Basiscode

Basiscode is a concept and accompanying software library designed to separate algorithmic specifications from the basis in which data is represented. It provides a basis-agnostic intermediate representation and tooling that allow developers to write computations in a canonical form and then transform or optimize them for different basis choices, such as Cartesian coordinates, Fourier bases, or custom orthonormal bases. By abstracting the basis, basiscode aims to improve portability across numerical backends and enable targeted optimizations for specific hardware.

At its core, basiscode treats computations as transformations between basis representations. It supports management of bases, automatic lowering of high-level operations to basis-aware primitives, and mechanisms to compose complex workflows from simple building blocks. The approach emphasizes reproducibility, cache-friendly data layouts, and the ability to compare results across bases. This separation can help with interoperability between libraries and with exploring alternative numerical representations without rewriting algorithms.

Key features include:

- Basis-aware representations and a type system that tracks basis context

- Transformation and lowering passes that map high-level operations to basis primitives

- Interoperability with common numeric libraries and data formats

- Performance-oriented scheduling, vectorization, and backend simulations

- Debugging, tracing, and reproducible results across different bases

Applications span linear algebra, signal processing, computer graphics, and scientific computing, with use in machine learning research and compiler optimization workflows. Basiscode remains a niche concept with multiple independent implementations and evolving standards. Supporters cite improved portability and hardware-aware performance, while critics point to added complexity and a steeper learning curve.