一般化した二重指数分割に基づく数値表現法  [in Japanese] A Generalized Numerical Representation Based on Double Exponential Cut  [in Japanese]

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Abstract

浜田の提案したURR (Universal Representation of Real numbers)表現は絶対値が1から離れるに従って,急速に精度が悪化するという欠点がある.この欠点を改善するために一般化した二重指数分割に基づく数値表現法を提案する.URR表現は二重指数±2±2mで実数を大まかに近似するが,本論文ではこれを±p±qmと一般化した.この一般化した表現ではpとqを大きくすることで,大きな実数に対してURR表現よりも少ないビット数で近似できるようになる.特にp=4,q=16と選ぶことによって,URR表現に比べ広範囲で精度の良い二重指数分割に基づく数値表現法となる.この一般化した数値表現は数々のURR表現の長所を有し,急速な精度の悪化も抑えている.この数値表現で実際に簡単な数値計算を行い,URR表現に比べ精度が良い本数値表現の有効性を検証した.A precision of URR(Universal Representation of Real numbers)which was proposed by Hamada goes to worse rapidly when the absolute value goes away from 1.We proposed generalized numerical representation based on the double exponential cut for the improvement to the serious drawback of URR.URR approximates real numbers with double exponential form of ±2±2m.We generalized the base of double expential cut ±p±qm in this paper.With larger p and q,our representation can approximate large numbers,spending lesser bit length than URR.Especially,our numerical representation with parameters of p=4,q=16 is preciser than URR.The generalized representation also has the same merit as in URR,and it canescape from the demerit in URR.We verified the effectiveness of our representation with simple numerical calculation.

A precision of URR (Universal Representation of Real numbers) which was proposed by Hamada goes to worse rapidly when the absolute value goes away from 1. We proposed generalized numerical representation based on the double exponential cut for the improvement to the serious drawback of URR. URR approximates real numbers with double exponential form of ±2^<±2>^m. We generalized the base of double expential cut as ±p^<±q>^m in this paper. With larger p and q, our representation can approximate large numbers, spending lesser bit length than URR. Especially, our numerical representation with parameters of p=4, q=16 is preciser than URR. The generalized representation also has the same merit as in URR, and it can escape from the demerit in URR. We verified the effectiveness of our representaion with simple numerical calculation.

Journal

  • Transactions of Information Processing Society of Japan

    Transactions of Information Processing Society of Japan 39(3), 511-518, 1998-03-15

    Information Processing Society of Japan (IPSJ)

References:  11

Codes

  • NII Article ID (NAID)
    110002722057
  • NII NACSIS-CAT ID (NCID)
    AN00116647
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • ISSN
    1882-7764
  • NDL Article ID
    4422819
  • NDL Source Classification
    ZM13(科学技術--科学技術一般--データ処理・計算機)
  • NDL Call No.
    Z14-741
  • Data Source
    CJP  NDL  NII-ELS  IPSJ 
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