fhelium.experimental.bootstrap.polynomial.chebyshev

Binary-decomposition evaluation of encrypted Chebyshev series.

BinaryDecompositionChebyshevEvaluator

class View source

BinaryDecompositionChebyshevEvaluator(skip_near_zero: float = 0.0)

Evaluate a Chebyshev series through shared doubling identities.

The evaluator builds only basis elements required by nonzero terms. It recursively uses

$$T_{2n}(x)=2T_n(x{)}^2-1,T_{2n+1}(x)=2T_n(x)T_{n+1}(x)-T_1(x),$$

Shared basis nodes are retained until their last polynomial or recurrence consumer. Depth-specific $T_1$ copies serve the odd recurrences. Basis-node scales follow the input scale through each product and group rescale; the advanced copies of $T_1$ use that same recurrence. Coefficient products built from basis values at one depth are accumulated before one shared rescale; the resulting depth groups are then aligned and added. This keeps intermediate inputs near the approximation's bounded domain and exposes the critical-path depth.

The coordinate, tensor axes, arithmetic-state preconditions, functional behavior, per-product transitions, output depth, active prime_ids, and depth-dependent scale schedule match BalancedPowerEvaluator; only the polynomial basis and multiplication DAG differ.

Attributes

Name	Type	Default/value
skip_near_zero	float	0.0

operation_inventory

method

def operation_inventory(polynomial: PolynomialApproximation) -> dict[str, int]: ...

Return multiplying operations in the shared basis schedule.

required_depths

method

def required_depths(polynomial: PolynomialApproximation) -> int: ...

Count the deepest shared basis node plus its coefficient rescale.

relinearization_depths

method

def relinearization_depths(polynomial: PolynomialApproximation, *, input_depth: int=0) -> tuple[int, ...]: ...

Return product-input depths of the required shared basis nodes.

evaluate

method

def evaluate(arithmetic: BootstrapArithmetic, ciphertext: Ciphertext, polynomial: PolynomialApproximation, *, relinearization_key: RelinearizationKey | EvaluationKeySet | Mapping[int, RelinearizationKey] | None=None) -> Ciphertext: ...

Build required $T_n(x)$ values, align term depths, and sum them.

Terms at or below skip_near_zero are omitted. A constant-only polynomial consumes one depth, as reported by required_depths. The method is functional and returns a two-component coefficient-domain standard-RNS Q value at the arithmetic owner's target scale.