Generic Scalar Type

Summary

Every operation in the library is written generically over a scalar type from the start, rather than hardcoded against a single concrete numeric type such as f64.

Scope

Applies to every function, algorithm, and data structure in the crate that operates on numeric values — vectors, matrices, sparse formats, and the algorithms defined over them.

Decision

Operations are written against a scalar type parameter rather than a fixed concrete type. The set of capabilities that type parameter must provide — basic arithmetic, whichever elementary functions are actually needed, identity values, and so on — is defined incrementally, as each capability is actually required by the mathematics being implemented, rather than specified upfront in full.

Constraints

• The library must remain usable with f32 on resource-constrained targets that lack double-precision floating-point hardware, and with f64 elsewhere, without maintaining two separate codebases for the two cases.
• Generality must be established before substantial algorithm code exists, so that switching or adding a numeric type later does not force a disruptive rewrite of function signatures across the crate.
• The scalar abstraction should not grow capability the current mathematics doesn’t need; each new requirement is added only when an algorithm actually needs it, in keeping with the same discipline applied to the crate’s other core traits.

Status

Implemented. All operations across the crate are generic over the scalar type; f32 and f64 are the concrete types currently in use, with room for further scalar types (such as fixed-point) if a real need for one arises.