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distlink computes the minimum orbital intersection distance (MOID), or global minimum of the distance between the points lying on two Keplerian ellipses by finding all stationary points of the distance function, based on solving an algebraic polynomial equation of 16th degree. The program tracks numerical errors and carefully treats nearly degenerate cases, including practical cases with almost circular and almost coplanar orbits. Benchmarks confirm its high numeric reliability and accuracy, and even with its error-controlling overheads, this algorithm is a fast MOID computation method that may be useful in processing large catalogs. Written in C++, the library also includes auxiliary functions.