Bio-Inspired Imprecise Computational Blocks for Efficient VLSI Implementation of Soft-Computing Applications
01 Apr 2010-IEEE Transactions on Circuits and Systems I-regular Papers (IEEE PressPUB767Piscataway, NJ, USA)-Vol. 57, Iss: 4, pp 850-862
TL;DR: It is shown that these proposed Bio-inspired Imprecise Computational blocks (BICs) can be exploited to efficiently implement a three-layer face recognition neural network and the hardware defuzzification block of a fuzzy processor.
Abstract: The conventional digital hardware computational blocks with different structures are designed to compute the precise results of the assigned calculations. The main contribution of our proposed Bio-inspired Imprecise Computational blocks (BICs) is that they are designed to provide an applicable estimation of the result instead of its precise value at a lower cost. These novel structures are more efficient in terms of area, speed, and power consumption with respect to their precise rivals. Complete descriptions of sample BIC adder and multiplier structures as well as their error behaviors and synthesis results are introduced in this paper. It is then shown that these BIC structures can be exploited to efficiently implement a three-layer face recognition neural network and the hardware defuzzification block of a fuzzy processor.
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27 May 2013
TL;DR: This paper reviews recent progress in the area, including design of approximate arithmetic blocks, pertinent error and quality measures, and algorithm-level techniques for approximate computing.
Abstract: Approximate computing has recently emerged as a promising approach to energy-efficient design of digital systems. Approximate computing relies on the ability of many systems and applications to tolerate some loss of quality or optimality in the computed result. By relaxing the need for fully precise or completely deterministic operations, approximate computing techniques allow substantially improved energy efficiency. This paper reviews recent progress in the area, including design of approximate arithmetic blocks, pertinent error and quality measures, and algorithm-level techniques for approximate computing.
921 citations
TL;DR: This paper proposes logic complexity reduction at the transistor level as an alternative approach to take advantage of the relaxation of numerical accuracy, and demonstrates the utility of these approximate adders in two digital signal processing architectures with specific quality constraints.
Abstract: Low power is an imperative requirement for portable multimedia devices employing various signal processing algorithms and architectures. In most multimedia applications, human beings can gather useful information from slightly erroneous outputs. Therefore, we do not need to produce exactly correct numerical outputs. Previous research in this context exploits error resiliency primarily through voltage overscaling, utilizing algorithmic and architectural techniques to mitigate the resulting errors. In this paper, we propose logic complexity reduction at the transistor level as an alternative approach to take advantage of the relaxation of numerical accuracy. We demonstrate this concept by proposing various imprecise or approximate full adder cells with reduced complexity at the transistor level, and utilize them to design approximate multi-bit adders. In addition to the inherent reduction in switched capacitance, our techniques result in significantly shorter critical paths, enabling voltage scaling. We design architectures for video and image compression algorithms using the proposed approximate arithmetic units and evaluate them to demonstrate the efficacy of our approach. We also derive simple mathematical models for error and power consumption of these approximate adders. Furthermore, we demonstrate the utility of these approximate adders in two digital signal processing architectures (discrete cosine transform and finite impulse response filter) with specific quality constraints. Simulation results indicate up to 69% power savings using the proposed approximate adders, when compared to existing implementations using accurate adders.
637 citations
TL;DR: New metrics are proposed for evaluating the reliability as well as the power efficiency of approximate and probabilistic adders and it is shown that the MED is an effective metric for measuring the implementation accuracy of a multiple-bit adder and that the NED is a nearly invariant metric independent of the size of an adder.
Abstract: Addition is a fundamental function in arithmetic operation; several adder designs have been proposed for implementations in inexact computing. These adders show different operational profiles; some of them are approximate in nature while others rely on probabilistic features of nanoscale circuits. However, there has been a lack of appropriate metrics to evaluate the efficacy of various inexact designs. In this paper, new metrics are proposed for evaluating the reliability as well as the power efficiency of approximate and probabilistic adders. Reliability is analyzed using the so-called sequential probability transition matrices (SPTMs). Error distance (ED) is initially defined as the arithmetic distance between an erroneous output and the correct output for a given input. The mean error distance (MED) and normalized error distance (NED) are then proposed as unified figures that consider the averaging effect of multiple inputs and the normalization of multiple-bit adders. It is shown that the MED is an effective metric for measuring the implementation accuracy of a multiple-bit adder and that the NED is a nearly invariant metric independent of the size of an adder. The MED is, therefore, useful in assessing the effectiveness of an approximate or probabilistic adder implementation, while the NED is useful in characterizing the reliability of a specific design. Since inexact adders are often used for saving power, the product of power and NED is further utilized for evaluating the tradeoffs between power consumption and precision. Although illustrated using adders, the proposed metrics are potentially useful in assessing other arithmetic circuit designs for applications of inexact computing.
453 citations
Cites background or methods from "Bio-Inspired Imprecise Computationa..."
...The recently proposed LOA is based on such a design [7]....
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...Hardware structure of the lower-part-OR adder [7]....
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...The bioinspired lowerpart OR adder (LOA) [7] is based on approximate logic, whose truth table is slightly different from the original truth table of a full adder....
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TL;DR: The results show that the proposed designs accomplish significant reductions in power dissipation, delay and transistor count compared to an exact design; moreover, two of the proposed multiplier designs provide excellent capabilities for image multiplication with respect to average normalized error distance and peak signal-to-noise ratio.
Abstract: Inexact (or approximate) computing is an attractive paradigm for digital processing at nanometric scales. Inexact computing is particularly interesting for computer arithmetic designs. This paper deals with the analysis and design of two new approximate 4-2 compressors for utilization in a multiplier. These designs rely on different features of compression, such that imprecision in computation (as measured by the error rate and the so-called normalized error distance) can meet with respect to circuit-based figures of merit of a design (number of transistors, delay and power consumption). Four different schemes for utilizing the proposed approximate compressors are proposed and analyzed for a Dadda multiplier. Extensive simulation results are provided and an application of the approximate multipliers to image processing is presented. The results show that the proposed designs accomplish significant reductions in power dissipation, delay and transistor count compared to an exact design; moreover, two of the proposed multiplier designs provide excellent capabilities for image multiplication with respect to average normalized error distance and peak signal-to-noise ratio (more than 50 dB for the considered image examples).
447 citations
Cites background or methods from "Bio-Inspired Imprecise Computationa..."
...Addition and multiplication are widely used operations in computer arithmetic; for addition full-adder cells have been extensively analyzed for approximate computing [2], [3], [4]....
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...In [4], an imprecise array multiplier is used for neural network applications by omitting some of the least significant bits in the partial products (and thus removing some adders in the array)....
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...Several approximate multipliers have been proposed in the literature [4], [5], [6], [7]....
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03 Mar 2012
TL;DR: An ISA extension that provides approximate operations and storage is described that gives the hardware freedom to save energy at the cost of accuracy and Truffle, a microarchitecture design that efficiently supports the ISA extensions is proposed.
Abstract: Disciplined approximate programming lets programmers declare which parts of a program can be computed approximately and consequently at a lower energy cost. The compiler proves statically that all approximate computation is properly isolated from precise computation. The hardware is then free to selectively apply approximate storage and approximate computation with no need to perform dynamic correctness checks.In this paper, we propose an efficient mapping of disciplined approximate programming onto hardware. We describe an ISA extension that provides approximate operations and storage, which give the hardware freedom to save energy at the cost of accuracy. We then propose Truffle, a microarchitecture design that efficiently supports the ISA extensions. The basis of our design is dual-voltage operation, with a high voltage for precise operations and a low voltage for approximate operations. The key aspect of the microarchitecture is its dependence on the instruction stream to determine when to use the low voltage. We evaluate the power savings potential of in-order and out-of-order Truffle configurations and explore the resulting quality of service degradation. We evaluate several applications and demonstrate energy savings up to 43%.
423 citations
Cites background from "Bio-Inspired Imprecise Computationa..."
...Imprecise integer logic blocks have also been designed [20]....
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References
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01 Jan 1999
6,012 citations
"Bio-Inspired Imprecise Computationa..." refers methods in this paper
...The network MSE is determined as the average MSE values of the network outputs for all testing and training patterns based on [42]...
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TL;DR: In this paper, the authors present a survey of the state-of-the-art in the field of digital integrated circuits, focusing on the following: 1. A Historical Perspective. 2. A CIRCUIT PERSPECTIVE.
Abstract: (NOTE: Each chapter begins with an Introduction and concludes with a Summary, To Probe Further, and Exercises and Design Problems.) I. THE FABRICS. 1. Introduction. A Historical Perspective. Issues in Digital Integrated Circuit Design. Quality Metrics of a Digital Design. 2. The Manufacturing Process. The CMOS Manufacturing Process. Design Rules-The Contract between Designer and Process Engineer. Packaging Integrated Circuits. Perspective-Trends in Process Technology. 3. The Devices. The Diode. The MOS(FET) Transistor. A Word on Process Variations. Perspective: Technology Scaling. 4. The Wire. A First Glance. Interconnect Parameters-Capitance, Resistance, and Inductance. Electrical Wire Models. SPICE Wire Models. Perspective: A Look into the Future. II. A CIRCUIT PERSPECTIVE. 5. The CMOS Inverter. The Static CMOS Inverter-An Intuitive Perspective. Evaluating the Robustness of the CMOS Inverter: The Static Behavior. Performance of CMOS Inverter: The Dynamic Behavior. Power, Energy, and Energy-Delay. Perspective: Technology Scaling and Its Impact on the Inverter Metrics. 6. Designing Combinational Logic Gates in CMOS. Static CMOS Design. Dynamic CMOS Design. How to Choose a Logic Style? Perspective: Gate Design in the Ultra Deep-Submicron Era. 7. Designing Sequential Logic Circuits. Timing Metrics for Sequential Circuits. Classification of Memory Elements. Static Latches and Registers. Dynamic Latches and Registers. Pulse Registers. Sense-Amplifier Based Registers. Pipelining: An Approach to Optimize Sequential Circuits. Non-Bistable Sequential Circuits. Perspective: Choosing a Clocking Strategy. III. A SYSTEM PERSPECTIVE. 8. Implementation Strategies for Digital ICS. From Custom to Semicustom and Structured-Array Design Approaches. Custom Circuit Design. Cell-Based Design Methodology. Array-Based Implementation Approaches. Perspective-The Implementation Platform of the Future. 9. Coping with Interconnect. Capacitive Parasitics. Resistive Parasitics. Inductive Parasitics. Advanced Interconnect Techniques. Perspective: Networks-on-a-Chip. 10. Timing Issues in Digital Circuits. Timing Classification of Digital Systems. Synchronous Design-An In-Depth Perspective. Self-Timed Circuit Design. Synchronizers and Arbiters. Clock Synthesis and Synchronization Using a Phased-Locked Loop. Future Directions and Perspectives. 11. Designing Arithmetic Building Blocks. Datapaths in Digital Processor Architectures. The Adder. The Multiplier. The Shifter. Other Arithmetic Operators. Power and Spped Trade-Offs in Datapath Structures. Perspective: Design as a Trade-off. 12. Designing Memory and Array Structures. The Memory Core. Memory Peripheral Circuitry. Memory Reliability and Yield. Power Dissipation in Memories. Case Studies in Memory Design. Perspective: Semiconductor Memory Trends and Evolutions. Problem Solutions. Index.
2,744 citations
"Bio-Inspired Imprecise Computationa..." refers background in this paper
...An Array multiplier with a -bit multiplicand and -bit multiplier array multiplier consists of similar cells called carry-save adder (CSA) array whose cells are shown by squares, followed by a -bit vector merging adder (whose cells are shown by rounded squares) to convert the carry-save redundant form into regular binary format [34]....
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Book•
21 May 2004
TL;DR: The authors draw upon extensive industry and classroom experience to introduce todays most advanced and effective chip design practices, and present extensively updated coverage of every key element of VLSI design, and illuminate the latest design challenges with 65 nm process examples.
Abstract: For both introductory and advanced courses in VLSI design, this authoritative, comprehensive textbook is highly accessible to beginners, yet offers unparalleled breadth and depth for more experienced readers. The Fourth Edition of CMOS VLSI Design: A Circuits and Systems perspective presents broad and in-depth coverage of the entire field of modern CMOS VLSI Design. The authors draw upon extensive industry and classroom experience to introduce todays most advanced and effective chip design practices. They present extensively updated coverage of every key element of VLSI design, and illuminate the latest design challenges with 65 nm process examples. This book contains unsurpassed circuit-level coverage, as well as a rich set of problems and worked examples that provide deep practical insight to readers at all levels.
2,355 citations
"Bio-Inspired Imprecise Computationa..." refers background in this paper
...5(b) illustrates the internal gate-level structure of each CSA array and also vector merging adder cell [35]....
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...Each cell contains a 2-input AND gate that forms partial product and a full-adder (CSA) to add the partial product into the running sum [35]....
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...Although our main focus is on unsigned multiplication, the basic structure and operation of the signed and unsigned BAM are the same [35]....
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Book•
01 Jan 1980
TL;DR: Students of science and engineering are shown the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving.
Abstract: Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION.
1,024 citations