Arbitrary-precision integer multiplication is the core kernel of many applications including scientific computing, cryptographic algorithms, etc. Existing acceleration of arbitrary-precision integer multiplication includes CPUs, GPUs, FPGAs, and ASICs. To leverage the hardware intrinsics low-bit function units (32/64-bit), arbitrary-precision integer multiplication can be calculated using Karatsuba decomposition, and Schoolbook decomposition by decomposing the two large operands into several small operands, generating a set of low-bit multiplications that can be processed either in a spatial or sequential manner on the low-bit function units, e.g., CPU vector instructions, GPU CUDA cores, FPGA digital signal processing (DSP) blocks. Among these accelerators, reconfigurable computing, e.g., FPGA accelerators are promised to provide both good energy efficiency and flexibility. We implement the state-of-the-art (SOTA) FPGA accelerator and compare it with the SOTA libraries on CPUs and GPUs. Surprisingly, in terms of energy efficiency, we find that the FPGA has the lowest energy efficiency, i.e., 0.29x of the CPU and 0.17x of the GPU with the same generation fabrication. Therefore, key questions arise: Where do the energy efficiency gains of CPUs and GPUs come from? Can reconfigurable computing do better? If can, how to achieve that? We first identify that the biggest energy efficiency gains of the CPUs and GPUs come from the dedicated vector units, i.e., vector instruction units in CPUs and CUDA cores in GPUs. FPGA uses DSPs and lookup tables (LUTs) to compose the needed computation, which incurs overhead when compared to using vector units directly. New reconfigurable computing, e.g., “FPGA+vector units” is a novel and feasible solution to improve energy efficiency. In this paper, we propose to map arbitrary-precision integer multiplication onto such a “FPGA+vector units” platform, i.e., AMD/Xilinx Versal ACAP architecture, a heterogeneous reconfigurable computing platform that features 400 AI engine tensor cores (AIE) running at 1 GHz, FPGA programmable logic (PL), and a general-purpose CPU in the system fabricated with the TSMC 7nm technology. Designing on Versal ACAP incurs several challenges and we propose AIM: Arbitrary-precision Integer Multiplication on Versal ACAP to automate and optimize the design. AIM accelerator is composed of AIEs, PL, and CPU. AIM framework includes analytical models to guide design space exploration and AIM automatic code generation to facilitate the system design and on-board design verification. We deploy the AIM framework on three different applications, including large integer multiplication (LIM), RSA, and Mandelbrot, on the AMD/Xilinx Versal ACAP VCK190 evaluation board. Our experimental results show that compared to existing accelerators, AIM achieves up to 12.6x, and 2.1x energy efficiency gains over the Intel Xeon Ice Lake 6346 CPU, and NVidia A5000 GPU respectively, which brings reconfigurable computing the most energy-efficient platform among CPUs and GPUs.
more »
« less
Swarm Model Checking on the {GPU}
We present Grapple, a new and powerful framework for explicit-state model checking on GPUs. Grapple is based on swarm verification (SV), a model-checking technique wherein a collection or swarm of small, memory- and time-bounded verification tests (VTs) are run in parallel to perform state-space exploration. SV achieves high state-space coverage via diversification of the search strategies used by constituent VTs. Grapple represents a swarm implementation for the GPU. In particular, it runs a parallel swarm of internally-parallel VTs, which are implemented in a manner that specifically targets the GPU architecture and the SIMD parallelism its computing cores offer. Grapple also makes effective use of the GPU shared memory, eliminating costly inter-block communication overhead. We conducted a comprehensive performance analysis of Grapple focused on the various design parameters, including the size of the queue structure, implementation of guard statements, and nondeterministic exploration order. Tests are run with multiple hardware configurations, including on the Amazon cloud. Our results show that Grapple performs favorably compared to the SPIN swarm and a prior non-swarm GPU implementation. Although a recently debuted FPGA swarm is faster, the deployment process to the FPGA is much more complex than Grapple's.
more »
« less
- Award ID(s):
- 1918225
- NSF-PAR ID:
- 10185187
- Date Published:
- Journal Name:
- International journal on software tools for technology transfer
- ISSN:
- 1433-2779
- Page Range / eLocation ID:
- 94-113
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Finkbeiner, B. ; Wies, T. (Ed.)Stochastic model checking (SMC) is a formal verification technique for the analysis of systems with probabilistic behavior. Scalability has been a major limiting factor for SMC tools to analyze real-world systems with large or infinite state spaces. The infinite-state Continuous-time Markov Chain (CTMC) model checker, STAMINA, tackles this problem by selectively exploring only a portion of a model’s state space, where a majority of the probability mass resides, to efficiently give an accurate probability bound to properties under verification. In this paper, we present two major improvements to STAMINA, namely, a method of calculating and distributing estimated state reachability probabilities that improves state space truncation efficiency and combination of the previous two CTMC analyses into one for generating the probability bound. Demonstration of the improvements on several benchmark examples, including hazard analysis of infinite-state combinational genetic circuits, yield significant savings in both run-time and state space size (and hence memory), compared to both the previous version of STAMINA and the infinite-state CTMC model checker INFAMY. The improved STAMINA demonstrates significant scalability to allow for the verification of complex real-world infinite-state systems.more » « less
-
null (Ed.)Sequential consistency (SC) is the most intuitive memory consistency model and the easiest for programmers and hardware designers to reason about. However, the strict memory ordering restrictions imposed by SC make it less attractive from a performance standpoint. Additionally, prior high-performance SC implementations required complex hardware structures to support speculation and recovery. In this article, we introduce the lockstep SC consistency model (LSC), a new memory model based on SC but carefully defined to accommodate the data parallel lockstep execution paradigm of GPUs. We also describe an efficient LSC implementation for an APU system-on-chip (SoC) and show that our implementation performs close to the baseline relaxed model. Evaluation of our implementation shows that the geometric mean performance cost for lockstep SC is just 0.76% for GPU execution and 6.11% for the entire APU SoC compared to a baseline with a weaker memory consistency model. Adoption of LSC in future APU and SoC designs will reduce the burden on programmers trying to write correct parallel programs, while also simplifying the implementation and verification of systems with heterogeneous processing elements and complex memory hierarchies. 1more » « less
-
The continued growth in the processing power of FPGAs coupled with high bandwidth memories (HBM), makes systems like the Xilinx U280 credible platforms for linear solvers which often dominate the run time of scientific and engineering applications. In this paper, we present Callipepla, an accelerator for a preconditioned conjugate gradient linear solver (CG). FPGA acceleration of CG faces three challenges: (1) how to support an arbitrary problem and terminate acceleration processing on the fly, (2) how to coordinate long-vector data flow among processing modules, and (3) how to save off-chip memory bandwidth and maintain double (FP64) precision accuracy. To tackle the three challenges, we present (1) a stream-centric instruction set for efficient streaming processing and control, (2) vector streaming reuse (VSR) and decentralized vector flow scheduling to coordinate vector data flow among modules and further reduce off-chip memory access latency with a double memory channel design, and (3) a mixed precision scheme to save bandwidth yet still achieve effective double precision quality solutions. To the best of our knowledge, this is the first work to introduce the concept of VSR for data reusing between on-chip modules to reduce unnecessary off-chip accesses and enable modules working in parallel for FPGA accelerators. We prototype the accelerator on a Xilinx U280 HBM FPGA. Our evaluation shows that compared to the Xilinx HPC product, the XcgSolver, Callipepla achieves a speedup of 3.94×, 3.36× higher throughput, and 2.94× better energy efficiency. Compared to an NVIDIA A100 GPU which has 4× the memory bandwidth of Callipepla, we still achieve 77% of its throughput with 3.34× higher energy efficiency. The code is available at https://github.com/UCLA-VAST/Callipepla.more » « less
-
We present FireSim, an open-source simulation platform that enables cycle-exact microarchitectural simulation of large scale-out clusters by combining FPGA-accelerated simulation of silicon-proven RTL designs with a scalable, distributed network simulation. Unlike prior FPGA-accelerated simulation tools, FireSim runs on Amazon EC2 F1, a public cloud FPGA platform, which greatly improves usability, provides elasticity, and lowers the cost of large-scale FPGA-based experiments. We describe the design and implementation of FireSim and show how it can provide sufficient performance to run modern applications at scale, to enable true hardware-software co-design. As an example, we demonstrate automatically generating and deploying a target cluster of 1,024 3.2 GHz quad-core server nodes, each with 16 GB of DRAM, interconnected by a 200 Gbit/s network with 2 microsecond latency, which simulates at a 3.4 MHz processor clock rate (less than 1,000x slowdown over real-time). In aggregate, this FireSim instantiation simulates 4,096 cores and 16 TB of memory, runs ~ 14 billion instructions per second, and harnesses 12.8 million dollars worth of FPGAs-at a total cost of only ~ $100 per simulation hour to the user. We present several examples to show how FireSim can be used to explore various research directions in warehouse-scale machine design, including modeling networks with high-bandwidth and low-latency, integrating arbitrary RTL designs for a variety of commodity and specialized datacenter nodes, and modeling a variety of datacenter organizations, as well as reusing the scale-out FireSim infrastructure to enable fast, massively parallel cycle-exact single-node microarchitectural experimentation.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/978-3-030-30923-7_6
