Verification circuit for Lagrange interpolation. Two arrays as input and an array of polynomial coefficients as output. The size of arrays is 2^n. It is recommended to build components, which work for any n, but you can fix n = n' (thus you can fix the number of rows).
$\displaystyle {\begin{aligned}\ell {j}(x)&={\frac {(x-x{0})}{(x_{j}-x_{0})}}\cdots {\frac {(x-x_{j-1})}{(x_{j}-x_{j-1})}}{\frac {(x-x_{j+1})}{(x_{j}-x_{j+1})}}\cdots {\frac {(x-x_{k})}{(x_{j}-x_{k})}}\[10mu]&=\prod {\begin{smallmatrix}0\leq m\leq k\m\neq j\end{smallmatrix}}{\frac {x-x{m}}{x_{j}-x_{m}}}.\end{aligned}}$
//|------|------|------ - ---- | ------ ------ -| ------ ------ | ------ - ----|
//| a | b | W2 | W3 | W4 | W5 |
//|------|------|------ c ---- | ------ sx [0] -| ------ sr [0] | ------ r ----|
//| 2 | 4 |-0.114286 | -189 |21.6 |13.5 |
//| 3 | 8 |0.333333 | 111 |-12.6857 |-12.75 |
//| 9 | 7 |0.0833333 | -19 |2.17143 |3.5 |
//| 7 | 10 |-0.25 | 1 |-0.114286 | -0.25 |
//|------|------|------ ------ | ------ sx [1] -|------ sr [1] -|------ ------ -|
//| | | | -126 |-42 |
//| | | | 95 |31.6667 |
//| | | | -18 |-6 |
//| | | | 1 |0.333333 |
//|------|------|------ ------ | ------ sx [2] -|------ sr [2] -|
//| | | | -42 |-3.5 |
//| | | | 41 |3.41667 |
//| | | | -12 |-1 |
//| | | | 1 |0.0833333 |
//|------|------|------ ------ | ------ sx [3] -|------ sr [3] -|
//| | | | -54 |13.5 |
//| | | | 51 |-12.75 |
//| | | | -14 |3.5 |
//| | | | 1 |-0.25 |
//|------|------|------ ------ | ------ ------ -|------ ------ -|