Generic rings in C (experimental)

Generic Flint-style rings in C using void pointers + context objects.

The idea is to support fully generic recursive constructions of rings (polynomials, fractions, power series, matrices, etc.) over arbitrary user-defined base rings.

Principles/goals/benefits

• Small code size, fast compilation.
• Possible to pack data efficiently (down to 1 byte / element).
• Plain C, similar interface to existing Flint code.
• Data layouts backwards compatible with most existing Flint types.
• Support all unusual cases in Flint/Arb/Calcium uniformly (error handling, inexact rings, noncomputable rings, context objects), with a uniform interface.
• Support fast stack based allocation of temporary variables and arrays (with safe limits).
• Fully in-place operations.
• Allow fast (a few cycles) runtime construction of context objects. (May be on the order of hundreds of cycles when constructing a new method table; this could be optimized.)
• Possibility to use generic default methods or provide optimized versions (e.g. for vector operations).

Disadvantages

• Potentially a few cycles overhead for each dynamic function lookup and function call. Precludes intra-method compiler optimizations and inlining (however, providing custom vector methods should partially compensate for this).
• Less compiler protection against type errors.
• Some function call signatures need to change in ways that make the interface less convenient (for uniformity).