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128 lines
3.6 KiB
Plaintext
128 lines
3.6 KiB
Plaintext
/*
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* randrun - perform a run test on rand()
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*
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* If X(j) < X(j+1) < ... X(j+k) >= X(j+k+1), then we have a run of 'k'.
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* We ignore the run breaker, X(j+k+1), and start with X(j+k+2) when
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* considering a new run in order to make our runs chi independent.
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*
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* See Knuth's "Art of Computer Programming - 2nd edition",
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* Volume 2 ("Seminumerical Algorithms"), Section 3.3.2.
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* "G. Run test", pp. 65-68,
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* "problem #14", pp. 74, 536.
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*
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* We use the suggestion in problem #14 to allow an application of the
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* chi-square test and to make estimating the run length probs easy.
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*/
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/*
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* Copyright 1995 by Landon Curt Noll. All Rights Reserved.
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*
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* Permission to use, copy, modify, and distribute this software and
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* its documentation for any purpose and without fee is hereby granted,
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* provided that the above copyright, this permission notice, and the
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* disclaimer below appear in all of the following:
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*
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* * supporting documentation
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* * source copies
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* * source works derived from this source
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* * binaries derived from this source or from derived source
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*
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* LANDON CURT NOLL DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
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* INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO
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* EVENT SHALL LANDON CURT NOLL BE LIABLE FOR ANY SPECIAL, INDIRECT OR
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* CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF
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* USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR
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* OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
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* PERFORMANCE OF THIS SOFTWARE.
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*/
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define randrun(run_cnt)
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{
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local i; /* index */
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local max_run; /* longest run */
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local long_run_cnt; /* number of runs longer than MAX_RUN */
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local run; /* current run length */
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local tally_sum; /* sum of all tally values */
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local last; /* last random number */
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local current; /* current random number */
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local MAX_RUN = 9; /* max run we will keep track of */
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local mat tally[1:MAX_RUN]; /* tally of length of a rise run of 'x' */
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local mat prob[1:MAX_RUN]; /* prob[x] = probability of 'x' length run */
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/*
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* parse args
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*/
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if (param(0) == 0) {
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run_cnt = 65536;
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}
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/*
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* run setup
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*/
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max_run = 0; /* no runs yet */
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long_run_cnt = 0; /* no long runs set */
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current = rand(); /* our first number */
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run = 1;
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/*
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* compute the run length probabilities
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*
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* A run length of 'r' occurs with a probability of:
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*
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* 1/r! - 1/(r+1)!
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*/
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for (i=1; i <= MAX_RUN; ++i) {
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prob[i] = 1.0/fact(i) - 1.0/fact(i+1);
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}
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/*
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* look at a number of random number trials
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*/
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for (i=0; i < run_cnt; ++i) {
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/* get our current number */
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last = current;
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current = rand();
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/* look for a run break */
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if (current < last) {
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/* record the stats */
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if (run > max_run) {
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max_run = run;
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}
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if (run > MAX_RUN) {
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++long_run_cnt;
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} else {
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++tally[run];
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}
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/* start a new run */
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current = rand();
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run = 1;
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/* note the continuing run */
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} else {
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++run;
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}
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}
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/* determine the number of runs found */
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tally_sum = matsum(tally) + long_run_cnt;
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/*
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* print the stats
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*/
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printf("rand run test used %d values to produce %d runs\n",
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run_cnt, tally_sum);
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for (i=1; i <= MAX_RUN; ++i) {
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printf("length=%d\tprob=%9.7f\texpect=%d \tcount=%d \terr=%9.7f\n",
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i, prob[i], round(tally_sum*prob[i]), tally[i],
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(tally[i] - round(tally_sum*prob[i]))/tally_sum);
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}
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printf("length>%d\t\t\t\t\tcount=%d\n", MAX_RUN, long_run_cnt);
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printf("max length=%d\n", max_run);
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}
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if (config("lib_debug") >= 0) {
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print "randrun([run_length]) defined";
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}
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