Python Matrix Exponentiation -

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i use python 2.x or 3.x raise 2x2 matrix initially

0 1 1 1

to exponent of 10¹⁹ or less. (that is, let m = matrix, m^10¹⁹).

however, don't want use numpy.

(by way, is fibonacci generator )

ok, way you're asking question means stand no chance of achieving this. i'll explain; please don't offended:

python wrong tool, , you're trying exclude helpers make little less wrong. you're trying numerical math in purest form -- , python scripting language can take advantage of numerical efficiency when using native libraries. 1 of these numpy, you've noticed (but didn't write) doesn't work, because numbers big fast when calculating mⁿ larger n.
even if there magic way optimize algorithm in matter allow matrix-matrix multiplication in single instruction , you'd need instruction count , check whether still should multiplying calculate mⁿ, calculation take 2*10¹⁹ instructions. assuming have 8 cpus can 4 billions of per second, still take little less 20 years. need here proper math. like, strong math. can find diagonal form such m = u d u^-1; u being unitary , d being diagonal matrix. then, using matrix exponential e, can e^m = u e^d u. classical exponential rules apply, can calculate e^{m^10¹⁹}. that's still ugly, terminate @ time can consider safer. however, luck implementing without degree in numerical mathematics.

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