Sorry if I'm mistaken with the place to ask the question (maybe I should go to stackoverflow.com/mathoverflow.net?).
I wonder if there is a proof that when evaluating extended Euclidean algorithm the Bézout's coefficients (that is s and t in identity as + bt = gcd(a, b)) will not exceed some reasonable values (depending on a, b, I guess). In particular implementation on some general-purpose programming language I'm interested in overflow correctness of the program.
To be precise I can mention that I use Victor Shoup's description of the algorithm (4.2 in his book “A Computational Introduction to Number Theory and Algebra” freely available from his homepage).