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Improvement of the π Calculation Algorithm and Implementation of Fast Multiple-Precision Computation

  • OOURA Takuya
    Research Institute for Mathematical Sciences, Kyoto University

Bibliographic Information

Other Title
  • 円周率公式の改良と高速多倍長計算の実装
  • エンシュウリツ コウシキ ノ カイリョウ ト コウソク タバイチョウ ケイサン ノ ジッソウ

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Abstract

In this paper, we derive efficient quadratic and quartic iteration algorithms from the improvement of Gauss'arithmetic-geometric mean (AGM) algorithm. The number of multiplications in the improved quadratic algorithm is only half the number of the original algorithm, but the number of the square root operations in the improved AGM iterations is equal to the number of the original algorithm. So we derive an efficient simultaneous Newton iteration for the square root calculation. Next, weimplement a fast multiple-precision computation for the proposed algorithms and estimate the number of floating point operations and the execution time to compute the AGM iterations.

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Details

  • CRID
    1390001205767416704
  • NII Article ID
    110001883724
  • NII Book ID
    AN10367166
  • ISSN
    09172246
    24240982
  • DOI
    10.11540/jsiamt.9.4_165
  • NDL BIB ID
    4931788
  • Text Lang
    ja
  • Data Source
    • JaLC
    • NDL
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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