fhelium.experimental.bootstrap.presets.cosine

Preconfigured full-slot callables using cosine double-angle reduction.

Each function returns a fhelium.experimental.bootstrap.FullSlotBootstrap. Callers may inspect, replace, or directly construct every component.

The versioned logn16 names identify component profiles. Their documented end-to-end configuration is derived from Preset.slots32768_scale50_depth27_int64 and galois_generator=5. Construction validates transform slot counts, structural-base/default-scale proximity, and depth.

cosine_depth_refresh_logn16_7_32_bound512_v1

function View source

def cosine_depth_refresh_logn16_7_32_bound512_v1(engine: Engine) -> FullSlotBootstrap: ...

Construct a versioned degree-32 cosine callable for raw bound $B=512$.

The modular-reduction component uses seven double-angle iterations and a degree-32 Chebyshev seed. It is intended for callers that establish both raw branch coordinates within $[-512,512]$; the narrower bound reduces the reducer's declared depth relative to the $B=1024$ profiles. Construction does not certify an encrypted range or application error.

cosine_depth_refresh_logn16_8_28_s2c3_v1

function View source

def cosine_depth_refresh_logn16_8_28_s2c3_v1(engine: Engine) -> FullSlotBootstrap: ...

Construct the 8/28 profile with three SlotsToCoeffs stages.

CoeffsToSlots retains the two-stage schedule of cosine_depth_refresh_logn16_8_28_v1. SlotsToCoeffs uses three collapsed radix-2 stages with inspected BSGS steps 8, 256, and 4096. The additional inverse-transform rescale advances the output by one depth and reduces the direct rotation-key inventory for the documented logN16 map. This factory retains the same $B=1024$ range precondition and does not choose a direct, composed, or mixed rotation-key inventory.

cosine_depth_refresh_logn16_8_28_v1

function View source

def cosine_depth_refresh_logn16_8_28_v1(engine: Engine) -> FullSlotBootstrap: ...

Construct the versioned 8/28 cosine full-slot callable.

The transform design matches cosine_depth_refresh_logn16_v1. Its modular-reduction component uses a degree-28 Chebyshev seed followed by eight double-angle iterations, fused normalization, and raw input bound $B=1024$. It has the same documented $N=2^{16}$, 50-bit, generator-5 deployment requirements and the same caller-established encrypted range. Application tests determine whether its numerical behavior is suitable for a workload.

Parameters

• engine: Engine supplying slot count and Galois convention.

Returns

A full-slot callable configured for the supplied Engine.

cosine_depth_refresh_logn16_v1

function View source

def cosine_depth_refresh_logn16_v1(engine: Engine) -> FullSlotBootstrap: ...

Construct the versioned 7/44 cosine full-slot callable.

The composition uses two collapsed radix-2 stages in each transform, BSGS baby step 16, a degree-44 Chebyshev cosine seed, seven double-angle iterations, and raw periodic-reduction input bound $B=1024$. Input normalization $x=r/B$ is fused into CoeffsToSlots.

The documented deployment configuration is derived from Preset.slots32768_scale50_depth27_int64 and uses galois_generator=5. The input is a full-slot ciphertext at bootstrap.input_depth = engine.max_depth - 1. Entry preparation uses its actual scale; the resulting raw real and imaginary branch coordinates must lie within $[-1024,1024]$. The factory does not enforce the deployment identity or encrypted range; it invokes FullSlotBootstrap's structural and depth validation. Applications test their own range and error distribution. Online execution requires the rotation, relinearization, and conjugation keys reported by the returned callable.

Parameters

• engine: Engine supplying slot count and Galois convention.

Returns

A full-slot callable configured for the supplied Engine.