Choosing a Pascal numerical library

This page is an informational map of Pascal numerical libraries for someone choosing a foundation for Free Pascal work. It uses only facts verified from upstream projects and this repository; see the comparison policy below.

Position

mathlib-fp is intended as a general-purpose numerical library for Free Pascal with four deliberate characteristics: an MIT licence with no paid tier, a complete implementation in Object Pascal source within this repository, no mandatory third-party numerical runtime, and documentation and qualification material organised as a learning path. These characteristics are described for mathlib-fp itself; this page makes no claim that they are unique or that any other library lacks them.

Known current gaps

The capability inventory is the authority for what mathlib-fp does not yet support. The main gaps and their roadmap destinations are:

• Special-function families — documented real-double Bessel, elliptic, Jacobi elliptic, exponential-integral, and Gauss hypergeometric functions are stable in 2.2.0; complex branches and analytic continuation remain unsupported.
• Advanced spectral families — real and complex Schur, Hessenberg, nonsymmetric real eigen, and generalized eigen paths are stable in 2.2.0; polynomial, shift-invert, and interior-target eigensystems remain deferred.
• Stiff and implicit ODEs — v2.3.0 adds a dense SDIRK2 solver alongside the explicit, non-stiff path, as described in the stiff and implicit ODE gate.
• Advanced sparse direct algorithms — no fill-reducing symbolic ordering, multifrontal/supernodal, distributed, out-of-core, or GPU path exists; the destination is the 2.4 Sparse Direct II gate.
• Parallel/SIMD dispatch and advanced iterative variants — no stable thread-pool or vector-intrinsic API and no block/flexible Krylov or multigrid; the destination is the performance acceleration track.
• Advanced DSP design and wavelets — equiripple, advanced IIR families, and broader wavelets are conditional; the destination is the Signal Processing II lane.
• Conditional statistics and data science — survival/factor analysis, robust covariance, GLMs, boosting, and broader forecasting are not activated; the destination is the Statistics II and Data Analysis II lanes.
• General model/decomposition persistence — only selected model adapters are stable; the destination is the Persistence and interchange II lane.
• Global and discrete optimisation — no reproducible global-optimisation baseline and no committed MILP/MINLP capability; the destination is the Global and discrete optimisation lane.

Engineering differentiators

mathlib-fp maintains several documentation and verification practices that are part of its release process:

• versioned web and offline documentation built from the same reviewed sources as the repository Markdown;
• beginner recipes and domain learning routes that lead with the double-real, allocating path;
• a machine-readable capability inventory (capabilities.json) that drives a human-readable status page;
• a qualification programme with accuracy budgets, independent references, adversarial fixtures, and release-specific evidence reports;
• runnable documentation examples whose claimed output is checked.

These are described as characteristics of mathlib-fp; this page does not assert that no other compared library does similar things.

Comparison policy

This page is informational, not advertising. It is reviewed at least once per major release. Claims are linked to evidence where practical, unknown facts are distinguished from unsupported capabilities, and no library is declared superior on the basis of raw function counts.

Sources

• FPC NumLib — FPC NumLib unit reference.
• DMath — DMath/TPMath page.
• LMath — SourceForge LMath project.
• MtxVec — Dew Research.
• ALGLIB for Delphi — ALGLIB Project.
• AMath/DAMath + MPArith — Wolfgang Ehrhardt.
• mrMath — github.com/mikerabat/mrmath.
• numerik — github.com/ariaghora/numerik.
• FastMath — github.com/neslib/FastMath.
• mathlib-fp — github.com/ikelaiah/mathlib-fp.

URLs that are not already present in this repository's documentation or the verified fact set are deliberately omitted rather than invented.