Recursive Reduction of Series for Multiple-precision Evaluation and its Application to Pi Calculation

4 Citations 4 References

Bibliographic Information

Other Title
  • 級数の集約による多倍長数の計算法とπの計算への応用

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Description

Multiple-precision mathematical constants, such as π or e are known to be calculated by sum of series. On the other hand, much faster calculation method that use iteration are known for some constants such as π. For the case of π, N digits calculation time by method of sum of series is said to be O(N^2), and that of iterational method is O(N(logN)^2).Thus, for large N, iterational method is far more efficient than that of sum of series. In this paper, we propose a fast algorithm of calculating sum of series in O(N(logN)^3)time by recursively reducing adjacent terms of series. With this algorithm, calculation time of sum of series become comparable to that of iterational method in case of large N. Experimental results on calculating 32, 000 to 530 million digits of π showed that the Chudnovsky formula which uses sum of series can be calculated faster than the Gauss-Legendre method which uses iterational method.

Journal

  • IPSJ SIG Notes

    IPSJ SIG Notes 74 31-36, 1998-12-11

    Information Processing Society of Japan (IPSJ)

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Details 詳細情報について

  • CRID
    1572261552107558400
  • NII Article ID
    110002932333
  • NII Book ID
    AN10463942
  • Text Lang
    ja
  • Data Source
    • CiNii Articles

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