diff options
Diffstat (limited to 'AufgabeFFP2.hs')
| -rw-r--r-- | AufgabeFFP2.hs | 36 |
1 files changed, 18 insertions, 18 deletions
diff --git a/AufgabeFFP2.hs b/AufgabeFFP2.hs index 7ed19fc..aef3bfb 100644 --- a/AufgabeFFP2.hs +++ b/AufgabeFFP2.hs | |||
| @@ -6,33 +6,33 @@ where | |||
| 6 | -- primality check | 6 | -- primality check |
| 7 | isPrime :: Integer -> Bool | 7 | isPrime :: Integer -> Bool |
| 8 | isPrime n = n > 1 && | 8 | isPrime n = n > 1 && |
| 9 | foldr (\p r -> | 9 | foldr (\p r -> |
| 10 | p*p > n | 10 | p*p > n |
| 11 | || ( | 11 | || ( |
| 12 | (n `mod` p) /= 0 | 12 | (n `mod` p) /= 0 |
| 13 | && r | 13 | && r |
| 14 | ) | 14 | ) |
| 15 | ) | 15 | ) |
| 16 | True primes | 16 | True primes |
| 17 | 17 | ||
| 18 | -- series of primes | 18 | -- series of primes |
| 19 | primes :: [Integer] | 19 | primes :: [Integer] |
| 20 | primes = 2:filter isPrime [3,5..] | 20 | primes = 2:filter isPrime [3,5..] |
| 21 | 21 | ||
| 22 | -- pairs of (p,p+2) | p,p+2 <- primes | 22 | -- pairs of (p,p+2) | p,p+2 <- primes |
| 23 | -- generate all pairs with map and then filter only the valid ones | 23 | -- generate all pairs with map and then filter only the valid ones |
| 24 | -- pair is valid if the second component n is a prime | 24 | -- pair is valid if the second component n is a prime |
| 25 | pps :: [(Integer, Integer)] | 25 | pps :: [(Integer, Integer)] |
| 26 | pps = filter (\(_,x) -> isPrime x) $ map (\p -> (p,p+2)) primes | 26 | pps = filter (\(_,x) -> isPrime x) $ map (\p -> (p,p+2)) primes |
| 27 | 27 | ||
| 28 | ------------------------------------------------------------------------------- | 28 | ------------------------------------------------------------------------------- |
| 29 | 29 | ||
| 30 | -- 2 | 30 | -- 2 |
| 31 | 31 | ||
| 32 | -- generates powers of 2 | 32 | -- generates powers of 2 |
| 33 | pof2s :: [Integer] | 33 | pof2s :: [Integer] |
| 34 | pof2s = [1] ++ map (2*) pof2s | 34 | pof2s = [1] ++ map (2*) pof2s |
| 35 | 35 | ||
| 36 | -- calculates 2^n | 36 | -- calculates 2^n |
| 37 | pow :: Int -> Integer | 37 | pow :: Int -> Integer |
| 38 | pow 0 = 1 | 38 | pow 0 = 1 |
| @@ -70,7 +70,7 @@ f z k = g z k h | |||
| 70 | -- actual function g (converts Int to Integer for more precision) | 70 | -- actual function g (converts Int to Integer for more precision) |
| 71 | g :: Int -> Int -> (Integer -> Integer -> Float) -> Float | 71 | g :: Int -> Int -> (Integer -> Integer -> Float) -> Float |
| 72 | g z k h = sum $ map (h $ fromIntegral z) [0..(fromIntegral k)] | 72 | g z k h = sum $ map (h $ fromIntegral z) [0..(fromIntegral k)] |
| 73 | 73 | ||
| 74 | -- helper function h using mem-table for the power-series (z^i) and for factorial (i!) | 74 | -- helper function h using mem-table for the power-series (z^i) and for factorial (i!) |
| 75 | hMT :: Integer -> Integer -> Float | 75 | hMT :: Integer -> Integer -> Float |
| 76 | hMT z i = (fromInteger $ pofNs z !! (fromInteger i)) / (fromInteger $ facs !! (fromInteger i)) | 76 | hMT z i = (fromInteger $ pofNs z !! (fromInteger i)) / (fromInteger $ facs !! (fromInteger i)) |
| @@ -86,15 +86,15 @@ h z i = (fromInteger $ z^i) / (fromInteger $ fac i) | |||
| 86 | -- gets the digits of an integer as a list | 86 | -- gets the digits of an integer as a list |
| 87 | digits :: Integer -> [Integer] | 87 | digits :: Integer -> [Integer] |
| 88 | digits x | 88 | digits x |
| 89 | | x<=0 = [] | 89 | | x<=0 = [] |
| 90 | | otherwise = (digits $ x `div` 10)++[x `mod` 10] | 90 | | otherwise = (digits $ x `div` 10)++[x `mod` 10] |
| 91 | 91 | ||
| 92 | -- calculates the goedel-number for the given integer | 92 | -- calculates the goedel-number for the given integer |
| 93 | -- returns 0 for non-positive numbers | 93 | -- returns 0 for non-positive numbers |
| 94 | gz :: Integer -> Integer | 94 | gz :: Integer -> Integer |
| 95 | gz n | 95 | gz n |
| 96 | | n<=0 = 0 | 96 | | n<=0 = 0 |
| 97 | | otherwise = product $ zipWith (^) primes (digits n) | 97 | | otherwise = product $ zipWith (^) primes (digits n) |
| 98 | 98 | ||
| 99 | -- goedel-number generator | 99 | -- goedel-number generator |
| 100 | gzs :: [Integer] | 100 | gzs :: [Integer] |
