The implementation of inverse functions provided by most interval arithmetic software libraries is restricted to bijective functions and to the principal branch of multivalued functions. On the other hand, some algorithms—most notably, constraint propagation algorithms—require multivalued inverse functions as well. We present in details in this paper the algorithms to implement interval arithmetic extensions of the following multivalued inverse functions: the inverse integral power, the inverse cosine, the inverse sine, the inverse tangent, the inverse hyperbolic cosine, and the inverse multiplication. The issues raised by their effective as well as efficient implementation with floating-point numbers in the gaol C++ library are carefully addressed.