Related papers: Recursive function templates as a solution of line…
Vector operations play an important role in high performance computing and are typically provided by highly optimized libraries that implement the BLAS (Basic Linear Algebra Subprograms) interface. In C++ templates and operator overloading…
In the last decade, Expression Templates (ET) have gained a reputation as an efficient performance optimization tool for C++ codes. This reputation builds on several ET-based linear algebra frameworks focused on combining both elegant and…
This paper explores the relationship between C++ templates and partial evaluation. Templates were designed to support generic programming, but unintentionally provided the ability to perform compile-time computations and code generation.…
Template metaprogramming is a popular technique for implementing compile time mechanisms for numerical computing. We demonstrate how expression templates can be used for compile time symbolic differentiation of algebraic expressions in C++…
Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often…
Performance, genericity and flexibility are three valuable qualities for scientific environments that tend to be antagonistic. C++ provides excellent support for both performances and genericity thanks to its support for (class and…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for…
Expression templates are a well-known set of techniques for improving the efficiency of operator overloading-based forward mode automatic differentiation schemes in the C++ programming language by translating the differentiation from…
The main purpose of this paper is to propose five programs in C++ for matrix computations and solving recurrent equations systems with entries in max plus algebra.
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,…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
C++ does not support run-time resolution of template type arguments. To circumvent this restriction, we can instantiate a template for all possible combinations of type arguments at compile time and then select the proper instance at run…
To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries such as LAPACK commonly implement operations as blocked algorithms. However, to achieve next-to-optimal performance…
The main purpose of this paper is to propose six programs in C++ for matrix computations and solving recurrent equations systems with entries in min plus algebra.
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…
The C++ Standard Template Library is the flagship example for libraries based on the generic programming paradigm. The usage of this library is intended to minimize the number of classical C/C++ errors, but does not warrant bug-free…
Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage…
Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…
We present a new method for large language models to solve compositional tasks. Although they have shown strong performance on traditional language understanding tasks, large language models struggle to solve compositional tasks, where the…