One Method - All Error-Metrics: A Three-Stage Approach for Error-Metric Evaluation in Approximate Computing

Froehlich, Saman; Grose, Daniel; Drechsler, Rolf

doi:10.23919/date.2019.8715138

Cited by 23 publications

(23 citation statements)

References 6 publications

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“…It is not a challenging task to provide limitations on the metrics, such as terminating the program when a certain error-rate or a certain average-case error is exceeded. Moreover, the authors in [17] did not claim their work to be 100% accurate to the actual error metrics (as they did not provide the values for the errors). In addition, they did not provide all the input combinations that produced errors and they only calculated the metrics.…”

Section: Experimental Results On Benchmark Addersmentioning

confidence: 99%

“…Recently, Froehlich et al [17] proposed a formal three-stage approach for the determination of all error-metrics for an approximate circuit. The determination of several error-metrics was facilitated by the main bulk of the work being done by a Gröbner reduction and an Algebraic Decision Diagram (ADD) that did not need to be repeated for different error metrics.…”

Section: Related Workmentioning

confidence: 99%

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Error metrics determination in functionally approximated circuits using SAT solvers

2020

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Approximate computing is an emerging design paradigm that offers trade-offs between output accuracy and computation efforts by exploiting some applications' intrinsic error resiliency. Computation of error metrics is of paramount importance in approximate circuits to measure the degree of approximation. Most of the existing techniques for evaluating error metrics apply simulations which may not be effective for evaluation of large complex designs because of an immense increase in simulation runtime and a decrease in accuracy. To address these deficiencies, we present a novel methodology that employs SAT (Boolean satisfiability) solvers for fast and accurate determination of error metrics specifically for the calculation of an average-case error and the maximum error rate in functionally approximated circuits. The proposed approach identifies the set of all errors producing assignments to gauge the quality of approximate circuits for real-life applications. Additionally, the proposed approach provides a test generation method to facilitate design choices, and acts as an important guide to debug the approximate circuits to discover and locate the errors. The effectiveness of the approach is demonstrated by evaluating the error metrics of several benchmark-approximated adders of different sizes. Experimental results on benchmark circuits show that the proposed SAT-based methodology accurately determines the maximum error rate and an average-case error within acceptable CPU execution time in one go, and further provides a log of error-generating input assignments. OPEN ACCESSCitation: Abed S, Behiry AAMR, Ahmad I (2020) Error metrics determination in functionally approximated circuits using SAT solvers. PLoS ONE 15(1): e0227745. https://doi.org/10.

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Section: Experimental Results On Benchmark Addersmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Error metrics determination in functionally approximated circuits using SAT solvers

2020

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“…Due to scalability issues, the results were presented for small sequential multipliers based on an 8-bit adder and some less complex circuits only. In addition, Symbolic Computer Algebra (SCA) has been used to determine various error metrics [18], [19]. The latter approach uses Algebraic Decision Diagrams (ADDs) that has the ability to determine the mean relative error for which no other formal technique exists.…”

Section: B Exact Error Analysis Of Approximate Circuitsmentioning

confidence: 99%

“…Using a subset of all possible input vectors can cause a substantial difference between the estimated and real error [7], [8]. Hence, various analytical and formal approaches have been proposed and applied for exact quantification of the error of the approximate circuits [9]- [19]. In this paper, we will focus on the formal approaches because they do not make any assumption on the structure of the approximate circuits and they can be applied to determine almost every error metric.…”

Section: Introductionmentioning

confidence: 99%

Formal Methods for Exact Analysis of Approximate Circuits

Vašíček

2019

IEEE Access

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Approximate circuits are digital circuits that are intentionally designed in such a way that the specification is violated in terms of functionality in order to obtain some improvements in power consumption, performance or area, in comparison with fully functional circuits. To design the approximate circuits, the synthesis tools rely on the availability of a procedure checking, whether the synthesized circuits meet a specification and/or provides information about circuit quality. Compared to the traditional circuit design flow, the nature of the approximate circuits involves replacing the strict functional equivalence checking with a more advanced approach that enables us to quantify or guarantee the degree of similarity. The most common technique is to employ a circuit simulator for analysing responses for all input vectors. This approach allows us to simultaneously perform checking and quality assessment, but the exhaustive enumeration of the input vectors is tractable only for a small number of inputs. To avoid excessive runtimes, a subset of all possible input vectors is typically used for complex circuits. This causes us, however, to lose the ability to guarantee that the quality of the synthesized circuits is within an acceptable range given in the specification. The main goal of this paper is to show how to adopt formal methods such as binary decision diagrams and satisfiability solvers for exhaustive analysis of approximate circuits without explicit enumeration of all input vectors. We survey the methods for exact computation of the most important error parameters used in the context of approximate computing, propose improved algorithms and provide a detailed analysis of their performance. The methods are benchmarked on a large set of key approximate circuits consisting of nearly 2,000 unique arithmetic instances with 8-, 12-, 16-, and 32-bit operands which helps us to identify the best algorithm and method for computation of a desired error parameter.

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“…Moreover, it remains an essential tool for the development and use of videos. In a nutshell, essential applications, including PPT presentation, are wireless network technology contributions [2].…”

Section: Introductionmentioning

confidence: 99%

Construction of Video Courses of Physical Education and Health Education in Colleges and Universities under the MOOC Platform

Shuai

2021

Mobile Information Systems

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In the traditional construction process of educational video courses for physical and health education in universities, numerous problems are encountered, such as small storage capacity, significant delay error, and decreased information throughput rate. Therefore, an educational video course for physical and health education in universities based on the Massive Open Online Course (MOOC) platform is constructed. The course is built by constructing a creative environment for video courses, establishing a video course model under the MOOC platform, and the caching code design for video courses. Upon numerous modifications and test runs, with the campus network’s help, the construction of a network teaching video for physical and health theory courses is realized. Our proposed approach’s experimental result shows that the designed course’s frame rate is 10% higher than that of the traditional course designing. The node’s storage capacity is up to 130%, the delay error is significantly reduced, and the information throughput rate is not affected by the increase of network load.

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One Method - All Error-Metrics: A Three-Stage Approach for Error-Metric Evaluation in Approximate Computing

Cited by 23 publications

References 6 publications

Error metrics determination in functionally approximated circuits using SAT solvers

Error metrics determination in functionally approximated circuits using SAT solvers

Formal Methods for Exact Analysis of Approximate Circuits

Construction of Video Courses of Physical Education and Health Education in Colleges and Universities under the MOOC Platform

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