CASTA: CUDA-Accelerated Static Timing Analysis for VLSI Designs

Static timing analysis (STA) is an essential yet time-consuming task during the circuit design flow to ensure the correctness and performance of the design. Thanks to the advancement of general-purpose computing on graphics processing units (GPUs), new possibilities and challenges have arisen for boosting the performance of STA. In this work, we present an efficient and holistic GPU-accelerated STA engine. We accelerate major STA tasks, including levelization, delay computation, graph propagation, and multicorner analysis, by developing high-performance GPU kernels and data structures. By dividing the STA workloads into CPU–GPU concurrent tasks with managed dependencies, our acceleration framework supports versatile incremental updates. Furthermore, we have extended our approach to multicorner analysis by exploring a large amount of corner-level data parallelism using GPU computing. Our implementation based on the open-source STA engine OpenTimer has achieved up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.07\times $ </tex-math></inline-formula> speed-up on single corner analysis, and up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$25.67\times $ </tex-math></inline-formula> speed-up on multicorner analysis on TAU 2015 contest designs and a 14-nm technology.

To exploit the benefits of throughput-optimized processors such as GPUs, applications need to be redesigned to achieve performance and efficiency. In this work, we present techniques to speed up statistical timing analysis on throughput processors. We draw upon advancements in improving the efficiency of Monte Carlo based statistical static timing analysis (MC SSTA) using techniques to reduce the sample size or smart sampling techniques. An efficient smart sampling technique, Stratification + Hybrid Quasi Monte Carlo (SH-QMC), is implemented on a GPU based on NVIDIA CUDA architecture. We show that although this application is based on MC analysis with straightforward parallelism available, achieving performance and efficiency on the GPU requires exposing more parallelism and finding locality in computations. This is in contrast with random sampling based algorithms which are inefficient in terms of sample size but can keep resources utilized on a GPU. We show that SH-QMC implemented on a Multi GPU is twice as fast as a single STA on a CPU for benchmark circuits considered. In terms of an efficiency metric, which measures the ability to convert a reduction in sample size to a corresponding reduction in runtime w.r.t a random sampling approach, we achieve 73.9% efficiency with the proposed approaches compared to 4.3% for an implementation involving performing computations on smart samples in parallel. Another contribution of the paper is a critical graph analysis technique to improve the efficiency of Monte Carlo based SSTA, leading to 2--9X further speedup.

We describe a procedure based on an existing static timing analysis tool for selecting path delay faults to target during test generation. The use of an existing static timing analysis tool ensures that a state-of-the-art process can be used for estimating path delays. However, static timing analysis, by itself, can be inaccurate as it does not take into consideration conditions that are necessary for detecting path delay faults. In the proposed method, these conditions are captured as what are called input necessary assignments, which static timing analysis tools are able to use. By providing the static timing analysis process with the input necessary assignments for a selected path, the static timing analysis process can estimate the delay of the path more accurately. It can also identify additional paths whose delays are at least as high as those of the selected paths. Thus, feeding back the input necessary assignments to the static timing analysis process enhances the correlation between static timing analysis and actual timing of tests on silicon. The result is a set of potentially detectable path delay faults associated with critical paths based on more accurate estimates of the path delays that can be exhibited by a test set, compared with the set that would be obtained by static timing analysis alone.

As design size gets larger and becomes more complicated with feature integration, the runtime for Static Timing Analysis (STA) becomes more of a concern. Due to time-to-market pressure, the validation of the design is performed in parallel with the physical synthesis flow; therefore it is not uncommon to find last minute critical logic bugs during final design integration iterations. However, timing verification needs to be run on full-chip level to ensure that the check is comprehensive. This paper proposes a method to isolate only those logics which are affected by the Engineering Change Order (ECO) for STA. This simplification will allow faster ECO iteration to enable a more efficient timing convergence. The proposed method is also suitable to be used for multithreading in STA engines to speed-up timing verification due to ECO changes. Engineering Change Order (ECO), Static Timing Analysis (STA), Incremental Static Timing Analysis, VLSI design

Static timing analysis (STA) is an integral part in the overall design flow because it verifies the expected timing behaviors of a circuit. However, as the circuit complexity continues to enlarge, there is an increasing need for enhancing the performance of existing STA algorithms using emerging heterogeneous parallelism that comprises manycore central processing units (CPUs) and graphics processing units (GPUs). In this paper, we introduce several state-of-the-art STA techniques, including task-based parallelism, task graph partition, and GPU kernel algorithms, all of which have brought significant performance benefits to STA applications. Motivated by these successful results, we will introduce a task-parallel programming system to generalize our solutions to benefit broader scientific computing applications.

In this paper, we explore the implementation of Monte Carlo based statistical static timing analysis (SSTA) on a Graphics Processing Unit (GPU). SSTA via Monte Carlo simulations is a computationally expensive, but important step required to achieve design timing closure. It provides an accurate estimate of delay variations and their impact on design yield. The large number of threads that can be computed in parallel on a GPU suggests a natural fit for the problem of Monte Carlo based SSTA to the GPU platform. Our implementation performs multiple delay simulations at a single gate in parallel. A parallel implementation of the Mersenne Twister pseudo-random number generator on the GPU, followed by Box-Muller transformations (also implemented on the GPU) is used for generating gate delay numbers from a normal distribution. The μ and σ of the pin-to-output delay distributions for all inputs and for every gate, are obtained using a memory lookup, which benefits from the large memory bandwidth of the GPU. Threads which execute in parallel have no data/control dependencies on each other. All threads compute identical instructions, but on different data, as required by the Single Instruction Multiple Data (SIMD) programming semantics of the GPU. Our approach is implemented on a NVIDIA GeForce GTX 8800 GPU card. Our results indicate that our approach can obtain an average speedup of about 260x as compared to a serial CPU implementation. With the recently announced quad 8800 GPU cards, we estimate that our approach would attain a speedup of over 785x. The correctness of the Monte Carlo based SSTA implemented on a GPU has been verified by comparing its results with a CPU based implementation.

Graphics processing units (GPUs) 1 have enjoyed increasing popularity in recent years, which benefits from, for example, general-purpose GPU (GPGPU) for parallel programs and new computing paradigms, such as the Internet of Things (IoT). GPUs hold great potential in providing effective solutions for big data analytics while the demands for processing large quantities of data in real time are also increasing. However, the pervasive presence of GPUs on mobile devices presents great challenges for GPGPU, mainly because GPGPU integrates a large amount of processor arrays and concurrent executing threads (up to hundreds of thousands). In particular, the root causes of performance loss in a GPGPU program can not be revealed in detail by current approaches. In this article, we propose MiC (Multi-level Characterization), a framework that comprehensively characterizes GPGPU kernels at the instruction, Basic Block (BBL), and thread levels. Specifically, we devise Instruction Vectors (IV) and Basic Blocks Vectors (BBV), a Thread Similarity Matrix (TSM), and a Divergence Flow Statistics Graph (DFSG) to profile information in each level. We use MiC to provide insights into GPGPU kernels through the characterizations of 34 kernels from popular GPGPU benchmark suites such as Compute Unified Device Architecture (CUDA) Software Development Kit (SDK), Rodinia, and Parboil. In comparison with Central Processing Unit (CPU) workloads, we conclude the key findings as follows: (1) There are comparable Instruction-Level Parallelism (ILP); (2) The BBL count is significantly smaller than CPU workloads—only 22.8 on average; (3) The dynamic instruction count per thread varies from dozens to tens of thousands and it is extremely small compared to CPU benchmarks; (4) The Pareto principle (also called 90/10 rule) does not apply to GPGPU kernels while it pervasively exists in CPU programs; (5) The loop patterns are dramatically different from those in CPU workloads; (6) The branch ratio is lower than that of CPU programs but higher than pure GPU workloads. In addition, we have also shown how TSM and DFSG are used to characterize the branch divergence in a visual way, to enable the analysis of thread behavior in GPGPU programs. In addition, we show an optimization case for a GPGPU kernel from the bottleneck identified through its characterization result, which improves 16.8% performance.

New computational architectures, such as multi-core processors and graphics processing units (GPUs), pose challenges to application developers. Although in the case of general-purpose GPU programming, environments and toolkits such as CUDA and OpenCL have simplified application development, different ways of thinking about memory access, storage, and program execution are required. This paper presents a strategy for implementing a specific signal processing technique for blind-source separation: infomax independent component analysis (ICA). Common linear algebra operations are mapped to a low cost programmable graphics card using the OpenCL programming toolkit. Because many components of ICA are inherently parallel, ICA computations can be accelerated by low cost parallel hardware. Experimental results on simulated and speech signals indicate that efficiency gains and scalability are achievable through general-purpose GPU implementation, and suggest that important applications in telecommunications, speech processing, and biomedical signal analysis can benefit from these new architectures. The utilization of low cost GPUs for programming may potentially facilitate real-time applications of previously offline algorithms.

One of the critical issues in MTCMOS design is how to estimate a circuit delay quickly. In this paper, we propose a delay modeling and static timing analysis (STA) methodology targeting at MTCMOS circuits. In the proposed method, we prepare a delay look-up table (LUT) consisting of the input slew, the output load capacitance, the virtual ground length, and a power-switch size. Using this LUT, we compute a circuit delay for each logic cell by applying the linear interpolation. Experimental results show that the proposed methodology enables to estimate the critical path delay in a good accuracy.

Nowadays graphics processing units (GPUs) have become popular parallel computing platforms known as General-Purpose GPU (GPGPU) computing. GPUs thereby are chosen by some security researchers as cryptographic accelerators to secure massive volumes of transactions. However, their security issues are ignored in spite of their popularity and performance. There are some possible information leakages faced with malicious attacks or even in the normal GPU computing. Our objective is to secure the confidentiality of cryptographic keys in GPU computing environments and provide easy-to-use programming with few constraints. In this paper, we propose a prototype in Linux, a system of GPGPU computing solution empowered by GPU virtualization technology, which keeps encrypted keys in guest machine to protect secret keys from leakage even in the event of full system compromise. With the API interception and redirection of CUDA, applications in Virtual Machines (VMs) can access the GPU device in a transparent way. Besides, we use virtio, a dedicated virtual I/O device, to transfer data between virtual and host machines in high performance. In our current study, we evaluate our prototype with the GPU implementation of ECC. We show that it can protect private keys of GPU cryptographic computation and it also incurs low performance penalty compared with the native environment, therefore demonstrating the prototype is secure and requires reasonable overhead.

Aging is an important determinant for the reliability of circuit designs and has been addressed by a number of protection techniques based on static timing analysis (STA). The timing reported by STA, however, is often too optimistic without considering the functional behavior of the circuit. Furthermore, signal probability has also been found to be a significant factor in the aging effect. As such, we present in this paper a timing-critical path analysis that takes function and aging into account as well as signal probability. Functional timing analysis (FTA) eliminates the false paths and generates more accurate timing. Furthermore, machine learning can be used to build models for predicting the timing of each cell for various aging lifetimes and signal probabilities. Experimental results indicate that there can be a difference of up to 6% on path delay between STA and FTA. The path ranks also differ for most of the benchmark circuits after considering aging with signal probability, resulting in the delay differences of up to 6.12 %. In conclusion, it is necessary to consider function, aging, and signal probability simultaneously when analyzing timing-critical paths in a circuit design.

Graphics processing units (GPUs) are providing increasingly higher performance with programmable internal processors, namely vertex processors (VPs) and fragment processors (FPs). Such newly added capabilities motivate us to perform general-purpose computation on GPUs (GPGPU) beyond graphics applications. Although VPs and FPs are connected in a pipeline, many GPGPU implementations utilize only FPs as a computational engine in the GPU. Therefore, such implementations may result in lower performance due to highly loaded FPs (as compared to VPs) being a performance bottleneck in the pipeline execution. The objective of our work is to improve the performance of GPGPU programs by eliminating this bottleneck. To achieve this, we present a code motion technique that is capable of reducing the FP workload by moving assembly instructions appropriately from the FP program to the VP program. We also present the definition of such movable instructions that do not change the I/O specification between the CPU and the GPU. The experimental results show that (1) our technique improves the performance of a Gaussian filter program with reducing execution time by approximately 40% and (2) it successfully reduces the FP workload in 10 out of 18 GPGPU programs.

Static timing analysis techniques are widely used to verify the timing behavior of large digital designs implemented predominantly in conventional static CMOS. These techniques, however, are not sufficient to completely verify the dynamic circuit families now finding favor in high-performance designs. In this paper, we describe an approach that extends static timing analysis to a high-performance dynamic CMOS logic family called self-resetting CMOS (SRCMOS). Due to the circuit structure employed in SRCMOS, designs naturally decompose into a hierarchy of gates and macros; timing analysis must address and preferably exploit this hierarchy. At the gate level, three categories of constraints on pulse timing arise from considering the effects of pulse width, overlap, and collisions. Timing analysis is performed at the macro level, by a) performing timing tests at macro boundaries and b) using macro-level delay models. We define various macro-level timing tests which ensure that fundamental gate-level timing constraints are satisfied. We extend the standard delay model to handle leading and trailing edges of signal pulses, across-chip variations, trading of signals, and slow and fast operating conditions. We have developed an SRCMOS timing analyzer based on this approach; the analyzer implemented as extensions to a standard static timing analysis program, thus facilitating its integration into an existing design system and methodology.

Recent static timing analysis (STA) tools have utilized task dependency graph (TDG) parallelism to enhance the STA runtime performance. Although TDG parallelism shows promising speedup, the overhead of scheduling a TDG can become dominant as the TDG becomes larger. To minimize the scheduling overhead, several TDG partitioning algorithms have been proposed to reduce the TDG size without affecting its task parallelism. Despite improved performance, existing TDG partitioners all fall short of incremental partitioning, limiting their practical use in STA tools that support timing-driven operations. To overcome this limitation, we propose iTAP, an incremental TDG partitioner to fully leverage the power of TDG partitioning in task-parallel STA applications. Compared to a state-of-the-art full TDG partitioner, iTAP enhances the overall STA performance by up to 2.97×.

Two benchmark tests were carried out to analyze the performance of OpenFOAM-based CFD solvers using General-Purpose computing on Graphics Processing Units(GPGPU). In the present study, RapidCFD, which is an implementation of OpenFOAM capable of running most of the functions of OpenFOAM on GPUs, was used to apply GPGPU to OpenFOAM. The numerical simulations of 1) 3D lid-driven cavity incompressible flows and 2) steady flows around a motorbike were conducted on two kinds of CPU, single-GPU, and multi-GPU systems, and the computational times were analyzed. For the test of cavity flows, as the number of cells increased, the performance and the scalability of GPGPU were improved. When the number of cells was 2503, a system with 8-GPUs showed the highest performance with 42 times of speedup over a CPU system. For the test of flows around a motorbike, a system with 8-GPUs showed the highest performance with 20 times of speedup over a CPU system. For both single precision and double precision calculations, the performance improvements using GPGPU were efficient. The results demonstrate that GPGPU would be more efficient than computing on CPUs when computing large-scale flows and practical problems that require massive parallelism.