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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Implementation and Synthesis of Math Library Functions

Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately puts development of such functions out of reach for all but the most experienced experts. To address this, we introduce MegaLibm, a domain-specific language for implementing, testing, and tuning math library implementations. MegaLibm is safe, modular, and tunable. Implementations in MegaLibm can automatically detect mathematical mistakes like sign flips via semantic wellformedness checks, and components like range reductions can be implemented in a modular, composable way, simplifying implementations. Once the high-level algorithm is done, tuning parameters like working precisions and evaluation schemes can be adjusted through orthogonal tuning parameters to achieve the desired speed and accuracy. MegaLibm also enables math library developers to work interactively, compiling, testing, and tuning their implementations and invoking tools like Sollya and type-directed synthesis to complete components and synthesize entire implementations. MegaLibm can express 8 state-of-the-art math library implementations with comparable speed and accuracy to the original C code, and can synthesize 5 variations and 3 from-scratch implementations with minimal guidance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

MatRIS: Multi-level Math Library Abstraction for Heterogeneity and Performance Portability using IRIS Runtime

Vendor libraries are tuned for a specific architecture and are not portable to others. Moreover, they lack support for heterogeneity and multi-device orchestration, which is required for efficient use of contemporary HPC and cloud resources. To address these challenges, we introduce MatRIS—a multilevel math library abstraction for scalable and performance-portable sparse/dense BLAS/LAPACK operations using IRIS runtime. The MatRIS-IRIS co-design introduces three levels of abstraction to make the implementation completely architecture agnostic and provide highly productive programming. We demonstrate that MatRIS is portable without any change in source code and can fully utilize multi-device heterogeneous systems by achieving high performance and scalability on Summit, Frontier, and a CADES cloud node equipped with four NVIDIA A100 GPUs and four AMD MI100 GPUs. A detailed performance study is presented in which MatRIS demonstrates multi-device scalability. When compared, MatRIS provides competitive and even better performance than libraries from vendors and other third parties.

Monil, M. A. H.↗
DOE OSTI2022

SparseLU, A Novel Algorithm and Math Library for Sparse LU Factorization

Decomposing sparse matrices into lower and upper triangular matrices (sparse LU factorization) is a key operation in many computational scientific applications. We developed SparseLU, a sparse linear algebra library that implements a new algorithm for LU factorization on general sparse matrices. The new algorithm divides the input matrix into tiles to which OpenMP tasks are created for factorization computation, where only tiles that contain nonzero elements are computed. For comparative performance analysis, we used the reference library SuperLU. Testing was performed on synthetically generated matrices which replicate the conditions of the real-world matrices. SparseLU is able to reach a mean speedup of ~29× compared to SuperLU.

Valero Lara, Pedro↗
DOE OSTI2024

Ginkgo - A math library designed to accelerate Exascale Computing Project science applications

Large-scale simulations require efficient computation across the entire computing hierarchy. A challenge of the Exascale Computing Project (ECP) was to reconcile highly heterogeneous hardware with the myriad of applications that were required to run on these supercomputers. Mathematical software forms the backbone of almost all scientific applications, providing efficient abstractions and operations that are crucial to harness the performance of computing systems. Ginkgo is one such mathematical software library, nurtured by ECP, providing high-performance, user-friendly, and performance portable interfaces for applications in ECP and beyond. In this paper, we elaborate on Ginkgo’s philosophy of high-performance software that is sustainable, reproducible, and easy to use. We showcase the wide feature set of solvers and preconditioners available in Ginkgo and the central concepts involved in their design. We elaborate on four different ECP software integrations: MFEM, PeleLM + SUNDIALS, XGC, and ExaSGD that use Ginkgo to accelerate their science runs. Performance studies of different problems from these applications highlight the effectiveness of Ginkgo and the benefits incurred by these ECP applications.

Cojean, Terry↗
DOE OSTI2023

Finding inputs that trigger floating-point exceptions in heterogeneous computing via Bayesian optimization

Testing code for floating-point exceptions is crucial as exceptions can quickly propagate and produce unreliable numerical answers. The state-of-the-art to test for floating-point exceptions in heterogeneous systems is quite limited and solutions require the application’s source code, which precludes their use in accelerated libraries where the source is not publicly available. We present an approach to find inputs that trigger floating-point exceptions in black-box CPU or GPU functions, i.e., functions where the source code and information about input bounds are unavailable. Our approach is the first to use Bayesian optimization (BO) to identify such inputs and uses novel strategies to overcome the challenges that arise in applying BO to this problem. Here, we implement our approach in the XSCOPE framework and demonstrate it on 58 functions from the CUDA Math Library and 81 functions from the Intel Math Library. XSCOPE is able to identify inputs that trigger exceptions in about 73% of the tested functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Kokkos v.4.0

SAND2023-07883O Kokkos software implements C++ performance portability programming models, tools and math libraries, which enables science and engineering software developers to use single-source codes for a wide range of computer architectures. Kokkos also provides implementations of existing and proposed C++ standard features that support programming model and math libraries that are used for implementing performance-portable scientific and engineering applications. The Kokkos libraries provide algorithms, data structures, and tools to enable high-performance computing developers to write performance-portable code. Capabilities fall into three broad categories: Kokkos Core, Kokkos Kernels, and Kokkos Tools. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2024

MatRIS: Addressing the Challenges for Portability and Heterogeneity Using Tasking for Matrix Decomposition (Cholesky)

The ubiquitous in-node heterogeneity of HPC and cloud computing platforms makes software portability and performance optimization extremely challenging. Described here, the MatRIS multilevel math library abstraction framework employs tasking to alleviate these difficulties. MatRIS includes the IRIS task-based runtime on the bottom level and exposes different layers of abstraction to render algorithms architecturally agnostic. MatRIS ensures the decomposition and creation of tasks that represent the necessary encapsulation of the optimized kernels from both vendor and open-source math libraries. Once built, MatRIS can select different combinations of accelerators at runtime, making it portable even on diverse heterogeneous architectures. By leveraging the IRIS runtime’s features for managing heterogeneity, MatRIS deploys algorithms that remove the need to specify orchestration and data transfer. This study describes how the serial task abstraction of a tiled Cholesky factorization is made portable and scalable in the case of multi-device and multi-vendor heterogeneity on a node with NVIDIA and AMD GPUs by using MatRIS. First, we demonstrate that Cholesky in MatRIS provides multi-GPU scalability that offers competitive performance versus cuSolverMG. Then, we present the challenges and opportunities for heterogeneous execution.

Monil, M. A. H.↗
DOE OSTI2022

Providing performance portable numerics for Intel GPUs

Summary With discrete Intel GPUs entering the high‐performance computing landscape, there is an urgent need for production‐ready software stacks for these platforms. In this article, we report how we enable the Ginkgo math library to execute on Intel GPUs by developing a kernel backed based on the DPC++ programming environment. We discuss conceptual differences between the CUDA and DPC++ programming models and describe workflows for simplified code conversion. We evaluate the performance of basic and advanced sparse linear algebra routines available in Ginkgo's DPC++ backend in the hardware‐specific performance bounds and compare against routines providing the same functionality that ship with Intel's oneMKL vendor library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Co-design for Particle Applications at Exascale

Co-design across the Exascale Computing Project (ECP) has been critical for both enabling science applications and bringing disparate communities together. Developing and porting applications to the various high-performance computing (HPC) architectures on pre-exascale and exascale computers has been quite challenging due to the diversity of hardware features and software stacks. The Co-design Center for Particle Applications (CoPA) has developed and enhanced the Cabana and PROGRESS/BML libraries to facilitate the creation of new particle applications, make existing particle applications exascale capable, and allow teams to explore new capabilities. Particle methods from atomistic, mesoscale, continuum, through cosmological scales have been built with Cabana, along with new possibilities for application coupling. Similarly, the PROGRESS/BML library has enabled quantum particle applications with linear algebra solvers to use advanced hardware. Across these CoPA-developed libraries, the co-design abstraction layer combines performance portability with math library support to facilitate separation of concerns and directly support science runs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

OpenMP Target Task: Tasking and Target Offloading on Heterogeneous Systems

This work evaluated the use of OpenMP tasking with target GPU offloading as a potential solution for programming productivity and performance on heterogeneous systems. Also, it is proposed a new OpenMP specification to make the implementation of heterogeneous codes simpler by using OpenMP target task, which integrates both OpenMP tasking and target GPU offloading in a single OpenMP pragma. As a test case, the authors used one of the most popular and widely used Basic Linear Algebra Subprogram Level-3 routines: triangular solver (TRSM). To benefit from the heterogeneity of the current high-performance computing systems, the authors propose a different parallelization of the algorithm by using a nonuniform decomposition of the problem. This work used target GPU offloading inside OpenMP tasks to address the heterogeneity found in the hardware. This new approach can outperform the state-of-the-art algorithms, which use a uniform decomposition of the data, on both the CPU-only and hybrid CPU-GPU systems, reaching speedups of up to one order of magnitude. The performance that this approach achieves is faster than the IBM ESSL math library on CPU and competitive relative to a highly optimized heterogeneous CUDA version. One node of Oak Ridge National Laboratory’s supercomputer, Summit, was used for performance analysis.

Valero Lara, Pedro↗
DOE OSTI2023

IRIS-DMEM: Efficient Memory Management for Heterogeneous Computing

This paper proposes an efficient data memory management approach for the Intelligent RuntIme System (IRIS) heterogeneous computing framework along with new data transfer policies. IRIS provides a task-based programming model for extreme heterogeneous computing (e.g., CPU, GPU, DSP, FPGA) with support for today's most important programming languages (e.g., OpenMP, OpenCL, CUDA, HIP, OpenACC). However, the IRIS framework either forces the programmer to introduce data transfer commands for each task or relies on suboptimal memory management for automatic and transparent data transfers. The work described here extends IRIS with novel heterogeneous memory handling and introduces novel data transfer policies by employing the Distributed data MEMory handler (DMEM) for efficient and optimal movement of data among the various computing resources. The proposed approach achieves performance gains of up to 7× for tiled LU factorization and tiled DGEMM (i.e., matrix multiplication) benchmarks. Moreover, this approach also reduces data transfers by up to 71% when compared to previous IRIS heterogeneous memory management handlers. This work compares the performance results of the IRIS framework's novel DMEM with the StarPU runtime and MAGMA math library for GPUs. Experiments show a performance gain of up to 1.95× over StarPU and 2.1× over MAGMA.

Miniskar, Narasinga Rao↗
DOE OSTI2025

ChatHPC: Building the Foundations for a Productive and Trustworthy AI-Assisted HPC Ecosystem

ChatHPC democratizes large language models for the high-performance computing (HPC) community by providing the infrastructure, ecosystem, and knowledge needed to apply modern generative AI technologies to rapidly create specific capabilities for critical HPC components while using relatively modest computational resources. Our divide-and-conquer approach focuses on creating a collection of reliable, highly specialized, and optimized AI assistants for HPC based on the cost-effective and fast Code Llama fine-tuning processes and expert supervision. We target major components of the HPC software stack, including programming models, runtimes, I/O, tooling, and math libraries. Thanks to AI, ChatHPC provides a more productive HPC ecosystem by boosting important tasks related to portability, parallelization, optimization, scalability, and instrumentation, among others. With relatively small datasets (on the order of KB), the AI assistants, which are created in a few minutes by using one node with two NVIDIA H100 GPUs and the ChatHPC library, can create new capabilities with Meta’s 7-billion parameter Code Llama base model to produce high-quality software with a level of trustworthiness of up to 90% higher than the 1.8-trillion parameter OpenAI ChatGPT-4o model for critical programming tasks in the HPC software stack.

Young, Aaron [ORNL] (ORCID:0000000254484667)↗
DOE OSTI2025

Real Vector Framework

SAND2025-11463O The Real Vector Framework (RVF) is a modern and flexible C++ vector math library for developing scientific computing software that involves vector computations. RVF allows an opt-in approach to functionality that parallels the familiar base-class and override structures of object-oriented programming. Users can reuse and customize the code without inheritance entanglements and dynamic dispatch, while enabling seamless interoperability between diverse container types. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

von Winckel, Gregory [Sandia National Lab. (SNL-CA↗
DOE OSTI2022

Towards Enhancing Coding Productivity for GPU Programming Using Static Graphs

The main contribution of this work is to increase the coding productivity of GPU programming by using the concept of Static Graphs. GPU capabilities have been increasing significantly in terms of performance and memory capacity. However, there are still some problems in terms of scalability and limitations to the amount of work that a GPU can perform at a time. To minimize the overhead associated with the launch of GPU kernels, as well as to maximize the use of GPU capacity, we have combined the new CUDA Graph API with the CUDA programming model (including CUDA math libraries) and the OpenACC programming model. We use as test cases two different, well-known and widely used problems in HPC and AI: the Conjugate Gradient method and the Particle Swarm Optimization. In the first test case (Conjugate Gradient) we focus on the integration of Static Graphs with CUDA. In this case, we are able to significantly outperform the NVIDIA reference code, reaching an acceleration of up to 11x thanks to a better implementation, which can benefit from the new CUDA Graph capabilities. In the second test case (Particle Swarm Optimization), we complement the OpenACC functionality with the use of CUDA Graph, achieving again accelerations of up to one order of magnitude, with average speedups ranging from 2x to 4x, and performance very close to a reference and optimized CUDA code. Our main target is to achieve a higher coding productivity model for GPU programming by using Static Graphs, which provides, in a very transparent way, a better exploitation of the GPU capacity. The combination of using Static Graphs with two of the current most important GPU programming models (CUDA and OpenACC) is able to reduce considerably the execution time w.r.t. the use of CUDA and OpenACC only, achieving accelerations of up to more than one order of magnitude. Finally, we propose an interface to incorporate the concept of Static Graphs into the OpenACC Specifications.

58 GEOSCIENCES↗
DOE OSTI2023

Understanding SYCL Portability for Pseudorandom Number Generation: a Case Study with Gene-Expression Connectivity Mapping

Towards the goal of improving functional and performance portability of SYCL, we study a bioinformatics application that has been accelerated with CUDA and fast pseudorandom number generation on a GPU. We describe the experience of migrating pseudorandom number generation from CUDA to SYCL, evaluate the performance of pseudorandom number generators using the CUDA random number generation library, suggest the support of the XORWOW pseudorandom number generator in the oneAPI math kernel library (oneMKL) interface for performance portability, and identify the performance gap using the MKL interface in SYCL that supports pseudorandom number generation with third-party libraries. We hope that the results are valuable for the development of the SYCL ecosystem.

Jin, Zheming↗
DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗