From: "Benjamin J. Tilly" <ben_tilly@...>
Date: 2001-05-08T08:03:48+09:00
Subject: [ruby-talk:14827] Re: Integer division oddness

>===== Original Message From "Mike T. Miller" <mtm@csoft.net> =====
>Ok, I think I understand now.  But to clarify, when you mention
>the range as [0,1) you are referring to the remainder with respect
>to the denominator, right?

I am talking the remainder as a floating point once you divide by
the denominatory.  Thinking integers the range is 0...d (note the
triple ., that means that d is not in the range).

>So given
>
>  n % d = m
>
>then
>
>  0 <= m < d

Supposed to be.

>Is that it? But this doesn't hold if d is negative: 10 % -9 = -8
>Argh!  Maybe I still don't quite get it.
>
You have it right, and I would call that answer a bug in Ruby.

Thinking this through carefully can be surprisingly hard.  I
remember with my silly Math::Fleximal in Perl having to eventually
just write down 4 cases first before I could get the logic right:

 4/ 3 =  1* 3 + 1
 4/-3 = -1*-3 + 1
-4/ 3 = -2* 3 + 2
-4/-3 =  2*-3 + 2

Given my druthers, this is the behaviour I want to see from division
and modulus.

Cheers,
Ben

PS Math::Fleximal is on CPAN for those who want to see absolutely
   pointless code...