fhelium.engine.ntt

Engine-owned NTT plans, parameter tables, and execution backends.

CompactPowerOfTwoRadixNttBackend

class View source

CompactPowerOfTwoRadixNttBackend(*, policy: CompactFixedRadixPolicy, ntt_tables: CompactPowerOfTwoRadixTables, rns_params: torch.Tensor)

Execute radix-4/8/16 digits with radix-specific CUDA butterflies.

forward_montgomery_

method

def forward_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

forward_to_montgomery_

method

def forward_to_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

forward_to_montgomery

method

def forward_to_montgomery(operand: torch.Tensor, parameter_row_start: int) -> torch.Tensor: ...

inverse_montgomery_

method

def inverse_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_standard_lazy_

method

def inverse_to_standard_lazy_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_standard_

method

def inverse_to_standard_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_centered_

method

def inverse_to_centered_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

CompactPowerOfTwoRadixTables

class View source

CompactPowerOfTwoRadixTables(forward_outer_twiddles: torch.Tensor, inverse_outer_twiddles: torch.Tensor, forward_radix_root_powers: torch.Tensor, inverse_radix_root_powers: torch.Tensor)

Packed outer twists and roots for strict fixed-radix digits.

Outer shapes are [limb, N - 1] and root shapes are [limb, radix] in canonical QP row order. Conversion mutates each integral table from standard to Montgomery residues in place.

Attributes

Name	Type	Default/value
forward_outer_twiddles	torch.Tensor
inverse_outer_twiddles	torch.Tensor
forward_radix_root_powers	torch.Tensor
inverse_radix_root_powers	torch.Tensor

convert_twiddles_to_montgomery_

method

def convert_twiddles_to_montgomery_(rns_params: torch.Tensor) -> None: ...

CompactRadix2NttBackend

class View source

CompactRadix2NttBackend(*, policy: CompactRadix2Policy, ntt_tables: CompactRadix2Tables, rns_params: torch.Tensor)

Compute butterfly indices in CUDA from canonical compact twiddles.

forward_montgomery_

method

def forward_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

forward_to_montgomery_

method

def forward_to_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

forward_to_montgomery

method

def forward_to_montgomery(operand: torch.Tensor, parameter_row_start: int) -> torch.Tensor: ...

inverse_montgomery_

method

def inverse_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_standard_lazy_

method

def inverse_to_standard_lazy_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_standard_

method

def inverse_to_standard_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_centered_

method

def inverse_to_centered_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

CompactRadix2Tables

class View source

CompactRadix2Tables(forward_twiddles: torch.Tensor, inverse_twiddles: torch.Tensor)

Canonical [limb, N] twiddle rows for production kernels.

Rows align exactly with canonical QP parameter columns. Conversion mutates each integral table from standard to Montgomery residues in place.

Attributes

Name	Type	Default/value
forward_twiddles	torch.Tensor
inverse_twiddles	torch.Tensor

convert_twiddles_to_montgomery_

method

def convert_twiddles_to_montgomery_(rns_params: torch.Tensor) -> None: ...

IndexedRadix2NttBackend

class View source

IndexedRadix2NttBackend(*, policy: IndexedRadix2Policy, ntt_tables: IndexedRadix2Tables, rns_params: torch.Tensor)

Execute the indexed radix-2 schedule on CPU or CUDA.

forward_montgomery_

method

def forward_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

forward_to_montgomery_

method

def forward_to_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

forward_to_montgomery

method

def forward_to_montgomery(operand: torch.Tensor, parameter_row_start: int) -> torch.Tensor: ...

inverse_montgomery_

method

def inverse_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_standard_lazy_

method

def inverse_to_standard_lazy_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_standard_

method

def inverse_to_standard_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

inverse_to_centered_

method

def inverse_to_centered_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

IndexedRadix2Tables

class View source

IndexedRadix2Tables(forward_even_indices: torch.Tensor, forward_odd_indices: torch.Tensor, forward_twiddles: torch.Tensor, inverse_even_indices: torch.Tensor, inverse_odd_indices: torch.Tensor, inverse_twiddles: torch.Tensor)

Schedules and stage-expanded twiddles for indexed execution.

Index tensors are torch.int32 on the backend device. Twiddle tensors are integral [limb, stage, butterfly] rows aligned with canonical QP parameter columns; they begin in standard form and are converted in place to Montgomery form without changing shape, dtype, device, or storage.

Attributes

Name	Type	Default/value
forward_even_indices	torch.Tensor
forward_odd_indices	torch.Tensor
forward_twiddles	torch.Tensor
inverse_even_indices	torch.Tensor
inverse_odd_indices	torch.Tensor
inverse_twiddles	torch.Tensor

convert_twiddles_to_montgomery_

method

def convert_twiddles_to_montgomery_(rns_params: torch.Tensor) -> None: ...

NttBackend

class View source

NttBackend()

Bases: Protocol

Representation-explicit NTT operations consumed by RnsRuntime.

Method names state both the input and output representation. forward consumes coefficient-domain data and produces NTT-domain data; inverse performs the reverse transition. montgomery and standard identify the residue representation. A trailing underscore means that the operand is mutated in place.

parameter_row_start is the zero-based start of the operand's prime-row interval in the backend's complete canonical QP tables. Implementations use it to select the exact per-prime twiddles, roots, and RNS parameters; they must not infer prime identity from operand.size(-2).

The protocol intentionally contains no radix, grouping, or table-layout fields. Those are construction-time properties of a concrete backend, not semantic differences visible to RnsRuntime.

Every operand is a dense integral tensor on one execution device [*batch, limb, coefficient_or_ntt_index] with final extent $N=2^{\mathtt{logN}}$. A concrete backend is usable only on devices for which its native schemas have dispatcher implementations. CPU engines use indexed radix-2 execution. There is no broadcasting. Limb j is aligned with canonical parameter row parameter_row_start + j and therefore with that row's exact prime $q_i$. All tables use the same dtype/device.

Let ${\psi }_i$ be the prepared primitive $2N$-th root modulo $q_i$ and $\mathrm{br}(k)$ the logN-bit reversal. The stored NTT order is

$$A_i[k]=\sum _{n=0}^{N-1}{a}_i[n]{\psi }_i^{(2\mathrm{br}(k)+1)n}(\mathrm{mod}{q}_i).$$

The inverse implements the corresponding normalized inverse with $N^{-1}mod{q}_i$. Transform kernels accept and return lazy representatives in $[0,2q_i)$ except inverse_to_standard_ (canonical $[0,q_i)$) and inverse_to_centered_ (centered representatives). A trailing underscore preserves and mutates operand storage; the functional forward allocates an output that does not alias any input.

Attributes

Name	Type	Default/value
name	str

forward_montgomery_

method

def forward_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

Map coefficient/Montgomery to NTT/Montgomery in place.

forward_to_montgomery_

method

def forward_to_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

Map coefficient/standard to NTT/Montgomery in place.

forward_to_montgomery

method

def forward_to_montgomery(operand: torch.Tensor, parameter_row_start: int) -> torch.Tensor: ...

Return NTT/Montgomery output without mutating or aliasing input.

inverse_montgomery_

method

def inverse_montgomery_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

Map NTT/Montgomery to coefficient/Montgomery in place.

inverse_to_standard_lazy_

method

def inverse_to_standard_lazy_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

Map in place to lazy coefficient/standard residues in $[0,2q_i)$.

inverse_to_standard_

method

def inverse_to_standard_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

Map in place to coefficient/standard residues in $[0,q_i)$.

inverse_to_centered_

method

def inverse_to_centered_(operand: torch.Tensor, parameter_row_start: int) -> None: ...

Map in place to centered coefficient/standard residues.

NttTables

data View source

NttTables = IndexedRadix2Tables | CompactRadix2Tables | CompactPowerOfTwoRadixTables

create_ntt_backend

function View source

def create_ntt_backend(policy: NttBackendPolicy, *, ntt_tables: NttTables, rns_params: torch.Tensor) -> NttBackend: ...

Construct an executor only from a matching policy/table pair.

prepare_ntt_tables

function View source

def prepare_ntt_tables(policy: NttBackendPolicy, ckks_config: CkksConfig, *, materialize_parameter_rows: MaterializeParameterRows, device: torch.device) -> NttTables: ...

Build a plan and return separately allocated backend table tensors.

Prime rows follow the config's canonical level-zero QP order exactly. Returned tensors use ckks_config.torch_dtype on device and remain in standard representation until RnsRuntime converts them in place.