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I haven't studied your algorithm in detail (too much other work) but I think you are using the Spigot algorithm?
If I understand correctly, the Spigot algorithm is the one I use in the earlier program I published, which finds digits of PI starting from the beginning. Crucially it uses an array, so the number of digits you can find depends (in principle) on the amount of memory available.
The most recent program, which finds digits starting at a specified position, has very small memory requirements. There is no array, and therefore the digits which you can find do not depend, even in principle, on the memory available. The general method is called the BBP Formula after the discoverers Bailey-Borwein-Plouffe.
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