From: Ramakrishnan Muthukrishnan <ram@rkrishnan.org>
Date: Mon, 22 Dec 2014 16:52:43 +0000 (+0530)
Subject: hw6: fib4 using Matrix operation
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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