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From: avg@diablo.ARPA (Allen VanGelder)
Newsgroups: net.lang
Subject: Re: Integer division: a winner declared
Message-ID: <127@diablo.ARPA>
Date: Sat, 15-Feb-86 21:47:13 EST
Article-I.D.: diablo.127
Posted: Sat Feb 15 21:47:13 1986
Date-Received: Mon, 17-Feb-86 05:23:48 EST
References: <11610@ucbvax.BERKELEY.EDU> <5100003@ccvaxa> <548@ism780c.UUCP> <1970@peora.UUCP>
Reply-To: avg@diablo.UUCP (Allen VanGelder)
Organization: Stanford University
Lines: 18
Keywords: semi-:-) re the winner, Knuth, Ada, C

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

(a mod b) is the answer to the question,
	"What element in the field Z_b is congruent to a?"
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.

I can't imagine implementing -5/3 = -2.  If you really need this, I
would assume you also need the Ada "mod" on the same numbers.  So do
	m = a mod b;
	q = (a - m) / b;
with very little overhead.