fhelium.backend.rns.automorphism

Coefficient indexing and RNS execution of polynomial automorphisms.

coefficient_galois_gather_indices

function View source

def coefficient_galois_gather_indices(ring_dimension: int, galois_element: int, device: str | torch.device='cpu') -> tuple[torch.Tensor, torch.Tensor]: ...

Return gathers implementing ${\sigma }_g:X\mapsto X^g$.

The returned device tensors have shapes [coefficient] with dtypes torch.int32 and torch.int8. For an integral coefficient-domain residue tensor [..., coefficient], destination j reads source_indices[j] and multiplies by source_sign[j]. No RNS limb or batch axis is represented in the tables, so the gather broadcasts across both without mutation.

apply_coefficient_galois_automorphism

function View source

def apply_coefficient_galois_automorphism(residues: torch.Tensor, galois_element: int, moduli: torch.Tensor) -> torch.Tensor: ...

Return non-aliasing coefficient residues for ${\sigma }_g$.

residues has integral [*batch, limb, coefficient] layout on one device in either standard or Montgomery representation. The gather and sign change preserve that representation and prime-row order. moduli is a same-dtype/device vector containing the modulus for each limb; reducing against it maps signed gather results into $[0,q_i)$ representatives before any NTT or key-switch consumer. The output has identical shape, dtype, and device, owns independent storage, and neither input is mutated.

NativeCoefficientAutomorphismImplementation

class View source

NativeCoefficientAutomorphismImplementation(name: str = 'native-coefficient-automorphism', supports_in_place: bool = False, operation_types: tuple[type[Operation], ...] = (rns.CoefficientAutomorphismOp,))

Apply one coefficient-domain Galois automorphism through the native op.

Attributes

Name	Type	Default/value
name	str	'native-coefficient-automorphism'
supports_in_place	bool	False
operation_types	tuple[type[Operation], ...]	(rns.CoefficientAutomorphismOp,)

resource_requirements

method

def resource_requirements(invocation: OperationInvocation) -> tuple[ResourceRequirement, ...]: ...

execute

method

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