libsnark：Lagrange interpolation at Roots of unity

libsnark\depends\libfqfft\libfqfft\evaluation_domain\domains\basic_radix2_domain_aux.tcc中的_basic_radix2_evaluate_all_lagrange_polynomials(…)函数的计算依据为《Behavior of the Lagrange Interpolants in the Roots of unity》论文中如下图的公式：

根据论文公式，令 w = e ( 1 m ) = e j ∗ 2 ∗ π m = c o s ( 2 ∗ π m ) + j ∗ s i n ( 2 ∗ π m ) w=e(\frac{1}{m})=e^{j*\frac{2*\pi}{m}} =cos(\frac{2*\pi}{m}) + j * sin(\frac{2*\pi}{m}) w=e(m1​)=ej∗m2∗π​=cos(m2∗π​)+j∗sin(m2∗π​) ⇓ \Downarrow ⇓ L m − 1 ( f , z ) = z m − 1 m ∗ ∑ k = 0 n − 1 w k ∗ f ( w k ) z − w k L_{m-1}(f,z) =\frac{z^m-1}{m}*\sum_{k=0}^{n-1}\frac{w^k*f(w^k)}{z-w^k} Lm−1​(f,z)=mzm−1​∗k=0∑n−1​z−wkwk∗f(wk)​ 令 z = t z=t z=t，可以推导出： u [ k ] = t m − 1 m ∗ w k ∗ 1 t − w k u[k]=\frac{t^m-1}{m} * w^k * \frac{1}{t-w^k} u[k]=mtm−1​∗wk∗t−wk1​ S [ k ] = f ( w k ) S[k]=f(w^k) S[k]=f(wk) 使得 L m − 1 ( f , t ) = u ⋅ S L_{m-1}(f,t) =u·S Lm−1​(f,t)=u⋅S(点乘)

/**
 * Compute the m Lagrange coefficients, relative to the set S={omega^{0},...,omega^{m-1}}, at the field element t.
 */
template
std::vector _basic_radix2_evaluate_all_lagrange_polynomials(const size_t m, const FieldT &t)
{
    if (m == 1)
    {
        return std::vector(1, FieldT::one());
    }

    if (m != (1u