Xref: utzoo comp.theory:372 comp.misc:8286 comp.lang.misc:4219
Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!wuarchive!decwrl!megatest!djones
From: djones@megatest.UUCP (Dave Jones)
Newsgroups: comp.theory,comp.misc,comp.lang.misc
Subject: Re: Modulus (Re: hashing function for strings)
Message-ID: <12120@goofy.megatest.UUCP>
Date: 23 Feb 90 03:02:29 GMT
References: <6197@bd.sei.cmu.edu>
Organization: Megatest Corporation, San Jose, Ca
Lines: 42

From article <6197@bd.sei.cmu.edu>, by firth@sei.cmu.edu (Robert Firth):
> In article <12099@goofy.megatest.UUCP> djones@megatest.UUCP (Dave Jones) writes:
> 
> [the 'contrary' view is that integer division should truncate towards zero]
> 
>>Several others have told me that it 'depends on what you're doing', but so
>>far nobody has come up with an example where the contrary view is a win.
> 
> That surprises me, since there is a standard example.

Several people posted candidates, but each was shot down in turn.

> You have a
> picture drawn on a Cartesian plane, symmetrical about the origin.
> You need to scale this picture by some factor - for example, you
> want to reduce its size by 50% linear.
> 
> The obvious coordinate transformation is (x',y') = (x/2,y/2).  If
> division truncates towards zero, fine; otherwise, the scaled picture
> is no longer symmetrical (and typically the viewer can perceive
> the asymmetry).

I presume that since we are using integer division, the image is
some kind of a bitmap, right?

This has the ring of truth to it, although it seems somewhat contrived.
(How often do you have a *symetrical* digitized picture laying about that
you want to scale by 1/2?) It has the ring of truth, because the problem
with the 'contrary' view is precicely that it's graph is symetrical about
the y-axix, which makes translating it sideways impossible. And here we have
a picture which is symetrical about the y-axis. If there is a case where
the 'contrary view' prevails, it will be something like this.

But I'm still not convinced. A picture undergoing this transformatinon will
be 'pinched' along both the x and y-axes, whether it is symetrical or not.
This may or may not be obvious, depending on the picture. But I would think
that the 'creases' down the middle would often be noticeable, and would be a
direct consequence of the nastiness around zero.

(It may not matter, but is this really a valid way to scale down a
bitmap image? Seems bogus to me, because any two-by-two rectangle that
has even one dot in it will get transformed into a dot.)