International Technology Roadmap for Semiconductors 2003の要求清浄度について － シリコンウエハ表面と雰囲気環境に要求される清浄度, 分析方法の現状について －

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

Often as the most important arithmetic modules in a processor, adders, multipliers, and dividers determine the performance and energy efficiency of many computing tasks. The demand of higher speed and power efficiency, as well as the feature of error resilience in many applications (e.g., multimedia, recognition, and data analytics), have driven the development of approximate arithmetic design. In this article, a review and classification are presented for the current designs of approximate arithmetic circuits including adders, multipliers, and dividers. A comprehensive and comparative evaluation of their error and circuit characteristics is performed for understanding the features of various designs. By using approximate multipliers and adders, the circuit for an image processing application consumes as little as 47% of the power and 36% of the power-delay product of an accurate design while achieving similar image processing quality. Improvements in delay, power, and area are obtained for the detection of differences in images by using approximate dividers.

A Review, Classification, and Comparative Evaluation of Approximate Arithmetic Circuits

Interconnects have been shown to be a dominant source of energy consumption in modern day System-on-Chip (SoC) designs. With a large (and growing) number of electronic systems being designed with battery considerations in mind, minimizing the energy consumed in on-chip interconnects becomes crucial. Further, the use of nanometer technologies is making it increasingly important to consider reliability issues during the design of SoC communication architectures. Continued supply voltage scaling has led to decreased noise margins, making interconnects more susceptible to noise sources such as crosstalk, power supply noise, radiation induced defects, etc. The resulting transient faults cause the interconnect to behave as an unreliable transport medium for data signals. Therefore, fault tolerant communication mechanism, such as Automatic Repeat Request (ARQ), Forward Error Correction (FEC), etc., which have been widely used in the networking community, are likely to percolate to the SoC domain. This paper presents a survey of techniques for energy efficient on-chip communication. Techniques operating at different levels of the communication design hierarchy are described, including circuit-level techniques, such as low voltage signaling, architecture-level techniques, such as communication architecture selection and bus isolation, system-level techniques, such as communication based power management and dynamic voltage scaling for interconnects, and network-level techniques, such as error resilient encoding for packetized on-chip communication. Emerging technologies, such as Code Division Multiple Access (CDMA) based buses, and wireless interconnects are also surveyed.

A survey of techniques for energy efficient on-chip communication

This paper presents an architectural-space exploration methodology for designing approximate multipliers. Unlike state-of-the-art, our methodology generates various design points by adapting three key parameters: (1) different types of elementary approximate multiply modules, (2) different types of elementary adder modules for summing the partial products, and (3) selection of bits for approximation in a wide-bit multiplier design. Generation and exploration of such a design space enables a wide-range of multipliers with varying approximation levels, each exhibiting distinct area, power, and output quality, and thereby facilitates approximate computing at higher abstraction levels. We synthesized our designs using Synopsys Design Compiler with a TSMC 45nm technology library and verified using ModelSim gate-level simulations. Power and quality evaluations for various designs are performed using PrimeTime and behavioral models, respectively. The selected designs are then deployed in a JPEG application. For reproducibility and to facilitate further research and development at higher abstraction layers, we have released the RTL and behavioral models of these approximate multipliers and adders as an open-source library at https://sourceforge.net/projects/lpaclib/.

Architectural-space exploration of approximate multipliers

Approximate computing explores opportunities that emerge when applications can tolerate error or inexactness. These applications, which range from multimedia processing to machine learning, operate on inherently noisy and imprecise data. We can trade-off some loss in output value integrity for improved processor performance and energy-efficiency. As memory accesses consume substantial latency and energy, we explore load value approximation, a micro architectural technique to learn value patterns and generate approximations for the data. The processor uses these approximate data values to continue executing without incurring the high cost of accessing memory, removing load instructions from the critical path. Load value approximation can also inhibit approximated loads from accessing memory, resulting in energy savings. On a range of PARSEC workloads, we observe up to 28.6% speedup (8.5% on average) and 44.1% energy savings (12.6% on average), while maintaining low output error. By exploiting the approximate nature of applications, we draw closer to the ideal latency and energy of accessing memory.

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Load Value Approximation

Modern processors contain large last level caches (LLCs) that consume substantial energy and area yet are imperative for high performance. Cache designs have improved dramatically by considering reference locality. Data values are also a source of optimization. Compression and deduplication exploit data values to use cache storage more efficiently resulting in smaller caches without sacrificing performance. In multi-megabyte LLCs, many identical or similar values may be cached across multiple blocks simultaneously. This redundancy effectively wastes cache capacity. We observe that a large fraction of cache values exhibit approximate similarity. More specifically, values across cache blocks are not identical but are similar. Coupled with approximate computing which observes that some applications can tolerate error or inexactness, we leverage approximate similarity to design a novel LLC architecture: the Doppelganger cache. The Doppelganger cache associates the tags of multiple similar blocks with a single data array entry to reduce the amount of data stored. Our design achieves 1.55×, 2.55× and 1.41 × reductions in LLC area, dynamic energy and leakage energy without harming performance nor incurring high application error.

Doppelgänger: a cache for approximate computing

The cost of moving and storing data is still a fundamental concern for computer architects. Inefficient handling of data can be attributed to conventional architectures being oblivious to the nature of the values that these data bits carry. We observe the phenomenon of spatio-value similarity, where data elements that are approximately similar in value exhibit spatial regularity in memory. This is inherent to 1) the data values of real-world applications, and 2) the way we store data structures in memory. We propose the Bunker Cache, a design that maps similar data to the same cache storage location based solely on their memory address, sacrificing some application quality loss for greater efficiency. The Bunker Cache enables performance gains (ranging from 1.08x to 1.19x) via reduced cache misses and energy savings (ranging from 1.18x to 1.39x) via reduced off-chip memory accesses and lower cache storage requirements. The Bunker Cache requires only modest changes to cache indexing hardware, integrating easily into commodity systems.

The bunker cache for spatio-value approximation

Approximate computing is the idea that systems can gain performance and energy efficiency if they expend less effort on producing a “perfect” answer. Approximate computing techniques propose various ways of exposing and exploiting accuracy–efficiency tradeoffs. We present a taxonomy that classifies approximate computing techniques according to salient features: visibility, determinism, and coarseness. These axes allow us to address questions about the correctability, reproducibility, and control over accuracy–efficiency tradeoffs of different techniques. We use this taxonomy to inform research challenges in approximate architectures, compilers, and applications.

A Taxonomy of General Purpose Approximate Computing Techniques

General matrix multiplication (GEMM) is universal in various applications, such as signal processing, machine learning, and computer vision. Conventional GEMM hardware architectures based on binary computing exhibit low area and energy efficiency as they scale due to the spatial nature of number representation and computing. Unary computing, on the other hand, can be performed with extremely simple processing units, often just with a single logic gate. But currently there exist no efficient architectures for unary GEMM. In this paper, we present uGEMM, an area- and energy-efficient unary GEMM architecture enabled by novel arithmetic units. The proposed design relaxes previously-imposed constraints on input bit streams---low correlation and long stream length---and achieves superior area and energy efficiency over existing unary systems. Furthermore, uGEMM's output bit streams exhibit higher accuracy and faster convergence, enabling dynamic energy-accuracy scaling on resource-constrained systems.

Joshua San Miguel

Papers

Load Value Approximation

Doppelgänger: a cache for approximate computing

The bunker cache for spatio-value approximation

A Taxonomy of General Purpose Approximate Computing Techniques

uGEMM: unary computing architecture for GEMM applications