Related papers: Correct Approximation of IEEE 754 Floating-Point A…
Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
As the dimensions and operating voltages of computer electronics shrink to cope with consumers' demand for higher performance and lower power consumption, circuit sensitivity to soft errors increases dramatically. Recently, a new data-type…
Neural network algorithms simulated on standard computing platforms typically make use of high resolution weights, with floating-point notation. However, for dedicated hardware implementations of such algorithms, fixed-point synaptic…
Adversarial examples pose a security risk as they can alter decisions of a machine learning classifier through slight input perturbations. Certified robustness has been proposed as a mitigation where given an input $\mathbf{x}$, a…
Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…
One of the major bottlenecks in high-resolution Earth Observation (EO) space systems is the downlink between the satellite and the ground. Due to hardware limitations, on-board power limitations or ground-station operation costs, there is a…
Customizing the precision of data can provide attractive trade-offs between accuracy and hardware resources. We propose a novel form of vector computing aimed at arrays of custom-precision floating point data. We represent these vectors in…
Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…
The implementation of digital filters in processors based on fixed-point arithmetic can lead to problems related to the finite word-length. In particular, the processing of signals in such filters can produce overflows and unwanted noise…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…
We initiate the study of parallel quantum programming by defining the operational and denotational semantics of parallel quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
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…
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
Algorithms are ways of mapping problems to solutions. An algorithm is invertible precisely when this mapping is injective, such that the initial problem can be uniquely inferred from its solution. While invertible algorithms can be…