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Any PRNG with a finite state size is eventually periodic. The maximum period possible is $2^n$ for an $n$-bit state, but the average with a well mixed state is $2^{n/2}$. Here the hash function used is SHA-512, but the state is 1024 bits. A first guess would be a period of $2^{512}$, rather than the $2^{256}$ mephisto gives. Let's look at the cycles. Both ...


Yes, this PRG is theoretically periodic. Approximately after generating $2^{512}$ outputs a state will be generated that collides with a previous state. (A previous version of this answer said $2^{256}$ as I missed that two outputs are used for the state. Otus answer pointed out this mistake.) This follows from the birthday problem. However, $2^{512}$ is ...

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