White Paper from Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing

In numerical computations, precision of floating-point computations is a key factor to determine the performance (speed and energy-efficiency) as well as the reliability (accuracy and reproducibility). However, precision generally plays a contrary role for both. Therefore, the ultimate concept for maximizing both at the same time is the minimal-precision computing through precision-tuning, which adjusts the optimal precision for each operation and data. Several studies have been already conducted for it so far (e.g. Precimoniuos and Verrou), but the scope of those studies is limited to the precision-tuning alone. Hence, we aim to propose a broader concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. In 2019, we have started the Minimal-Precision Computing project to propose a more broad concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. Specifically, our system combines (1) a precision-tuning method based on Discrete Stochastic Arithmetic (DSA), (2) arbitrary-precision arithmetic libraries, (3) fast and accurate numerical libraries, and (4) Field-Programmable Gate Array (FPGA) with High-Level Synthesis (HLS). In this white paper, we aim to provide an overview of various technologies related to minimal- and mixed-precision, to outline the future direction of the project, as well as to discuss current challenges together with our project members and guest speakers at the LSPANC 2020 workshop; https://www.r-ccs.riken.jp/labs/lpnctrt/lspanc2020jan/

High Performance Reconfigurable Computing for Linear Algebra: Design and Performance Analysis

Field Programmable Gate Arrays (FPGAs) enable powerful performance acceleration for scientific computations because of their intrinsic parallelism, pipeline ability, and flexible architecture. This dissertation explores the computational power of FPGAs for an important scientific application: linear algebra. First of all, optimized linear algebra subroutines are presented based on enhancements to both algorithms and hardware architectures. Compared to microprocessors, these routines achieve significant speedup. Second, computing with mixed-precision data on FPGAs is proposed for higher performance. Experimental analysis shows that mixed-precision algorithms on FPGAs can achieve the high performance of using lower-precision data while keeping higher-precision accuracy for finding solutions of linear equations. Third, an execution time model is built for reconfigurable computers (RC), which plays an important role in performance analysis and optimal resource utilization of FPGAs. The accuracy and efficiency of parallel computing performance models often depend on mean maximum computations. Despite significant prior work, there have been no sufficient mathematical tools for this important calculation. This work presents an Effective Mean Maximum Approximation method, which is more general, accurate, and efficient than previous methods. Together, these research results help address how to make linear algebra applications perform better on high performance reconfigurable computing architectures

Numerical solutions of differential equations on FPGA-enhanced computers

Conventionally, to speed up scientific or engineering (S&E) computation programs on general-purpose computers, one may elect to use faster CPUs, more memory, systems with more efficient (though complicated) architecture, better software compilers, or even coding with assembly languages. With the emergence of Field Programmable Gate Array (FPGA) based Reconfigurable Computing (RC) technology, numerical scientists and engineers now have another option using FPGA devices as core components to address their computational problems. The hardware-programmable, low-cost, but powerful “FPGA-enhanced computer” has now become an attractive approach for many S&E applications. A new computer architecture model for FPGA-enhanced computer systems and its detailed hardware implementation are proposed for accelerating the solutions of computationally demanding and data intensive numerical PDE problems. New FPGAoptimized algorithms/methods for rapid executions of representative numerical methods such as Finite Difference Methods (FDM) and Finite Element Methods (FEM) are designed, analyzed, and implemented on it. Linear wave equations based on seismic data processing applications are adopted as the targeting PDE problems to demonstrate the effectiveness of this new computer model. Their sustained computational performances are compared with pure software programs operating on commodity CPUbased general-purpose computers. Quantitative analysis is performed from a hierarchical set of aspects as customized/extraordinary computer arithmetic or function units, compact but flexible system architecture and memory hierarchy, and hardwareoptimized numerical algorithms or methods that may be inappropriate for conventional general-purpose computers. The preferable property of in-system hardware reconfigurability of the new system is emphasized aiming at effectively accelerating the execution of complex multi-stage numerical applications. Methodologies for accelerating the targeting PDE problems as well as other numerical PDE problems, such as heat equations and Laplace equations utilizing programmable hardware resources are concluded, which imply the broad usage of the proposed FPGA-enhanced computers

Best practices for building hardware designs for living computational science applications

Scientific computing or Computational science, is a field of study where engineers and scientists use computer simulations to solve equations that model the physical world. In some cases, these equations come from the first principles of physics. In the past, these simulations were run on a single processor machine. However, due to various technological reasons, the performance of these machines are not likely to improve at the same rate as in the past. In order to improve the performance per watt of these simulations, special-purpose hardware accelerators can be used. This work mainly focuses on using FPGA-based hardware accelerators. In order to run these simulations on an FPGA accelerator, the application code needs to be re-factored into software and hardware sections. These faster simulations have motivated scientists to capture more behavior of the physical world. As additional behavior is captured, the application code needs to be re-factored each time, and a significant effort is required to re-build the design. Unfortunately, these multiple cycles of re-design reduces the overall productivity of scientists and engineers. This work proposes a set of hardware design guidelines for changing computational science codes or living computational science codes. These guidelines co-evolve the hardware with the software, reducing the overall effort of re-design and improving productivity. The design guidelines are evaluated for effectiveness, communicability, and broad applicability. Experimental results have shown that the overall re-design effort is reduced, and these guidelines are broadly applicable to a wide variety of scientific computing applications

Algorithm Architecture Co-design for Dense and Sparse Matrix Computations

abstract: With the end of Dennard scaling and Moore's law, architects have moved towards heterogeneous designs consisting of specialized cores to achieve higher performance and energy efficiency for a target application domain. Applications of linear algebra are ubiquitous in the field of scientific computing, machine learning, statistics, etc. with matrix computations being fundamental to these linear algebra based solutions. Design of multiple dense (or sparse) matrix computation routines on the same platform is quite challenging. Added to the complexity is the fact that dense and sparse matrix computations have large differences in their storage and access patterns and are difficult to optimize on the same architecture. This thesis addresses this challenge and introduces a reconfigurable accelerator that supports both dense and sparse matrix computations efficiently. The reconfigurable architecture has been optimized to execute the following linear algebra routines: GEMV (Dense General Matrix Vector Multiplication), GEMM (Dense General Matrix Matrix Multiplication), TRSM (Triangular Matrix Solver), LU Decomposition, Matrix Inverse, SpMV (Sparse Matrix Vector Multiplication), SpMM (Sparse Matrix Matrix Multiplication). It is a multicore architecture where each core consists of a 2D array of processing elements (PE). The 2D array of PEs is of size 4x4 and is scheduled to perform 4x4 sized matrix updates efficiently. A sequence of such updates is used to solve a larger problem inside a core. A novel partitioned block compressed sparse data structure (PBCSC/PBCSR) is used to perform sparse kernel updates. Scalable partitioning and mapping schemes are presented that map input matrices of any given size to the multicore architecture. Design trade-offs related to the PE array dimension, size of local memory inside a core and the bandwidth between on-chip memories and the cores have been presented. An optimal core configuration is developed from this analysis. Synthesis results using a 7nm PDK show that the proposed accelerator can achieve a performance of upto 32 GOPS using a single core.Dissertation/ThesisMasters Thesis Computer Engineering 201

Acceleration Techniques for Sparse Recovery Based Plane-wave Decomposition of a Sound Field

Plane-wave decomposition by sparse recovery is a reliable and accurate technique for plane-wave decomposition which can be used for source localization, beamforming, etc. In this work, we introduce techniques to accelerate the plane-wave decomposition by sparse recovery. The method consists of two main algorithms which are spherical Fourier transformation (SFT) and sparse recovery. Comparing the two algorithms, the sparse recovery is the most computationally intensive. We implement the SFT on an FPGA and the sparse recovery on a multithreaded computing platform. Then the multithreaded computing platform could be fully utilized for the sparse recovery. On the other hand, implementing the SFT on an FPGA helps to flexibly integrate the microphones and improve the portability of the microphone array. For implementing the SFT on an FPGA, we develop a scalable FPGA design model that enables the quick design of the SFT architecture on FPGAs. The model considers the number of microphones, the number of SFT channels and the cost of the FPGA and provides the design of a resource optimized and cost-effective FPGA architecture as the output. Then we investigate the performance of the sparse recovery algorithm executed on various multithreaded computing platforms (i.e., chip-multiprocessor, multiprocessor, GPU, manycore). Finally, we investigate the influence of modifying the dictionary size on the computational performance and the accuracy of the sparse recovery algorithms. We introduce novel sparse-recovery techniques which use non-uniform dictionaries to improve the performance of the sparse recovery on a parallel architecture