Floating-point numbers represent only a subset of real numbers. As such, floating-point arithmetic introduces approximations that can compound and have a significant impact on numerical simulations. We introduce encapsulated error, a new way to estimate ...

A general multi-purpose data structure for an efficient representation of conforming unstructured homogeneous meshes for scientific computations on CPU and GPU-based systems is presented. The data structure is provided as open-source software as part of ...

The article by Flegar et al. titled “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software” presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance ...

Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is used in many DNN software frameworks. However,...

“Code Generation for Generally Mapped Finite Elements” includes performance results for the finite element methods discussed in that manuscript. The authors provided a Zenodo archive with the Firedrake components and dependencies used, as well as the ...

We present a new algorithm for the 2D sliding window discrete Fourier transform. Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley-Tukey fast Fourier transform. ...

We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear halfspaces. We implement and evaluate randomized polynomial-time algorithms for accurately approximating the polytope’s ...

A Sparse Symmetric Indefinite Direct Solver for GPU Architectures includes performance results and comparisons of the developed GPU direct solver against a CPU direct solver. New performance data were gathered using software provided by the manuscript ...

The scientific community relies on the peer review process for assuring the quality of published material, the goal of which is to build a body of work we can trust. Computational journals such as the ACM Transactions on Mathematical Software (TOMS) use ...

We present a simple and efficient methodology for the development, tuning, and installation of matrix algorithms such as the hybrid Strassen's and Winograd's fast matrix multiply or their combination with the 3M algorithm for complex matrices (i.e., ...

We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra community for the development and ...

Modern architectures have complex memory hierarchies and increasing parallelism (e.g., multicores). These features make achieving and maintaining good performance across rapidly changing architectures increasingly difficult. Performance has become a ...

This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas from the IEEE 754 standard, by providing correct ...

The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems, and compilers to programming languages (see especially Section 8). ...

This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a ...

This article proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. A major goal is to design and develop a common framework to enable efficient, and portable, implementations of iterative algorithms for ...

We explain why we feel that the comparison betwen Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.

BTN is a collection of FORTRAN subroutines for solving unconstrained nonlinear optimization problems. It currently runs on both Intel hypercube computers (distributed memory) and Sequent computers (shared memory), and can take advantage of vector ...