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