Re: Rounding with Div and Mod operators

  "William Rayer" <william.rayer@virgin.net> writes:
> n = (n div d) * d + (n mod d)
>
> What is interesting about this rule is there seem to be two ways of
> rounding that satisfy it when n or d are negative - either we round
> integers to the next lowest value or we round towards zero.


The first is called floored division, the second symmetric division.


> My question is: which rounding system is preferred and does it matter?


It does matter in some applications. Which one is preferred depends
on the application, but in most cases that I have come across floored
division is preferred.


Therefore several languages have come up with operations for both
options: Ada has mod and rem (I don't know how it defines /), Forth
has fm/mod (floored) and sm/rem (symmetric).


And here's a little gem I have from Andrew Haley for doing floored
division of a double-precision integer by a single-precision integer
with single-precision results in terms of unsigned division; the
signed number representation is 2s complement:


denomsign=denom;
if (denom < 0) {
    denom = -denom;
    num = -num;
}
if (num < 0)
    num.hi += denom; /* single-precision add to the most significant part of
                                            the numerator. */
quot = num u/ denom;
rem = num u% denom;
if (denomsign<0)
    rem = -rem;


- anton
--
M. Anton Ertl Some things have to be seen to be believed
anton@mips.complang.tuwien.ac.at Most things have to be believed to be seen
http://www.complang.tuwien.ac.at/anton/home.html

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