Universal: Reliable, Reproducible, and Energy-Efficient Numerics

Omtzigt, E. Theodore L.; Quinlan, James

doi:10.1007/978-3-031-09779-9_7

Cited by 5 publications

(4 citation statements)

References 14 publications

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“…In order to verify that the proposed architectures are correct, exhaustive tests were generated with the reference software library Universal [37] for 8, 10 and 12-bit posits, as well as random/corner case tests for 16, 32 and 64-bit posits. All these tests were successful.…”

Section: Proposed Approachmentioning

confidence: 99%

Generating Posit-Based Accelerators With High-Level Synthesis

Murillo

Barrio

Botella

et al. 2023

IEEE Trans. Circuits Syst. I

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Recently, the posit number system has demonstrated a higher accuracy over standard floating-point arithmetic for many scientific applications. However, when it comes to implementing accelerators for these applications, the tool support for this arithmetic format is still missing, especially during the high-level synthesis (HLS) step. In this paper, we incorporate the posit data type into the high-level synthesis (HLS) design process, so that we can generate the register-transfer level (RTL) implementation directly from a given behavioral specification, but using posit numbers instead of the classical floating-point notations. Our evaluations show that, even if posit-based circuits require more area than their floating-point counterparts, they offer higher accuracy when using the same bitwidth. For example, using posit arithmetic can reduce computation errors by about two orders of magnitude when compared to using standard floating-point numbers. Our approach also includes an alternative to mitigate the high overheads of the posits and broadening the potential use of this format. We also propose a hybrid scheme that uses posit numbers only in the private local memory, while the accelerator operates in the classic floatingpoint notation. This solution is useful when the designers want to optimize local memories and data transfers, but still use legacy HLS tools that only support traditional floating-point notations.

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Section: Proposed Approachmentioning

confidence: 99%

Generating Posit-Based Accelerators With High-Level Synthesis

Murillo

Barrio

Botella

et al. 2023

IEEE Trans. Circuits Syst. I

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“…The exact result of the operation is computed using twice the number of bits and compared with the obtained result in both conventional and HUB 16-bit posit formats by calculating the relative error. The Universal library [7] was used to emulate the computation of such formats via software.…”

Section: A Error Analysismentioning

confidence: 99%

“…Nonetheless, one of the most promising contributions is the posit™ arithmetic, introduced in 2017 by John L. Gustafson [2]. Posit numbers (or posits) have shown promising results in a wide variety of areas, namely: signal processing [3], neural networks [4], [5], or linear algebra [6], [7], [8].…”

Section: Introductionmentioning

confidence: 99%

HUB Meets Posit: Arithmetic Units Implementation

Murillo,

Hormigo,

Barrio

et al. 2023

IEEE Trans. Circuits Syst. II

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The posit™ format was introduced in 2017 as an alternative to replacing the widespread IEEE 754. Posit arithmetic provides reproducible results across platforms and possesses tapered accuracy, among other improvements. Nevertheless, despite the advantages provided by such a format, their functional units are not as competitive as the IEEE 754 ones yet. The HUB approach was presented in 2016 to reduce the hardware cost of floating-point units. In this brief, we present HUB posit, a new format to mitigate the hardware overhead of posit units. Results show that it is possible to reach up to 15% and 12% in terms of area-delay product for adders and multipliers, respectively, while maintaining a similar level of accuracy. In addition, synthesis results show that HUB posit units are able to reach higher frequencies than conventional ones.

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“…Universal delivers software and hardware co-design capabilities to develop low and mixedprecision algorithms for reducing energy consumption in signal processing, Industry 4.0, machine learning, robotics, and high-performance computing applications (Omtzigt & Quinlan, 2022). The package includes command-line tools for visualizing and interrogating numeric encodings, an interface for setting and querying bits, and educational examples showcasing performance gain and numerical accuracy with the different number systems.…”

mentioning

confidence: 99%

Universal Numbers Library: Multi-format Variable Precision Arithmetic Library

Omtzigt¹,

Quinlan²

2023

JOSS

Self Cite

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Universal Numbers Library, or simply Universal, is a comprehensive, self-contained C++ header-only template library that provides implementations of various number representations and standard arithmetic operations on arbitrary configurations of integer and real numbers (Omtzigt et al., 2020). With its extensive collection of number systems, including integers, decimals, fixed-points, rationals, linear floats, tapered floats, logarithmic, SORNs, interval, level-index, and adaptive-precision binary and decimal integers and floats, Universal offers a robust verification suite for each system.Using a posit number as an example, the basic pattern to use a custom Universal type is: #include template Real MyKernel(const Real& a, const Real& b) { return a * b; // replace this with your kernel computation } constexpr double pi = 3.14159265358979323846; int main() {

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Universal: Reliable, Reproducible, and Energy-Efficient Numerics

Cited by 5 publications

References 14 publications

Generating Posit-Based Accelerators With High-Level Synthesis

Generating Posit-Based Accelerators With High-Level Synthesis

HUB Meets Posit: Arithmetic Units Implementation

Universal Numbers Library: Multi-format Variable Precision Arithmetic Library

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