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Divisibility tests are algorithms that can quickly decide if one integer is divisible by another. There are many tests but most are either of the trimming or summing variety. Our goals are to present Zbikowski's family of trimming tests as…
Faced with saturation of Moore's law and increasing dimension of data, system designers have increasingly resorted to parallel and distributed computing. However, distributed computing is often bottle necked by a small fraction of slow…
A generalized Chinese remainder theorem (CRT) for multiple integers from residue sets has been studied recently, where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known. A…
In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Quantum processors require rapid and high-fidelity simultaneous measurements of many qubits. While superconducting qubits are among the leading modalities toward a useful quantum processor, their readout remains a bottleneck. Traditional…
The current BigData era routinely requires the processing of large scale data on massive distributed computing clusters. Such large scale clusters often suffer from the problem of "stragglers", which are defined as slow or failed nodes. The…
Docker images are composed of multiple layers, each of which contains a set of instructions, and an archive of files. Layers allow Docker to separate a large build task into smaller ones, such that when a part of the program is changed,…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…
The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Judging whether an integer can be divided by prime numbers such as 2 or 3 may appear trivial to human beings, but can be less straightforward for computers. Here, we tested multiple deep learning architectures and feature engineering…
An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Modern computationally-heavy applications are often time-sensitive, demanding distributed strategies to accelerate them. On the other hand, distributed computing suffers from the bottleneck of slow workers in practice. Distributed coded…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We introduce an error resilient distributed computing method based on an extension of the channel polarization phenomenon to distributed algorithms. The method leverages an algorithmic split operation that transforms two identical compute…
Deep neural networks (DNNs) are of critical use in different domains. To accelerate DNN computation, tensor compilers are proposed to generate efficient code on different domain-specific accelerators. Existing tensor compilers mainly focus…
In this note, we represent integers in a type of factoradic notation. Rather than use the corresponding Lehmer code, we will view integers as permutations. Given a pair of integers n and k, we give a formula for n mod k in terms of the…