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As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…
We introduce fast-decodable indexing schemes for edit distance which can be used to speed up edit distance computations to near-linear time if one of the strings is indexed by an indexing string $I$. In particular, for every length $n$ and…
With ever-increasing computational demand for deep learning, it is critical to investigate the implications of the numeric representation and precision of DNN model weights and activations on computational efficiency. In this work, we…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
Index is an important component in database systems. Learned indexes have been shown to outperform traditional tree-based index structures for fixed-sized integer or floating point keys. However, the application of the learned solution to…
The FFT of three-dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on a large number of processors. Performance of many scientific…
Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are…
This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…
We study codes that are list-decodable under insertions and deletions. Specifically, we consider the setting where a codeword over some finite alphabet of size $q$ may suffer from $\delta$ fraction of adversarial deletions and $\gamma$…
In modern low-power embedded platforms, floating-point (FP) operations emerge as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy…
The majority of text is stored in UTF-8, which must be validated on ingestion. We present the lookup algorithm, which outperforms UTF-8 validation routines used in many libraries and languages by more than 10 times using commonly available…
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…
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…
Patients with motor control difficulties often "type" on a computer using a switch keyboard to guide a scanning cursor to text elements. We show how to optimize some parts of the design of switch keyboards by casting the design problem as…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…