Routine for linear interpolation on a grid

Write a function that, given increasing nodes $x_1<\dots<x_n$ with values $y_i$, returns a linearly interpolated value at a query point $x$.

Find the bracketing interval, then blend linearly. Binary-search for $x_i\le x\le x_{i+1}$ in $O(\log n)$ and return $y_i+(y_{i+1}-y_i)\tfrac{x-x_i}{x_{i+1}-x_i}$. Validate sorted, distinct nodes and decide a policy outside the grid (flat extrapolation, linear extrapolation or an error).