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This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed…
This paper proposes hardware converters for the microscaling format (MX-format), a reduced representation of floating-point numbers. We present an algorithm and a memory-free hardware model for converting 32 single-precision floating-point…
As recently demonstrated, Deep Neural Networks (DNN), usually trained using single precision IEEE 754 floating point numbers (binary32), can also work using lower precision. Therefore, 16-bit and 8-bit compressed format have attracted…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…
Coin-flipping is a fundamental task in two-party cryptography where two remote mistrustful parties wish to generate a shared uniformly random bit. While quantum protocols promising near-perfect security exist for weak coin-flipping -- when…
Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and…
In many machine learning applications, e.g., tree-based ensembles, floating point numbers are extensively utilized due to their expressiveness. Nowadays performing data analysis on embedded devices from dynamic data masses becomes…
We derive two probabilistic bounds for the relative forward error in the floating point summation of $n$ real numbers, by representing the roundoffs as independent, zero-mean, bounded random variables. The first probabilistic bound is based…
We describe a compression method for floating-point astronomical images that gives compression ratios of 6 -- 10 while still preserving the scientifically important information in the image. The pixel values are first preprocessed by…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…
We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite…
One of the major bottlenecks in high-resolution Earth Observation (EO) space systems is the downlink between the satellite and the ground. Due to hardware limitations, on-board power limitations or ground-station operation costs, there is a…
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…
Iterative methods with certified convergence for the computation of Gauss--Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be…
A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
8-bit integer inference, as a promising direction in reducing both the latency and storage of deep neural networks, has made great progress recently. On the other hand, previous systems still rely on 32-bit floating point for certain…
This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean…