The GNU Multiple Precision Library offers a function to calculate the modular multiplicative inverse of a multiple-precision number given the modulus (also a multiple-precision number). This program does the same, but shows all the steps of Euclid's Division Lemma, which is used to calculate the multiplicative inverse.
tfpf/Euclid-Extended_Algorithm
calculate the multiplicative inverse of a number (however large) using Euclid's Extended Division Lemma
C