module Exercise05 where

-- May or may not be useful: computes the logarithm base 2 (rounded down) of the given number.
-- You don't have to move this into the WETT tags if you want to use it.
log2 :: (Integral a, Num b) => a -> b
log2 = let go acc n = if n <= 1 then acc else go (acc + 1) (n `div` 2) in go 0

{-WETT-}
decompose :: [Integer] -> [Integer]
decompose ds = reverse $ rmLeadingZeors $ process [ product (map (`div` 2^i) ds) | i <- [pwr, pwr -1 .. 0]] 0 dim
    where
        dim = length ds
        pwr = minimum $ map log2 ds

process :: (Integral t, Num a) => [a] -> a -> t -> [a]
process [] _ _ = []
process (x:xs) acc dim = x-acc:process xs ((acc + (x-acc))*(2^dim)) dim

rmLeadingZeors :: (Eq a, Num a) => [a] -> [a]
rmLeadingZeors (0:xs) = rmLeadingZeors xs
rmLeadingZeors xs = xs

{-TTEW-}