Related papers: Number Parsing at a Gigabyte per Second
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
We describe how to compute very far decimals of $$\pi$$ and how to provide formal guarantees that the decimals we compute are correct. In particular, we report on an experiment where 1 million decimals of $$\pi$$ and the billionth…
On the string of finite length, a (genomic) transposition is defined as the operation of exchanging two consecutive substrings. The minimum number of transpositions needed to transform one into the other is the transposition distance, that…
Multiplication of n-digit integers by long multiplication requires O(n^2) operations and can be time-consuming. In 1970 A. Schoenhage and V. Strassen published an algorithm capable of performing the task with only O(n log(n)) arithmetic…
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…
This paper presents the analysis of the impact of a floating-point number precision reduction on the quality of text classification. The precision reduction of the vectors representing the data (e.g. TF-IDF representation in our case)…
Binary, or one-bit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this work, we study the problem of data classification from binary data and…
Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…
HalftimeHash is a new algorithm for hashing long strings. The goals are few collisions (different inputs that produce identical output hash values) and high performance. Compared to the fastest universal hash functions on long strings…
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
Traditional deep learning often overlooks bytes, the basic units of the digital world, where all forms of information and operations are encoded and manipulated in binary format. Inspired by the success of next token prediction in natural…
Given a combinatorial decomposition for a counting problem, we resort to the simple scheme of approximating large numbers by floating-point representations in order to obtain efficient Fully Polynomial Time Approximation Schemes (FPTASes)…
Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively…
Intel includes in its recent processors a powerful set of instructions capable of processing 512-bit registers with a single instruction (AVX-512). Some of these instructions have no equivalent in earlier instruction sets. We leverage these…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l;…
The recent surge of interest in Deep Neural Networks (DNNs) has led to increasingly complex networks that tax computational and memory resources. Many DNNs presently use 16-bit or 32-bit floating point operations. Significant performance…