Related papers: Implementation and Synthesis of Math Library Funct…
The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for change and avoiding maintainer overload. This includes dealing…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
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…
Recent large language models (LLMs) have demonstrated the ability to perform explicit multi-step reasoning such as chain-of-thought prompting. However, their intermediate steps often contain errors that can propagate leading to inaccurate…
Our RLibm project generates a single implementation for an elementary function that produces correctly rounded results for multiple rounding modes and representations with up to 32-bits. They are appealing for developing fast reference…
Standard library implementations of functions like sin and exp optimize for accuracy, not speed, because they are intended for general-purpose use. But applications tolerate inaccuracy from cancellation, rounding error, and…
We describe a new C++ library for multiprecision arithmetic for numbers in the order of 100--500 bits, i.e., representable with just a few limbs. The library is written in "optimizing-compiler-friendly" C++, with an emphasis on the use of…
Numerical software depends on fast, accurate implementations of mathematical primitives like sin, exp, and log. Modern superoptimizers can optimize floating-point kernels against a given set of such primitives, but a more fundamental…
While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits…
Continual learning enables AI systems to acquire new knowledge while retaining previously learned information. While traditional unimodal methods have made progress, the rise of Multimodal Large Language Models (MLLMs) brings new challenges…
Beginning programmers struggle with the complex grammar of modern programming languages like Java, and make lot of syntax errors. The diagnostic syntax error messages from compilers and IDEs are sometimes useful, but often the messages are…
Code optimization remains a core objective in software development, yet modern compilers struggle to navigate the enormous optimization spaces. While recent research has looked into employing large language models (LLMs) to optimize source…
Frontier Large language models (LLMs) like ChatGPT and Gemini can decipher cryptic compiler errors for novice programmers, but their computational scale, cost, and tendency to over-assist make them problematic for widespread pedagogical…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
MPI collective operations provide a standardized interface for performing data movements within a group of processes. The efficiency of collective communication operations depends on the actual algorithm, its implementation, and the…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including…
This paper provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element…
Mathematical reasoning represents a critical frontier in advancing large language models (LLMs). While step-by-step approaches have emerged as the dominant paradigm for mathematical problem-solving in LLMs, the quality of reasoning steps in…