pow.hpp

#pragma once
 
namespace barretenberg {
 
template <typename FF> struct PowUnivariate {
    // ζ_{l}, initialized as ζ_{0} = ζ
    // At round l, equals ζ^{ 2^l }
    FF zeta_pow;
    // ζ_{l+1}, initialized as ζ_{1} = ζ^2
    // Always equal to zeta_pow^2
    // At round l, equals ζ^{ 2^{l+1} }
    FF zeta_pow_sqr;
    // c_{l}, initialized as c_{0} = 1
    // c_{l} = ∏_{0 ≤ k < l-1} ( (1-u_{k}) + u_{k}⋅ζ_{k} )
    // At round d-1, equals pow(u_{0}, ..., u_{d-1}).
    FF partial_evaluation_constant = FF(1);
 
    // Initialize with the random zeta
    explicit PowUnivariate(FF zeta_pow)
        : zeta_pow(zeta_pow)
        , zeta_pow_sqr(zeta_pow.sqr())
    {}
 
    // Evaluate the monomial ((1−X_{l}) + X_{l}⋅ζ_{l}) in the challenge point X_{l}=u_{l}.
    FF univariate_eval(FF challenge) const { return (FF(1) + (challenge * (zeta_pow - FF(1)))); };
 
    void partially_evaluate(FF challenge)
    {
        FF current_univariate_eval = univariate_eval(challenge);
        zeta_pow = zeta_pow_sqr;
        // TODO(luke): for native FF, this could be self_sqr()
        zeta_pow_sqr = zeta_pow_sqr.sqr();
 
        partial_evaluation_constant *= current_univariate_eval;
    }
};
} // namespace barretenberg