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fhelium.backend.ntt ​

NTT numerical implementations, table preparation, and context-owned transforms.

NttContext provides policy-specific Tensor tables. NativeNttImplementation prepares operations over supplied Tensor operands and shares native calls with context transforms. Compile can select a schedule before preparing execution.

CompactPowerOfTwoRadixTables ​

class View source

python
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 QP row order. Conversion mutates each integral table from standard to Montgomery residues in place.

Attributes ​

NameTypeDefault/value
forward_outer_twiddlestorch.Tensor
inverse_outer_twiddlestorch.Tensor
forward_radix_root_powerstorch.Tensor
inverse_radix_root_powerstorch.Tensor

convert_twiddles_to_montgomery_ ​

method

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

CompactRadix2Tables ​

class View source

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

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

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

Attributes ​

NameTypeDefault/value
forward_twiddlestorch.Tensor
inverse_twiddlestorch.Tensor

convert_twiddles_to_montgomery_ ​

method

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

IndexedRadix2Tables ​

class View source

python
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 QP parameter columns; they begin in standard form and are converted in place to Montgomery form without changing shape, dtype, device, or storage.

Attributes ​

NameTypeDefault/value
forward_even_indicestorch.Tensor
forward_odd_indicestorch.Tensor
forward_twiddlestorch.Tensor
inverse_even_indicestorch.Tensor
inverse_odd_indicestorch.Tensor
inverse_twiddlestorch.Tensor

convert_twiddles_to_montgomery_ ​

method

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

NativeNttImplementation ​

class View source

python
NativeNttImplementation(name: str, required_backend_name: str | None, supports_in_place: bool = True, operation_types: tuple[type[Operation], ...] = _NTT_OPERATION_TYPES)

Bases: _TensorOperandImplementation

Execute logical NTT operations through one named schedule executor.

Attributes ​

NameTypeDefault/value
namestr
required_backend_namestr | None
supports_in_placeboolTrue
operation_typestuple[type[Operation], ...]_NTT_OPERATION_TYPES

select_ntt_schedule ​

method

python
def select_ntt_schedule(**facts): ...

prepare_operation ​

method

python
def prepare_operation(operation: Operation): ...

execute ​

method

python
def execute(invocation: OperationInvocation, values: tuple[torch.Tensor, ...], resources: tuple[BoundResource, ...], *, in_place: bool) -> tuple[torch.Tensor, ...]: ...

NttContext ​

class View source

python
NttContext(rns_context: RnsContext, ntt_backend: str | None=None)

Own one NTT policy and its tables, and use shared prepared transforms.

The context composes an RnsContext whose parameter tensor is passed unchanged to native NTT executors. Transform methods preserve prime rows and operand storage unless the method is the functional forward_to_montgomery variant.

tensor_operands ​

method

python
def tensor_operands(prime_ids: tuple[int, ...], *, inverse: bool) -> tuple[torch.Tensor, ...]: ...

Return native table views for the selected rows and transform direction.

Parameter generation belongs to this context. The returned Tensors can be supplied directly or placed in a Program's external material table.

forward_montgomery_ ​

method

python
def forward_montgomery_(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> None: ...

Apply the negacyclic forward NTT to Montgomery residues in place.

forward_to_montgomery_ ​

method

python
def forward_to_montgomery_(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> None: ...

Apply forward NTT and standard-to-Montgomery conversion in place.

forward_to_montgomery ​

method

python
def forward_to_montgomery(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> torch.Tensor: ...

Return the non-aliasing forward NTT/Montgomery transition.

inverse_montgomery_ ​

method

python
def inverse_montgomery_(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> None: ...

Apply normalized inverse NTT and keep Montgomery form.

inverse_to_standard_lazy_ ​

method

python
def inverse_to_standard_lazy_(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> None: ...

Inverse NTT to coefficient/standard lazy residues in place.

inverse_to_standard_ ​

method

python
def inverse_to_standard_(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> None: ...

Inverse NTT to coefficient/standard reduced residues in place.

inverse_to_centered_ ​

method

python
def inverse_to_centered_(a: torch.Tensor, *, include_p: bool=False, parameter_row_start: int | None=None) -> None: ...

Inverse NTT to centered coefficient/standard residues in place.

NttTables ​

data View source

python
NttTables = IndexedRadix2Tables | CompactRadix2Tables | CompactPowerOfTwoRadixTables

prepare_ntt_tables ​

function View source

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

Build a plan and return separately allocated backend table tensors.

Prime rows follow the config's depth-zero QP order. Returned tensors use the selected execution dtype on device and remain in standard representation until RnsContext converts them in place.