Floating-Point Inverse Square Root Algorithm Based on Taylor-Series Expansion

Wei, Jianglin; Kuwana, Anna; Kobayashi, Haruo; Kubo, Kazuyoshi; Tanaka, Yuuki

doi:10.1109/tcsii.2021.3062358

Cited by 9 publications

(1 citation statement)

References 16 publications

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“…The author realized that Taylor-series expansion has its conversion region; for some functions, it is very wide while for others, it is limited. Then we considered to apply it to some floating-point digital arithmetic circuits for good tradeoff among memory size, required numbers of additions/subtractions/multiplications, and computing accuracy [142,143].…”

Section: Floating-point Digital Arithmetic Circuit Based On Taylor-se...mentioning

confidence: 99%

How the Author's Group Came Up with Ideas in Analog/Mixed-Signal Circuit and System Area

KOBAYASHI

2024

IEICE Trans. Fundamentals

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This article reviews the author's group research achievements in analog/mixed-signal circuit and system area with introduction of how they came up with the ideas. Analog/mixed-signal circuits and systems have to be designed as well-balanced in many aspects, and coming up ideas needs some experiences and discussions with researchers. It is also heavily dependent on researchers. Here, the author's group own experiences are presented as well as their research motivations.

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Section: Floating-point Digital Arithmetic Circuit Based On Taylor-se...mentioning

confidence: 99%

How the Author's Group Came Up with Ideas in Analog/Mixed-Signal Circuit and System Area

KOBAYASHI

2024

IEICE Trans. Fundamentals

Self Cite

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Fast and accurate approximation algorithms for computing floating point square root

Kokosiński,

Gepner,

Moroz

et al. 2024

Numer Algor

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The square root is one of the most used functions in many different engineering and scientific applications. We propose new methods for calculating the square root function that are based on the Newton–Raphson method with Heron iteration. A modification of Heron’s formula combined with an improved selection of the magic constants enables a significant reduction of the maximum relative error (MRE). Simple modifications to the Newton–Raphson formula and the magic number method enable implementation on platforms with limited hardware resources, such as microcontrollers and FPGAs, with variable accuracy. Implementations of new approximation algorithms in the C programming language were carefully tested and evaluated against their software and hardware counterparts on the most popular platforms, e.g., CPUs from Intel, AMD and ARM, GPU from Nvidia and IPU from Graphcore. The proposed numerical algorithms are shown to be superior in terms of computational time, the number of clock cycles, accuracy, MRE, and root mean square deviation.

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Divide and Conquer: Floating-Point Exponential Calculation Based on Taylor-Series Expansion

Wei

Kuwana

Kobayashi

et al. 2021

2021 IEEE 14th International Conference on ASIC (ASICON)

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Floating-Point Inverse Square Root Algorithm Based on Taylor-Series Expansion

Cited by 9 publications

References 16 publications

How the Author's Group Came Up with Ideas in Analog/Mixed-Signal Circuit and System Area

How the Author's Group Came Up with Ideas in Analog/Mixed-Signal Circuit and System Area

Fast and accurate approximation algorithms for computing floating point square root

Divide and Conquer: Floating-Point Exponential Calculation Based on Taylor-Series Expansion

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