From mboxrd@z Thu Jan  1 00:00:00 1970
X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me
X-Spam-Level: **
X-Spam-Status: No, score=2.6 required=5.0 tests=BAYES_20,INVALID_DATE,
	REPLYTO_WITHOUT_TO_CC autolearn=no autolearn_force=no version=3.4.4
Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.BERKELEY.EDU
Path: utzoo!linus!decvax!bellcore!ulysses!ucbvax!brahms!gsmith
From: gsmith@brahms.BERKELEY.EDU (Gene Ward Smith)
Newsgroups: net.lang,net.lang.ada
Subject: Re: Integer division: a winner declared
Message-ID: <11957@ucbvax.BERKELEY.EDU>
Date: Fri, 21-Feb-86 03:34:35 EST
Article-I.D.: ucbvax.11957
Posted: Fri Feb 21 03:34:35 1986
Date-Received: Mon, 24-Feb-86 07:21:42 EST
References: <11610@ucbvax.BERKELEY.EDU> <5100003@ccvaxa> <548@ism780c.UUCP> <1970@peora.UUCP> <127@diablo.ARPA>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: gsmith@brahms.UUCP (Gene Ward Smith)
Organization: University of California, Berkeley
Keywords: semi-:-) re the winner, Knuth, Ada, C
Xref: linus net.lang:1918 net.lang.ada:645
List-Id: <comp.lang.ada>

In article <127@diablo.ARPA> avg@diablo.UUCP (Allen VanGelder) writes:

>Ada clearly has it right.  Knuth agrees, but spells "rem" differently.
>Ada examples:
>	   5/ 3   =  1		 5 rem  3 =  2		 5 mod  3 =  2
>	(-5)/ 3   = -1		-5 rem  3 = -2		-5 mod  3 =  1
>	   5/(-3) = -1		 5 rem -3 =  2		 5 mod -3 = -2
>	(-5)/(-3) =  1		-5 rem -3 = -2		-5 mod -3 = -1
>

   It looks like I need to unsay most of the bad things I said about Ada.
Sorry about that, Adaphiles, but at first I thought J. Eric Roskos was
saying Ada had two mod-type functions, but later decided he was saying it
had only one (since he said Knuth's was different). I hope foot-in-mouth
disease isn't catching.

>For b > 0, Z_b = {0,1,2,...,b-1} by standard definition.  For b < 0
>I am unaware of any standard definition, but we might as well define
>Z_b = {0,-1,-2,...,b+1}.  Note that b+1 is the multiplicative identity.

   There is a standard remainder defintion for negative b, but it really
doesn't matter; the Knuth/Ada definition is just fine.

>I can't imagine implementing -5/3 = -2.  If you really need this, I

   Just today I needed this. It took an extra (C language) function 
definition. I have *never in my life*, to the best of my recollection,
wanted or needed -5/2 = -1. It's not as important as mod by any means,
so I will just leave you with this thought: it's still wrong, but the 
situation is improving. Maybe the next "language to end all languages"
after Ada will finally get it right.

ucbvax!brahms!gsmith    Gene Ward Smith/UCB Math Dept/Berkeley CA 94720
ucbvax!weyl!gsmith      "Dumb problem. DUMB!!!"