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Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD)…

We extend the Stainless deductive verifier with floating-point support, providing the first automated verification support for floating-point numbers for a subset of Scala that includes polymorphism, recursion and higher-order functions. We…

Modern CNN are typically based on floating point linear algebra based implementations. Recently, reduced precision NN have been gaining popularity as they require significantly less memory and computational resources compared to floating…

To efficiently support Large Language Models (LLMs), modern GPGPU architectures have introduced new features and programming paradigms, such as warp specialization. These features enable temporal overlap between the producer and consumer,…

The rapid adaptation of data driven AI models, such as deep learning inference, training, Vision Transformers (ViTs), and other HPC applications, drives a strong need for runtime precision configurable different non linear activation…

Commercial FPGAs, such as AMD Versal devices, increasingly incorporate AI engines that exploit low-precision packed-SIMD fused multiply-accumulate (FMA) to achieve proportional throughput gains. However, trans-precision FMA (e.g.,…

Spectral analysis plays an important role in detection of damage in structures and deep learning. The choice of a floating-point format plays a crucial role in determining the accuracy and performance of spectral analysis. The IEEE Std…

In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable 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…

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…

The state-of-the-art hardware platforms for training Deep Neural Networks (DNNs) are moving from traditional single precision (32-bit) computations towards 16 bits of precision -- in large part due to the high energy efficiency and smaller…

Real-time multi-view point cloud reconstruction is a core problem in 3D vision and immersive perception, with wide applications in VR, AR, robotic navigation, digital twins, and computer interaction. Despite advances in multi-camera systems…

We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can…

Floating-point non-associativity makes fundamental deep learning operations, such as matrix multiplication (matmul) on GPUs, inherently non-deterministic. Despite this, the statistical structure of the resulting numerical error remains…

Emerging applications such as augmented reality and tactile Internet are compute-intensive and latency-sensitive, which hampers their running in constrained end devices alone or in the distant cloud. The stringent requirements of such…

Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in…

Posit arithmetic has emerged as a promising alternative to IEEE 754 floating-point representation, offering enhanced accuracy and dynamic range. However, division operations in posit systems remain challenging due to their inherent hardware…

The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…

In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…

Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…