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The accurate and efficient calculation of ordinary and generalized posterior distributions is an important problem in the several research fields such as decoding, AI, statistics and statistical mechanics. The condition of generalized posterior distributions is not given by the deterministic values such as X = x, but by the distributions such as P(X = x) = p. If the condition is P(X = x) = 1 then the generalized posterior distribution is an ordinary posterior distribution. A procedure using the sum of the e-projection 1 vectors is proposed. Since the procedure is suitable for parallel algorithms, an alternate algorithm for calculating generalized posterior distributions on log linear models is given by the procedure. The proposed algorithm works well for codes with short loops.