On 12/15/05, Jack Johnson <knapjack@gmail.com> wrote:

Not really, but all the talk about Singularity got me poking around
and I came across this:

------

How are the functions DIV and MOD defined?

The following answers are given by the Internal Working Document on
the Common Language Infrastructure (CLI).

result = value1 DIV value2 satisfies the following conditions:
|result| = |value1| / |value2|, and
sign(result) = +, if sign(value1) = sign(value2)
sign(result) = - , if sign(value1) # sign(value2)

result  = value1 MOD value2 satisfies the following conditions:
result = value1 - value2 * (value1 DIV value2), and
0 <= |result| < |value2|, and
sign(result) = sign(value1)

Please note that this definition of DIV and MOD differs from the
definition given in [M. Reiser, N. Wirth. Programming in Oberon. p.
36]:
x  = (x DIV y) * y + (x MOD y), and
0 <= (x MOD y) < y

( from http://www.bluebottle.ethz.ch/oberon.net/faq.html#ad_DivMod )

------

I kind of collect random, older computer science texts, so I cracked
open The Nature of Computation by Pohl and Shaw, which yields:

  "x MOD y = x - (x ÷ y) * y, where ÷ indicates integer division (i.e.
fractions are disregarded; equivalently, the result of the division is
truncated)."

So, what *is* -5 MOD 3?

-Jack