modular arithmetic

modular arithmetic
modulo arithmetic

   <mathematics> (Or "clock arithmetic") A kind of integer
   arithmetic that reduces all numbers to one of a fixed set
   [0..N-1] (this would be "modulo N arithmetic") by effectively
   repeatedly adding or subtracting N (the "modulus") until the
   result is within this range.

   The original mathematical usage considers only __equivalence__
   modulo N.  The numbers being compared can take any values,
   what matters is whether they differ by a multiple of N.
   Computing usage however, considers modulo to be an operator
   that returns the remainder after integer division of its first
   argument by its second.

   Ordinary "clock arithmetic" is like modular arithmetic except
   that the range is [1..12] whereas modulo 12 would be [0..11].

   (2003-03-28)