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this function constructs an interpolant using compactly supported cubic b splines. The advantage of using splines of compact support over traditional cubic splines is that compact support makes the splines well-conditioned. The interpolant is constructed in O(N) time and can be evaluated in constant time. Its error is O(h^4), and obeys the interpolating condition s(x_j) = f(x_j) for all samples. In addition, f' can be estimated from s', albeit with lower accuracy. This routine is cppcheck clean, and is clean under AddressSanitizer and MemorySanitizer.