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|
module e
/*
Approximation of the number e.
Result: A list containing the first NrDigits digits of e = [2,7,1,8,2,8,1,8,2,8,...].
*/
(<) infix 4 :: !Int !Int -> Bool
(<) a b = code inline {
ltI
}
(+) infixl 6 :: !Int !Int -> Int
(+) a b = code inline {
addI
}
(-) infixl 6 :: !Int !Int -> Int
(-) a b = code inline {
subI
}
(*) infixl 7 :: !Int !Int -> Int
(*) a b = code inline {
mulI
}
(/) infixl 7 :: !Int !Int -> Int
(/) a b = code inline {
divI
}
(==) infix 4 :: !Int !Int -> Bool
(==) a b = code inline {
eqI
}
(rem) infix 7 :: !Int !Int -> Int
(rem) a b = code inline {
remI
}
take :: Int [a] -> [a]
take 0 _ = []
take n [x:xs] = [x:take (n-1) xs]
hd :: [a] -> a
hd [x:xs] = x
tl :: [a] -> [a]
tl [_:xs] = xs
//import StdEnv
NrDigits :== 200 // The number of digits of the approximation of e
// Approximating e:
Approx_e::[Int]
Approx_e = [2:Expan ones] where ones= [1:ones]
// Expan expects an infinite list of ones and returns an infinite
// list containing the digits of the fraction of e ([7,1,8,2,8,...]).
Expan::[Int] -> [Int]
Expan f = [hd ten:Expan (tl ten)]
where
ten = Ten 2 f
Ten::Int [Int] -> [Int]
Ten c [p:q] | Safe k c = [k / c, k rem c + a1 : b1]
= [(k + a1) / c, (k + a1) rem c : b1]
where
a1 = hd ten
b1 = tl ten
ten = Ten (c+1) q
k = 10 * p
Safe::Int Int -> Bool
Safe k c = k/c == (k + 9)/c
/*
The Start rule returns the first NrDigits elements of the
list of digits returned by the function
'Approx_e' by means of the function take.
*/
Start::[Int]
Start = take NrDigits Approx_e
|
