The Remainder Operator

The remainder operator % computes the remainder that results when one number is divided by another. Specifically, suppose m and n are of some numeric type, where n ≠ 0. We can then define a quotient q and a remainder r as the unique values such that:

• qn + r = m;
• q is an integer;
• |qn| ≤ |m|; and
• |r| < |n|.

Then m % n gives r, and we can compute q by:

(m - r) / n

Another way to think about m % n is through the following algorithm to compute it:

1. Compute |m| / |n|, and remove any fractional part.
2. If m and n have the same sign, let q be the above result; otherwise, let q be the negative of the above result.
3. m % n is m - qn.

Examples:

• 7 % 3 = 1
• -9 % 5 = -4
• 8 % -3 = 2
• -10 % -4 = -2
• 6.4 % 1.3 = 1.2