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3+{- Toy program that outputs the n first digits of Pi.
5+ Inspired from http://www.haskell.org/haskellwiki/Shootout/Pidigits.
6+ The original ns and str lazy lists have been replaced by strict functions.
8+ Memory usage seems to be excessive. One of the branches of str is tail recursive, and
9+ the other one only needs to cons an extra Integer.
11+ For reference, the Haskell version runs in 0m0.230s when printing to /dev/null.
12+ It almost runs in constant space.
15+data F = mkF Integer Integer Integer
17+-- Prints the list of digits by groups of 10
18+loop : Nat -> Nat -> List Integer -> IO()
19+loop n k' Nil = putStrLn $ (pack $ Vect.replicate n ' ') ++ "\t:" ++ show k'
20+loop Z k' xs = do putStrLn ("\t:"++show k')
22+loop (S k) k' (x::xs) = do putStr (show x)
26+fn k = mkF k (4*k+2) (2*k+1)
28+flr : Integer -> F -> Integer
29+flr x (mkF q r t) = (q*x + r) `div` t
32+comp (mkF q r t) (mkF u v x) = mkF (q*u) (q*v+r*x) (t*x)
34+-- Returns the list of digits of pi. Memory hungry.
35+str : F -> Integer -> Nat -> List Integer
37+str z k (S n) = if(y == flr 4 z)
38+ then y :: str (comp (mkF 10 (-10*y) 1) z ) k n
39+ else str (comp z (fn k)) (k+1) (S n)
45+ let n = fromIntegerNat (the Integer (cast a))
46+ let l = str (mkF 1 0 1) 1 n