Related papers: Relative error due to a single bit-flip in floatin…

We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…

This paper presents two sufficient conditions to ensure a faithful evaluation of polynomial in IEEE-754 floating point arithmetic. Faithfulness means that the computed value is one of the two floating point neighbours of the exact result;…

The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…

Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…

A divide-and-conquer cryptanalysis can often be mounted against some keystream generators composed of several (nonlinear) independent devices combined by a Boolean function. In particular, any parity-check relation derived from the periods…

The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…

The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits ("qubits") are susceptible to two types of error, corresponding to flips of the…

Given a set $\cal P$ of points in the Euclidean plane and two triangulations of $\cal P$, the flip distance between these two triangulations is the minimum number of flips required to transform one triangulation into the other.…

The differences between the sets in which ideal arithmetics takes place and the sets of floating point numbers are outlined. A set of classical problems in correct numerical evaluation is presented, to increase the awareness of newcomers to…

The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…

We show how to simulate a roll of a fair $n$-sided die by one flip of a biased coin with probability $1/n$ of coming up heads, followed by $3\lfloor\log_2 n \rfloor+1$ flips of a fair coin.

Coin flipping is a fundamental cryptographic primitive that enables two distrustful and far apart parties to create a uniformly random bit [Blu81]. Quantum information allows for protocols in the information theoretic setting where no…

Physical instantiations of a bit of information are subject to thermal noise that can trigger unintended bit-flip errors. Bits implemented with CMOS technology typically operate in regimes that reliably suppress these errors with a large…

This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming…

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…

We propose, experimentally realize and study possible applications of a new type of logic element: random flip-flop. By definition it operates similarly to a conventional flip-flop except that it functions with probability of 1/2 otherwise…

How to turn the flip of a coin into a random variable whose expected value equals a scattering amplitude? We answer this question by constructing a numerical algorithm to evaluate curve integrals - a novel formulation of scattering…

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…

Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…

For any discrete probability distributions with bounded entropy, we can generate exactly a random variate using only a finite expected number of perfect coin flips. A perfect coin flip is the outcome of an unbiased Bernoulli random…