Improvement of the π Calculation Algorithm and Implementation of Fast Multiple-Precision Computation
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- OOURA Takuya
- Research Institute for Mathematical Sciences, Kyoto University
Bibliographic Information
- Other Title
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- 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.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 9 (4), 165-172, 1999
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390001205767416704
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- NII Article ID
- 110001883724
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 4931788
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed