Related papers: Customizable Precision of Floating-Point Arithmeti…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying…
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
Thanks to the computational power of modern cluster machines, numerical simulations can provide, with an unprecedented level of details, new insights into fluid mechanics. However, taking full advantage of this hardware remains challenging…
We present a novel approach for designing complex approximate arithmetic circuits that trade correctness for power consumption and play important role in many energy-aware applications. Our approach integrates in a unique way formal methods…
In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…
We propose a compute shader based point cloud rasterizer with up to 10 times higher performance than classic point-based rendering with the GL_POINT primitive. In addition to that, our rasterizer offers 5 byte depth-buffer precision with…
Points-to analysis is the problem of approximating run-time values of pointers statically or at compile-time. Points-to sets are used to store the approximated values of pointers during points-to analysis. Memory usage and running time…
Many modern search domains comprise high-dimensional vectors of floating point numbers derived from neural networks, in the form of embeddings. Typical embeddings range in size from hundreds to thousands of dimensions, making the size of…
Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training…
Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low…
The number of IoT devices is expected to continue its dramatic growth in the coming years and, with it, a growth in the amount of data to be transmitted, processed and stored. Compression techniques that support analytics directly on the…
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…
While advancements in quantization have significantly reduced the computational costs of inference in deep learning, training still predominantly relies on complex floating-point arithmetic. Low-precision fixed-point training presents a…
This piece of work presents a meaningful example for the advantages of using bitwise operations for creating effective algorithms in programming. A task connected with mathematical modeling in weaving industry is examined and computed.
In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface…
With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…