core Design

Design goal

arithmetic extends LunaFlow from algebraic structure into analytic capability, while keeping semantics explicit and backend-specific.

Analytic behavior is split into many small traits instead of one large “real number” interface.
Unchecked and checked surfaces coexist so callers can choose between direct backend behavior and explicit contextual validation.
The checked layer shares common types such as ArithmeticContext and ArithmeticError.
Enclosure-style relations are separated from scalar comparison to avoid semantic lies.
Integer-family instances stay narrow and only expose operations that remain closed on those types.

This package does not define vectors, matrices, complex numbers, or symbolic objects.
It does not hide branch-cut or exceptional-value semantics behind one vague abstraction.