RFR: 8376223: Add modeling interfaces for algebraic structures: groups, rings, and fields

[Joe Darcy]

On Fri, 23 Jan 2026 19:50:49 GMT, Joe Darcy <darcy at openjdk.org> wrote:

> First cut at adding modeling interfaces for the algebraic structures of rings, groups, and fields.

> Oh: I said all that because it came up _twice_; the other was:
> 
> > so at least ordered fields would be skipped.
> 
> But the real numbers are an ordered field and a type like `Double` (setting aside the special values) IS modeling the real numbers. The fact that it's an imperfect _representation_ of the type it models, that suffers from saturation/overflow, imho does not change its nature. imho we should not think of `Double` as having anything to do with algebraic "finite fields" even though as a representation it is hopelessly finite.

To be pedantic, for IEEE 754 floating-point, the specific mathematical object being approximated is not the real numbers (a field with lots of fun bonus properties), but the _extended_ real numbers -- the reals augmented with positive and negative infinity values. Due to the infinities, the extended reals are none of a group, ring, or field, but they do have some useful algebraic properties.

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PR Comment: https://git.openjdk.org/valhalla/pull/1957#issuecomment-3792791469