Concept

Modular arithmetic

Related publications (72)

“Transplanting the human mind into inanimate matter”: Leibniz’s Reckoning Machine Seen from a Media Perspective

Between 1672 and 1694, the German mathematician Gottfried Wilhelm Leibniz (1646-1716) attempted to design a reckoning machine that would be able to perform the four basic arithmetic operations on multiple-digit numbers. Working closely with the French cloc ...

2020

MATHICSE Technical Report : Fast QR decomposition of HODLR matrices

Daniel Kressner, Ana Susnjara

The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as they proceed indi- ...

MATHICSE2018

Improving Circuit Mapping Performance Through MIG-based Synthesis for Carry Chains

Giovanni De Micheli, Paolo Ienne, Mathias Soeken, Grace Zgheib, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù, Xifan Tang, Ana Petkovska, Zhufei Chu

Hard-wired carry chains in FPGAs are designed to improve efficiency of important arithmetic primitives. Although they are proven to be effective for arithmetic-rich functions, there are very few studies on the optimization opportunities of carry chains for ...

ACM2017

An improvement on the number of simplices in F-q(d)

Van Thang Pham

Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...

Elsevier Science Bv2017

Solving quantified linear arithmetic by counterexample-guided instantiation

Viktor Kuncak, Andrew Joseph Reynolds

This paper presents a framework to derive instantiation-based decision procedures for satisfiability of quantified formulas in first-order theories, including its correctness, implementation, and evaluation. Using this framework we derive decision procedur ...

2017

Towards a Compiler for Reals

Viktor Kuncak, Eva Darulova

Numerical software, common in scientific computing or embedded systems, inevitably uses a finite-precision approximation of the real arithmetic in which most algorithms are designed. In many applications, the roundoff errors introduced by finite-precision ...

2017

Experimental observations and modelling of intrinsic rotation reversals in tokamaks

Basil Duval, Yann Camenen, Emiliano Fable, Alessandro Bortolon

The progress made in understanding spontaneous toroidal rotation reversals in tokamaks is reviewed and current ideas to solve this ten-year-old puzzle are explored. The paper includes a summarial synthesis of the experimental observations in AUG, C-Mod, KS ...

Iop Publishing Ltd2017

A modular approach to learning manipulation strategies from human demonstration

Aude Billard, Miao Li, Ravin Luis De Souza

Object manipulation is a challenging task for robotics, as the physics involved in object interaction is complex and hard to express analytically. Here we introduce a modular approach for learning a manipulation strategy from human demonstration. Firstly w ...

Springer Verlag2016

Authenticated Encryption with Variable Stretch

Serge Vaudenay, Damian Vizár, Reza Reyhanitabar

In conventional authenticated-encryption (AE) schemes, the ciphertext expansion, a.k.a.stretch or tag length, is a constant or a parameter of the scheme that must be fixed per key. However, using variable-length tags per key can be desirable in practice or ...

Springer-Verlag Berlin2016

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015

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