The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Tiga algoritma darab untuk operasi bahagi titik terapung dibandingkan: kaedah Newton-Raphson, algoritma Goldschmidt, dan kaedah naif yang hanya mengira bentuk pengembangan siri Taylor bagi salingan. Siri ini juga menyediakan asas teori untuk algoritma Goldschmidt. Adalah diketahui umum bahawa, kaedah Newton-Raphson dan algoritma Goldschmidt, yang pertama adalah lebih tepat manakala yang kedua adalah lebih pantas pada unit saluran paip. Walau bagaimanapun, sedikit yang dilaporkan mengenai kaedah naif. Dalam laporan ini, kami menganalisis kelajuan dan ketepatan setiap kaedah dan membentangkan keputusan ujian berangka, yang kami jalankan untuk mengesahkan kesahihan analisis ketepatan. Pada asasnya, perbandingan dibuat dalam konteks pelaksanaan perisian (cth , perpustakaan makro) dan pematuhan dengan pembundaran IEEE Standard 754 tidak dipertimbangkan. Ia ditunjukkan bahawa kaedah naif berguna dalam tetapan realistik di mana bilangan lelaran adalah kecil dan kaedah itu dilaksanakan pada unit titik terapung saluran paip dengan konfigurasi berganda-terkumpul. Dalam keadaan sedemikian, kaedah naif memberikan hasil yang lebih tepat dengan kependaman sedikit lebih rendah, berbanding dengan algoritma Goldschmidt, dan jauh lebih pantas daripada tetapi lebih rendah sedikit dari segi ketepatan kepada kaedah Newton-Raphson.
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Salinan
Takashi AMISAKI, Umpei NAGASHIMA, Kazutoshi TANABE, "Floating-Point Divide Operation without Special Hardware Supports" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 1, pp. 173-177, January 1999, doi: .
Abstract: Three multiplicative algorithms for the floating-point divide operation are compared: the Newton-Raphson method, Goldschmidt's algorithm, and a naive method that simply calculates a form of the Taylor series expansion of a reciprocal. The series also provides a theoretical basis for Goldschmidt's algorithm. It is well known that, of the Newton-Raphson method and Goldschmidt's algorithm, the former is the more accurate while the latter is the faster on a pipelined unit. However, little is reported about the naive method. In this report, we analyze the speed and accuracy of each method and present the results of numerical tests, which we conducted to confirm the validity of the accuracy analysis. Basically, the comparison are made in the context of software implementation (e. g. , a macro library) and compliance with the IEEE Standard 754 rounding is not considered. It is shown that the naive method is useful in a realistic setting where the number of iterations is small and the method is implemented on a pipelined floating-point unit with a multiply-accumulate configuration. In such a situation, the naive method gives a more accurate result with a slightly lower latency, as compared with Goldschmidt's algorithm, and is much faster than but slightly inferior in accuracy to the Newton-Raphson method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_1_173/_p
Salinan
@ARTICLE{e82-a_1_173,
author={Takashi AMISAKI, Umpei NAGASHIMA, Kazutoshi TANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Floating-Point Divide Operation without Special Hardware Supports},
year={1999},
volume={E82-A},
number={1},
pages={173-177},
abstract={Three multiplicative algorithms for the floating-point divide operation are compared: the Newton-Raphson method, Goldschmidt's algorithm, and a naive method that simply calculates a form of the Taylor series expansion of a reciprocal. The series also provides a theoretical basis for Goldschmidt's algorithm. It is well known that, of the Newton-Raphson method and Goldschmidt's algorithm, the former is the more accurate while the latter is the faster on a pipelined unit. However, little is reported about the naive method. In this report, we analyze the speed and accuracy of each method and present the results of numerical tests, which we conducted to confirm the validity of the accuracy analysis. Basically, the comparison are made in the context of software implementation (e. g. , a macro library) and compliance with the IEEE Standard 754 rounding is not considered. It is shown that the naive method is useful in a realistic setting where the number of iterations is small and the method is implemented on a pipelined floating-point unit with a multiply-accumulate configuration. In such a situation, the naive method gives a more accurate result with a slightly lower latency, as compared with Goldschmidt's algorithm, and is much faster than but slightly inferior in accuracy to the Newton-Raphson method.},
keywords={},
doi={},
ISSN={},
month={January},}
Salinan
TY - JOUR
TI - Floating-Point Divide Operation without Special Hardware Supports
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 173
EP - 177
AU - Takashi AMISAKI
AU - Umpei NAGASHIMA
AU - Kazutoshi TANABE
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 1999
AB - Three multiplicative algorithms for the floating-point divide operation are compared: the Newton-Raphson method, Goldschmidt's algorithm, and a naive method that simply calculates a form of the Taylor series expansion of a reciprocal. The series also provides a theoretical basis for Goldschmidt's algorithm. It is well known that, of the Newton-Raphson method and Goldschmidt's algorithm, the former is the more accurate while the latter is the faster on a pipelined unit. However, little is reported about the naive method. In this report, we analyze the speed and accuracy of each method and present the results of numerical tests, which we conducted to confirm the validity of the accuracy analysis. Basically, the comparison are made in the context of software implementation (e. g. , a macro library) and compliance with the IEEE Standard 754 rounding is not considered. It is shown that the naive method is useful in a realistic setting where the number of iterations is small and the method is implemented on a pipelined floating-point unit with a multiply-accumulate configuration. In such a situation, the naive method gives a more accurate result with a slightly lower latency, as compared with Goldschmidt's algorithm, and is much faster than but slightly inferior in accuracy to the Newton-Raphson method.
ER -