|Your definition of divFloorRem (and probably divCeilingRem as well)
|doesn't seem to be quite right, because I end up with
| (-4) `mod` (-3) == -4
|because divTruncateRem (-4) (-3) is (1,-1).
|
|The condition in the "if" should be something like
| signum r == -signum d
|rather than r<0. (Something like this is in the definition of
|`mod` on page 89 in 1.2beta.)
|
|Stefan Kahrs
Right, thanks. I've committed the error of forgetting that the
divisor can be negative. I did the rounding methods first, where
the "divisor" is 1, and then did the division methods by (incorrect!)
analogy. You'd think that after n years of struggling with with
definitions like these, I'd be able to get them right!
So, as you say, this can be fixed thus:
divFloorRem n d = if signum r == - signum d then (q-1, r+d) else qr
where qr@(q,r) = divTruncateRem n d
divCeilingRem n d = if signum r == signum d then (q+1, r-d) else qr
where qr@(q,r) = divTruncateRem n d
Another way:
divFloorRem n d = if r < 0 then (q-1, r+d) else qr
where
qr@(q,r) = divTruncateRem n' d'
(n', d') = if d < 0 then ((-n),(-d)) else (n,d)
divCeilingRem n d = if r > 0 then (q+1, r-d) else qr
where
qr@(q,r) = divTruncateRem n' d'
(n', d') = if d < 0 then ((-n),(-d)) else (n,d)
--Joe
