Efficient digital implementation of a multi-precision square-root algorithm

In high performance computing systems and signal processing, there is a basic set of mathematical functions that are essential. While addition, subtraction and multiplication are well understood, there is less literature on square-rooting, which is a particularly time- and resource-consuming functio...

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Veröffentlicht in:	Chronic diseases and translational medicine Jg. 13; H. 2; S. 110 - 117
Hauptverfasser:	Beasley, Alexander E, Watson, Robert J, Clarke, Christopher T
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Beijing The Institution of Engineering and Technology 01.03.2019 John Wiley & Sons, Inc
Schlagworte:	Accuracy Algorithms Approximation CAD Computer aided design double‐precision inputs efficient digital implementation error analysis field programmable gate arrays floating point arithmetic half‐precision inputs IEEE‐754R standard floating‐point numbers input mantissa mathematical functions MFLOP modern high‐performance computing systems multiprecision square‐root algorithm normalised error Number systems optimisation performance optimised variants Research Article signal processing Software square‐root function traditional nonrestoring algorithms valuable resources mathematical functions field programmable gate arrays error analysis signal processing half-precision inputs square-root function efficient digital implementation MFLOP floating point arithmetic IEEE-754R standard floating-point numbers optimisation modern high-performance computing systems normalised error double-precision inputs input mantissa performance optimised variants valuable resources multiprecision square-root algorithm traditional nonrestoring algorithms
ISSN:	1751-8601, 1751-861X, 2095-882X, 1751-861X, 2589-0514
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Zusammenfassung:	In high performance computing systems and signal processing, there is a basic set of mathematical functions that are essential. While addition, subtraction and multiplication are well understood, there is less literature on square-rooting, which is a particularly time- and resource-consuming function. Traditional non-restoring algorithms produce a mantissa half the length of the input mantissa, causing a loss of precision. This study presents a method for increasing the accuracy of this algorithm. It is shown to work for all IEEE-754R standard floating-point numbers. Error analysis shows a 57-fold (for half-precision) and 134e6-fold improvement (for double-precision) in the normalised error, equivalent to at most 1 Units of Least Precision. Resource and performance optimised variants are analysed and their throughput analysed. On an Intel Stratix V device, performance optimised implementations achieve a throughput of 717 MFLOPs. Resource optimised implementations on a low-cost device require only 127 Adaptive Logic Modules and 232 registers, with a throughput of 8.56 MFLOPs. All implementations are DSP block and memory free, saving valuable resources. The maximum throughput of the presented design is 15.5 times greater than that proposed by Pimentel et al. and two orders of magnitude greater than typical multiply-accumulate methods.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1751-8601 1751-861X 2095-882X 1751-861X 2589-0514
DOI:	10.1049/iet-cdt.2018.5051