fromRational broken for Ratio a

[daniel.is.fischer]

The Fractional instance for Ratio a in GHC.Real defines

    fromRational (x:%y) =  fromInteger x :% fromInteger y

For fixed-width Integral types, that produces invalid results:

Prelude Data.Ratio> fromRational (1 % 2^32) :: Ratio Int
1 % 0
Prelude Data.Ratio> fromRational (3 % (2^32+9)) :: Ratio Int
3 % 9

Via toRational, these can be ported back to Rational.

Ratio a is generally broken for fixed-width types:

Prelude Data.Ratio> 1 % (minBound :: Int)
(-1) % (-2147483648)

but the particular brokenness of fromRational can be alleviated by reducing:

    fromRational (x:%y) = fromInteger x % fromInteger y

{-# RULES
"fromRational/id"  fromRational = id :: Rational -> Rational
  #-}

I think it's better to throw a divide by zero error than to produce invalid results here.

[daniel.is.fischer]

Patch with the suggested change. I don't see anything else we could do.

Please review and merge.

[simonmar]

Applied, thanks!

Mon Oct 18 18:01:09 PDT 2010  Daniel Fischer <daniel.is.fischer@web.de>
  * FIX #4335
  fromRational :: Rational -> Ratio a produced invalid results for fixed-width
  types a. Reduce the fraction to avoid that.

[igloo]

Merged.