Integral operators quot vs. div

Question

To quote section 6.4.2 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 of div is truncated toward negative infinity.

The div function is often the more natural one to use, whereas the quot function corresponds to the machine instruction on modern machines, so it's somewhat more efficient.

The two behave differently when dealing with negative numbers. Consider:

Hugs> (-20) `divMod` 3
(-7,1)
Hugs> (-20) `quotRem` 3
(-6,-2)

Here, -7 * 3 + 1 = -20 and -6 * 3 + (-2) = -20, but the two ways give you different answers.

Also, see here: http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html

The definition for quot is "integer division truncated toward zero", whereas the definition for div is "integer division truncated toward negative infinity".