fhelium.experimental.bootstrap.presets.exponential

Preconfigured full-slot callables using exponential-squaring reduction.

The versioned profile is documented for a configuration derived from Preset.slots32768_scale50_levels27_int64 with base_prime_bits=50 and an engine using galois_generator=5. The factory composes public components; it does not certify encrypted range or application error.

exponential_depth_refresh_logn16_d16_v1

function View source

def exponential_depth_refresh_logn16_d16_v1(engine: CkksEngine) -> FullSlotBootstrap: ...

Construct the versioned degree-16 exponential full-slot callable.

The composition uses two collapsed radix-2 stages in each transform, BSGS baby step 16, a degree-16 balanced-power exponential seed, repeated squaring for raw input bound $B=1024$, fused normalization $x=r/B$, and sine extraction by conjugation.

The measured configuration is derived from Preset.slots32768_scale50_levels27_int64 with base_prime_bits=50 and is bound to an engine using galois_generator=5. It accepts a final-public-level input near default scale with both raw branch coordinates in $[-1024,1024]$. The function does not enforce the deployment identity or encrypted range; FullSlotBootstrap checks structural-scale proximity, transform shape, and depth. Application tests must establish numerical suitability and level budget. Online execution requires rotation, relinearization, and conjugation keys.

Parameters

• engine: Engine supplying slot count and Galois convention.

Returns

An engine-bound full-slot callable ready for evaluation.