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

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

caching every required $T_n$ and each depth-specific $T_1$ for one call. 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 executed by evaluate.

Alignment includes operand advancement within odd recurrences, the shared depth chain for $T_1=x$, and advancement between coefficient depth groups. rescale_operations counts one coefficient rescale per occupied basis depth rather than one per coefficient product.

required_depths

method

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

Count the deepest required recurrence plus coefficient product.

evaluate

method

def evaluate(arithmetic: BootstrapArithmetic, ciphertext: Ciphertext, polynomial: PolynomialApproximation, *, relinearization_key: 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. As in the power evaluator, the constant-only case deliberately consumes one depth so its execution agrees with required_depths. The method is functional and returns a two-component coefficient-domain standard-RNS Q value at the arithmetic owner's target scale.