Probabilistic Error Analysis of Approximate Adders and Multipliers

Mazahir, Sana; Ayub, Muhammad Kamran; Hasan, Osman; Shafique, Muhammad

doi:10.1007/978-3-319-99322-5_5

Cited by 8 publications

(10 citation statements)

References 24 publications

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“…Low-level approximate circuits are modeled based on a lookup table technique, which characterizes the statistical properties of approximate hardware and uses a regression-based technique for composing statistics to formulate output quality [40,50]. An analytical error analysis approach for approximate adders can predict, evaluate, and compare the accuracy of various approximate adders and multipliers [41,51]. These existing works mostly focus on low-level error estimation or high-level program analysis.…”

Section: Error Estimation Methodsmentioning

confidence: 99%

“…It calculates the output quality of approximate configuration with a few formulas very quickly. However, these analytical models are usually limited to certain approximate sites such as approximate adders or approximate multipliers for calculation [40,41], approximate SRAM/DRAM/SSD/PCM [42][43][44][45] for storage, and approximate data transmission for communication [31][32][33][34][35][36]. Particularly, there are a variety of accuracy-power/performance tradeoffs for a specified approximate component.…”

Section: Introductionmentioning

confidence: 99%

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HEAP: A Holistic Error Assessment Framework for Multiple Approximations Using Probabilistic Graphical Models

Jiao

2020

Electronics

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Approximate computing has been a good paradigm of energy-efficient accelerator design. Accurate and fast error estimation is critical for appropriate approximate techniques selection so that power saving (or performance improvement) can be maximized with acceptable output quality in approximate accelerators. In the paper, we propose HEAP, a Holistic Error assessment framework to characterize multiple Approximate techniques with Probabilistic graphical models (PGM) in a joint way. HEAP maps the problem of evaluating errors induced by different approximate techniques into a PGM issue, including: (1) A heterogeneous Bayesian network is represented by converting an application’s data flow graph, where various approximate options are {precise, approximate} two-state X*-type nodes, while input or operating variables are {precise, approximate, unacceptable} three-state X-type nodes. These two different kinds of nodes are separately used to configure the available approximate techniques and track the corresponding error propagation for guaranteed configurability; (2) node learning is accomplished via an approximate library, which consists of probability mass functions of multiple approximate techniques to fast calculate each node’s Conditional Probability Table by mechanistic modeling or empirical modeling; (3) exact inference provides the probability distribution of output quality at three levels of precise, approximate, and unacceptable. We do a complete case study of 3 × 3 Gaussian kernels with different approximate configurations to verify HEAP. The comprehensive results demonstrate that HEAP is helpful to explore design space for power-efficient approximate accelerators, with just 4.18% accuracy loss and 3.34 × 105 speedup on average over Mentor Carlo simulation.

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Section: Error Estimation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

HEAP: A Holistic Error Assessment Framework for Multiple Approximations Using Probabilistic Graphical Models

Jiao

2020

Electronics

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“…This can easily happen when a Matlab circuit model is used instead of a gate-level description and a less generic, but more efficient gate-level simulator. Twenty-five hours are reported when analyzing 14-bit adders in [26] and more than 19 years are estimated when performing the exhaustive simulation of 20-bit adders [9]. So as to avoid excessive run-times and enable the analysis of complex circuits, many authors simplify the problem and evaluate the functionality of approximate circuits by applying a subset of all possible input vectors.…”

Section: B Exact Error Analysis Of Approximate Circuitsmentioning

confidence: 99%

“…In order to address the inaccuracy of the Monte-Carlo simulation, various statistical and analytical methods have been proposed [7]- [9], [11], [12]. The common feature of these techniques is that the error is expressed as a function of circuit parameters like the number of inputs, the number of truncated bits, carry-chain length, the number of subcomponents, etc.…”

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%

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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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A novel lightweight CNN-based error-reduced carry prediction approximate full adder design for multimedia applications

Nishanth,

Sulochana

2024

Neural Comput & Applic

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Probabilistic Error Analysis of Approximate Adders and Multipliers

Cited by 8 publications

References 24 publications

HEAP: A Holistic Error Assessment Framework for Multiple Approximations Using Probabilistic Graphical Models

HEAP: A Holistic Error Assessment Framework for Multiple Approximations Using Probabilistic Graphical Models

Formal Methods for Exact Analysis of Approximate Circuits

A novel lightweight CNN-based error-reduced carry prediction approximate full adder design for multimedia applications

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