Re: Rounding with Div and Mod operators

wclodius@aol.com says...
> I'm writing a compiler for a new language which is to include the
> integer division and integer remainder operators (div and mod). I have
> some questions about the way these operators do rounding with negative
> operands and would appreciate any feedback.


I notice that several people have mentioned the "two" forms of
div/mod. I few years back I compared this on quite a few languages
and found the *three* definitions in actual use (and, no, it was so
long ago that I don't remember which definition was used by which
language). The three definitions are (using |x| to mean absolute
value of x and sgn(x) to mean the sign of x, -1, 0, +1)...


1. sgn(x % y) = sgn(x)
0 <= |x % y| <= |y|


2. sgn(x % y) = sgn(y)
0 <= |x % y| <= |y|


3. 0 <= x % y
0 <= x % y < |y|


I believe that there are quite a few more ways in which it could be
defined from a theoretical point of view, but these are the only ones
I have seen in practice.
--
Michael Lee Finney
michael.finney@acm.org

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