LOW POWER AND LOW AREA MULTIPLICATION CIRCUITS THROUGH PARTIAL PRODUCT PERFORATION

Focus on hardware-level approximation by introducing the partial product perforation technique for designing approximate multiplication circuits. The partial product perforation method for creating approximate multipliers. It omit the generation of some partial products, thus reducing the number of partial products that have to be accumulated; we decrease the area, power. The major contributions of this work, the software-based perforation technique on the design of hardware circuits, obtaining the optimized design solutions regarding the power–area–error tradeoffs. Analyze in a mathematically rigorous manner the arithmetic accuracy of partial product perforation and prove that it delivers a bounded and predictable output error. Error analysis is not bound to specific multiplier architecture and can be applied with error guarantees to every multiplication circuit regardless of its architecture that compared with the respective exact design, the partial product perforation. Index Terms: Approximate Arithmetic Circuits, Approximate Computing, Approximate Multiplier, Error Analysis & Low Power

Compressor based approximate multiplier architectures for media processing applications

Approximate computing is an attractive technique to gain substantial improvement in the area, speed, and power in applications where exact computation is not required. This paper proposes two improved multiplier designs based on a new 4:2 approximate compressor circuit to simplify the hardware at the partial product reduction stage. The proposed multiplier designs are targeted towards error-tolerant applications. Exhaustive error and hardware analysis has been carried out on the existing and proposed multiplier designs. The results prove that the proposed approximate multiplier architecture performs better than the existing architectures without significant compromise on quality metrics. Experimental results show that die-area and power consumed are reduced upto 28%, and 25.29% respectively in comparison with the existing designs without significant compromise on accuracy

Designing Approximate Computing Circuits with Scalable and Systematic Data-Driven Techniques

Semiconductor feature size has been shrinking significantly in the past decades. This decreasing trend of feature size leads to faster processing speed as well as lower area and power consumption. Among these attributes, power consumption has emerged as the primary concern in the design of integrated circuits in recent years due to the rapid increasing demand of energy efficient Internet of Things (IoT) devices. As a result, low power design approaches for digital circuits have become of great attractive in the past few years. To this end, approximate computing in hardware design has emerged as a promising design technique. It provides design opportunities to improve timing and energy efficiency by relaxing computing quality. This technique is feasible because of the error-resiliency of many emerging resource-hungry computational applications such as multimedia processing and machine learning. Thus, it is reasonable to utilize this characteristic to trade an acceptable amount of computing quality for energy saving. In the literature, most prior works on approximate circuit design focus on using manual design strategies to redesign fundamental computational blocks such as adders and multipliers. However, the manual design techniques are not suitable for system level hardware due to much higher design complexity. In order to tackle this challenge, we focus on designing scalable, systematic and general design methodologies that are applicable on any circuits. In this paper, we present two novel approximate circuit design methods based on machine learning techniques. Both methods skip the complicated manual analysis steps and primarily look at the given input-error pattern to generate approximate circuits. Our first work presents a framework for designing compensation block, an essential component in many approximate circuits, based on feature selection. Our second work further extends and optimizes this framework and integrates data-driven consideration into the design. Several case studies on fixed-width multipliers and other approximate circuits are presented to demonstrate the effectiveness of the proposed design methods. The experimental results show that both of the proposed methods are able to automatically and efficiently design low-error approximate circuits

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

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

Energy-Efficient Approximate Multiplication for Digital Signal Processing and Classification Applications

The need to support various digital signal processing (DSP) and classification applications on energy-constrained devices has steadily grown. Such applications often extensively perform matrix multiplications using fixed-point arithmetic while exhibiting tolerance for some computational errors. Hence, improving the energy efficiency of multiplications is critical. In this brief, we propose multiplier architectures that can tradeoff computational accuracy with energy consumption at design time. Compared with a precise multiplier, the proposed multiplier can consume 58% less energy/op with average computational error of ∼ 1 %. Finally, we demonstrate that such a small computational error does not notably impact the quality of DSP and the accuracy of classification applications. © 1993-2012 IEEE.1