2019-03-18 00:46:56 +08:00
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{-''' mbinary
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2019-03-06 19:11:01 +08:00
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#######################################################################
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# File : fibonacci.hs
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.github.io
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# Github: https://github.com/mbinary
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# Created Time: 2019-02-03 19:42
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# Description: matrix pow and fast pow:
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calculate big number fibonacci item. for negative item, use f(n) = f(n+2)-f(n+1)
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#######################################################################
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2019-03-18 00:46:56 +08:00
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-}
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2019-03-06 19:11:01 +08:00
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module Fibonacci where
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fib :: Integer -> Integer
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fib n = let p = if n>0 then n-2 else 2-n
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mat = if n>0 then [1,1,1,0] else [0,1,1,-1]
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m = matrix_pow mat p
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in m!!0+m!!1
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matrix_pow mat n = if n<=0 then [1,0,0,1]
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else let v = if (mod n 2==0) then [1,0,0,1] else mat
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m2 = matrix_mul mat mat
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remain = matrix_pow m2 (div n 2)
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in matrix_mul v remain
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matrix_mul a b = [ a!!0 * b!!0 +a!!1 * b!!2,a!!0 * b!!1 +a!!1 * b!!3,a!!2 * b!!0 +a!!3 * b!!2, a!!2 * b!!1+a!!3 * b!!3]
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