Towards Lattice Quantum Chromodynamics on FPGA devices

In this paper we describe a single-node, double precision Field Programmable Gate Array (FPGA) implementation of the Conjugate Gradient algorithm in the context of Lattice Quantum Chromodynamics. As a benchmark of our proposal we invert numerically the Dirac-Wilson operator on a 4-dimensional grid on three Xilinx hardware solutions: Zynq Ultrascale+ evaluation board, the Alveo U250 accelerator and the largest device available on the market, the VU13P device. In our implementation we separate software/hardware parts in such a way that the entire multiplication by the Dirac operator is performed in hardware, and the rest of the algorithm runs on the host. We find out that the FPGA implementation can offer a performance comparable with that obtained using current CPU or Intel's many core Xeon Phi accelerators. A possible multiple node FPGA-based system is discussed and we argue that power-efficient High Performance Computing (HPC) systems can be implemented using FPGA devices only.Comment: 17 pages, 4 figure

Scalable Energy-efficient Microarchitectures with Computational Error Tolerance

Dennard scaling of conventional semiconductor technology has reached its limit resulting in issues pertaining to leakage current and threshold voltage. Energy-savings found at the transistor level by simply lowering supply voltage are no longer available for these devices (e.g., MOSFETs) and has reached the Landauer-Shannon limit. Recent proposals of minivolt switch technologies aim to extend the technology scaling roadmap by maintaining a high on/off ratio of drain current with a much lower supply voltage. However, high intermittent error probabilities in millivolt switches constraints their Vdd reduction for traditional architectures. Thus, there is an urgent need for scalable and energy-efficient micro-architectures with computational error-tolerance. This thesis systematically leverages the error detection and correction properties of the Redundant Residue Number System (RRNS) by varying the number of non-redundant (n) and redundant (r) components (residues), and selects and discusses trade-offs about configuration points from a two-dimensional (n, r)-RRNS design plane that meet certain capabilities of error detection and/or correction. Being able to efficiently handle resilience in this (n, r)-RRNS plane significantly improves reliability, allowing further Vdd reduction and energy savings. First, the necessary implementation details of RRNS cores are discussed. Second, scalable RRNS micro-architectures that simultaneously support both error-correction and checkpointing with restart capabilities for uncorrectable errors are proposed. Third, novel RRNS-based adaptive checkpointing&restart mechanisms are designed that automatically guarantee reliability while minimizing the energy-delay product (EDP). Finally, the RRNS design space is explored to find the optimal (n, r) configuration points. For similar reliability when compared to a conventional binary core (running at high Vdd) without computational error tolerance, the proposed RRNS scalable micro-architecture reduces EDP by 53% on average for memory-intensive workloads and by 67% on average for non-memory-intensive workloads. This thesis's second topic is to alleviate fault rate and power consumption issues of exascale computing. Faults in High-Performance Computing (HPC) have become an urgent challenge with estimated Mean Time Between Failures (MTBF) of exascale system projected as only several minutes with contemporary methodologies. Unfortunately, existing error-tolerance technologies in the context of HPC systems have serious deficiencies such as insufficient error-tolerance coverage, high power consumption, and difficult integration with existing workloads. Considering Department of Energy (DOE) guidelines that limit exascale power consumption to 20 MW, this thesis highlights the issue of energy usage and proposes a thread-level fault tolerance mechanism compatible with current state-of-the art exascale programming models while simultaneously meeting the requirements of full system error protection. Additionally, an efficient micro-architecture and corresponding mechanisms that can support thread level RRNS are discussed. Experimental results show that this strategy reduces energy consumption by 62.25% and the Energy-Delay-Product by 58.67% on average when compared with state-of-the-art black box resilience techniques.Ph.D

Harnessing resilience: biased voltage overscaling for probabilistic signal processing

A central component of modern computing is the idea that computation requires determinism. Contrary to this belief, the primary contribution of this work shows that useful computation can be accomplished in an error-prone fashion. Focusing on low-power computing and the increasing push toward energy conservation, the work seeks to sacrifice accuracy in exchange for energy savings. Probabilistic computing forms the basis for this error-prone computation by diverging from the requirement of determinism and allowing for randomness within computing. Implemented as probabilistic CMOS (PCMOS), the approach realizes enormous energy sav- ings in applications that require probability at an algorithmic level. Extending probabilistic computing to applications that are inherently deterministic, the biased voltage overscaling (BIVOS) technique presented here constrains the randomness introduced through PCMOS. Doing so, BIVOS is able to limit the magnitude of any resulting deviations and realizes energy savings with minimal impact to application quality. Implemented for a ripple-carry adder, array multiplier, and finite-impulse-response (FIR) filter; a BIVOS solution substantially reduces energy consumption and does so with im- proved error rates compared to an energy equivalent reduced-precision solution. When applied to H.264 video decoding, a BIVOS solution is able to achieve a 33.9% reduction in energy consumption while maintaining a peak-signal-to-noise ratio of 35.0dB (compared to 14.3dB for a comparable reduced-precision solution). While the work presented here focuses on a specific technology, the technique realized through BIVOS has far broader implications. It is the departure from the conventional mindset that useful computation requires determinism that represents the primary innovation of this work. With applicability to emerging and yet to be discovered technologies, BIVOS has the potential to contribute to computing in a variety of fashions.PhDCommittee Chair: Anderson, David; Committee Member: Conte, Thomas; Committee Member: Ferri, Bonnie; Committee Member: Hasler, Paul; Committee Member: Mooney, Vincen

Chapter One – An Overview of Architecture-Level Power- and Energy-Efficient Design Techniques

Power dissipation and energy consumption became the primary design constraint for almost all computer systems in the last 15 years. Both computer architects and circuit designers intent to reduce power and energy (without a performance degradation) at all design levels, as it is currently the main obstacle to continue with further scaling according to Moore's law. The aim of this survey is to provide a comprehensive overview of power- and energy-efficient “state-of-the-art” techniques. We classify techniques by component where they apply to, which is the most natural way from a designer point of view. We further divide the techniques by the component of power/energy they optimize (static or dynamic), covering in that way complete low-power design flow at the architectural level. At the end, we conclude that only a holistic approach that assumes optimizations at all design levels can lead to significant savings.Peer ReviewedPostprint (published version

The Effects of Approximate Multiplication on Convolutional Neural Networks

This paper analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can be performed more efficiently in hardware accelerators. The study identifies the critical factors in the convolution, fully-connected, and batch normalization layers that allow more accurate CNN predictions despite the errors from approximate multiplication. The same factors also provide an arithmetic explanation of why bfloat16 multiplication performs well on CNNs. The experiments are performed with recognized network architectures to show that the approximate multipliers can produce predictions that are nearly as accurate as the FP32 references, without additional training. For example, the ResNet and Inception-v4 models with Mitch-$w$6 multiplication produces Top-5 errors that are within 0.2% compared to the FP32 references. A brief cost comparison of Mitch-$w$6 against bfloat16 is presented, where a MAC operation saves up to 80% of energy compared to the bfloat16 arithmetic. The most far-reaching contribution of this paper is the analytical justification that multiplications can be approximated while additions need to be exact in CNN MAC operations.Comment: 12 pages, 11 figures, 4 tables, accepted for publication in the IEEE Transactions on Emerging Topics in Computin

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

From FPGA to ASIC: A RISC-V processor experience

This work document a correct design flow using these tools in the Lagarto RISC- V Processor and the RTL design considerations that must be taken into account, to move from a design for FPGA to design for ASIC