Module rns 

Level 0 — ℤ. RNS integers over the adaptive Basis, and Garner CRT.

Balanced residues (no sign-magnitude)

Residues are stored canonically in [0, p) for each prime p, but the value they encode is the balanced (symmetric) integer in (-M/2, M/2], where M = ∏ p. Reconstruction folds u ∈ [0, M) to u - M when 2u > M.

There is no negative flag: subtraction is the channel-parallel (a + p - b) % p, with no magnitude comparison and no BigInt in the loop. The sign of a value is an Archimedean question — it is answered by the crate::ball::Ball in the crate::adelic::Adelic carrier, never by the residues (which are constitutionally blind to size).

All primes are GPU-eligible ((2^15, 2^16)), so every channel op — add, sub, and even (a*b) — fits in a u32 with no u128 intermediate.

Structs

RnsInt

An exact integer in balanced RNS form (Level 0 of the tower).

Functions

add_channel

One channel’s add: (a + b) % m. Fits u32 (a, b < 2^16).

crt_balanced

Garner CRT followed by balanced (symmetric) folding into (-M/2, M/2].

garner_crt

Garner’s algorithm: reconstruct the unsigned integer in [0, M) from its balanced-canonical residues. All intermediates stay within u64.

mul_channel

One channel’s multiply: (a * b) % m. Fits u32 (a, b < 2^16).

sub_channel

One channel’s subtract: (a + m - b) % m. No magnitude comparison.