The frem(x, y) function returns r = x - y*n where n is the integer nearest the exact value x/y. The value of n is taken to be even in the case of a tie.

The rounding mode is not considered for this computation. If r = 0, then its sign is set to that of x.

If y is real, frem(x, y) maps onto complex numerics.

This function signals invalid_operation if y is unordered with 0 (unless y is already a NaN).

Note:  If m and n are integers, frem(m, n) is not necessarily the same mathematical value as irem(m, n), since frem() computes by using the nearest integer to the quotient m/n, not the integer quotient of m by n.

The frem command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.