Related papers: Number Parsing at a Gigabyte per Second

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…

We consider the prospect of a processor that can perform interval arithmetic at the same speed as conventional floating-point arithmetic. This makes it possible for all arithmetic to be performed with the superior security of interval…

Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…

Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our…

Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a…

Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process,…

Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…

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…

Reducing hardware overhead of neural networks for faster or lower power inference and training is an active area of research. Uniform quantization using integer multiply-add has been thoroughly investigated, which requires learning many…

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…

Within numerical reasoning, understanding numbers themselves is still a challenge for existing language models. Simple generalisations, such as solving 100+200 instead of 1+2, can substantially affect model performance (Sivakumar and…

Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…

A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very…

We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…

We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…

We report (to our knowledge) the first evaluation of Constraint Satisfaction as a computational framework for solving closest string problems. We show that careful consideration of symbol occurrences can provide search heuristics that…

In this paper we use ternary representation of numbers for compressing text data. We use a binary map for ternary digits and introduce a way to use the binary 11-pair, which has never been use for coding data before, and we futher use…

This paper introduces a binary encoding that supports arbitrarily large, small and precise decimals. It completely preserves information and order. It does not rely on any arbitrary use-case-based choice of calibration and is readily…

How should text dataset sizes be compared across languages? Even for content-matched (parallel) corpora, UTF-8 encoded text can require a dramatically different number of bytes for different languages. In our work, we define the byte…

Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for…