Xref: utzoo comp.misc:8385 comp.lang.misc:4321 comp.arch:14370
Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!mcsun!ukc!edcastle!lfcs!db
From: db@lfcs.ed.ac.uk (Dave Berry)
Newsgroups: comp.misc,comp.lang.misc,comp.arch
Subject: Re: Modulus
Message-ID: <2573@castle.ed.ac.uk>
Date: 2 Mar 90 13:37:47 GMT
References: <981@m1.cs.man.ac.uk> <12115@goofy.megatest.UUCP>
Reply-To: db@lfcs.ed.ac.uk (Dave Berry)
Organization: Laboratory for the Foundations of Computer Science, Edinburgh U
Lines: 52

In article <12115@goofy.megatest.UUCP> djones@megatest.UUCP (Dave Jones) writes:
>Just now I did a little experimenting. On Sun-3, release 4.3.  In both C
>and Pascal, division is correct, but mod is wrong.
>
>In other words, they have it exactly backwards from the ANSI Pascal
>Standard. Not right mathematically. Not right according  to the standard.
>You got to wonder, how come?

Almost certainly becasue that's how the hardware does it.  Almost all
processors implements integer division and modulus that way.o

Questions to comp.arch readers (who I've just tuned in):

1. Is the "normal" method for calculating integer division and modulus
   intrinsically faster than the mathematically expected definition (that
   rounds towards minus infinity), or is it just convention that it's
   implemented this way?

2. If everyone was suddenly to agree that the mathematically expected
   definition should be adopted as a standard, could it be done quicker
   in hardware than with software over the existing hardware?


There is some weight to arguments that languages should support the
round towards zero versions.  Standard ML defines div and mod the
mathematically expected way, and this has produced criticism from
some users and implementers that use of these operators on positive
arguments is unnecessarily penalised, since they can't use the versions
provided by the hardware.  It is possible that the definition might
be amended to support both definitions.

I note that the ISO draft proposal for standard computer arithmetic
(published in SIGPLAN notices, Jan. 1990) allows either or both versions
of div and mod.


For reference, the Definition of Standard ML defines div and mod as follows:

  i mod d, i div d return integers r, q determined by the equation
  d * q + r = i, where either 0 <= r < d or d < r <= 0.  Thus r has
  the same sign as d.  [An exception is raised] if d = 0.

  [nb. the operators used in this definition are those of arithmetic,
   not of the language.]

What sign i mod d should have when d < 0 (in an arbitrary language, not ML)
was discussd in several other articles recently.

 Dave Berry, LFCS, Edinburgh Uni.      db%lfcs.ed.ac.uk@nsfnet-relay.ac.uk

"The thought of someone sharing one's own preferences without also sharing
 one's aversions strikes most people as utterly inconceivable." - C. A. Tripp.