Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

Graillat, Stef; Jézéquel, Fabienne; Picot, Romain; Févotte, François; Lathuilière, Bruno

doi:10.1016/j.jocs.2019.07.004

Cited by 24 publications

(30 citation statements)

References 15 publications

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“…A second phase performs a statistical refinement to join the precision bindings derived from different input sets. Other tools adopt more advanced techniques but their search space is restricted to standard FP types (e.g., PROMISE [8] and Precimonious [14]), or in other cases they are limited to the analysis of functional expressions (e.g., FPTuner [4] and PRECISA [13]). As a final consideration, all these tool do not enable the analysis of the dynamic range associated to a fixed-format FP type.…”

Section: Related Workmentioning

confidence: 99%

A transprecision floating-point platform for ultra-low power computing

Tagliavini

Mach

Rossi

et al. 2018

2018 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE)

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In modern low-power embedded platforms, the execution of floating-point (FP) operations emerges as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy consumed by a core and its data memory is related to FP computations. The adoption of FP formats requiring a lower number of bits is an interesting opportunity to reduce energy consumption, since it allows to simplify the arithmetic circuitry and to reduce the memory bandwidth required to transfer data between memory and registers by enabling vectorization. From a theoretical point of view, the adoption of multiple FP types perfectly fits with the principle of transprecision computing, allowing fine-grained control of approximation while meeting specified constraints on the precision of final results. In this paper we propose an extended FP type system with complete hardware support to enable transprecision computing on low-power embedded processors, including two standard formats (binary32 and binary16) and two new formats (binary8 and binary16alt). First, we introduce a software library that enables exploration of FP types by tuning both precision and dynamic range of program variables. Then, we present a methodology to integrate our library with an external tool for precision tuning, and experimental results that highlight the clear benefits of introducing the new formats. Finally, we present the design of a transprecision FP unit capable of handling 8-bit and 16-bit operations in addition to standard 32bit operations. Experimental results on FP-intensive benchmarks show that up to 90% of FP operations can be safely scaled down to 8-bit or 16-bit formats. Thanks to precision tuning and vectorization, execution time is decreased by 12% and memory accesses are reduced by 27% on average, leading to a reduction of energy consumption up to 30%. I. INTRODUCTIONNowadays most embedded applications involving numerical computations with large dynamic range are performed using binary64 (double-precision) or binary32 (single-precision) floating-point (FP) formats, described by the IEEE 754 standard [18]. In these applications, the execution of FP operations emerges as a major contributor to the energy consumption. To provide experimental evidence of this insight, we have executed a set of FP-intensive applications on PULPino [7], an open-source ULP microcontroller. Results show that 30% of the energy consumption of the core is actually due to FP operations. Moreover, an additional 20% is spent in moving FP operands from data memory to registers and vice versa. To provide a compromise between energy cost and dynamic range, IEEE 754 introduces a 16-bit format referred to as binary16 (half-precision). The introduction of binary16 represents a first step to increase the energy efficiency of FP computations, but software development flows for ULP systems still lack a methodology to evaluate the effect of reduced-precision FP variables on application requirements. In practice,...

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Section: Related Workmentioning

confidence: 99%

A transprecision floating-point platform for ultra-low power computing

Tagliavini

Mach

Rossi

et al. 2018

2018 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE)

View full text Add to dashboard Cite

show abstract

“…This speedup is up to 5.5 if 4 correct digits are requested for matrix multiplication. In the numerical experiments carried out with the two-precision version of PROMISE [9], lower speedup has been obtained (up to 1.3). In this case, speedup was measured w.r.t.…”

Section: Autotuning Of Floating-point Types With Three Possible Precimentioning

confidence: 97%

“…The PROMISE (PRecision OptiMISE) software [9,10] is based on CADNA and aims at optimizing floating-point type declarations in simulation codes. The sequel relies on Definition 1 that makes clear the notion of decimal significant digits in common between two numbers.…”

Section: The Promise Softwarementioning

confidence: 99%

“…with single and double precision variables. PROMISE has been successfully tested on programs implementing several numerical algorithms including linear system solving and also on an industrial code that solves the neutron transport equations [9]. In this section, we aim at showing the feasiblity of using PROMISE to automatically provide modified programs with variable declarations in single, double, and quadruple precision.…”

Section: Autotuning Of Floating-point Types With Three Possible Precimentioning

confidence: 99%

“…We describe in this paper the functionalities added to the CADNA library for the control of accuracy of binary128 results. Furthermore we show how these modifications have enabled the improvement of the PROMISE 4 software [9,10] that is based on CADNA and aims at optimizing the precision of variables in numerical codes. Indeed, from a required accuracy of the results, PROMISE automatically determines the appropriate precision for each floating-point variable in a code.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical validation in quadruple precision using stochastic arithmetic

Graillat¹,

Jézéquel²,

Picot³

et al.

Kalpa Publications in Computing

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Discrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floating-point variables, i.e. having 113-bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113-bit mantissa length variables. This new version of CADNA has been successfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision.

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Numerical Validation of Half Precision Simulations

Jézéquel

Hoseininasab

Hilaire

2021

Advances in Intelligent Systems and Computing

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In this article, we show how to control the numerical quality of half precision computations using stochastic arithmetic. The CADNA library that is used to estimate rounding errors and detect numerical instabilities in floating-point codes has been improved and extended to support half precision. A performance gain up to a factor 20 has been observed w.r.t. accuracy estimation in arbitrary precision. Furthermore we present how to generate codes mixing half, single, and double precision with a requested accuracy on results providing a user-defined numerical quality of the code. Control of robustness and floating-point auto-tuning taking into account half precision have been successfully performed on various numerical simulations, in particular a control application.

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Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

Cited by 24 publications

References 15 publications

A transprecision floating-point platform for ultra-low power computing

A transprecision floating-point platform for ultra-low power computing

Numerical validation in quadruple precision using stochastic arithmetic

Numerical Validation of Half Precision Simulations

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