September 2017 Update

Task/Bernoulli-numbers/Haskell/bernoulli-numbers-1.hs

@@ -0,0 +1,23 @@
+import Data.Ratio
+import System.Environment
+
+main = getArgs >>= printM . defaultArg
+  where
+    defaultArg as =
+      if null as
+        then 60
+        else read (head as)
+
+printM m =
+  mapM_ (putStrLn . printP) .
+  takeWhile ((<= m) . fst) . filter (\(_, b) -> b /= 0 % 1) . zip [0 ..] $
+  bernoullis
+
+printP (i, r) =
+  "B(" ++ show i ++ ") = " ++ show (numerator r) ++ "/" ++ show (denominator r)
+
+bernoullis = map head . iterate (ulli 1) . map berno $ enumFrom 0
+  where
+    berno i = 1 % (i + 1)
+    ulli _ [_] = []
+    ulli i (x:y:xs) = (i % 1) * (x - y) : ulli (i + 1) (y : xs)

Task/Bernoulli-numbers/Haskell/bernoulli-numbers-2.hs

@@ -0,0 +1,17 @@
+import Data.Ratio (numerator, denominator, (%))
+
+bernouillis :: Integer -> [Rational]
+bernouillis =
+  let faulhaber rs n = (:) =<< (-) 1 . sum $ zipWith ((*) . (n %)) [2 ..] rs
+  in fmap head . tail . scanl faulhaber [] . enumFromTo 0
+
+bernouilliTable :: Integer -> String
+bernouilliTable =
+  let row i x =
+        [ concat ["B(", show i, ") = ", show n, "/", show (denominator x)]
+        | let n = numerator x
+        , n /= 0 ]
+  in unlines . concat . zipWith row [0 ..] . bernouillis
+
+main :: IO ()
+main = putStrLn (bernouilliTable 60)

Task/Bernoulli-numbers/Haskell/bernoulli-numbers.hs

@@ -1,17 +0,0 @@
-module Main where
-
-import Data.Ratio
-import System.Environment
-
-main = getArgs >>=  printM . defaultArg where
-    defaultArg as = if null as then 60 else read (head as)
-
-printM m = mapM_ (putStrLn . printP) . takeWhile ((<= m).fst)
-           . filter (\(_,b) -> b /= 0%1) . zip [0..]  $ bernoullis
-
-printP (i,r) = "B(" ++ show i ++ ")=" ++ show (numerator r) ++ "/" ++ show (denominator r)
-
-bernoullis =  map head . iterate (ulli 1) . map berno $ enumFrom 0 where
-    berno i = 1 % (i+1)
-    ulli _ [_] = []
-    ulli i (x:y:xs) = (i%1)*(x-y) : ulli (i+1) (y:xs)