From: Ramakrishnan Muthukrishnan Date: Mon, 22 Dec 2014 16:52:43 +0000 (+0530) Subject: hw6: fib4 using Matrix operation X-Git-Url: https://git.rkrishnan.org/pf/content/en/seg/priv/simplejson/rgr-080307.php?a=commitdiff_plain;h=136b9a5fe04b0dc7ca3b390c169cb933ab38188a;p=yorgey.git hw6: fib4 using Matrix operation --- diff --git a/hw6/Fibonacci.hs b/hw6/Fibonacci.hs index 15b563b..39f3349 100644 --- a/hw6/Fibonacci.hs +++ b/hw6/Fibonacci.hs @@ -96,3 +96,18 @@ instance Fractional (Stream Integer) where r fibs3 :: Stream Integer fibs3 = x' / (streamRepeat 1 - x' - x' * x') + +-- exercise 7 +data Matrix = Matrix Integer Integer Integer Integer + +instance Num Matrix where + (*) :: Matrix -> Matrix -> Matrix + (*) (Matrix a1 b1 c1 d1) (Matrix a2 b2 c2 d2) = + Matrix (a1*a2 + b1*c2) (a1*b2 + b1*d2) (c1*a2 + d1*c2) (c1*b2 + d1*d2) + +fib4 :: Integer -> Integer +fib4 0 = 0 +fib4 n = let f0 = (Matrix 1 1 1 0) + (Matrix _ b _ _) = f0 ^ n + in + b