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From: radford@calgary.UUCP (Radford Neal)
Newsgroups: net.arch
Subject: Re: Right shift vs. divide (change divide!)
Message-ID: <49@calgary.UUCP>
Date: Fri, 17-Jan-86 03:07:39 EST
Article-I.D.: calgary.49
Posted: Fri Jan 17 03:07:39 1986
Date-Received: Fri, 17-Jan-86 12:15:26 EST
References: <124000005@ima.UUCP> <4772@alice.UUCP> <1016@turtlevax.UUCP>, <32@calgary.UUCP> <345@mcgill-vision.UUCP>
Organization: University of Calgary, Calgary, Alberta
Lines: 34

>      Only reason I can see for a  mathematician -- for anyone -- to want
> it  to   work  this  way  is   that  then  x-(y*(x/y))  is  always  >=0.
> Unfortunately, doing  this  breaks other nice  properties, in particular
> that  x/y  equals -((-x)/y).   It  therefore  means that  hardware can't
> handle  negative  numbers  by  simply  negating  before  and  after  the
> operation.    I  don't  see  why you aren't satisfied with  -3/2=-1  and
> -3%2=-1.   You still  have  that x=(x%y)+(y*(x/y)), which is  really all
> mathematicians demand, as far as I know (flame retardant:  my  knowledge
> of number theory is limited to undergrad level).

In applications where number theory is relevant there is a powerful
demand that

      x%y = (x+y)%y

which isn't true with truncate toward zero division.

>      What do you want done with -3/-2 or 3/-2?

Beets me. I'm rather confused as to when people actually use negative
divisors and what should be done about them. But as a first cut I might
go for:

    7/3 = 2     7%3 = 1
   -7/3 = -3   -7%3 = 2
    7/-3 = -2   7%-3 = 1
   -7/-3 = 3   -7%-3 = 2

This preserves the properties that

   x = (x/y)*y + x%y   and   0 <= x%y < |y|

      Radford Neal
      University of Calgary