From: Michael Ulm <michael.ulm@...>
Date: 2008-03-04T19:59:27+09:00
Subject: Re: Why not "truncation towards zero"?

Artem Voroztsov wrote:
> Is it intentional that  (-1/2)  gives -1 ?

I say not only is it intentional, but in this case Ruby gets it Right(TM).

> Please, give me links if there is any rationale.

No links, but rounding to minus infinity is mathematically and conceptionally
the simplest way to do it. The benefit is, that there are fewer special
cases to deal with when numbers get negative.

-C code snipped-

> 
> It looks like  standard C9x  states not only  equation b*(a/b) + a%b == a
> but also "truncation towards zero".

This equation is fulfilled in Ruby as well. It also shows one reason why
the C implementation is worse. To make this equation correct for negative a,
the expression  a%b  has to be negative as well. So, the range of values for
 a%b  differs for positive and negative values of a, whereas in Ruby it is
always in the range (0...b). This is tremendously useful.

> 
> 
> In http://www.open-std.org/JTC1/SC22/WG14/www/docs/C99RationaleV5.10.pdf
> one  could read (6.5.5, page 74):
>   .. In Fortran, however, the result will always
>   truncate toward zero, and the overhead seems to be acceptable to the
> numeric
>   programming  community. Therefore, C99 now requires similar behavior, which
>   should facilitate porting of code from Fortran to C...

So, this is saying, C does this because of backwards compatibility with
Fortran, which didn't get it right. There is no reason for Ruby to be
backwards compatible with Fortran.

HTH,

Michael