Modulo operation

• Not to be confused with: Modulus operation - which is another name for absolute value

Definition

For $a\in\mathbb{N}_0$ and $b\in\mathbb{N}$ "$a$ modulo $b$", written usually as a%b in most programming languages or using a mod(a,b) function is the remainder of dividing $a$ by $b$.

Implementation

I write this page because I have used:

• $$a\% b\eq \Bigg(a-b\cdot$$ $$\text{Floor}$$ $${\left(\frac{a}{b}\right)}\Bigg)$$
  • Caveat:This only works for non-negative values!
    TODO: Proof?

See also

• Division algorithm and Integer division
• idiv (x86) and div (x86)

Extensions

• What about negative numbers?
• $2.5$ mod $1$ is safely and obviously $0.5$ - this is quite common.