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April 26, 2017 05:20
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compute fibonacci(n)%m for very large n
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| from Goulib.math2 import digits, identity | |
| def mod_matmul(A,B, mod=0): | |
| return [[sum(a*b for a,b in zip(A_row,B_col))%mod for B_col in zip(*B)] for A_row in A] | |
| def mod_matpow(M, power, mod=0): | |
| result = identity(2) | |
| for power in digits(power,2,True): | |
| if power: | |
| result = mod_matmul(result, M, mod) | |
| M = mod_matmul(M, M, mod) | |
| return result | |
| def fibonacci(n,mod=0): | |
| return mod_matpow([[1,1],[1,0]],n,mod)[0][1] | |
| print(fibonacci(int(1E19),1000000007)) # gives 647754067 |
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see https://www.drgoulu.com/2017/04/25/comment-calculer-le-1e19-eme-terme-de-la-suite-de-fibonacci/
all functions are available in https://github.com/goulu/Goulib math2 module with better documentation ...