Stefan Heinzmann wrote:
is there a library for Haskell that implements scaled integers, i.e. integers with a fixed scale factor so that the scale factor does not need to be stored, but is part of the type?
In particular it would be useful (i.e. for signal processing) to have numbers based on Int scaled such that they fall into the range [-1.0 .. 1.0). Or other scale factors which are powers of 2. Addition and subtraction would then map to the ordinary operations for Int, while Multiplication and Division would have to apply the scale factor to correct the result of normal Int operations (which would be a shift operation).
I'm answering myself, as I've come up with a naïve and probably embarrassing first try, which I'm presenting here below so that I can improve my (so far very limited) Haskell skills. Division isn't efficient yet, I just wanted some solution to allow trying it out. I'm sure this can be improved a lot, either in style or in efficiency. So please comment. Cheers Stefan --------------------------------------------------------------------- module ShiftedInt (Int0B31) where import Data.Int import Data.Bits import Data.Ratio data Int0B31 = Int0b31 Int32 instance Show Int0B31 where show (Int0b31 a) = show ((fromIntegral a) * sfD) instance Fractional Int0B31 where fromRational a = Int0b31(fromInteger(quot((numerator a)*sfI) (denominator a))) (/) (Int0b31 a) (Int0b31 b) = fromRational ((fromIntegral a) % (fromIntegral b)) instance Num Int0B31 where negate (Int0b31 a) = Int0b31 (negate a) abs (Int0b31 a) = Int0b31 (abs a) signum (Int0b31 a) = Int0b31 (signum a) fromInteger a = Int0b31 (fromInteger a) (+) a b = a + b (*) (Int0b31 a) (Int0b31 b) = Int0b31 (mul64 (fromIntegral a) (fromIntegral b)) instance Ord Int0B31 where (<=) (Int0b31 a) (Int0b31 b) = a <= b instance Eq Int0B31 where (==) (Int0b31 a) (Int0b31 b) = a == b mul64 :: Int64 -> Int64 -> Int32 mul64 a b = fromIntegral ((a * b) `shift` shiftamount) sfD = 2.0 ^^ shiftamount sfI = 2 ^ (-shiftamount) shiftamount = -31 ---------------------------------------------------------------------