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
-
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