Chains of recurrences technique was introduced as an "aggressive" technique for
loop optimization. It was later extended to multidimensional case that corresponds
to the nested loop optimization problem and was used to accelerate massive numeric
computations over the regular intervals in such applications as for example
mathematical plotting. Recently this technique in very rudimentary form was adopted
by compiler developers. For example it has been adopted in the well-known
mainstream GCC 4.0 compiler under the name of "Scalar Evolutions".
In our talk we will briefly introduce this technique and discuss its applications together
with several our own (Maple, C, Java, VHDL) implementations.