37 lines
1.2 KiB
Haskell
37 lines
1.2 KiB
Haskell
import Data.Ratio ((%), denominator, numerator)
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import Data.Bool (bool)
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-- ignoring the task-given pi sequence: sucky convergence
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-- pie = zip (3:repeat 6) (map (^2) [1,3..])
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pie = zip (0 : [1,3 ..]) (4 : map (^ 2) [1 ..])
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sqrt2 = zip (1 : repeat 2) (repeat 1)
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napier = zip (2 : [1 ..]) (1 : [1 ..])
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-- truncate after n terms
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cf2rat n = foldr (\(a, b) f -> (a % 1) + ((b % 1) / f)) (1 % 1) . take n
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-- truncate after error is at most 1/p
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cf2rat_p p s = f $ map ((\i -> (cf2rat i s, cf2rat (1 + i) s)) . (2 ^)) [0 ..]
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where
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f ((x, y):ys)
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| abs (x - y) < (1 / fromIntegral p) = x
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| otherwise = f ys
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-- returns a decimal string of n digits after the dot; all digits should
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-- be correct (doesn't mean it's the best approximation! the decimal
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-- string is simply truncated to given digits: pi=3.141 instead of 3.142)
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cf2dec n = ratstr n . cf2rat_p (10 ^ n)
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where
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ratstr l a = show t ++ '.' : fracstr l n d
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where
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d = denominator a
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(t, n) = quotRem (numerator a) d
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fracstr 0 _ _ = []
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fracstr l n d = show t ++ fracstr (l - 1) n1 d
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where
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(t, n1) = quotRem (10 * n) d
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main :: IO ()
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main = mapM_ putStrLn [cf2dec 200 sqrt2, cf2dec 200 napier, cf2dec 200 pie]
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