Merge branch 'dev'

2 files changed, 125 insertions, 1 deletions

diff --git a/AufgabeFFP2.hs b/AufgabeFFP2.hs
index e66b7a8..7993c01 100644
--- a/AufgabeFFP2.hs
+++ b/AufgabeFFP2.hs
@@ -38,4 +38,59 @@ 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 hMT
+
+-- function g without memoization (uning hSlow)
+f :: Int -> Int -> Float
+f z k = g z k h
+
+-- actual function g (converts Int to Integer for more precision)
+g :: Int -> Int -> (Integer -> Integer -> Float) -> Float
+g z k h = sum $ map (h $ fromIntegral z) [1..(fromIntegral k)]
+        
+-- helper function h using mem-table for the power-series (z^i) and for faculty (i!)
+hMT :: Integer -> Integer -> Float
+hMT z i = (fromInteger $ pofNs z !! (fromInteger i)) / (fromInteger $ facGen !! ((fromIntegral i)-1))
+
+-- helper function h without memoization
+h :: Integer -> Integer -> Float
+h z i =  (fromInteger $ z^i) / (fromInteger $ fac i)
+
+-------------------------------------------------------------------------------
+
+-- 4
+
+-- gets the digits of an integer as a list
+digits :: Integer -> [Integer]
+digits x
+        | x<=0 = []
+        | otherwise = (digits $ x `div` 10)++[x `mod` 10]
+
+-- calculates the goedel-number for the given integer
+-- returns 0 for non-positive numbers
+gz :: Integer -> Integer
+gz n
+        | n<=0 = 0
+        | otherwise = product $ zipWith (^) primes (digits n)
+
+-- goedel-number generator
+gzs :: [Integer]
+gzs = map (gz) [1..]
diff --git a/TestAufgabeFFP2.hs b/TestAufgabeFFP2.hs
new file mode 100644
index 0000000..0df8612
--- /dev/null
+++ b/TestAufgabeFFP2.hs
@@ -0,0 +1,69 @@
+module Main where
+
+import Test.HUnit
+import Control.Monad
+import AufgabeFFP2
+
+assertBoolF :: String -> Bool -> Assertion
+assertBoolF msg b =  when b (assertFailure msg)
+
+-------------------------------------------------------------------------------
+-- 1
+
+pps1 :: Test
+pps1 = TestCase (assertEqual "pps"
+        [(3,5),(5,7),(11,13),(17,19),(29,31),(41,43), (59,61),(71,73),(101,103),(107,109)]
+        (take 10 pps))
+
+pps2 :: Test
+pps2 = TestCase (assertEqual "pps"
+        (347,349)
+        (pps!!20))
+        
+pps3 :: Test
+pps3 = TestCase (assertEqual "pps"
+        (809,811)
+        (head (drop 30 pps)))
+
+ppsTests = TestList [pps1, pps2, pps3]
+
+-------------------------------------------------------------------------------
+-- 2
+
+-------------------------------------------------------------------------------
+-- 3
+
+-------------------------------------------------------------------------------
+-- 4
+
+gz1 :: Test
+gz1 = TestCase (assertEqual "gz"
+        144
+        (gz 42))
+
+gz2 :: Test
+gz2 = TestCase (assertEqual "gz"
+        400
+        (gz 402))
+
+gzs1 :: Test
+gzs1 = TestCase (assertEqual "gzs"
+        144
+        (gzs!!41))
+
+gzs2 :: Test
+gzs2 = TestCase (assertEqual "gzs"
+        400
+        (gzs!!401))
+
+
+gzTests = TestList [gz1, gz2, gzs1, gzs2]
+
+-------------------------------------------------------------------------------
+
+tests :: [Test]
+tests = [ppsTests, gzTests]
+
+main = do
+        forM tests $ \test ->
+                runTestTT test