Re: [Caml-list] Integer arithmetic: mod

["Vesa Karvonen" <vesa.karvonen@housemarque.fi>]

IIRC, the appendix on arithmetic in Computer Architecture: A Quantitative
Approach by Hennessy and Patterson (ISBN: 1558603298) has some rather
convincing arguments on the superior definition of integer div and mod. Well
worth reading.

Regards,
  Vesa Karvonen

----- Original Message -----
From: "Xavier Leroy" <xavier.leroy@inria.fr>
To: "Edmund GRIMLEY EVANS" <edmundo@rano.org>
Cc: <caml-list@inria.fr>
Sent: Monday, November 19, 2001 17:49
Subject: Re: [Caml-list] Integer arithmetic: mod


> > I strongly advise against leaving the meaning of any built-in or
> > library function or operator as implementation-defined. If you do this
> > you will get unportable programs and inefficient programs (because
> > people who want their programs to be portable will be forced to define
> > their own versions of the functions).
>
> I can agree with this argument.
>
> > In my opinion and in most people's opinion, as far as I can tell, if
> > you're starting afresh, the best way to define integer division is as
> > rounding downwards. Integer remainder, to be consistent with this, has
> > the sign of the divisor. There are lots of arguments that support this
> > type of division, both mathematical and practical, and the only
> > arguments against it seem to involve compatibility: the other sort of
> > division is faster on some widely used hardware, is required by some
> > widely used programming languages and assumed by some existing
> > software.
>
> Well, all hardware today implements round-towards-zero for division,
> and this is unlikely to change in the future since ISO C9x requires
> this behavior, so this will remain the behavior of "/" in OCaml.
> We certainly do not want to penalize the existing programs that use
> "/" and "mod" correctly, i.e. on positive arguments.
>
> I'm favorable to providing proper Euclidean division and modulus as
> library functions.  But: I disagree with your statement that
>
> > the best way to define integer division is as
> > rounding downwards. Integer remainder, to be consistent with this, has
> > the sign of the divisor.
>
> The way I learned Euclidean division in college is that the quotient q
> and the modulus r of a divided by b are defined by
>
>         a = b * q + r  with 0 <= r < |b|
>
> e.g. the modulus is never negative, and division does not necessarily
> rounds downwards.  I believe what mathematically-oriented minds really
> want is a modulus that is always positive.
>
> Any mathematician on this list who could look it up in Bourbaki?
>
> - Xavier Leroy
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