Integer division that rounds up

Introduction

Usual integer division rounds down: ${\frac {a}{b}}=\left\lfloor {\frac {a}{b}}\right\rfloor$ for $a,b\in \mathbb {N} ,b\neq 0$. To round up (if overflow is not an issue), you can use following algorithm with the usual roundig down division: Failed to parse (syntax error): {\displaystyle q = \frac{x+y-1}{y} = \left \lceiling \frac xy \right \rceiling. }