In many programming languages, a % b is simply a - b*(a/b), where '/' is integer (truncated toward 0) division. I'm alright with this because: 1. this computat

In many programming languages, a % b is simply a - b*(a/b), where '/' is integer (truncated toward 0) division. I'm alright with this because: 1. this computation is typically more efficient on silicon optimized for arithmetic, 2. this computation is unambiguous and more straightforward to people who are unfamiliar with modular arithmetic, especially when negative a and b are involved, and 3. in contexts where the mathematical remainder 0 <= r < abs(b) is needed, b is typically always known. It is easy to see that knowing a % b and b it is easy to recover r, but knowing b and r, one may not recover a % b (we don't know if it was positive or negative).