Flexible Multiple-Precision Fused Arithmetic Units for Efficient Deep Learning Computation

Deep Learning has achieved great success in recent years. In many fields of applications, such as computer vision, biomedical analysis, and natural language processing, deep learning can achieve a performance that is even better than human-level. However, behind this superior performance is the expensive hardware cost required to implement deep learning operations. Deep learning operations are both computation intensive and memory intensive. Many research works in the literature focused on improving the efficiency of deep learning operations. In this thesis, special focus is put on improving deep learning computation and several efficient arithmetic unit architectures are proposed and optimized for deep learning computation. The contents of this thesis can be divided into three parts: (1) the optimization of general-purpose arithmetic units for deep learning computation; (2) the design of deep learning specific arithmetic units; (3) the optimization of deep learning computation using 3D memory architecture. Deep learning models are usually trained on graphics processing unit (GPU) and the computations are done with single-precision floating-point numbers. However, recent works proved that deep learning computation can be accomplished with low precision numbers. The half-precision numbers are becoming more and more popular in deep learning computation due to their lower hardware cost compared to the single-precision numbers. In conventional floating-point arithmetic units, single-precision and beyond are well supported to achieve a better precision. However, for deep learning computation, since the computations are intensive, low precision computation is desired to achieve better throughput. As the popularity of half-precision raises, half-precision operations are also need to be supported. Moreover, the deep learning computation contains many dot-product operations and therefore, the support of mixed-precision dot-product operations can be explored in a multiple-precision architecture. In this thesis, a multiple-precision fused multiply-add (FMA) architecture is proposed. It supports half/single/double/quadruple-precision FMA operations. In addition, it also supports 2-term mixed-precision dot-product operations. Compared to the conventional multiple-precision FMA architecture, the newly added half-precision support and mixed-precision dot-product only bring minor resource overhead. The proposed FMA can be used as general-purpose arithmetic unit. Due to the support of parallel half-precision computations and mixed-precision dot-product computations, it is especially suitable for deep learning computation. For the design of deep learning specific computation unit, more optimizations can be performed. First, a fixed-point and floating-point merged multiply-accumulate (MAC) unit is proposed. As deep learning computation can be accomplished with low precision number formats, the support of high precision floating-point operations can be eliminated. In this design, the half-precision floating-point format is supported to provide a large dynamic range to handle small gradients for deep learning training. For deep learning inference, 8-bit fixed-point 2-term dot-product computation is supported. Second, a flexible multiple-precision MAC unit architecture is proposed. The proposed MAC unit supports both fixed-point operations and floating-point operations. For floating-point format, the proposed unit supports one 16-bit MAC operation or sum of two 8-bit multiplications plus a 16-bit addend. To make the proposed MAC unit more versatile, the bit-width of exponent and mantissa can be flexibly exchanged. By setting the bit-width of exponent to zero, the proposed MAC unit also supports fixed-point operations. For fixed-point format, the proposed unit supports one 16-bit MAC or sum of two 8-bit multiplications plus a 16-bit addend. Moreover, the proposed unit can be further divided to support sum of four 4-bit multiplications plus a 16-bit addend. At the lowest precision, the proposed MAC unit supports accumulating of eight 1-bit logic AND operations to enable the support of binary neural networks. Finally, a MAC architecture based on the posit format, a promising numerical format in deep learning computation, is proposed to facilitate the use of posit format in deep learning computation. In addition to the above mention arithmetic units, an improved hybrid memory cube (HMC) architecture is proposed for weight-sharing deep neural network processing. By modifying the HMC instruction set and HMC logic layer, the major part of the deep learning computation can be accomplished inside memory. The proposed design reduces the memory bandwidth requirements and thus reduces the energy consumed by memory data transfer

The Algorithms for FPGA Implementation of Sparse Matrices Multiplication

In comparison to dense matrices multiplication, sparse matrices multiplication real performance for CPU is roughly 5--100 times lower when expressed in GFLOPs. For sparse matrices, microprocessors spend most of the time on comparing matrices indices rather than performing floating-point multiply and add operations. For 16-bit integer operations, like indices comparisons, computational power of the FPGA significantly surpasses that of CPU. Consequently, this paper presents a novel theoretical study how matrices sparsity factor influences the indices comparison to floating-point operation workload ratio. As a result, a novel FPGAs architecture for sparse matrix-matrix multiplication is presented for which indices comparison and floating-point operations are separated. We also verified our idea in practice, and the initial implementations results are very promising. To further decrease hardware resources required by the floating-point multiplier, a reduced width multiplication is proposed in the case when IEEE-754 standard compliance is not required

Implementation of the OPU Instruction Set Architecture on the Microsemi Polarfire 300 Field-Programmable Gate Array

Deep learning is a fast-growing field with numerous promising applications that, unfortunately, demands large computing power for both training and inference tasks. To meet this demand, numerous hardware accelerators have thus been designed. Currently, however, these platforms are being developed independently from each other, and, as a result, there is a lack of compatibility between them. Notably, there is a need for standardization of the interface between hardware accelerators and software. UCLA's OPU is an ISA that aims at solving this issue. Contrary to general-purpose ISAs, OPU is designed to adequately express the computations involved in deep learning models, which allows for simple compilation and efficient cores. Prior to this work, only two fully-featured cores implementing the OPU ISA had been designed, both targeted at Xilinx SRAM-based FPGAs. However, flash-based FPGAs can offer several advantages thanks to their different technology. They are more secure, more reliable, and can yield a lower power consumption. All three of these characteristics being potentially highly valuable for deep learning accelerators, especially those embedded in edge devices, a new OPU core is here developed and mapped to a flash-based FPGA. More specifically, the potential of the MPF300 FPGA as a platform for the OPU ISA is evaluated. This represents the first OPU core implemented on an FPGA that is not manufactured by Xilinx. In addition, this design is also the first OPU core capable of operating on floating-point numbers, which simplifies the compilation of models. As such, this work contributes to the diversification of the catalog of available OPU cores, which increases the relevance of this ISA.While prior work affirms that, on Xilinx FPGAs, 8-bit floating-point arithmetic is more area-efficient than 8-bit integer arithmetic, the opposite is found in this work for Microsemi FPGAs. As a consequence, it is established that the optimum manner to perform large floating-point dot products on the MPF300 is to convert the operands to wider integers, on the device, then complete the computations using integer arithmetic. In contrast to Xilinx FPGAs, 5-bit mantissas are here preferred over 4-bit mantissas. Additionally, due to the lower ratio of the number of LUTs to DSPs of the MPF300, the relative resource utilization is found to be significantly higher here compared to the existing implementations. This new OPU core is found to be in average 1.7 times more energy-efficient than the existing similarly-sized implementation of the OPU ISA. Furthermore, the new core is in average 2 times faster than the Nvidia Jetson Nano platform, while consuming the same amount of power. These results further prove the relevance of the OPU ISA. In addition, this demonstrates that flash-based FPGAs, too, are a viable option for deep learning acceleration. The scarcity of these FPGAs in the relevant literature is thus not justified. Nevertheless, analysis of the core shows that the layout of modern FPGAs is in general suboptimal for the task of machine learning acceleration. In particular, the placement of the hard resources of the device tends to cause congestion on the device that reduces performance. This suggests the need for the development of specialized FPGAs for this task

Using reconfigurable computing technology to accelerate matrix decomposition and applications

Matrix decomposition plays an increasingly significant role in many scientific and engineering applications. Among numerous techniques, Singular Value Decomposition (SVD) and Eigenvalue Decomposition (EVD) are widely used as factorization tools to perform Principal Component Analysis for dimensionality reduction and pattern recognition in image processing, text mining and wireless communications, while QR Decomposition (QRD) and sparse LU Decomposition (LUD) are employed to solve the dense or sparse linear system of equations in bioinformatics, power system and computer vision. Matrix decompositions are computationally expensive and their sequential implementations often fail to meet the requirements of many time-sensitive applications. The emergence of reconfigurable computing has provided a flexible and low-cost opportunity to pursue high-performance parallel designs, and the use of FPGAs has shown promise in accelerating this class of computation. In this research, we have proposed and implemented several highly parallel FPGA-based architectures to accelerate matrix decompositions and their applications in data mining and signal processing. Specifically, in this dissertation we describe the following contributions: • We propose an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices. • We implement a floating-point Hestenes-Jacobi architecture for SVD, which is capable of analyzing arbitrary sized matrices. • We introduce a novel deeply pipelined reconfigurable architecture for QRD, which can be dynamically configured to perform either Householder transformation or Givens rotation in a manner that takes advantage of the strengths of each. • We design a configurable architecture for sparse LUD that supports both symmetric and asymmetric sparse matrices with arbitrary sparsity patterns. • By further extending the proposed hardware solution for SVD, we parallelize a popular text mining tool-Latent Semantic Indexing with an FPGA-based architecture. • We present a configurable architecture to accelerate Homotopy l1-minimization, in which the modification of the proposed FPGA architecture for sparse LUD is used at its core to parallelize both Cholesky decomposition and rank-1 update. Our experimental results using an FPGA-based acceleration system indicate the efficiency of our proposed novel architectures, with application and dimension-dependent speedups over an optimized software implementation that range from 1.5ÃÂ to 43.6ÃÂ in terms of computation time

Evaluation of floating-point sum or difference of products in carry-save domain

An architecture to evaluate a 24-bit floating-point sum or difference of products using modified sequential carry-save multipliers with extensive pipelining is described. The basic building block of the architecture is a carry-save multiplier with built-in mantissa alignment for the summation during the multiplication cycles. A carry-save adder, capable of mantissa alignment, correctly positions products with the current carry-save sum. Carry propagation in individual multipliers is avoided and is only required once to produce the final result

When FPGAs are better at floating-point than microprocessors

It has been shown that FPGAs could outperform high-end microprocessors on floating-point computations thanks to massive parallelism. However, most previous studies re-implement in the FPGA the operators present in a processor. This is a safe and relatively straightforward approach, but it doesn't exploit the greater flexibility of the FPGA. This article is a survey of the many ways in which the FPGA implementation of a given floating-point computation can be not only faster, but also more accurate than its microprocessor counterpart. Techniques studied here include custom precision, specific accumulator design, dedicated architectures for coarser operators which have to be implemented in software in processors, and others. A real-world biomedical application illustrates these claims. This study also points to how current FPGA fabrics could be enhanced for better floating-point support

ARITHMETIC LOGIC UNIT ARCHITECTURES WITH DYNAMICALLY DEFINED PRECISION

Modern central processing units (CPUs) employ arithmetic logic units (ALUs) that support statically defined precisions, often adhering to industry standards. Although CPU manufacturers highly optimize their ALUs, industry standard precisions embody accuracy and performance compromises for general purpose deployment. Hence, optimizing ALU precision holds great potential for improving speed and energy efficiency. Previous research on multiple precision ALUs focused on predefined, static precisions. Little previous work addressed ALU architectures with customized, dynamically defined precision. This dissertation presents approaches for developing dynamic precision ALU architectures for both fixed-point and floating-point to enable better performance, energy efficiency, and numeric accuracy. These new architectures enable dynamically defined precision, including support for vectorization. The new architectures also prevent performance and energy loss due to applying unnecessarily high precision on computations, which often happens with statically defined standard precisions. The new ALU architectures support different precisions through the use of configurable sub-blocks, with this dissertation including demonstration implementations for floating point adder, multiply, and fused multiply-add (FMA) circuits with 4-bit sub-blocks. For these circuits, the dynamic precision ALU speed is nearly the same as traditional ALU approaches, although the dynamic precision ALU is nearly twice as large

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

Energy-Efficiency Evaluation of FPGAs for Floating-Point Intensive Workloads

In this work we describe a method to measure the computing performance and energy-efficiency to be expected of an FPGA device. The motivation of this work is given by their possible usage as accelerators in the context of floating-point intensive HPC workloads. In fact, FPGA devices in the past were not considered an efficient option to address floating-point intensive computations, but more recently, with the advent of dedicated DSP units and the increased amount of resources in each chip, the interest towards these devices raised. Another obstacle to a wide adoption of FPGAs in the HPC field has been the low level hardware knowledge commonly required to program them, using Hardware Description Languages (HDLs). Also this issue has been recently mitigated by the introduction of higher level programming framework, adopting so called High Level Synthesis approaches, reducing the development time and shortening the gap between the skills required to program FPGAs wrt the skills commonly owned by HPC software developers. In this work we apply the proposed method to estimate the maximum floating-point performance and energy-efficiency of the FPGA embedded in a Xilinx Zynq Ultrascale+ MPSoC hosted on a Trenz board

Design and implementation of an out of order execution engine of floating point arithmetic operations

In this thesis, work is undertaken towards the design in hardware description languages and implementation in FPGA of an out of order execution engine of floating point arithmetic operations. This thesis work, is part of a project called Lagarto