From 12ad8b53c5be7e22975082baa715e96aa2f1b9dd Mon Sep 17 00:00:00 2001
From: Matthias Wisniowski <matthias.wisniowski@gmail.com>
Date: Sun, 25 Mar 2012 19:04:12 +0200
Subject: First implementation for 2.3

hFast and hSlow diverge in values, reason unknown.
e.g. consider >> map (\x -> hFast x x) [1..15] << (similar for hSlow)
hSlow has the wrong values after 10.
---
 AufgabeFFP2.hs | 38 +++++++++++++++++++++++++++++++++++++-
 1 file changed, 37 insertions(+), 1 deletion(-)

diff --git a/AufgabeFFP2.hs b/AufgabeFFP2.hs
index e66b7a8..e4e646b 100644
--- a/AufgabeFFP2.hs
+++ b/AufgabeFFP2.hs
@@ -38,4 +38,40 @@ powFast :: Int -> Integer
 powFast 0 = 1
 powFast n = pof2s !! (n-1) + pof2s !! (n-1)
 
--------------------------------------------------------------------------------
\ No newline at end of file
+-------------------------------------------------------------------------------
+
+-- 3
+
+-- power series of N
+pofNs :: Integer -> [Integer]
+pofNs n = [1] ++ (map (n*) $ pofNs n)
+
+-- faculty function
+fac :: Integer -> Integer
+fac n = product [1..n]
+
+-- stream of faculties
+facGen :: [Integer]
+facGen = map (fac) [1..]
+
+-- function g with memoization (using hFast)
+fMT :: Int -> Int -> Float
+fMT z k = g z k hFast
+
+-- function g without memoization (uning hSlow)
+f :: Int -> Int -> Float
+f z k = g z k hSlow
+
+-- actual function g
+g :: Int -> Int -> (Int -> Int -> Float) -> Float
+g z k h = sum $ map (h z) [1..k]
+	
+-- helper function h using mem-table for the power-series (z^i) and for faculty (i!)
+hFast :: Int -> Int -> Float
+hFast z i = (fromInteger $ pofNs (fromIntegral z) !! i) / (fromInteger $ facGen !! (i-1))
+
+-- helper function h without memoization
+hSlow :: Int -> Int -> Float
+hSlow z i = (fromIntegral $ z^i) / (fromInteger $ fac $ fromIntegral i)
+
+-------------------------------------------------------------------------------
-- 
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