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

Approximation can increase performance or reduce power consumption with a simplified or inaccurate circuit in application contexts where strict requirements are relaxed. For applications related to human senses, approximate arithmetic can be used to generate sufficient results rather than absolutely accurate results. Approximate design exploits a tradeoff of accuracy in computation versus performance and power. However, required accuracy varies according to applications, and 100% accurate results are still required in some situations. In this paper, we propose an accuracy-configurable approximate (ACA) adder for which the accuracy of results is configurable during runtime. Because of its configurability, the ACA adder can adaptively operate in both approximate (inaccurate) mode and accurate mode. The proposed adder can achieve significant throughput improvement and total power reduction over conventional adder designs. It can be used in accuracy-configurable applications, and improves the achievable tradeoff between performance/power and quality. The ACA adder achieves approximately 30% power reduction versus the conventional pipelined adder at the relaxed accuracy requirement.

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Accuracy-configurable adder for approximate arithmetic designs

Modern digital IC designs have a critical operating point, or “wall of slack”, that limits voltage scaling. Even with an error-tolerance mechanism, scaling voltage below a critical voltage - so-called overscaling - results in more timing errors than can be effectively detected or corrected. This limits the effectiveness of voltage scaling in trading off system reliability and power. We propose a design-level approach to trading off reliability and voltage (power) in, e.g., microprocessor designs. We increase the range of voltage values at which the (timing) error rate is acceptable; we achieve this through techniques for power-aware slack redistribution that shift the timing slack of frequently-exercised, near-critical timing paths in a power- and area-efficient manner. The resulting designs heuristically minimize the voltage at which the maximum allowable error rate is encountered, thus minimizing power consumption for a prescribed maximum error rate and allowing the design to fail more gracefully. Compared with baseline designs, we achieve a maximum of 32.8% and an average of 12.5% power reduction at an error rate of 2%. The area overhead of our techniques, as evaluated through physical implementation (synthesis, placement and routing), is no more than 2.7%.

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Slack redistribution for graceful degradation under voltage overscaling

Current processor designs have a critical operating point that sets a hard limit on voltage scaling. Any scaling beyond the critical voltage results in exceeding the maximum allowable error rate, i.e., there are more timing errors than can be effectively and gainfully detected or corrected by an error-tolerance mechanism. This limits the effectiveness of voltage scaling as a knob for reliability/power tradeoffs. In this paper, we present power-aware slack redistribution, a novel design-level approach to allow voltage/reliability tradeoffs in processors. Techniques based on power-aware slack redistribution reapportion timing slack of the frequently-occurring, near-critical timing paths of a processor in a power- and area-efficient manner, such that we increase the range of voltages over which the incidence of operational (timing) errors is acceptable. This results in soft architectures — designs that fail gracefully, allowing us to perform reliability/power tradeoffs by reducing voltage up to the point that produces maximum allowable errors for our application. The goal of our optimization is to minimize the voltage at which a soft architecture encounters the maximum allowable error rate, thus maximizing the range over which voltage scaling is possible and minimizing power consumption for a given error rate. Our experiments demonstrate 23% power savings over the baseline design at an error rate of 1%. Observed power reductions are 29%, 29%, 19%, and 20% for error rates of 2%, 4%, 8%, and 16% respectively. Benefits are higher in the face of error recovery using Razor. Area overhead of our techniques is up to 2.7%.

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Designing a processor from the ground up to allow voltage/reliability tradeoffs

The well-studied gate-sizing optimization is a major contributor to IC power-performance tradeoffs. Viable optimizers must accurately model circuit timing, satisfy a variety of constraints, scale to large circuits, and effectively utilize a large (but finite) number of possible gate configurations, including V t and L g . Within the research-oriented infrastructure used in the ISPD 2012 Gate Sizing Contest, we develop a metaheuristic approach to gate sizing that integrates timing and power optimization, and handles several types of constraints. Our solutions are evaluated using a rigorous protocol that computes circuit delay with Synopsys PrimeTime. Our implementation Trident outperforms the best-reported results on all but one of the ISPD 2012 benchmarks. Compared to the 2012 contest winner, we further reduce leakage power by an average of 43%.

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Sensitivity-guided metaheuristics for accurate discrete gate sizing

We propose a logic synthesis methodology with a novel low-power circuit structure for ternary logic. The proposed methodology synthesizes a ternary function as a ternary logic gate using carbon nanotube field-effect transistors (CNTFETs). The circuit structure uses the body effect to mitigate the excessive power consumption for the third logic value. Energy-efficient ternary logic circuits are designed with a combination of synthesized low-power ternary logic gates. The proposed methodology is applicable to both unbalanced (0, 1, 2) and balanced (−1, 0, 1) ternary logic. To verify the improvement in energy efficiency, we have designed various ternary arithmetic logic circuits using the proposed methodology. The proposed ternary full adder has a significant improvement in the power-delay product (PDP) over previous designs. Ternary benchmark circuits have been designed to show that complex ternary functions can be designed to more efficient circuits with the proposed methodology.

Seokhyeong Kang

Papers

Accuracy-configurable adder for approximate arithmetic designs

Slack redistribution for graceful degradation under voltage overscaling

Designing a processor from the ground up to allow voltage/reliability tradeoffs

Sensitivity-guided metaheuristics for accurate discrete gate sizing

A Logic Synthesis Methodology for Low-Power Ternary Logic Circuits