Continued fraction: Difference between revisions

Content added Content deleted
m (→‎Version 1: added √½ to the generalized showing of √s. -- ~~~~)
m (→‎{{header|Haskell}}: fix small bug)
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-- truncate after n terms
-- truncate after n terms
--cf2rat :: (Integral a) => Int -> [(a, a)] -> Ratio a
cf2rat n = foldr (\(a,b) f -> (a%1) + ((b%1) / f)) (1%1) . take n
cf2rat n = foldr (\(a,b) f -> (a%1) + ((b%1) / f)) (1%1) . take n


-- truncate after error is at most 1/p
-- truncate after error is at most 1/p
--cf2rat_p :: (Integral a, Integral b) => b -> [(a, a)] -> Ratio a
cf2rat_p p s = f $ map (\i -> (cf2rat i s, cf2rat (1+i) s)) $ map (2^) [0..]
⚫
where f ((x,y):ys) = if abs (x-y) < (1/fromIntegral p) then x else f ys
cf2rat_p p s = f $ map ((flip cf2rat) s) $ map (2^) [0..]
⚫
where f (x:y:ys) = if abs (x - y) < (1/fromIntegral p)
then x
else f (y:ys)


-- returns a decimal string of n digits after the dot; all digits should
-- returns a decimal string of n digits after the dot; all digits should
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-- string is simply truncated to given digits: pi=3.141 instead of 3.142)
-- string is simply truncated to given digits: pi=3.141 instead of 3.142)
cf2dec n = (ratstr n) . cf2rat_p (10^n) where
cf2dec n = (ratstr n) . cf2rat_p (10^n) where
--ratstr :: Integral a => Int -> Ratio a -> String
ratstr l a = (show t) ++ '.':fracstr l n d where
ratstr l a = (show t) ++ '.':fracstr l n d where
d = denominator a
d = denominator a
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