Speeding up Exact Real Arithmetic on Fast Binary Cauchy Sequences by Using Memoization Based on Quantized Precision

• Item type: Trans(1)
• 公開日: 2017-06-16
• タイトル: Speeding up Exact Real Arithmetic on Fast Binary Cauchy Sequences by Using Memoization Based on Quantized Precision
• タイトル / 言語: en
• タイトル: Speeding up Exact Real Arithmetic on Fast Binary Cauchy Sequences by Using Memoization Based on Quantized Precision
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: [通常論文] Fast Binary Cauchy Sequence, exact real arithmetic, lazy evaluation, memoization, Haskell library
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_6501
• 資源タイプ: journal article
• 著者所属: Hiroshima City University
• 著者所属(英): en
• 著者所属(英): Hiroshima City University
• 著者名: Hideyuki, Kawabata
• 著者名(英): Hideyuki, Kawabata
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Exact Real Arithmetic on Fast Binary Cauchy Sequences (FBCSs) provides us a simple and fairly fast way to obtain numerical results of arbitrary precision. The arithmetic on FBCSs can be implemented concisely in a lazy functional language with unlimited-length integer arithmetic, such that each FBCS is represented by a function that generates approximated values with respect to requested precisions. However, application of the arithmetic on FBCSs to programs such as matrix computations, that usually involve large amount of references to common subexpressions, requires care to avoid the blowup of the amount of computation caused by the fact that approximated values are not shared among multiple references. Although simple memoization might alleviate the situation, the effect would be limited since required precisions for subexpressions tend to be various. In this paper, we present an extended design of the arithmetic on FBCSs that enables the memoization based on quantized precision, that is expected to enlarge the reuse rate and reduce the amount of computation without sacrificing the properties of the arithmetic to be exact arithmetic. Numerical experiments by using our prototype libraries in Haskell demonstrated that our approach possesses the potential to outperform existing implementations by orders of magnitude in speed and memory consumption.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.25(2017) (online); ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Exact Real Arithmetic on Fast Binary Cauchy Sequences (FBCSs) provides us a simple and fairly fast way to obtain numerical results of arbitrary precision. The arithmetic on FBCSs can be implemented concisely in a lazy functional language with unlimited-length integer arithmetic, such that each FBCS is represented by a function that generates approximated values with respect to requested precisions. However, application of the arithmetic on FBCSs to programs such as matrix computations, that usually involve large amount of references to common subexpressions, requires care to avoid the blowup of the amount of computation caused by the fact that approximated values are not shared among multiple references. Although simple memoization might alleviate the situation, the effect would be limited since required precisions for subexpressions tend to be various. In this paper, we present an extended design of the arithmetic on FBCSs that enables the memoization based on quantized precision, that is expected to enlarge the reuse rate and reduce the amount of computation without sacrificing the properties of the arithmetic to be exact arithmetic. Numerical experiments by using our prototype libraries in Haskell demonstrated that our approach possesses the potential to outperform existing implementations by orders of magnitude in speed and memory consumption.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.25(2017) (online); ------------------------------
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA11464814
• 書誌情報: 情報処理学会論文誌プログラミング（PRO）; 巻 10, 号 3, 発行日 2017-06-16
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7802
• 出版者 / 言語: ja
• 出版者: 情報処理学会