
mod(+Number1, +Number2, -Result)

   Evaluates the modulus Number1 mod Number2 and unifies the resulting value
with Result.



Arguments
   Number1             Integer.
   Number2             Integer.
   Result              A variable or integer.

Type
   Arithmetic

Description
   This predicate is used by the ECLiPSe compiler to expand evaluable
   arithmetic expressions.  So the call to mod(Number1, Number2, Result) is
   equivalent to

    Result is Number1 mod Number2

    which should be preferred for portability.

    The modulus operation computes the remainder corresponding to the
    flooring division div.  The following relation always holds:

    X =:= (X mod Y) + (X div Y) * Y.

    The result Result is either zero, or has the same sign as Number2.

   In coroutining mode, if Number1 or Number2 are uninstantiated, the call
   to mod/3 is delayed until these variables are instantiated.

   CAUTION: The behaviour of mod was changed for standard compliance!
   In ECLiPSe versions up to 5.8, mod computed the remainder corresponding
   to the truncating division //, and thus gave different results for
   arguments with opposite signs.  Moreover, the operator precedence was
   changed from op(300,xfx,mod) to op(400,yfx,mod), which means that
   a*b mod c is now parsed as (a*b)mod c rather than a*(b mod c).


Modes and Determinism
   mod(+, +, -) is det

Exceptions
     4 --- Number1 or Number2 is not instantiated (non-coroutining mode    only).
     5 --- Result is a number but not an integer.
     5 --- Number1 or Number2 is a number but not an integer.
    20 --- Illegal arithmetic operation: Number2 is zero
    24 --- Number1 or Number2 is not of a numeric type.
    24 --- Result is neither a number nor a variable.

Examples
   
Success:
      X is 10 mod 3.		(gives X = 1)

      mod( 10,  3,  1).
      mod(-10,  3,  2).
      mod( 10, -3, -2).
      mod(-10, -3,  1).

      mod( 11,  3,  2).
Fail:
      mod(1, 2, 3).
Error:
      mod(A, 2, 6).              (Error 4).
      mod(6, 2.0, 3.0).          (Error 5).
      mod(2, 0, Result).         (Error 20).
      mod(4 + 2, 2, 12).         (Error 24).
      mod(5, 2, r).              (Error 24).


See Also
   is / 2, div / 3, rem / 3
