Swiss researchers declare new record for exact pi figure
phys.org
phys.org
In my naive ignorance, I can't see how you 'retrieve' more digits past the number of decimal places supported by whatever device you're calculating on.
(Numbers typically are in binary and multiplication uses more advanced algorithms than the ones taught in primary school, but those are implementation details)
See https://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic.
That formula allows one to compute the n-th hex digit of pi without having to calculate all digits before it (a fairly weird result. AFAIK, the search for a similar formula to compute decimal digits still is on). It is a lot faster for large n.
They won’t use that for all hex digits because isn’t as fast as other formulas if you want all hex digits.
That may not detect all hardware glitches (a single bit flip in RAM or on disk late in the process may go unnoticed, for example), but will detect bugs in their code or compiler, as errors in calculation will result in all digits being correct only by chance after some point where the calculation deviates.