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
본 논문에서는 로그(기록2x) 다중 도메인 분할 방법에 의한 IEEE754 바이너리32 정확도 부동 소수점 수. 일반 가수(1≤x<2)에 2, 4, 8, …을 곱합니다(또는 동등하게 1, 2, 3, … 비트를 왼쪽으로 시프트함).x<4), (4≤x<8), (8≤x<16),…를 고려하고 Taylor 계열 확장을 적용합니다. 해당 지역에서는 기울기가 f(x)=로그2 x ~에 관하여 x (1 ≤ 의 영역에 비해 완만합니다.x<2), 필요한 용어 수가 줄어듭니다. 또한 엔지니어의 설계에 가장 적합한 알고리즘을 선택하고 최고의 하드웨어 장치를 구축하기 위해 하드웨어의 덧셈, 뺄셈, 곱셈 횟수와 LUT(Look-Up Table) 크기 간의 균형을 고려합니다.
Jianglin WEI
Gunma University
Anna KUWANA
Gunma University
Haruo KOBAYASHI
Gunma University
Kazuyoshi KUBO
Oyama National College of Technology
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Jianglin WEI, Anna KUWANA, Haruo KOBAYASHI, Kazuyoshi KUBO, "IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 7, pp. 1020-1027, July 2022, doi: 10.1587/transfun.2021EAP1076.
Abstract: In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log2x) of IEEE754 binary32 accuracy floating-point number by a multi-domain partitioning method. The general mantissa (1≤x<2) is multiplied by 2, 4, 8, … (or equivalently left-shifted by 1, 2, 3, … bits), the regions of (2≤x<4), (4≤x<8), (8≤x<16),… are considered, and Taylor-series expansion is applied. In those regions, the slope of f(x)=log2 x with respect to x is gentle compared to the region of (1≤x<2), which reduces the required number of terms. We also consider the trade-offs among the numbers of additions, subtractions, and multiplications and Look-Up Table (LUT) size in hardware to select the best algorithm for the engineer's design and build the best hardware device.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1076/_p
부
@ARTICLE{e105-a_7_1020,
author={Jianglin WEI, Anna KUWANA, Haruo KOBAYASHI, Kazuyoshi KUBO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division},
year={2022},
volume={E105-A},
number={7},
pages={1020-1027},
abstract={In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log2x) of IEEE754 binary32 accuracy floating-point number by a multi-domain partitioning method. The general mantissa (1≤x<2) is multiplied by 2, 4, 8, … (or equivalently left-shifted by 1, 2, 3, … bits), the regions of (2≤x<4), (4≤x<8), (8≤x<16),… are considered, and Taylor-series expansion is applied. In those regions, the slope of f(x)=log2 x with respect to x is gentle compared to the region of (1≤x<2), which reduces the required number of terms. We also consider the trade-offs among the numbers of additions, subtractions, and multiplications and Look-Up Table (LUT) size in hardware to select the best algorithm for the engineer's design and build the best hardware device.},
keywords={},
doi={10.1587/transfun.2021EAP1076},
ISSN={1745-1337},
month={July},}
부
TY - JOUR
TI - IEEE754 Binary32 Floating-Point Logarithmic Algorithms Based on Taylor-Series Expansion with Mantissa Region Conversion and Division
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1020
EP - 1027
AU - Jianglin WEI
AU - Anna KUWANA
AU - Haruo KOBAYASHI
AU - Kazuyoshi KUBO
PY - 2022
DO - 10.1587/transfun.2021EAP1076
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2022
AB - In this paper, an algorithm based on Taylor series expansion is proposed to calculate the logarithm (log2x) of IEEE754 binary32 accuracy floating-point number by a multi-domain partitioning method. The general mantissa (1≤x<2) is multiplied by 2, 4, 8, … (or equivalently left-shifted by 1, 2, 3, … bits), the regions of (2≤x<4), (4≤x<8), (8≤x<16),… are considered, and Taylor-series expansion is applied. In those regions, the slope of f(x)=log2 x with respect to x is gentle compared to the region of (1≤x<2), which reduces the required number of terms. We also consider the trade-offs among the numbers of additions, subtractions, and multiplications and Look-Up Table (LUT) size in hardware to select the best algorithm for the engineer's design and build the best hardware device.
ER -