Birthday Spacings Test

Choose m birthdays in a "year" of n days. List the spacings between the birthdays. Let j be the number of values that occur more than once in that list, then j is asymptotically Poisson distributed with mean m^3/(4n). Experience shows n must be quite large, say n>=2^18, for comparing the results to the Poisson distribution with that mean. This test uses n=2^24 and m=2^10, so that the underlying distribution for j is taken to be Poisson with lambda=2^30/(2^26)=16. A sample of 200 j''s is taken, and a chi-square goodness of fit test provides a p value. The first test uses bits 1-24 (counting from the left) from integers in the specified file. Then the file is closed and reopened, then bits 2-25 of the same integers are used to provide birthdays, and so on to bits 9-32. Each set of bits provides a p-value, and the nine p-values provide a sample for a KSTEST.