Related papers: lrsarith: a small fixed/hybrid arithmetic C librar…

Recent advancements in large language models (LLMs) underscore the need for stronger reasoning capabilities to solve complex problems effectively. While Chain-of-Thought (CoT) reasoning has been a step forward, it remains insufficient for…

In this paper, we describe a new hybrid algorithm for computing all singular triplets above a given threshold and provide its implementation in MATLAB/Octave and R. The high performance of our codes and ease at which they can be used,…

Large language models (LLMs) have catalyzed an upsurge in automatic code generation, garnering significant attention for register transfer level (RTL) code generation. Despite the potential of RTL code generation with natural language, it…

Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…

We propose a novel framework that provides constructive feedback to an LLM in the "guess-and-check" paradigm by formally verifying its own thinking process and detecting local reasoning errors. We apply this framework to the loop invariant…

This report presents some early results on code generation targeting tensor cores on NVIDIA GPUs using the MLIR compiler infrastructure. The state-of-the-art in high-performance deep learning today is primarily driven by manually optimized…

There are numerous examples of problems in symbolic algebra in which the required storage grows far beyond the limitations even of the distributed RAM of a cluster. Often this limitation determines how large a problem one can solve in…

In this article we present PARSIR (PARallel SImulation Runner), a package that enables the effective exploitation of shared-memory multi-processor machines for running discrete event simulation models. PARSIR is a compile/run-time…

MERLIN is an accelerator physics library written in C++ which can be used for a range of accelerator tracking simulations, including collimation in hadron colliders. Recently MERLIN has been upgraded to provide a robust tool for HL-LHC…

We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as…

When implementing functionality which requires sparse matrices, there are numerous storage formats to choose from, each with advantages and disadvantages. To achieve good performance, several formats may need to be used in one program,…

Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer…

Efficient code retrieval is critical for developer productivity, yet existing benchmarks largely focus on Python and rarely stress-test robustness beyond superficial lexical cues. To address the gap, we introduce an automated pipeline for…

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset.…

The paper reports on a computer algebra program LSSS (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially efficient for very large sparse systems that have a solution…

In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…

This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…

Constraint Handling Rules (CHR) is a rule-based programming language that rewrites collections of constraints. It is typically embedded into a general-purpose language. There exists a plethora of implementation for numerous host languages.…

Parallel dataflow systems have become a standard technology for large-scale data analytics. Complex data analysis programs in areas such as machine learning and graph analytics often involve control flow, i.e., iterations and branching.…

We present ProFit, a new code for Bayesian two-dimensional photometric galaxy profile modelling. ProFit consists of a low-level C++ library (libprofit), accessible via a command-line interface and documented API, along with high-level R…