A Survey on Approximate Multiplier Designs for Energy Efficiency: From Algorithms to Circuits

Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially in error-resilient applications. The computation error and energy efficiency largely depend on how and where the approximation is introduced into a design. Thus, this article aims to provide a comprehensive review of the approximation techniques in multiplier designs ranging from algorithms and architectures to circuits. We have implemented representative approximate multiplier designs in each category to understand the impact of the design techniques on accuracy and efficiency. The designs can then be effectively deployed in high-level applications, such as machine learning, to gain energy efficiency at the cost of slight accuracy loss.Comment: 38 pages, 37 figure

Approximate Computing Survey, Part II: Application-Specific & Architectural Approximation Techniques and Applications

The challenging deployment of compute-intensive applications from domains such Artificial Intelligence (AI) and Digital Signal Processing (DSP), forces the community of computing systems to explore new design approaches. Approximate Computing appears as an emerging solution, allowing to tune the quality of results in the design of a system in order to improve the energy efficiency and/or performance. This radical paradigm shift has attracted interest from both academia and industry, resulting in significant research on approximation techniques and methodologies at different design layers (from system down to integrated circuits). Motivated by the wide appeal of Approximate Computing over the last 10 years, we conduct a two-part survey to cover key aspects (e.g., terminology and applications) and review the state-of-the art approximation techniques from all layers of the traditional computing stack. In Part II of our survey, we classify and present the technical details of application-specific and architectural approximation techniques, which both target the design of resource-efficient processors/accelerators & systems. Moreover, we present a detailed analysis of the application spectrum of Approximate Computing and discuss open challenges and future directions.Comment: Under Review at ACM Computing Survey

Design and Evaluation of Approximate Logarithmic Multipliers for Low Power Error-Tolerant Applications

In this work, the designs of both non-iterative and iterative approximate logarithmic multipliers (LMs) are studied to further reduce power consumption and improve performance. Non-iterative approximate LMs (ALMs) that use three inexact mantissa adders, are presented. The proposed iterative approximate logarithmic multipliers (IALMs) use a set-one adder in both mantissa adders during an iteration; they also use lower-part-or adders and approximate mirror adders for the final addition. Error analysis and simulation results are also provided; it is found that the proposed approximate LMs with an appropriate number of inexact bits achieve a higher accuracy and lower power consumption than conventional LMs using exact units. Compared with conventional LMs with exact units, the normalized mean error distance (NMED) of 16-bit approximate LMs is decreased by up to 18% and the power-delay product (PDP) has a reduction of up to 37%. The proposed approximate LMs are also compared with previous approximate multipliers; it is found that the proposed approximate LMs are best suitable for applications allowing larger errors, but requiring lower energy consumption and low power. Approximate Booth multipliers fit applications with less stringent power requirements, but also requiring smaller errors. Case studies for error-tolerant computing applications are provided

Approximate Computing Survey, Part I: Terminology and Software & Hardware Approximation Techniques

The rapid growth of demanding applications in domains applying multimedia processing and machine learning has marked a new era for edge and cloud computing. These applications involve massive data and compute-intensive tasks, and thus, typical computing paradigms in embedded systems and data centers are stressed to meet the worldwide demand for high performance. Concurrently, the landscape of the semiconductor field in the last 15 years has constituted power as a first-class design concern. As a result, the community of computing systems is forced to find alternative design approaches to facilitate high-performance and/or power-efficient computing. Among the examined solutions, Approximate Computing has attracted an ever-increasing interest, with research works applying approximations across the entire traditional computing stack, i.e., at software, hardware, and architectural levels. Over the last decade, there is a plethora of approximation techniques in software (programs, frameworks, compilers, runtimes, languages), hardware (circuits, accelerators), and architectures (processors, memories). The current article is Part I of our comprehensive survey on Approximate Computing, and it reviews its motivation, terminology and principles, as well it classifies and presents the technical details of the state-of-the-art software and hardware approximation techniques.Comment: Under Review at ACM Computing Survey

Improving the Hardware Performance of Arithmetic Circuits using Approximate Computing

An application that can produce a useful result despite some level of computational error is said to be error resilient. Approximate computing can be applied to error resilient applications by intentionally introducing error to the computation in order to improve performance, and it has been shown that approximation is especially well-suited for application in arithmetic computing hardware. In this thesis, novel approximate arithmetic architectures are proposed for three different operations, namely multiplication, division, and the multiply accumulate (MAC) operation. For all designs, accuracy is evaluated in terms of mean relative error distance (MRED) and normalized mean error distance (NMED), while hardware performance is reported in terms of critical path delay, area, and power consumption. Three approximate Booth multipliers (ABM-M1, ABM-M2, ABM-M3) are designed in which two novel inexact partial product generators are used to reduce the dimensions of the partial product matrix. The proposed multipliers are compared to other state-of-the-art designs in terms of both accuracy and hardware performance, and are found to reduce power consumption by up to 56% when compared to the exact multiplier. The function of the multipliers is verified in several image processing applications. Two approximate restoring dividers (AXRD-M1, AXRD-M2) are proposed along with a novel inexact restoring divider cell. In the first divider, the conventional cells are replaced with the proposed inexact cells in several columns. The second divider computes only a subset of the trial subtractions, after which the divisor and partial remainder are rounded and encoded so that they may be used to estimate the remaining quotient bits. The proposed dividers are evaluated for accuracy and hardware performance alongside several benchmarking designs, and their function is verified using change detection and foreground extraction applications. An approximate MAC unit is presented in which the multiplication is implemented using a modified version of ABM-M3. The delay is reduced by using a fused architecture where the accumulator is summed as part of the multiplier compression. The accuracy and hardware savings of the MAC unit are measured against several works from the literature, and the design is utilized in a number of convolution operations

Energy-efficient embedded machine learning algorithms for smart sensing systems

Embedded autonomous electronic systems are required in numerous application domains such as Internet of Things (IoT), wearable devices, and biomedical systems. Embedded electronic systems usually host sensors, and each sensor hosts multiple input channels (e.g., tactile, vision), tightly coupled to the electronic computing unit (ECU). The ECU extracts information by often employing sophisticated methods, e.g., Machine Learning. However, embedding Machine Learning algorithms poses essential challenges in terms of hardware resources and energy consumption because of: 1) the high amount of data to be processed; 2) computationally demanding methods. Leveraging on the trade-off between quality requirements versus computational complexity and time latency could reduce the system complexity without affecting the performance. The objectives of the thesis are to develop: 1) energy-efficient arithmetic circuits outperforming state of the art solutions for embedded machine learning algorithms, 2) an energy-efficient embedded electronic system for the \u201celectronic-skin\u201d (e-skin) application. As such, this thesis exploits two main approaches: Approximate Computing: In recent years, the approximate computing paradigm became a significant major field of research since it is able to enhance the energy efficiency and performance of digital systems. \u201cApproximate Computing\u201d(AC) turned out to be a practical approach to trade accuracy for better power, latency, and size . AC targets error-resilient applications and offers promising benefits by conserving some resources. Usually, approximate results are acceptable for many applications, e.g., tactile data processing,image processing , and data mining ; thus, it is highly recommended to take advantage of energy reduction with minimal variation in performance . In our work, we developed two approximate multipliers: 1) the first one is called \u201cMETA\u201d multiplier and is based on the Error Tolerant Adder (ETA), 2) the second one is called \u201cApproximate Baugh-Wooley(BW)\u201d multiplier where the approximations are implemented in the generation of the partial products. We showed that the proposed approximate arithmetic circuits could achieve a relevant reduction in power consumption and time delay around 80.4% and 24%, respectively, with respect to the exact BW multiplier. Next, to prove the feasibility of AC in real world applications, we explored the approximate multipliers on a case study as the e-skin application. The e-skin application is defined as multiple sensing components, including 1) structural materials, 2) signal processing, 3) data acquisition, and 4) data processing. Particularly, processing the originated data from the e-skin into low or high-level information is the main problem to be addressed by the embedded electronic system. Many studies have shown that Machine Learning is a promising approach in processing tactile data when classifying input touch modalities. In our work, we proposed a methodology for evaluating the behavior of the system when introducing approximate arithmetic circuits in the main stages (i.e., signal and data processing stages) of the system. Based on the proposed methodology, we first implemented the approximate multipliers on the low-pass Finite Impulse Response (FIR) filter in the signal processing stage of the application. We noticed that the FIR filter based on (Approx-BW) outperforms state of the art solutions, while respecting the tradeoff between accuracy and power consumption, with an SNR degradation of 1.39dB. Second, we implemented approximate adders and multipliers respectively into the Coordinate Rotational Digital Computer (CORDIC) and the Singular Value Decomposition (SVD) circuits; since CORDIC and SVD take a significant part of the computationally expensive Machine Learning algorithms employed in tactile data processing. We showed benefits of up to 21% and 19% in power reduction at the cost of less than 5% accuracy loss for CORDIC and SVD circuits when scaling the number of approximated bits. 2) Parallel Computing Platforms (PCP): Exploiting parallel architectures for near-threshold computing based on multi-core clusters is a promising approach to improve the performance of smart sensing systems. In our work, we exploited a novel computing platform embedding a Parallel Ultra Low Power processor (PULP), called \u201cMr. Wolf,\u201d for the implementation of Machine Learning (ML) algorithms for touch modalities classification. First, we tested the ML algorithms at the software level; for RGB images as a case study and tactile dataset, we achieved accuracy respectively equal to 97% and 83.5%. After validating the effectiveness of the ML algorithm at the software level, we performed the on-board classification of two touch modalities, demonstrating the promising use of Mr. Wolf for smart sensing systems. Moreover, we proposed a memory management strategy for storing the needed amount of trained tensors (i.e., 50 trained tensors for each class) in the on-chip memory. We evaluated the execution cycles for Mr. Wolf using a single core, 2 cores, and 3 cores, taking advantage of the benefits of the parallelization. We presented a comparison with the popular low power ARM Cortex-M4F microcontroller employed, usually for battery-operated devices. We showed that the ML algorithm on the proposed platform runs 3.7 times faster than ARM Cortex M4F (STM32F40), consuming only 28 mW. The proposed platform achieves 15 7 better energy efficiency than the classification done on the STM32F40, consuming 81mJ per classification and 150 pJ per operation

Playing with number representations and operator-level approximations

International audienceEnergy consumption is one of the major issues in computing today shared by all domains in computer science, from high-performance computing to embedded systems. The two main factors that influence energy consumption is the execution time and data volume. In the recent years, approximation is receiving renewed interests to improve both speed and energy consumption in embedded systems. Many applications in embedded systems do not require high precision/accuracy, and both software designers and hardware designers often seek for a golden point of the compromise between accuracy, speed, energy, and area cost in several layers with a broad range from application, software levels to architecture, circuit levels. Various techniques for approximate computing (AC) augment the design space by providing another set of design knobs for performance-accuracy trade-off. Stochastic computing (SC) is also seen as an alternative to conventional computing, since requiring less hardware and being more tolerant to soft errors at the expense of higher latency. SC uses a probabilistic model of computation and requires less hardware to implement complex operations. This talk will review the main techniques for operator-level approximations using various number representations and by playing with data word-length and types of operators, to show their benefit and drawbacks in terms of energy efficiency. We will also introduce the basic concepts of stochastic computing as well as its advantages in terms of robustness to errors and fair limitations