Data commit

Task/Arithmetic-geometric-mean/Haskell/arithmetic-geometric-mean.hs

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+-- Return an approximation to the arithmetic-geometric mean of two numbers.
+-- The result is considered accurate when two successive approximations are
+-- sufficiently close, as determined by "eq".
+agm :: (Floating a) => a -> a -> ((a, a) -> Bool) -> a
+agm a g eq = snd $ until eq step (a, g)
+  where
+    step (a, g) = ((a + g) / 2, sqrt (a * g))
+
+-- Return the relative difference of the pair.  We assume that at least one of
+-- the values is far enough from 0 to not cause problems.
+relDiff :: (Fractional a) => (a, a) -> a
+relDiff (x, y) =
+  let n = abs (x - y)
+      d = (abs x + abs y) / 2
+  in n / d
+
+main :: IO ()
+main = do
+  let equal = (< 0.000000001) . relDiff
+  print $ agm 1 (1 / sqrt 2) equal