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From: franka@mmintl.UUCP (Frank Adams)
Newsgroups: net.arch
Subject: Re: Right shift vs. divide (change divide!)
Message-ID: <1032@mmintl.UUCP>
Date: Tue, 14-Jan-86 05:03:11 EST
Article-I.D.: mmintl.1032
Posted: Tue Jan 14 05:03:11 1986
Date-Received: Fri, 17-Jan-86 06:15:36 EST
References: <124000005@ima.UUCP> <4772@alice.UUCP> <1016@turtlevax.UUCP> <32@calgary.UUCP> <285@mips.UUCP>
Reply-To: franka@mmintl.UUCP (Frank Adams)
Organization: Multimate International, E. Hartford, CT
Lines: 30

In article <285@mips.UUCP> hansen@mips.UUCP (Craig Hansen) writes:
>So now we've seen every possible solution: ignore it,
>fix arithmetic right shift, and now fix divide!
>
>There are indeed two consistent definitions of divide,
>both of which satisfy the relation:
>
>	x = (x / y) * y + (x % y)
>
>The two definitions basically amount to evaluating x/y
>by (1) rounding toward -infinity and (2) rounding toward zero.
>Each have their own advantages:

There is another important definition, which is to round to the nearest
integer.  (This is subdivided by what one does with a fractional part
of exactly one half.)  Uses for the rounded quotient should be quite
obvious.

The remainder in this case is the remainder with the smallest possible
absolute value.  This is useful in a variety of number-theoretic
applications; as a simple example, Euclid's algorithm will terminate
faster using the least absolute remainder.


I will note also that I fairly often want to do a division and round
up instead of down.  This is especially common when dealing with
arrays whose first element is 1, not 0.

Frank Adams                           ihpn4!philabs!pwa-b!mmintl!franka
Multimate International    52 Oakland Ave North    E. Hartford, CT 06108