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When the shape parameter, α, is integral, generating gamma random variables with a digital computer is straightforward. There is no simple method for generating gamma random variates with non-integral shape parameters. A common procedure is to approximately generate such random variables by use of the so-called probability switch method. Another procedure, which is exact, is due to Jöhnk. This paper presents a rejection method for exactly generating gamma random variables when α is greater than 1. The efficiency of the rejection method is shown to be better than the efficiency of Jöhnk's method. The paper concludes that when α is non-integral the following mix of procedures yields the best combination of accuracy and efficiency: (1) when α is less than 1, use Jöhnk's method; (2) when 1 is less than α and α is less than 5, use the rejection method; (3) when α is greater than 5, use the probability switch method. [ABSTRACT FROM AUTHOR]

Current methods for mechanical program verification require a complete predicate specification on each loop. Because this is tedious and error prone, producing a program with complete, correct predicates is reasonably difficult and would be facilitated by machine assistance. This paper discusses techniques for mechanically synthesizing loop predicates. Two classes of techniques are considered: (1) heuristic methods which derive loop predicates from boundary conditions and/or partially specified inductive assertions: (2) extraction methods which use input predicates and appropriate weak interpretations to obtain certain classes of loop predicates by an evaluation on the weak interpretation. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the analysis of performance of the various key-to-address transformation methods. In this approach the keys in a file arc assumed to have been selected from the key space according to a certain probabilistic selection algorithm. All files with the same number of keys selected from this key space will be suitably weighted in accordance with the algorithm, and the average performance of the transformation methods on these files will be used as the potential of these methods. Using this analysis, methods with the same overall performance can be classified and key distributions partial to certain transformations can be identified. All this can be done analytically. The approach is applied to a group of transformation methods using files whose keys are selected randomly. [ABSTRACT FROM AUTHOR]