ADR 0015 — Arithmetic type is a first-class template parameter

Accepted · 2026-05-20 · cortex/docs/adr/0015-type-generic-arithmetic.md

Status: Accepted Date: 2026-05-20 Source: docs/arch/cortex-repo.md, Data structure abstractions (MTL5) and Non-linear Least Squares; CLAUDE.md Related: ADR-0003, ADR-0013

Context

The KPU targets mixed-precision arithmetic: number formats chosen per operator for energy and accuracy, not locked to IEEE-754 double. Studying and deploying that requires the same algorithm code to run in many number systems. MTL5 (linear algebra) and Universal (posits, cfloat, fixed-point, LNS, …) are designed for exactly this.

Decision

• Math (branes::math) and SDK operators are templated on the scalar type and constrained by concepts (LinearAlgebraScalar, OrderedField, …), never hardcoded to double or float.
• MTL5 is the linear-algebra layer (dense/sparse types, ITL Krylov solvers, sparse direct solvers); Universal supplies the number systems. Non-linear least squares is a header-only addition on top of MTL5.
• C++20 is required (concepts, std::span) and must not be lowered.

Consequences

• New math must instantiate for the validated arithmetic set (IEEE double/float, Universal posit/cfloat/fixed-point). The type-smoke and Kalman-filter-over-posits tests catch regressions when MTL5 or Universal is bumped.
• Generic code may only use operations the concepts guarantee. Gaps in upstream genericity are fixed upstream (e.g. stillwater-sc/mtl5#538).
• Compile times are higher (ADR-0003, mitigated by sccache).