From the haskell report:
The quot, rem, div, and mod class methods satisfy these laws if y is non-zero:
(x `quot` y)*y + (x `rem` y) == x (x `div` y)*y + (x `mod` y) == x
quot
is integer division truncated toward zero, while the result ofdiv
is truncated toward negative infinity.
For example:
Prelude> (-12) `quot` 5
-2
Prelude> (-12) `div` 5
-3
What are some examples of where the difference between how the result is truncated matters?
Many languages have a "mod" or "%" operator that gives the remainder after division with truncation towards 0; for example C, C++, and Java, and probably C#, would say:
(-11)/5 = -2
(-11)%5 = -1
5*((-11)/5) + (-11)%5 = 5*(-2) + (-1) = -11.
Haskell's quot
and rem
are intended to imitate this behaviour. I can imagine compatibility with the output of some C program might be desirable in some contrived situation.
Haskell's div
and mod
, and subsequently Python's / and %, follow the convention of mathematicians (at least number-theorists) in always truncating down division (not towards 0 -- towards negative infinity) so that the remainder is always nonnegative. Thus in Python,
(-11)/5 = -3
(-11)%5 = 4
5*((-11)/5) + (-11)%5 = 5*(-3) + 4 = -11.
Haskell's div
and mod
follow this behaviour.