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I wonder how do they check all those digits are exact? Do they compute it two or more different ways? It is not possible to design a physical test for that prec
by informatimago 5y ago
I wonder how do they check all those digits are exact? Do they compute it two or more different ways? It is not possible to design a physical test for that precision. But even mathematically, if there's an error in the middle of the digits, what test can we perform to detect it?
- Someone 5y agoThey probably verify some of their hex digits (including those reported by earlier records, on the off chance that you find a difference) using https://en.wikipedia.org/wiki/Bellard%27s_formula https://en.wikipedia.org/wiki/Bellard%27s_formula. 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.