Re: Integers and Mathematical Correctness

[Wilhelm Spickermann <wilhelm.spickermann@t-online.de>]

--On Thursday, November 01, 2001 18:54:34 +0000 David Starner 
<dvdeug@x8b4e53cd.dhcp.okstate.edu> wrote:

> Basically, a division is correct if
>
> dividend / divisor = quotient, modulus
> 	implies that
> (quotient * divisor) + modulus = dividend
> 	But
> (-2 * 2) + 1 = -3 = (-1 * 2) + -1.
> The first is division floored to negative infinity, and the
> second is  division symmetric around zero, and either are
> valid. Forth-83 picked

Both Equations are valid, but only the first one (the first 
part) uses a modulus -- the second one uses a remainder. A 
modulus can take only abs(divisor) different values while a 
remainder can take 2*abs(divisor)-1 different values.

Wilhelm