Or if you don't want to pay for laziness at all you could build your memo array
imperatively (but purely):
import Data.Array.IArray(elems,(!),inRange)
import Data.Array.MArray(newArray_,writeArray,readArray)
import Data.Array.Unboxed(UArray)
import Data.Array.ST(runSTUArray,STUArray)
import Control.Monad(forM_)
import Data.List(zipWith3)
ackMemoSize :: Int
ackMemoSize = 12;
ackList :: [Int]
ackList = 0:1:2:zipWith3 (\ i j k -> i+j+k) ackList (tail ackList) (tail (tail
ackList))
ackMemo :: UArray Int Int
ackMemo = runSTUArray $ do -- the $ works with ghc 6.10, hooray
a <- newArray_ (0,ackMemoSize)
writeArray a 0 0
writeArray a 1 1
writeArray a 2 2
let op i x | i > ackMemoSize = return ()
| otherwise = do
writeArray a i x
y <- readArray a (i-3)
op (succ i) $! (2*x-y) -- could use (2*x) intead
op 3 (0+1+2)
return a
ack :: Int -> Int
ack i | inRange (0,ackMemoSize) i = ackMemo ! i
| otherwise = error "outsize memorized range for ack"
test = (take (succ ackMemoSize) ackList) == (elems ackMemo)
&& (ackList !! ackMemoSize) == (ack ackMemoSize)
Which should have very good performance in building ackMemo (the first time it
is used).
By changing the (2*x-y) to (2*x) I think you get the sum-of-all-previous-entries
behavior.
Cheers,
Chris
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