Algorithm S (Serial Test)

This algorithm calculates Kolmogorov-Smirnov statistics and
probabilities for sets of successive independent random pairs.
The upper range (R) of the data set is specified by the user.
First, 100 chi-square probabilities are calculated and stored.
These probabilities are used to calculate Kolmogorov-Smirnov
statistics and probabilities which are printed.

Inputs:

C = Number of Categories           (= S^2)
P = Number of Pairs of Variates
S = Number of Entries in Data Set
U() = Uniform Random Number Generator Function Under Test

S1. [Initialize.]  Set k <- 0, m <- 0, F <- C - 1.

S2. [Generate Data for KS test.]  Execute Steps S3 to S7 100 times,
    then go on to S8.

S3. [Calculate next chi-square statistic.]  Set SoS <- 0, t <- 0,
    m <- 0, and set Occurs[j] <- 0, 1 <= j <= C. (We will execute
    step S4 P times. Steps S5 and S6 complete the calculation.)

S4. [Tally Next Observation.]  Set x <- U() mod S, y <- U() mod S,
    and v = x * S + y.  Set Occurs[v] <- Occurs[v] + 1.  Increase t.
    If t < P, repeat this step.

S5. [Calculate sum of squares.]  Set SoS <= SoS + Occurs[m]^2, and
    m <- m + 1.  If m < C, repeat this step.

S6. [Finish chi-square statistic.]  Set XSQ <- (C/P) * SoS - P.

S7. [Calculate p-value.]  Execute function chdtr() to get p-value.
    Set k <- k + 1. Then, set ProbXSQ[k] <- chdtr(F, XSQ). If k < 100,
    return to step S3.

S8. [Calculate K-S data.]  Execute function KSCalc() to get K-S
    statistics and probabilities.  There will be four quantities
    produced - Kn+, Pn+, Kn-, Pn-.

S9. [Print Results.]  Print Kn+, Pn+, Kn-, Pn-.