One Way of Estimating Frequencies of Jumps in a Program.

For the segmentation of a program it is useful to have a reasonable estimation of the values of S_ij, where S_ij is the mean value of the number of jumps from the ith instruction on to the ith instruction in the run time. In the cases where the S_ij, are estimated directly, the structure of the whole program must be generally taken into account; therefore it is very difficult for the programmer and/or the translator to obtain a good estimation of the S_ij. It is easier to estimate not S_ij, but the quantities p_ij = S_ij·c_i,/∑_j^N=1 S_ij, where c, is an arbitrary positive constant for each i. Although the p_ij are, for each i, proportional to S_ij, the estimation of p_ij is easier, because we must estimate only the "probabilities" of events where instruction l_j, is executed after instruction l_i. This estimation can often be done without considering the structure of the whole program. In the first part of the paper, using the theory of the Markov chains, an algorithm for the computation of the S_ij from the p , is found, and some ways of obtaining estimates of the p_ij are given. In the second part a variant of this algorithm is derived, avoiding the necessity of computation involving large matrices. [ABSTRACT FROM AUTHOR]