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These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of log ⁡ ( 2 ) \\log {(2)} or π \\pi on a modest work station in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of π \\pi , the billionth hexadecimal digits of π 2 , log ⁡ ( 2 ) \\pi ^{2}, \\; \\log (2) and log 2 ⁡ ( 2 ) \\log ^{2}(2) , and the ten billionth decimal digit of log ⁡ ( 9 / 10 ) \\log (9/10) . 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On the rapid computation of various polylogarithmic constants 论文

On the rapid computation of various polylogarithmic constants · 相关文章