Crate adele_ring 

adele-ring — exact multi-base arithmetic engine

adele-ring represents numbers across multiple prime channels using the Residue Number System (RNS). Because the channels are mutually independent (no carry propagation), arithmetic is embarrassingly parallel and maps onto both CPU threads (rayon) and GPU threads (wgpu).

On top of the RNS substrate sits a number tower that keeps every value at the cheapest exact level it can:

Level	Set	Type
0	ℤ	rns::RnsInt
1	ℚ	rational::RnsRational
2	ℚ̄	algebraic::AlgebraicNumber
3	ℝ_c	computable::ComputableReal
4	𝒮	symbolic::SymbolicExpr

The crate name uses a hyphen (adele-ring) but the Rust path uses an underscore (adele_ring), per Rust’s identifier rules.

Re-exports

pub use algebraic::AlgebraicNumber;

pub use algebraic::Polynomial;

pub use backend::executor;

pub use backend::ArithmeticBackend;

pub use backend::Executor;

pub use batch::RnsBatch;

pub use computable::Computable;

pub use computable::ComputableReal;

pub use dispatch::DispatchPlan;

pub use dispatch::Dispatcher;

pub use rational::RnsRational;

pub use rns::garner_crt;

pub use rns::Channels;

pub use rns::RnsInt;

pub use symbolic::IdentityGraph;

pub use symbolic::SymbolicExpr;

pub use tower::TowerLevel;

pub use tower::TowerValue;

Modules

algebraic

Level 2 — ℚ̄. Exact algebraic numbers as (minimal polynomial, isolating interval) pairs.

backend

The ArithmeticBackend trait and the Executor that selects between CPU and GPU at runtime. All batch math in the crate flows through the Executor — it never hard-codes a backend.

batch

RnsBatch — the single flat buffer format shared by both backends.

computable

Level 3 — ℝ_c. Computable reals: numbers stored as algorithms that produce a rational approximation to any requested precision, rather than as digits.

cpu

CpuBackend — the always-available backend, using rayon to parallelize over batch items (and, for single values, over channels above a threshold).

dispatch

Base-aware ALU dispatcher.

gpu

GpuBackend — wgpu compute-shader implementation of ArithmeticBackend.

primes

Prime utilities, factorization, and channel (base) selection.

rational

Level 1 — ℚ. Exact rational arithmetic over the RNS substrate.

rns

Level 0 — ℤ. RNS integers and the core CRT reconstruction.

symbolic

Level 4 — 𝒮. Symbolic expression trees and an identity graph.

tower

The number tower router. Every value carries a TowerLevel; operations try to stay at the lowest (cheapest) level they can, dropping down when a result simplifies (e.g. √2·√2 = 2) and rising only when forced.

Constants

RAYON_CHANNEL_THRESHOLD

Channel-count threshold above which single-value operations parallelize over channels with rayon. Below it, sequential is faster (task overhead ~50ns vs channel op ~1ns: break-even around 8–16 channels).