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# mod(+Number1, +Number2, -Result)

Evaluates the modulus Number1 mod Number2 and unifies the resulting value
with Result.
*Number1*
- Integer.
*Number2*
- Integer.
*Result*
- A variable or integer.

## 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

### Exceptions

*(4) instantiation fault *
- Number1 or Number2 is not instantiated (non-coroutining mode only).
*(5) type error *
- Number1 or Number2 is a number but not an integer.
*(20) arithmetic exception *
- Illegal arithmetic operation: Number2 is zero
*(24) number expected *
- Number1 or Number2 is not of a numeric type.

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

## See Also

is / 2, div / 3, rem / 3