Function extrapolate_over_subspace 

pub fn extrapolate_over_subspace<F: BinaryField, E: FieldOps + From<F>>(
    subspace: &BinarySubspace<F>,
    values: &[E],
    z: E,
) -> E

Extrapolate a polynomial from its evaluations over a binary subspace to a point.

Given evaluations of a polynomial on all points of a binary subspace, computes the polynomial’s value at an arbitrary point z using Lagrange interpolation. This is equivalent to computing the inner product of values with the Lagrange basis evaluations at z, but avoids materializing the full vector of Lagrange evaluations.

Algorithm

Exploits the additive group structure of binary subspaces: all barycentric weights are identical, so a single weight w = (∏_{j=1}^{n-1} domain[j])^{-1} is computed once. The interpolated value is then w * Σ_i values[i] * ∏_{j≠i} (z - domain[j]), evaluated via a single linear pass using a prefix-product accumulator (same technique as EvaluationDomain::extrapolate).

Complexity

• Time: O(n) where n = subspace size
• Space: O(1) beyond the input