HIGH PRECISION INTEGER ADDITION, SUBTRACTION AND MULTIPLICATION WITH A GRAPHICS PROCESSING UNIT

Modern computing paradigms, such as cloud computing, are increasingly adopting GPUs to boost their computing capabilities primarily due to the heterogeneous nature of AI/ML/deep learning workloads. However, the energy consumption of GPUs is a critical problem. Dynamic Voltage Frequency Scaling (DVFS) is a widely used technique to reduce the dynamic power of GPUs. Yet, configuring the optimal clock frequency for essential performance requirements is a non-trivial task due to the complex nonlinear relationship between the application’s runtime performance characteristics, energy, and execution time. It becomes more challenging when different applications behave distinctively with similar clock settings. Simple analytical solutions and standard GPU frequency scaling heuristics fail to capture these intricacies and scale the frequencies appropriately. In this regard, we propose a data-driven frequency scaling technique by predicting the power and execution time of a given application over different clock settings. We collect the data from application profiling and train the models to predict the outcome accurately. The proposed solution is generic and can be easily extended to different kinds of workloads and GPU architectures. Furthermore, using this frequency scaling by prediction models, we present a deadline-aware application scheduling algorithm to reduce energy consumption while simultaneously meeting their deadlines. We conduct real extensive experiments on NVIDIA GPUs using several benchmark applications. The experiment results have shown that our prediction models have high accuracy with the average RMSE values of 0.38 and 0.05 for energy and time prediction, respectively. Also, the scheduling algorithm consumes 15.07% less energy as compared to the baseline policies.

Most Computational Fluid Dynamics (CFD) applications solve the Naiver-Stokes equations using various discretization methods like Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), etc. The most compute-intensive process in CFD algorithms is the pressure Poisson solver. Solving the pressure Poisson equation requires the solution of a set of linear simultaneous equations. As the problem size/complexity increases, so does the effort and time invested in solving the equations. This study presents fast and robust iterative solvers and the acceleration of the same using the Graphics Processing Unit (GPU) architecture. Serial versions of the codes are implemented in the C language and the parallelization on GPU is achieved using Compute Unified Device Architecture (CUDA). For this study, a two-dimensional heat conduction problem is considered. FDM is used for discretization. Iterative solvers Conjugate Gradient and Multi Grid methods have been implemented in serial and parallel. The performance enhancement with single GPU and CPU system over a single CPU in terms of computing time is reported. It is seen that multigrid algorithms are superior in convergence and nearly 13 times speed-up has been obtained through GPU acceleration using CUDA, for a grid size of 2048 X 2048. The tests have been done on a cluster with Intel(R) Xeon(R) CPU E5-2670 CPU and NVIDIA K10 GPU.

SummaryMany e‐business or social network servers have been constructed on cloud. On such open environments, private data of massive users have to be protected by encrypting, such as using Advanced Encryption Standard (AES), and furthermore, this process must be finished in a short time for users' better experience. This gives huge pressure on cloud servers, especially common servers, such as web servers. We urgently need an inexpensive and highly efficient method to relieve cloud servers' pressure. Fortunately, many cores of a graphics processing unit (GPU) can undertake this hard mission because of stronger computing power and lower price. The GPU environments can be virtualized on demand by cloud through the vCUDA technology. Of course, for those clouds not equipped with a GPU, a central processing unit (CPU) can still work as multithreads in parallel. Thus, in a cloud, AES can be parallelized using many cores of a GPU or multicores of a CPU with high efficiency and low cost. For typical cloud applications, such as web services, there are massive users and each one has short plaintext. If we simply parallelize AES in such an application, we cannot obtain better performance because of the GPU's extra data transferring cost. Thus, we coalesce the massive users' data and cut these data into same‐length slices for improving the performance of parallel AES as much as possible. So we design six parallel AES algorithms using GPU parallelism or CPU parallelism, which differ in parallel scope and whether data are coalesced or cut to slices. Specifically, they are coalescent and sliced GPU (GCS), coalescent and unsliced GPU, uncoalescent GPU, coalescent and sliced CPU, coalescent and unsliced CPU, and uncoalescent CPU. Moreover, we implement them on two representative platforms and evaluate their performance. Through comparing their performance, GCS has the best performance among these algorithms. In a cloud with Nvidia GPUs, GCS is a more powerful algorithm for massive users' data encrypting, relatively. Copyright © 2015 John Wiley & Sons, Ltd.

List mode based image reconstruction is continuously gaining ground in PET imaging. The centerpiece of this reconstruction is the ray projector which unfortunately also represents the most time consuming part of the reconstruction process. Graphics processing units (GPU) represent today a cheap alternative to getting high computation power in medical imaging. However, only few GPU adapted methods have been proposed within the PET image reconstruction context, especially concerning the ray projector. In this work we propose and evaluate a new projector called DDA-ELL, which has the advantage of being applicable to both CPU and GPU architectures. The proposed projector was incorporated and evaluated within the 3D-OPLEM reconstruction algorithm implemented on both CPU and GPU architectures. Quantitative and qualitative performance evaluation was performed using simulated phantom and clinical datasets. We have shown that the proposed ray projector reconstructed images lead to improved noise and contrast characteristics compared to the widely used iterative Siddon approach. The speedup reached by the CPU version of our method compared to the iterative Siddon method was 11, while the GPU version was nearly 140 times faster.

A direct simulation Monte Carlo (DSMC) method is implemented on graphical processing unit (GPU) architecture to simulate the deposition phenomena that occur on a glass panel during modern organic light emitting diodes (OLED) manufacturing processes with a huge number of simulated particles because a fully three-dimensional (3D) particle simulation is required to accurately predict deposition thickness and uniformity on the substrate in a low-pressure environment. To examine the accuracy and efficiency of the newly developed DSMC code running on GPU architecture, verification and validation tests were performed by solving several benchmarking problems. Under three conditions which have been applied in previous OLED deposition process test experiments, the new DSMC model successfully simulates the transport of organic material evaporated from the heated nozzle array and its deposition onto a glass panel inside a low-pressure chamber. The uniformity and normalized thickness between the DSMC and experimental results for the three test cases are then compared. The normalized thickness of the organic material deposited to the large glass panel calculated from the DSMC is found to have an error of less than 4%, and the uniformity values calculated from the absolute deposition thickness show good agreement with those obtained from experimental data in all test cases.

The graphics processing unit (GPU) became an undoubtedly important computing engine for high-performance computing. With massive parallelism and easy programmability, GPU has been quickly adopted by various emerging computing domains including gaming, artificial intelligence, security, virtual reality, and so on. With its huge success in the market, GPU execution and its architecture became one of the essential topics in parallel computing today. The goal of this chapter is to provide readers with a basic understanding of GPU architecture and its programming model. This chapter explores the historical background of current GPU architecture, basics of various programming interfaces, core architecture components such as shader pipeline, schedulers and memories that support SIMT execution, various types of GPU device memories and their performance characteristics, and some examples of optimal data mapping to memories. Several recent studies are also discussed that helped advance the GPU architecture from the perspectives of performance, energy efficiency, and reliability.

Implementation of Image Enhancement Algorithms and Recursive Ray Tracing using CUDA

The General Purpose Graphics Processing Unit has secured a prominent position in the High-Performance Computing world due to its performance gain and programmability. Understanding the relationship between Graphics Processing Unit (GPU) power consumption and program features can aid developers in building energy-efficient sustainable applications. In this work, we propose a static analysis-based power model built using machine learning techniques. We have investigated six machine learning models across three NVIDIA GPU architectures: Kepler, Maxwell, and Volta with Random Forest, Extra Trees, Gradient Boosting, CatBoost, and XGBoost reporting favorable results. We observed that the XGBoost technique-based prediction model is the most efficient technique with an R 2 value of 0.9646 on Volta Architecture. The dataset used for these techniques includes kernels from different benchmarks suits, sizes, nature (e.g., compute-bound, memory-bound), and complexity (e.g., control divergence, memory access patterns). Experimental results suggest that the proposed solution can help developers precisely predict GPU applications power consumption using program analysis across GPU architectures. Developers can use this approach to refactor their code to build energy-efficient GPU applications.

Graphics processing units function well as high performance computing devices for scientific computing. The non-standard processor architecture and high memory bandwidth allow graphics processing units (GPUs) to provide some of the best performance in terms of FLOPS per dollar. Recently these capabilities became accessible for general purpose computations with the CUDA programming environment on NVIDIA GPUs and ATI Stream Computing environment on ATI GPUs. Many applications in computational science are constrained by memory access speeds and can be accelerated significantly by using GPUs as the compute engine. Using graphics processing units as a compute engine gives the personal desktop computer a processing capacity that competes with supercomputers. Graphics Processing Units represent an energy efficient architecture for high performance computing in flow simulations and many other fields. This document reviews the graphic processing unit and its features and limitations.

Monte Carlo simulation (MCS) plays a key role in medical applications, especially for emission tomography and radiotherapy. However MCS is also associated with long calculation times that prevent its use in routine clinical practice. Recently, graphics processing units (GPU) became in many domains a low cost alternative for the acquisition of high computational power. The objective of this work was to develop an efficient framework for the implementation of MCS on GPU architectures. Geant4 was chosen as the MCS engine given the large variety of physics processes available for targeting different medical imaging and radiotherapy applications. In addition, Geant4 is the MCS engine behind GATE which is actually the most popular medical applications' simulation platform. We propose the definition of a global strategy and associated structures for such a GPU based simulation implementation. Different photon and electron physics effects are resolved on the fly directly on GPU without any approximations with respect to Geant4. Validations have shown equivalence in the underlying photon and electron physics processes between the Geant4 and the GPU codes with a speedup factor of 80–90. More clinically realistic simulations in emission and transmission imaging led to acceleration factors of 400–800 respectively compared to corresponding GATE simulations.

We propose a generalized method for adapting and optimizing algorithms for efficient execution on modern graphics processing units (GPU). The method consists of several steps. First, build a control flow graph (CFG) of the algorithm. Next, transform the CFG into a tree of loops and merge non-parallelizable loops into parallelizable ones. Finally, map the resulting loops tree to the tree of GPU computational units, unrolling the algorithm’s loops as necessary for the match. The mapping should be performed bottom-up, from the lowest GPU architecture levels to the highest ones, to minimize off-chip memory access and maximize register file usage. The method provides programmer with a convenient and robust mental framework and strategy for GPU code optimization. We demonstrate the method by adapting to a GPU the DPLL backtracking search algorithm for solving the Boolean satisfiability problem (SAT). The resulting GPU version of DPLL outperforms the CPU version in raw tree search performance sixfold for regular Boolean satisfiability problems and twofold for irregular ones.

We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.

The architecture of the latest Graphic Processing Unit (GPU) has surpassed the previous application-specific stream architecture. This has led to an architecture consisting of a number of uniform programmable units integrated on the same chip which facilitate the general-purpose computing beyond the graphic processing. With the multiple programmable units executing in parallel, the latest GPU shows superior performance. Furthermore, programmers can have a direct control on the GPU pipeline using easy-to-use parallel programming environments, whereas they had to rely on specific graphics API's in the past. These advances in hardware and software make General-Purpose GPU (GPGPU) computing widespread. In this paper, using the latest GPU and its software environment, we parallelize a computationally demanding financial application and optimize its performance. We also analyze the performance results compared with those obtained using CPU only. Experimental results show that GPU can achieve a superior performance, greater than 190x, compared with the CPU-only case.

The Smith Waterman algorithm for sequence alignment is one of the main tools of bioinformatics. It is used for sequence similarity searches and alignment of similar sequences. The high end Graphical Processing Unit (GPU), used for processing graphics on desktop computers, deliver computational capabilities exceeding those of CPUs by an order of magnitude. Recently these capabilities became accessible for general purpose computations thanks to CUDA programming environment on Nvidia GPUs and ATI Stream Computing environment on ATI GPUs. Here we present an efficient implementation of the Smith Waterman algorithm on the Nvidia GPU. The algorithm achieves more than 3.5 times higher per core performance than previously published implementation of the Smith Waterman algorithm on GPU, reaching more than 70% of theoretical hardware performance. The differences between current and earlier approaches are described showing the example for writing efficient code on GPU.

Network coding has recently been widely applied in various networks for system throughput improvement and/or resilience to network dynamics. However, the computational overhead introduced by the network coding operations is not negligible and has become the cornerstone for real deployment of network coding. In this paper, we exploit the computing power of contemporary Graphic Processing Units (GPUs) to accelerate the network coding operations. We proposed three parallel algorithms that maximize the parallelism of the encoding and decoding processes, i.e., the power of GPUs is fully utilized. This paper also shares our optimization design choices and our workarounds to the challenges encountered in working with GPUs. With our implementation of the algorithms, we are able to achieve up to 12 times of speedup over the highly optimized CPU counterpart, using the NVIDIA GPU and the Computer Unified Device Architecture (CUDA) programming model.