I read the following link.
That compute $F_n$ in $O(\log n)$, but i can't find the space complexity of this matrix form of $F_n$.
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The algorithm uses a constant number of $2 \times 2$ matrices which contain Fibonacci numbers $F_m$ for $m \leq n$, as well as a few indices ranging up to $n$.
This should be enough information to compute the space complexity of the algorithm, whether expressed in machine words or in bits.
As an aside, since $F_n$ grows exponentially in $n$, it is misleading to count only the number of arithmetic operations, rather than the bit complexity of the computation.