divide,mod,quo,rem

Usage

divide(a, b)
a mod n
a mod b
a quo b
a rem b

Signatures

divide:	(%,%) $\to$ (%, %)
mod,quo,rem:	(%,%) $\to$ %
mod:	(%,MachineInteger) $\to$ MachineInteger

Parameter	Type	Description
a,b	%	integers, $b \ne 0$
n	MachineInteger	a nonzero machine integer

Returns

$a$ mod $b$ (resp. $a$ mod $n$) returns $m$ such that $0 \le m < \vert b\vert$ (resp. $0 \le m < \vert n\vert$) and $a \equiv m \pmod b$ (resp $n$), while $a$ rem $b$ returns $r$ such that $-\vert b\vert < r < \vert b\vert$ and $a \equiv r \pmod b$, $a$ quo $b$ returns $(a - (a$ rem $b)) / b$, and divide(a, b) returns the pair (a quo b, a rem b).

Remarks

mod returns a unique remainder modulo b, but is more expensive to compute than rem, and is not guaranteed to be compatible with the result of quo. The version whose second argument is a MachineInteger allows for more efficient implementations.