High speed modified carry save adder using a structure of multiplexers

Adders are the heart of data path circuits for any processor in digital computer and signal processing systems. Growth in technology keeps supporting efficient design of binary adders for high speed applications. In this paper, a fast and area-efficient modified carry save adder (CSA) is presented. A multiplexer based design of full adder is proposed to implement the structure of the CSA. The proposed design of full adder is employed in designing all stages of traditional CSA. By modifying the design of full adder in CSA, the complexity and area of the design can be reduced, resulting in reduced delay time. The VHDL implementations of CSA adders including (the proposed version, traditional CSA, and modified CSAs presented in literature) are simulated using Quartus II synthesis software tool with the altera FPGA EP2C5T144C6 device (Cyclone II). Simulation results of 64-bit adder designs demonstrate the average improvement of 17.75%, 1.60%, and 8.81% respectively for the worst case time, thermal power dissipation and number of FPGA logic elements

Optimisations arithmétiques et synthèse de haut niveau

High-level synthesis (HLS) tools offer increased productivity regarding FPGA programming.However, due to their relatively young nature, they still lack many arithmetic optimizations.This thesis proposes safe arithmetic optimizations that should always be applied.These optimizations are simple operator specializations, following the C semantic.Other require to a lift the semantic embedded in high-level input program languages, which are inherited from software programming, for an improved accuracy/cost/performance ratio.To demonstrate this claim, the sum-of-product of floating-point numbers is used as a case study. The sum is performed on a fixed-point format, which is tailored to the application, according to the context in which the operator is instantiated.In some cases, there is not enough information about the input data to tailor the fixed-point accumulator.The fall-back strategy used in this thesis is to generate an accumulator covering the entire floating-point range.This thesis explores different strategies for implementing such a large accumulator, including new ones.The use of a 2's complement representation instead of a sign+magnitude is demonstrated to save resources and to reduce the accumulation loop delay.Based on a tapered precision scheme and an exact accumulator, the posit number systems claims to be a candidate to replace the IEEE floating-point format.A throughout analysis of posit operators is performed, using the same level of hardware optimization as state-of-the-art floating-point operators.Their cost remains much higher that their floating-point counterparts in terms of resource usage and performance. Finally, this thesis presents a compatibility layer for HLS tools that allows one code to be deployed on multiple tools.This library implements a strongly typed custom size integer type along side a set of optimized custom operators.À cause de la nature relativement jeune des outils de synthèse de haut-niveau (HLS), de nombreuses optimisations arithmétiques n'y sont pas encore implémentées. Cette thèse propose des optimisations arithmétiques se servant du contexte spécifique dans lequel les opérateurs sont instanciés.Certaines optimisations sont de simples spécialisations d'opérateurs, respectant la sémantique du C.D'autres nécéssitent de s'éloigner de cette sémantique pour améliorer le compromis précision/coût/performance.Cette proposition est démontré sur des sommes de produits de nombres flottants.La somme est réalisée dans un format en virgule-fixe défini par son contexte.Quand trop peu d’informations sont disponibles pour définir ce format en virgule-fixe, une stratégie est de générer un accumulateur couvrant l'intégralité du format flottant.Cette thèse explore plusieurs implémentations d'un tel accumulateur.L'utilisation d'une représentation en complément à deux permet de réduire le chemin critique de la boucle d'accumulation, ainsi que la quantité de ressources utilisées. Un format alternatif aux nombres flottants, appelé posit, propose d'utiliser un encodage à précision variable.De plus, ce format est augmenté par un accumulateur exact.Pour évaluer précisément le coût matériel de ce format, cette thèse présente des architectures d'opérateurs posits, implémentés avec le même degré d'optimisation que celui de l'état de l'art des opérateurs flottants.Une analyse détaillée montre que le coût des opérateurs posits est malgré tout bien plus élevé que celui de leurs équivalents flottants.Enfin, cette thèse présente une couche de compatibilité entre outils de HLS, permettant de viser plusieurs outils avec un seul code. Cette bibliothèque implémente un type d'entiers de taille variable, avec de plus une sémantique strictement typée, ainsi qu'un ensemble d'opérateurs ad-hoc optimisés

A high-performance inner-product processor for real and complex numbers.

A novel, high-performance fixed-point inner-product processor based on a redundant binary number system is investigated in this dissertation. This scheme decreases the number of partial products to 50%, while achieving better speed and area performance, as well as providing pipeline extension opportunities. When modified Booth coding is used, partial products are reduced by almost 75%, thereby significantly reducing the multiplier addition depth. The design is applicable for digital signal and image processing applications that require real and/or complex numbers inner-product arithmetic, such as digital filters, correlation and convolution. This design is well suited for VLSI implementation and can also be embedded as an inner-product core inside a general purpose or DSP FPGA-based processor. Dynamic control of the computing structure permits different computations, such as a variety of inner-product real and complex number computations, parallel multiplication for real and complex numbers, and real and complex number division. The same structure can also be controlled to accept redundant binary number inputs for multiplication and inner-product computations. An improved 2's-complement to redundant binary converter is also presented

A VLSI implementation of DCT using pass transistor technology

A VLSI design for performing the Discrete Cosine Transform (DCT) operation on image blocks of size 16 x 16 in a real time fashion operating at 34 MHz (worst case) is presented. The process used was Hewlett-Packard's CMOS26--A 3 metal CMOS process with a minimum feature size of 0.75 micron. The design is based on Multiply-Accumulate (MAC) cells which make use of a modified Booth recoding algorithm for performing multiplication. The design of these cells is straight forward, and the layouts are regular with no complex routing. Two versions of these MAC cells were designed and their layouts completed. Both versions were simulated using SPICE to estimate their performance. One version is slightly faster at the cost of larger silicon area and higher power consumption. An improvement in speed of almost 20 percent is achieved after several iterations of simulation and re-sizing

VLSI Circuits for Approximate Computing

Approximate Computing has recently emerged as a promising solution to enhance circuits performance by relaxing the requisite on exact calculations. Multimedia and Machine Learning constitute a typical example of error resilient, albeit compute-intensive, applications. In this dissertation, the design and optimization of approximate fundamental VLSI digital blocks is investigated. In chapter one the theoretical motivations of Approximate Computing, from the VLSI perspective, are discussed. In chapter two my research activity about approximate adders is reported. In this chapter approximate adders for both traditional non-error tolerant applications and error resilient applications are discussed. In chapter three precision-scalable units are investigated. Real-time precision scalability allows adapting the precision level of the unit with the precision requirements of the applications. In this context my research activities regarding approximate Multiply-and-Accumulate and memory units are described. In chapter four a precision-scalable approximate convolver for computer vision applications is discussed. This is composed of both the approximate Multiply-and-Accumulate and memory units, presented in the chapter three

A Study on Efficient Designs of Approximate Arithmetic Circuits

Approximate computing is a popular field where accuracy is traded with energy. It can benefit applications such as multimedia, mobile computing and machine learning which are inherently error resilient. Error introduced in these applications to a certain degree is beyond human perception. This flexibility can be exploited to design area, delay and power efficient architectures. However, care must be taken on how approximation compromises the correctness of results. This research work aims to provide approximate hardware architectures with error metrics and design metrics analyzed and their effects in image processing applications. Firstly, we study and propose unsigned array multipliers based on probability statistics and with approximate 4-2 compressors, full adders and half adders. This work deals with a new design approach for approximation of multipliers. The partial products of the multiplier are altered to introduce varying probability terms. Logic complexity of approximation is varied for the accumulation of altered partial products based on their probability. The proposed approximation is utilized in two variants of 16-bit multipliers. Synthesis results reveal that two proposed multipliers achieve power savings of 72% and 38% respectively compared to an exact multiplier. They have better precision when compared to existing approximate multipliers. Mean relative error distance (MRED) figures are as low as 7.6% and 0.02% for the proposed approximate multipliers, which are better than the previous state-of-the-art works. Performance of the proposed multipliers is evaluated with geometric mean filtering application, where one of the proposed models achieves the highest peak signal to noise ratio (PSNR). Second, approximation is proposed for signed Booth multiplication. Approximation is introduced in partial product generation and partial product accumulation circuits. In this work, three multipliers (ABM-M1, ABM-M2, and ABM-M3) are proposed in which the modified Booth algorithm is approximated. In all three designs, approximate Booth partial product generators are designed with different variations of approximation. The approximations are performed by reducing the logic complexity of the Booth partial product generator, and the accumulation of partial products is slightly modified to improve circuit performance. Compared to the exact Booth multiplier, ABM-M1 achieves up to 15% reduction in power consumption with an MRED value of 7.9 × 10-4. ABM-M2 has power savings of up to 60% with an MRED of 1.1 × 10-1. ABM-M3 has power savings of up to 50% with an MRED of 3.4 × 10-3. Compared to existing approximate Booth multipliers, the proposed multipliers ABM-M1 and ABM-M3 achieve up to a 41% reduction in power consumption while exhibiting very similar error metrics. Image multiplication and matrix multiplication are used as case studies to illustrate the high performance of the proposed approximate multipliers. Third, distributed arithmetic based sum of products units approximation is analyzed. Sum of products units are key elements in many digital signal processing applications. Three approximate sum of products models which are based on distributed arithmetic are proposed. They are designed for different levels of accuracy. First model of approximate sum of products achieves an improvement up to 64% on area and 70% on power, when compared to conventional unit. Other two models provide an improvement of 32% and 48% on area and 54% and 58% on power, respectively, with a reduced error rate compared to the first model. Third model achieves MRED and normalized mean error distance (NMED) as low as 0.05% and 0.009%. Performance of approximate units is evaluated with a noisy image smoothing application, where the proposed models are capable of achieving higher PSNR than existing state of the art techniques. Fourth, approximation is applied in division architecture. Two approximation models are proposed for restoring divider. In the first design, approximation is performed at circuit level, where approximate divider cells are utilized in place of exact ones by simplifying the logic equations. In the second model, restoring divider is analyzed strategically and number of restoring divider cells are reduced by finding the portions of divisor and dividend with significant information. An approximation factor $p$ is used in both designs. In model 1, the design with p=8 has a 58% reduction in both area and power consumption compared to exact design, with a Q-MRED of 1.909 × 10-2 and Q-NMED of 0.449 × 10-2. The second model with an approximation factor p=4 has 54% area savings and 62% power savings compared to exact design. The proposed models are found to have better error metrics compared to existing designs, with better performance at similar error values. A change detection image processing application is used for real time assessment of proposed and existing approximate dividers and one of the models achieves a PSNR of 54.27 dB

Energy-efficient Hardware Accelerator Design for Convolutional Neural Network

Department of Electrical EngineeringConvolutional neural network (CNN) is a class of deep neural networks, which shows a superior performance in handling images. Due to its performance, CNN is widely used to classify an object or detect the position of object from an image. CNN can be implemented on either edge devices or cloud servers. Since the cloud servers have high computational capabilities, CNN on cloud can perform a large number of tasks at once with a high throughput. However, CNN on the cloud requires a long round-trip time. To infer an image picture, data from a sensor should be uploaded to the cloud server, and processed information from CNN is transferred to the user. If an application requires a rapid response in a certain situation, the long round-trip time of cloud is a critical issue. On the other hand, an edge device has a very short latency, even though it has limited computing resources. In addition, since the edge device does not require the transmission of images over network, its performance would not be affected by the bandwidth of network. Because of these features, it is ef???cient to use the cloud for CNN computing in most cases, but the edge device is preferred in some applications. For example, CNN algorithm for autonomous car requires rapid responses. CNN on cloud requires transmission and reception of images through network, and it cannot respond quickly to users. This problem becomes more serious when a high-resolution input image is required. On the other hand, the edge device does not require the data transmission, and it can response very quickly. Edge devices would be also suitable for CNN applications involving privacy or security. However, the edge device has limited energy resource, the energy ef???ciency of the CNN accelerator is a very important issue. Embedded CNN accelerator consists of off-chip memory, host CPU and a hardware accelerator. The hardware accelerator consists of the main controller, global buffer and arrays of processing elements (PE). It also has a separate compression module and activation module. In this dissertation, we propose energy-ef???cient design in three different parts. First, we propose a time-multiplexing PE to increase the energy ef???ciency of multipliers. From the fact the feature maps have small values which are de???ned as non-outliers, we increase the energy ef???ciency for computing non-outliers. For further improving the energy efficiency of PE, approximate computing is also introduced. Method to optimize the trade-off between accuracy and energy is also proposed. Second, we investigate the energy-ef???cient accuracy recovery circuit. For the implementation of CNN on edge, CNN loops are usually tiled. During tiling of CNN loops, accuracy can be degraded. We analyze the accuracy reduction due to tiling and recover accuracy by extending et al. of partial sums with very small energy overhead. Third, we reduce energy consumption for DRAM accessing. CNN requires massive data transmission between on-chip and off-chip memory. The energy consumption of data transmission accounts for a large portion of total energy consumption. We propose a spatial correlation-aware compression algorithm to reduce the transmission of feature maps. In each of these three levels, this dissertation proposes novel optimization and design ???ows which increase the energy ef???ciency of CNN accelerator on edge.clos