Related papers: Modular SIMD arithmetic in Mathemagix
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…
Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
An integer adder for integers in the binary representation is one of the basic operations of any digital processor. For adding two integers of N bits each, the serial adder takes as many clock ticks. For achieving higher speeds, parallel…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
As we venture into the Intermediate-Scale Quantum (ISQ) era, the proficiency of modular arithmetic operations becomes pivotal for advancing quantum cryptographic algorithms. This study presents an array of quantum circuits, each…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over $\Q$, but it does not seem to be popular among…
In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as…
Integer factorization is a very hard computational problem. Currently no efficient algorithm for integer factorization is publicly known. However, this is an important problem on which it relies the security of many real world cryptographic…
Matrix-multiplication units (MXUs) are now prevalent in every computing platform. The key attribute that makes MXUs so successful is the semiring structure, which allows tiling for both parallelism and data reuse. Nonetheless,…
In~\cite{algorithmic} was given an algorithm that computes arithmetical structures on matrices. We use some of the ideas contained there to get an algorithm that computes arithmetical structures over dominated polynomials. A dominated…
We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is…
We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…
Given n positive integers, the Modular Subset Sum problem asks if a subset adds up to a given target t modulo a given integer m. This is a natural generalization of the Subset Sum problem (where m=+\infty) with ties to additive…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We present an Integer Linear Programming based approach to finding the optimal fusion strategy for combinator-based parallel programs. While combinator-based languages or libraries provide a convenient interface for programming parallel…