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From: earl@mips.UUCP (Earl Killian)
Newsgroups: net.math,net.lang.c,net.arch
Subject: Re: Integer division
Message-ID: <322@mips.UUCP>
Date: Thu, 6-Feb-86 16:03:42 EST
Article-I.D.: mips.322
Posted: Thu Feb  6 16:03:42 1986
Date-Received: Sun, 9-Feb-86 05:47:29 EST
References: <367@mcgill-vision.UUCP>
Organization: MIPS Computer Systems, Mountain View, CA
Lines: 23
Xref: watmath net.math:2806 net.lang.c:7797 net.arch:2482

Of the languages I'm familiar with, I believe integer division is
best handled in Common Lisp.  There are four functions of two
arguments: trunc, floor, ceil, and round.  Each divides the first
argument by the second and then rounds the result to an integer
using round to zero, round to -infinity, round to +infinity, and
round to nearest respectively.  The second return value is the
remainder of that division.

Thus:
(trunc 7 3)	=>  2,  1		; 2*3 + 1 = 7
(trunc -7 3)	=> -2, -1		; -2*3 + -1 = -7
(floor 7 3)	=>  2,  1		; 2*3 + 1 = 7
(floor -7 3)	=> -3,  2		; -3*3 + 2 = -7
(ceil 7 3)	=> 3, -2		; 3*3 + -2 = 7
(ceil -7 3)	=> -2, -1		; -2*3 + -1 = -7
(round 7 3)	=> 2, 1			; 2*3 + 1 = 7
(round -7 3)	=> -2, -1		; -2*3 + -1 = -7

The programmer picks what is appropriate.  I have found floor and ceil
to be the most useful, and trunc somewhat less.  I have never used round.

Actually these are also functions of one argument: (floor 3.5) => 3 0.5,
etc.