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Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
Neural network algorithms simulated on standard computing platforms typically make use of high resolution weights, with floating-point notation. However, for dedicated hardware implementations of such algorithms, fixed-point synaptic…
Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or…
Tensor Core is a mixed-precision matrix-matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense…
In several fields such as statistics, machine learning, and bioinformatics, categorical variables are frequently represented as one-hot encoded vectors. For example, given 8 distinct values, we map each value to a byte where only a single…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…
We examine the problem of optimizing classification tree evaluation for on-line and real-time applications by using GPUs. Looking at trees with continuous attributes often used in image segmentation, we first put the existing algorithms for…
This paper describes our experience developing polynomial approximations for trigonometric functions that produce correctly rounded results for multiple representations and rounding modes using the RLIBM approach. A key challenge with…
This paper describes the design and simulation of an 8-bit dedicated processor for calculating the Sine and Cosine of an Angle using CORDIC Algorithm (COordinate Rotation DIgital Computer), a simple and efficient algorithm to calculate…
The convergence characteristics of two viscous core corrections as used in straight-line segmentation methods are rigorously analysed. These are \emph{curvature corrections} that account for the induced velocity contribution at a point on a…
Tensor cores (TCs) are a type of Application-Specific Integrated Circuit (ASIC) and are a recent addition to Graphics Processing Unit (GPU) architectures. As such, TCs are purposefully designed to greatly improve the performance of Matrix…
Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors provides more possibilities for the development and implementation of quantum algorithms.…
Coherent Ising Machines (CIMs) have emerged as a hybrid form of quantum computing devices designed to solve NP-complete problems, offering an exciting opportunity for discovering optimal solutions. Despite challenges such as susceptibility…
This paper introduces a fast Central Processing Unit (CPU) implementation of geodesic morphological operations using stream processing. In contrast to the current state-of-the-art, that focuses on achieving insensitivity to the filter sizes…
Approximate computing techniques have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing…
An algorithm of particle-in-cell simulations is described and tested to aid further the actual design of simple vircators working on axially symmetric modes. The methods of correction of the numerical solution, have been chosen and jointly…
Object-oriented programming is often regarded as too inefficient for high-performance computing (HPC), despite the fact that many important HPC problems have an inherent object structure. Our goal is to bring efficient, object-oriented…
Many modern sequence alignment tools implement fast string matching using the space efficient data structure called FM-index. The succinct nature of this data structure presents unique challenges for the algorithm designers. In this paper,…
Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing…