 
Tim Smith       sdcrdcf!ism780c!tim || ima!ism780!tim || ihnp4!cithep!tim