• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.1
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• pp.173-180
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• 2022

Approximate Computing is a promising method for designing hardware-efficient computing systems. Approximate multiplication is one of key operations used in approximate computing methods for high performance and low power computing. An approximate 4-2 compressor can implement hardware-efficient circuits for approximate multiplication. In this paper, we propose an approximate multiplier with low area and low power characteristics. The proposed approximate multiplier architecture is segmented into three portions; an exact region, an approximate region, and a constant correction region. Partial product reduction in the approximation region are simplified using a new 4:2 approximate compressor, and the error due to approximation is compensated using a simple error correction scheme. Constant correction region uses a constant calculated with probabilistic analysis for reducing error. Experimental results of 8×8 multiplier show that the proposed design requires less area, and consumes less power than conventional 4-2 compressor-based approximate multiplier.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.449-457
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• 2000

The paper describes the study of global approximate optimization utilizing soft computing techniques such as genetic algorithms (GA's), neural networks (NN's), and fuzzy inference systems(FIS). GA's provide the increasing probability of locating a global optimum over the entire design space associated with multimodality and nonlinearity. NN's can be used as a tool for function approximations, a rapid reanalysis model for subsequent use in design optimization. FIS facilitates to handle the quantitative design information under the case where the training data samples are not sufficiently provided or uncertain information is included in design modeling. Properties of soft computing techniques affect the quality of global approximate model. Evolutionary fuzzy modeling (EFM) and adaptive neuro-fuzzy inference system (ANFIS) are briefly introduced for structural optimization problem in this context. The paper presents the success of EFM depends on how optimally the fuzzy membership parameters are selected and how fuzzy rules are generated.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.4
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• pp.671-678
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• 2022

Approximate computing is an computational technique that is acceptable degree of inaccurate results of accurate results. Approximate multiplication is one of the approximate computing methods for high-performance and low-power computing. In this paper, we propose a high-density, low-power, and high-speed approximate multiplier using approximate 4-2 compressor and improved full adder. The approximate multiplier with approximate 4-2 compressor consists of three regions of the exact, approximate and constant correction regions, and we compared them by adjusting the size of region by applying an efficient partial product reduction. The proposed approximate multiplier was designed with Verilog HDL and was analyzed for area, power and delay time using Synopsys Design Compiler (DC) on a 25nm CMOS process. As a result of the experiment, the proposed multiplier reduced area by 10.47%, power by 26.11%, and delay time by 13% compared to the conventional approximate multiplier.

• Journal of Korean Society for Quality Management
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• v.18 no.2
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• pp.25-32
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• 1990

This paper presents an approximate algorithm for computing Fault-tree probabilities. The method is essentially composed of three steps. In the first step, a Fault-tree is converted into a network form. In the second step, We change the network into a parallelized diagram. In the third step, the approximate fault-tree probability is calculated from the parallelized diagram. In this paper, in order to verify the method two hypothetical Fault-tree is used by examples. The results show that the method is very useful, even though it is an approximate technique, since it needs not to search the minimal cut sets and has the simple computing rontines.

• Transactions on Semiconductor Engineering
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• v.2 no.4
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• pp.58-68
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• 2024

Approximate computing is a promising approach that optimizes hardware components while tolerating some degree of accuracy loss. In particular, approximate multiplication is widely used as a key operation in computing systems that demand both high performance and low power consumption. Among various techniques, the approximate 4-2 compressor has gained attention for its ability to significantly enhance the performance and efficiency of approximate multiplier through benefits such as low power consumption, improved processing speed, and circuit simplification. A multiplier that computes the product of two n-bit numbers typically consists of three stages: partial product generation, partial product reduction, and adder. By using an approximate 4-2 compressor, the partial product reduction stage can be simplified, and errors introduced by approximation can be compensated for using error correction modules. Additionally, constant correction techniques can be employed to further reduce errors. This paper explores the characteristics of approximate 4-2 compressors and compares various models. Based on this analysis, we evaluate different error metrics and synthesis results for an 8×8 approximate multiplier. Furthermore, we conduct a comparative analysis by applying the multiplier to image processing tasks.

• Annual Conference of KIPS
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• 2019.05a
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• pp.479-481
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• 2019

본 연구에서는 이미지를 분류하는 인공 신경망 가속기를 최적화했고, 이를 구현하여 기존 인공 신경망 가속기와 성능을 비교 분석했다. FPGA(Field Programmable Fate Array) 보드를 이용하여 가속기를 구현했으며, 해당 보드의 내부 메모리인 BRAM 을 FIFO(First In First Out)구조로 설계하여 메모리 시스템을 구현했다. Approximate computing 기법을 효율적으로 적용하기 위해 FWL(Fractional Word Length)최적점을 분석했고, 이를 기반으로 인공 신경망 가속기의 부동 소수점 연산을 고정 소수점 연산으로 변환했다. 구현된 인공 신경망 가속기는 기존의 인공 신경망에 비해, 약 7.4%더 효율적인 전력소모량을 보였다.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1131-1141
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• 2010

We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Some numerical experiments are given to show the efficiency of the preconditioner.

• IEMEK Journal of Embedded Systems and Applications
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• v.16 no.5
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• pp.233-240
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• 2021

We propose a novel, highly accurate approximate multiplier using different types of inexact 4-2 compressors. The importance of low hardware costs leads us to develop approximate multiplication for error-resilient applications. Several rules are developed when selecting a topology for designing the proposed multiplier. Our highly accurate multiplier design considers the different error characteristics of adopted compressors, which achieves a good error distribution, including a low relative error of 0.02% in the 8-bit multiplication. Our analysis shows that the proposed multiplier significantly reduces power consumption and area by 45% and 26%, compared with the exact multiplier. Notably, a trade-off relationship between error characteristics and hardware costs can be achieved when considering those of existing highly accurate approximate multipliers. In the image blending, edge detection and image sharpening applications, the proposed 8-bit approximate multiplier shows better performance in terms of image quality metrics compared with other highly accurate approximate multipliers.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1132-1142
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• 2001

The paper describes the construction of global function approximation models for use in design optimization via global search techniques such as genetic algorithms. Two different approximation methods referred to as evolutionary fuzzy modeling (EFM) and neuro-fuzzy modeling (NFM) are implemented in the context of global approximate optimization. EFM and NFM are based on soft computing paradigms utilizing fuzzy systems, neural networks and evolutionary computing techniques. Such approximation methods may have their promising characteristics in a case where the training data is not sufficiently provided or uncertain information may be included in design process. Fuzzy inference system is the central system for of identifying the input/output relationship in both methods. The paper introduces the general procedures including fuzzy rule generation, membership function selection and inference process for EFM and NFM, and presents their generalization capabilities in terms of a number of fuzzy rules and training data with application to a three-bar truss optimization.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.6
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• pp.742-746
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• 2010

In this paper, we propose new randomness testing methods based on approximate periods in order to improve the previous randomness testing method using exact pattern matching. Finding approximate periods of random sequences enables us to search similarly repeated parts, but it has disadvantages since it takes long time. In this paper we propose randomness testing methods whose time complexity is O($n^2$) by reducing the time complexity of computing approximate periods from O($n^3$) to O($n^2$). Moreover, we perform some experiments to compare pseudo random number generated by AES cryptographic algorithms and true random number.