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.

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Approximate computing: An emerging paradigm for energy-efficient design

Approximate computing trades off computation quality with effort expended, and as rising performance demands confront plateauing resource budgets, approximate computing has become not merely attractive, but even imperative. In this article, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU, and FPGA), processor components, memory technologies, and so forth, as well as programming frameworks for AC. We classify these techniques based on several key characteristics to emphasize their similarities and differences. The aim of this article is to provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.

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A Survey of Techniques for Approximate Computing

Energy is increasingly a first-order concern in computer systems. Exploiting energy-accuracy trade-offs is an attractive choice in applications that can tolerate inaccuracies. Recent work has explored exposing this trade-off in programming models. A key challenge, though, is how to isolate parts of the program that must be precise from those that can be approximated so that a program functions correctly even as quality of service degrades.We propose using type qualifiers to declare data that may be subject to approximate computation. Using these types, the system automatically maps approximate variables to low-power storage, uses low-power operations, and even applies more energy-efficient algorithms provided by the programmer. In addition, the system can statically guarantee isolation of the precise program component from the approximate component. This allows a programmer to control explicitly how information flows from approximate data to precise data. Importantly, employing static analysis eliminates the need for dynamic checks, further improving energy savings. As a proof of concept, we develop EnerJ, an extension to Java that adds approximate data types. We also propose a hardware architecture that offers explicit approximate storage and computation. We port several applications to EnerJ and show that our extensions are expressive and effective; a small number of annotations lead to significant potential energy savings (10%-50%) at very little accuracy cost.

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EnerJ: approximate data types for safe and general low-power computation

High-performance parallel computer architecture and systems have been improved at a phenomenal rate. In the meantime, VLSI computer-aided design (CAD) software for multibillion-transistor IC design has become increasingly complex and requires prohibitively high computational resources. Recent studies have shown that, numerous CAD problems, with their high computational complexity, can greatly benefit from the fast-increasing parallel computation capabilities. However, parallel programming imposes big challenges for CAD applications. Fully exploiting the computational power of emerging general-purpose and domain-specific multicore/many-core processor systems, calls for fundamental research and engineering practice across every stage of parallel CAD design, from algorithm exploration, programming models, design-time and run-time environment, to CAD applications, such as verification, optimization, and simulation. This journal special section will cover recent progress on parallel CAD research, including algorithm foundations, programming models, parallel architectural-specific optimization, and verification. More specifically, papers with in-depth and extensive coverage of the following topics will be considered, as well as other topics relevant to the design of parallel CAD algorithms and software tools. 1. Parallel algorithm design and specification for CAD applications 2. Parallel programming models and languages of particular use in CAD 3. Runtime support and performance optimization for CAD applications 4. Parallel architecture-specific design and optimization for CAD applications 5. Parallel program debugging and verification techniques particularly relevant for CAD The papers should be submitted via the Manuscript Central website and should adhere to standard ACM TODAES formatting requirements (http://todaes.acm.org/). The page count limit is 25.

Parallel CAD: Algorithm Design and Programming Special Section Call for Papers TODAES: ACM Transactions on Design Automation of Electronic Systems

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%.

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Architecture support for disciplined approximate programming

This paper proposes the design of a ternary inverter that uses low current as input voltage is VDD/2. When the supply voltage is set to 1 V, current supplied by a voltage source as an input voltage VDD/2 is reduced by 22.75% from 1.89μΑ to 1.46μΑ. By connecting ternary inverters back-to-back, a trit-storage element is implemented as a ternary SRAM cell. This paper also presents the first verification of read/write schemes that consider noise margins.

Design and Analysis of a Low-Power Ternary SRAM

Resilient design techniques are used to (i) ensure correct operation under dynamic variations and to (ii) improve design performance (e.g., timing speculation). However, significant overheads (e.g., 16p and 14p energy penalties due to throughput degradation and additional circuits) are incurred by existing resilient design techniques. For instance, resilient designs require additional circuits to detect and correct timing errors. Further, when there is an error, the additional cycles needed to restore a previous correct state degrade throughput, which diminishes the performance benefit of using resilient designs. In this work, we describe an improved methodology for resilient design implementation to minimize the costs of resilience in terms of power, area, and throughput degradation. Our methodology uses two levers: selective-endpoint optimization (i.e., sensitivity-based margin insertion) and clock skew optimization. We integrate the two optimization techniques in an iterative optimization flow which comprehends toggle rate information and the trade-off between cost of resilience and margin on combinational paths. Since the error-detection network can result in up to 9p additional wirelength cost, we also propose a matching-based algorithm for construction of the error-detection network to minimize this resilience overhead. Further, our implementations comprehend the impacts of signoff corners (in particular, hold constraints, and use of typical vs. slow libraries) and process variation, which are typically omitted in previous studies of resilience trade-offs. Our proposed flow achieves energy reductions of up to 21p and 10p compared to a conventional (with only margin used to attain robustness) design and a brute-force implementation (i.e., a typical resilient design, where resilient endpoints are (greedily) instantiated at timing-critical endpoints), respectively. We show that these benefits increase in the context of an adaptive voltage scaling strategy.

An Improved Methodology for Resilient Design Implementation

A power-gating circuit and devices including the same are provided. The power-gating circuit includes a flip-flop configured to receive a first power supply voltage and a gated clock signal to operate and a switch circuit connected between a first power supply voltage source configured to supply the first power supply voltage and a second power supply voltage source configured to supply a second power supply voltage. The switch circuit includes a first switch configured to be connected between the first power supply voltage source and the second power supply voltage source and to operate in response to a clock enable signal and a second switch configured to be connected between the first power supply voltage source and the second power supply voltage source and to operate in response to the first power supply voltage.

Data-retained power-gating circuit and devices including the same

The portability of emerging computing systems demands further reduction in the power consumption of their components. Approximate computing can reduce power consumption by using a simplified or an inaccurate circuit. In this paper, the energy efficiency of a finite impulse response (FIR) filter is improved through approximate computing. We propose an approximate synthesis technique for an energy-efficient FIR filter with an acceptable level of accuracy. We employ the common subexpression elimination (CSE) algorithm to implement the FIR filter and replace conventional adder/subtractors with approximate ones. While yielding acceptable rates of accuracy, the proposed flow can attain a maximum energy saving of 50.7% in comparison with conventional FIR filter designs.

Novel approximate synthesis flow for energy-efficient FIR filter

Logic synthesis has been increasingly important to accelerate the development of high-level systems. However, in multi-valued logic, logic synthesis methods that can process emerging devices are deficient. We propose and automate a method to synthesize ternary logic circuits. Our design of ternary logic circuits is based on static gate design, and exploits carbon nanotube field-effect transistors. We optimize ternary logic circuits by minimizing the number of transistors with a modified Quine-McCluskey algorithm. Our proposed method has improved power-delay product by 52.72 % over the state-of-the-art method for a ternary half adder, and by 68.06 % for a ternary multiplier. We also have improved power-delay product by 37.30 % over the state-of-the-art method for a ternary full adder that has high load capacitance. Our design has an average of 42.43 % fewer transistors than the existing design for circuits that have large number of inputs. As circuits become larger, the improved power-delay product and reduced transistor count are advantageous.

Seokhyeong Kang

Papers

Design and Analysis of a Low-Power Ternary SRAM

An Improved Methodology for Resilient Design Implementation

Data-retained power-gating circuit and devices including the same

Novel approximate synthesis flow for energy-efficient FIR filter

Ternary Logic Synthesis with Modified Quine-McCluskey Algorithm