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| -rw-r--r-- | lec06/Fibonacci.hs | 20 |
1 files changed, 20 insertions, 0 deletions
diff --git a/lec06/Fibonacci.hs b/lec06/Fibonacci.hs index 375e5ef..afa2263 100644 --- a/lec06/Fibonacci.hs +++ b/lec06/Fibonacci.hs @@ -61,4 +61,24 @@ instance Num (Stream Integer) where where zip (Cons a0 sa) (Cons b0 sb) = Cons (a0,b0) (zip sa sb) (*) (Cons a0 sa) b@(Cons b0 sb) = Cons (a0*b0) $ (streamMap (*a0) sb + (sa*b)) +instance Fractional (Stream Integer) where + (/) a@(Cons a0 sa) b@(Cons b0 sb) = Cons (a0 `div` b0) $ streamMap (`div` b0) (sa-(a/b)*sb) + +fibs3 :: Stream Integer +fibs3 = x / (1 - x - (x*x)) + +-- Exercise 7 (Optional) + +data Matrix = M Integer Integer Integer Integer + +instance Num Matrix where + (*) (M a11 a12 a21 a22) (M b11 b12 b21 b22) = M (a11*b11+a12*b21) (a11*b12+a12*b22) (a21*b11+a22*b21) (a21*b12+a22*b22) + +fib4 :: Integer -> Integer +fib4 0 = 0 +fib4 n = take12 ((M 1 1 1 0)^n) + where take12 (M a11 a12 a21 a22) = a12 + +fibs4 :: Stream Integer +fibs4 = streamMap fib4 $ streamFromSeed (+1) 0 |