tpt-math

The numeric substrate for the TPT Solutions science / engineering / formal verification stack. tpt-math is a workspace of small, dependency-light, dual-licensed (MIT OR Apache-2.0) crates that wrap the best-of-breed pure-Rust math ecosystem (and, where no dual-licensed option exists, consolidate prior TPT crates) behind a coherent, no_std-friendly API.

It exists so that tpt-science, tpt-engineering, and tpt-formal can depend on one consistent set of math primitives instead of each re-wrapping the Rust math ecosystem ad hoc.

License posture. Per ADR-0007 every external dependency must be dual-licensed (MIT OR Apache-2.0) or more permissive. The crates that were Apache-2.0-only — nalgebra, clarabel, statrs, argmin, and faer — have been replaced with in-house implementations (see the crate map), so the workspace carries no Apache-2.0-only dependency. The remaining wrapped ecosystem crates (uom, rustfft, rand/rand_distr, num-*) are all dual-licensed.

Crate map

Crates are organised into layers; lower layers never depend on higher ones.

Scalar & units

Crate	Wraps / consolidates	no_std	Notes
tpt-math-numeric	num-traits, libm	yes	Scalar numeric trait glue.
tpt-math-units	uom (std disabled)	yes	Compile-time typed units.
tpt-math-units-dyn	tpt-units-runtime	no	Runtime dimension-checked units.

Exact & linear algebra

Crate	Wraps / consolidates	no_std	Notes
tpt-math-exact	num-bigint, num-rational	yes (alloc)	Exact rational + interval arithmetic.
tpt-math-linalg-dense	— (in-house; was faer)	yes (alloc)	Dense DVector/DMatrix, column-major Vec storage; storage backend for tpt-math-linalg / -optimize.
tpt-math-linalg	tpt-math-linalg-dense (in-house)	yes	Dimensionally-checked vectors/matrices over the in-house dense backend.
tpt-math-linalg-fixed	— (in-house)	yes	Const-generic fixed-size vectors/matrices + closed-form det/inverse; no allocator.
tpt-math-linalg-complex	— (in-house)	yes (alloc)	Complex-valued matrices, complex LU/Cholesky, QR eigenvalue solver for EM/quantum.
tpt-math-linalg-sparse	— (in-house)	yes (alloc)	Sparse COO/CSR/CSC + iterative CG/BiCGSTAB solvers; hand-rolled, complements tpt-fem-sparse.
tpt-math-geometry	tpt-math-linalg-fixed (in-house)	yes	Points, rotations, quaternions, isometries, projections; no nalgebra.

Geometry & spatial

Crate	Wraps / consolidates	no_std	Notes
tpt-math-geometry	tpt-math-linalg-fixed (in-house)	yes	Points, rotations, quaternions, isometries, projections; no nalgebra.
tpt-math-spatial	— (in-house)	yes	Featherstone 6-D spatial vectors, dual quaternions, screw theory; built on tpt-math-geometry / -linalg-fixed.

Graph & interpolation

Crate	Wraps / consolidates	no_std	Notes
tpt-math-graph	petgraph (dual Apache-2.0 OR MIT)	yes (alloc)	Thin wrap for adjacency / toposort / Dijkstra / A*; in-house max-flow on top.
tpt-math-interpolate	— (in-house)	yes (alloc)	RBF, ordinary Kriging, PCHIP, B-spline basis for scattered data / surrogates.

Probability

Crate	Wraps / consolidates	no_std	Notes
tpt-math-prob-core	—	yes	Shared Distribution/Sampler traits.
tpt-math-prob-dist	rand_distr	yes	Standard distributions.
tpt-math-prob-bayes	tpt-zero-bayes	no	Bayesian inference primitives.
tpt-math-prob-markov	tpt-zero-markov	no	Markov chains / HMM.
tpt-math-prob-monte-carlo	tpt-zero-monte-carlo	no	Monte Carlo methods.
tpt-math-prob-sampler	tpt-zero-sampler, tpt-zero-rand	yes	Sampling strategies.
tpt-math-prob	(umbrella)	no	Re-exports the five prob-* crates behind features.

Statistics, autodiff, symbolic

Crate	Wraps / consolidates	no_std	Notes
tpt-math-stats	in-house (special/dist); no statrs	no	Hypothesis tests / regression + in-house distributions & special functions.
tpt-math-autodiff-fwd	—	yes	Dual-number forward-mode autodiff.
tpt-math-autodiff-rev	— (in-house; was tpt-grad)	no	Reverse-mode / tape autodiff, built on tpt-math-autodiff-fwd.
tpt-math-autodiff	(umbrella)	no	Re-exports fwd + rev.
tpt-math-symbolic	tpt-sym	no	Permissive-license CAS; generic Coefficient, default f64, optional exact BigRational.

Optimisation & signal

Crate	Wraps / consolidates	no_std	Notes
tpt-math-optimize-general	— (in-house; was argmin)	no	Steepest descent, nonlinear conjugate gradient, Newton.
tpt-math-optimize-convex	— (in-house; was clarabel)	no	Dense primal-dual interior-point (Mehrotra) QP solver.
tpt-math-optimize	(umbrella)	no	Re-exports general + convex.
tpt-math-signal-fft	rustfft	no	FFT.
tpt-math-signal-filter	—	no	FIR/IIR filters, windowing.
tpt-math-signal	(umbrella)	no	Re-exports fft + filter.

Build order

tpt-math-numeric
  -> tpt-math-linalg-dense          (in-house dense storage; was faer)
  -> tpt-math-linalg-fixed          (in-house fixed-size)
       -> tpt-math-geometry
  -> tpt-math-units
       -> tpt-math-linalg           (wraps linalg-dense)
       -> tpt-math-units-dyn
       -> tpt-math-exact
            -> tpt-math-prob-core
                 -> tpt-math-prob-dist / -bayes / -markov / -monte-carlo / -sampler
                 -> tpt-math-prob            (umbrella)
            -> tpt-math-stats               (in-house; no statrs)
       -> tpt-math-linalg-sparse    (in-house; needs linalg-dense)
       -> tpt-math-linalg-complex   (in-house; needs linalg-dense)
  -> tpt-math-graph                 (wraps petgraph; needs numeric)
  -> tpt-math-interpolate           (in-house; needs linalg-dense)
  -> tpt-math-autodiff-fwd
       -> tpt-math-autodiff-rev
            -> tpt-math-autodiff            (umbrella)
  -> tpt-math-symbolic
  -> tpt-math-optimize-general      (in-house; was argmin)
       -> tpt-math-optimize-convex   (in-house QP; needs linalg-dense)
            -> tpt-math-optimize      (umbrella)
  -> tpt-math-signal-fft
       -> tpt-math-signal-filter
            -> tpt-math-signal        (umbrella)

Consuming tpt-math

Downstream repos depend only on the leaf / umbrella crates they need:

• tpt-science — reach for tpt-math-prob + tpt-math-stats (inference, Monte Carlo, hypothesis tests), tpt-math-autodiff (gradient-based solvers), tpt-math-optimize (parameter fitting), and tpt-math-signal (time-series / spectral analysis).
• tpt-engineering — reach for tpt-math-linalg + tpt-math-units (physically-dimensioned models), tpt-math-optimize-convex (QP/control problems), tpt-math-prob (uncertainty propagation), tpt-math-spatial (rigid-body / kinematics), tpt-math-linalg-sparse (FEM / large systems).
• tpt-formal — reach for tpt-math-exact (provably-exact arithmetic under verification), tpt-math-numeric / tpt-math-units (trusted scalar/unit primitives).
• tpt-fem — reach for tpt-math-linalg / -linalg-dense / -linalg-sparse / -linalg-complex and tpt-math-optimize for assembly and sparse solves.
• tpt-physics — reach for tpt-math-linalg, tpt-math-graph, tpt-math-spatial, and tpt-math-interpolate (surrogate modelling).

Repository layout

• crates/* — the 31 library workspace members.
• xtask/ — the developer-tooling crate (cargo xtask …).
• examples/ — tpt-math-examples, four unpublished cross-crate demos.
• Cargo.toml — workspace manifest (resolver = "2", shared [workspace.package]).
• deny.toml — license / advisory / source hygiene (dual-license policy, ADR 0007).
• spec.txt — the original build spec.
• todo.md — the per-phase build checklist.

Depending on tpt-math

Every crate in crates/* is published to crates.io — depend on them the usual way:

[dependencies]
tpt-math-linalg = "0.1"
tpt-math-prob    = "0.1"

To track main ahead of a release instead, depend on them directly from git:

[dependencies]
tpt-math-linalg = { git = "https://github.com/tpt-solutions/tpt-math", package = "tpt-math-linalg" }
tpt-math-prob    = { git = "https://github.com/tpt-solutions/tpt-math", package = "tpt-math-prob" }

Pin to a commit or tag for reproducibility. The workspace also ships local tooling so you can sanity-check an integration before publishing:

• Examples — examples/ (tpt-math-examples, unpublished) holds four runnable cross-crate programs (units+linalg, prob+stats, autodiff+optimize, symbolic+exact). Run them all with just examples or cargo run -p tpt-math-examples --bin <name>.
• Verification — cargo xtask check (or just check) runs cargo fmt --check, clippy with -D warnings, and cargo-deny. The no_std crates are built for thumbv6m-none-eabi via cargo xtask no-std.
• Policy docs — SECURITY.md (no-unsafe policy, deny.toml posture, panic/try_* convention, symbolic recursion caveat) and CONTRIBUTING.md (issues-only workflow, per-crate checklist, deny.toml license policy).

License

Every crate is MIT OR Apache-2.0. Author: TPT Solutions.