Related papers: Introduction to the GiNaC Framework for Symbolic C…
Although many active scientific codes use modern Fortran, most contemporary scientific software "libraries" are implemented in C and C++. Providing their numerical, algorithmic, or data management features to Fortran codes requires writing…
Modern unified programming models (such as CUDA and SYCL) that combine host (CPU) code and GPU code into the same programming language, same file, and same lexical scope lack adequate support for GPU code specialization, which is a key…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Every algorithm which can be executed on a computer can at least in principle be realized in hardware, i.e. by a discrete physical system. The problem is that up to now there is no programming language by which physical systems can…
By leveraging quantum-mechanical properties like superposition, entanglement, and interference, quantum computing (QC) offers promising solutions for problems that classical computing has not been able to solve efficiently, such as drug…
Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields $\mathbb{Q}(a_1,\ldots,a_n)$ where the extensions numbers $a_k$ may be…
Quantum computers have leaped from the theoretical realm into a race to large-scale implementations. This is due to the promise of revolutionary speedups, where achieving such speedup requires designing an algorithm that harnesses the…
Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
Despite the plethora of powerful software to spot bugs, identify performance bottlenecks or simply improve the overall quality of code, programming languages remain the first and most important tool of a developer. Therefore, appropriate…
We introduce an algebra qCCS of pure quantum processes in which no classical data is involved, communications by moving quantum states physically are allowed, and computations is modeled by super-operators. An operational semantics of qCCS…
This article introduces hinted dictionaries for expressing efficient ordered sets and maps functionally. As opposed to the traditional ordered dictionaries with logarithmic operations, hinted dictionaries can achieve better performance by…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
Q# is a standalone domain-specific programming language from Microsoft for writing and running quantum programs. Like most industrial languages, it was designed without a formal specification, which can naturally lead to ambiguity in its…
Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations.…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Distributed quantum computing (DQC) is a promising proposal for overcoming the scalability challenges of quantum computing. However, the evaluation of DQC hardware and software is difficult due to the relative dearth of classical simulation…
Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is…
Quantum computer programming is emerging as a new subject domain from multidisciplinary research in quantum computing, computer science, mathematics (especially quantum logic, lambda calculi, and linear logic), and engineering attempts to…