package/dieharder: drop rgb_operm

Fix the following build failure:

/home/autobuild/autobuild/instance-7/output-1/host/lib/gcc/m68k-buildroot-linux-uclibc/11.2.0/../../../../m68k-buildroot-linux-uclibc/bin/ld: dieharder-add_ui_rngs.o:(.data+0xd8): undefined reference to `rgb_operm'

Fixes:
 - http://autobuild.buildroot.org/results/7be339674291b39f8eddb8ad065f0988128ecfe9

Signed-off-by: Fabrice Fontaine <fontaine.fabrice@gmail.com>
Signed-off-by: Arnout Vandecappelle (Essensium/Mind) <arnout@mind.be>
(cherry picked from commit d0ffdb2bdd22432f6f269a43ceaf7f1e51d535b5)
Signed-off-by: Peter Korsgaard <peter@korsgaard.com>

package/dieharder/0005-Remove-defunct-rgb_operm.patch

@@ -0,0 +1,732 @@
+From 40d377b86c856f5a4510a6f5cd56be004873ad77 Mon Sep 17 00:00:00 2001
+From: =?UTF-8?q?Marcus=20M=C3=BCller?= <mueller@kit.edu>
+Date: Mon, 12 Oct 2020 21:30:12 +0200
+Subject: [PATCH] Remove defunct rgb_operm
+
+[Retrieved from:
+https://github.com/eddelbuettel/dieharder/pull/2/commits/40d377b86c856f5a4510a6f5cd56be004873ad77]
+Signed-off-by: Fabrice Fontaine <fontaine.fabrice@gmail.com>
+---
+ include/Makefile.am           |   1 -
+ include/dieharder/rgb_operm.h |  38 --
+ include/dieharder/tests.h     |   2 -
+ libdieharder/rgb_operm.c      | 633 ----------------------------------
+ 4 files changed, 674 deletions(-)
+ delete mode 100644 include/dieharder/rgb_operm.h
+ delete mode 100644 libdieharder/rgb_operm.c
+
+diff --git a/include/Makefile.am b/include/Makefile.am
+index f80b4ff..e4659cd 100644
+--- a/include/Makefile.am
++++ b/include/Makefile.am
+@@ -33,7 +33,6 @@ nobase_include_HEADERS = dieharder/copyright.h \
+ 	dieharder/rgb_lagged_sums.h \
+ 	dieharder/rgb_lmn.h \
+ 	dieharder/rgb_minimum_distance.h \
+-	dieharder/rgb_operm.h \
+ 	dieharder/rgb_persist.h \
+ 	dieharder/rgb_permutations.h \
+ 	dieharder/rgb_timing.h \
+diff --git a/include/dieharder/rgb_operm.h b/include/dieharder/rgb_operm.h
+deleted file mode 100644
+index c48fa37..0000000
+--- a/include/dieharder/rgb_operm.h
++++ /dev/null
+@@ -1,38 +0,0 @@
+-/*
+- * rgb_operm test header.
+- */
+-
+-/*
+- * function prototype
+- */
+-int rgb_operm(Test **test,int irun);
+-
+-static Dtest rgb_operm_dtest __attribute__((unused)) = {
+-  "RGB Overlapping Permuations Test",
+-  "rgb_operm",
+-  "\n\
+-#========================================================================\n\
+-#                 RGB Overlapping Permutations Test\n\
+-# Forms both the exact (expected) covariance matrix for overlapping\n\
+-# permutations of random integer and an empirical covariance matrix\n\
+-# formed from a long string of samples.  The difference is expected\n\
+-# to have a chisq distribution and hence can be transformed into a\n\
+-# sample p-value.  Note that this is one possible functional replacement\n\
+-# for the broken/defunct diehard operm5 test, but one that permits k (the\n\
+-# number of numbers in the overlapping permutation window) to be varied\n\
+-# from 2 to perhaps 8.\n\
+-#\n",
+-  100,     /* Default psamples */
+-  100000,  /* Default tsamples */
+-  1,       /* We magically make all the bit tests return a single histogram */
+-  rgb_operm,
+-  0
+-};
+-
+-/*
+- * Global variables.
+- *
+- * rgb_operm_k is the size of the overlapping window that is slid along
+- * a data stream of rands from x_i to x_{i+k} to compute c[][].
+- */
+-unsigned int rgb_operm_k;
+diff --git a/include/dieharder/tests.h b/include/dieharder/tests.h
+index 1674aed..b50dbe3 100644
+--- a/include/dieharder/tests.h
++++ b/include/dieharder/tests.h
+@@ -11,7 +11,6 @@
+ #include <dieharder/rgb_kstest_test.h>
+ #include <dieharder/rgb_lagged_sums.h>
+ #include <dieharder/rgb_minimum_distance.h>
+-#include <dieharder/rgb_operm.h>
+ #include <dieharder/rgb_permutations.h>
+ #include <dieharder/dab_bytedistrib.h>
+ #include <dieharder/dab_dct.h>
+@@ -80,7 +79,6 @@
+    RGB_PERMUTATIONS,
+    RGB_LAGGED_SUMS,
+    RGB_LMN,
+-   RGB_OPERM,
+    DAB_BYTEDISTRIB,
+    DAB_DCT,
+    DAB_FILLTREE,
+diff --git a/libdieharder/rgb_operm.c b/libdieharder/rgb_operm.c
+deleted file mode 100644
+index 15f8e9a..0000000
+--- a/libdieharder/rgb_operm.c
++++ /dev/null
+@@ -1,633 +0,0 @@
+-/*
+- * ========================================================================
+- * $Id: rgb_operm.c 252 2006-10-10 13:17:36Z rgb $
+- *
+- * See copyright in copyright.h and the accompanying file COPYING
+- * ========================================================================
+- */
+-
+-/*
+- * ========================================================================
+- * This is the revised Overlapping Permutations test.  It directly
+- * simulates the covariance matrix of overlapping permutations.  The way
+- * this works below (tentatively) is:
+- *
+- *    For a bit ntuple of length N, slide a window of length N to the
+- *    right one bit at a time.  Compute the permutation index of the
+- *    original ntuple, the permutation index of the window ntuple, and
+- *    accumulate the covariance matrix of the two positions.  This
+- *    can be directly and precisely computed as well.  The simulated
+- *    result should be distributed according to the chisq distribution,
+- *    so we subtract the two and feed it into the chisq program as a
+- *    vector to compute p.
+- *
+- * This MAY NOT BE RIGHT.  I'm working from both Marsaglia's limited
+- * documentation (in a program that doesn't do ANYTHING like what the
+- * documentation says it does) and from Nilpotent Markov Processes.
+- * But I confess to not quite understand how to actually perform the
+- * test in the latter -- it is very good at describing the construction
+- * of the target matrix, not so good at describing how to transform
+- * this into a chisq and p.
+- *
+- * FWIW, as I get something that actually works here, I'm going to
+- * THOROUGHLY document it in the book that will accompany the test.
+- *========================================================================
+- */
+-
+-#include <dieharder/libdieharder.h>
+-#define RGB_OPERM_KMAX 10
+-
+-/*
+- * Some globals that will eventually go in the test include where they
+- * arguably belong.
+- */
+-double fpipi(int pi1,int pi2,int nkp);
+-uint piperm(size_t *data,int len);
+-void make_cexact();
+-void make_cexpt();
+-int nperms,noperms;
+-double **cexact,**ceinv,**cexpt,**idty;
+-double *cvexact,*cvein,*cvexpt,*vidty;
+-
+-int rgb_operm(Test **test,int irun)
+-{
+-
+- int i,j,n,nb,iv,s;
+- uint csamples;   /* rgb_operm_k^2 is vector size of cov matrix */
+- uint *count,ctotal; /* counters */
+- uint size;
+- double pvalue,ntuple_prob,pbin;  /* probabilities */
+- Vtest *vtest;   /* Chisq entry vector */
+-
+- gsl_matrix_view CEXACT,CEINV,CEXPT,IDTY;
+-
+- /*
+-  * For a given n = ntuple size in bits, there are n! bit orderings
+-  */
+- MYDEBUG(D_RGB_OPERM){
+-   printf("#==================================================================\n");
+-   printf("# rgb_operm: Running rgb_operm verbosely for k = %d.\n",rgb_operm_k);
+-   printf("# rgb_operm: Use -v = %d to focus.\n",D_RGB_OPERM);
+-   printf("# rgb_operm: ======================================================\n");
+- }
+-
+- /*
+-  * Sanity check first
+-  */
+- if((rgb_operm_k < 0) || (rgb_operm_k > RGB_OPERM_KMAX)){
+-   printf("\nError:  rgb_operm_k must be a positive integer <= %u.  Exiting.\n",RGB_OPERM_KMAX);
+-   exit(0);
+- }
+-
+- nperms = gsl_sf_fact(rgb_operm_k);
+- noperms = gsl_sf_fact(3*rgb_operm_k-2);
+- csamples = rgb_operm_k*rgb_operm_k;
+- gsl_permutation * p = gsl_permutation_alloc(nperms);
+-
+- /*
+-  * Allocate memory for value_max vector of Vtest structs and counts,
+-  * PER TEST.  Note that we must free both of these when we are done
+-  * or leak.
+-  */
+- vtest = (Vtest *)malloc(csamples*sizeof(Vtest));
+- count = (uint *)malloc(csamples*sizeof(uint));
+- Vtest_create(vtest,csamples+1);
+-
+- /*
+-  * We have to allocate and free the cexact and cexpt matrices here
+-  * or they'll be forgotten when these routines return.
+-  */
+- MYDEBUG(D_RGB_OPERM){
+-   printf("# rgb_operm: Creating and zeroing cexact[][] and cexpt[][].\n");
+- }
+- cexact = (double **)malloc(nperms*sizeof(double*));
+- ceinv  = (double **)malloc(nperms*sizeof(double*));
+- cexpt  = (double **)malloc(nperms*sizeof(double*));
+- idty   = (double **)malloc(nperms*sizeof(double*));
+- cvexact = (double *)malloc(nperms*nperms*sizeof(double));
+- cvein   = (double *)malloc(nperms*nperms*sizeof(double));
+- cvexpt  = (double *)malloc(nperms*nperms*sizeof(double));
+- vidty   = (double *)malloc(nperms*nperms*sizeof(double));
+- for(i=0;i<nperms;i++){
+-   /* Here we pack addresses to map the matrix addressing onto the vector */
+-   cexact[i] = &cvexact[i*nperms];
+-   ceinv[i] = &cvein[i*nperms];
+-   cexpt[i] = &cvexpt[i*nperms];
+-   idty[i] = &vidty[i*nperms];
+-   for(j = 0;j<nperms;j++){
+-     cexact[i][j] = 0.0;
+-     ceinv[i][j] = 0.0;
+-     cexpt[i][j]  = 0.0;
+-     idty[i][j]   = 0.0;
+-   }
+- }
+-
+- make_cexact();
+- make_cexpt();
+-
+- iv=0;
+- for(i=0;i<nperms;i++){
+-   for(j=0;j<nperms;j++){
+-     cvexact[iv] = cexact[i][j];
+-     cvexpt[iv]  = cexpt[i][j];
+-     vidty[iv]   = 0.0;
+-   }
+- }
+-
+- CEXACT = gsl_matrix_view_array(cvexact, nperms, nperms);
+- CEINV  = gsl_matrix_view_array(cvein  , nperms, nperms);
+- CEXPT  = gsl_matrix_view_array(cvexpt , nperms, nperms);
+- IDTY   = gsl_matrix_view_array(vidty  , nperms, nperms);
+-
+- /*
+-  * Hmmm, looks like cexact isn't invertible.  Duh.  So it has eigenvalues.
+-  * This seems to be important (how, I do not know) so let's find out.
+-  * Here is the gsl ritual for evaluating eigenvalues etc.
+-  */
+-
+- gsl_vector *eval = gsl_vector_alloc (nperms);
+- gsl_matrix *evec = gsl_matrix_alloc (nperms,nperms);
+- /*
+- gsl_eigen_nonsymm_workspace* w =  gsl_eigen_nonsymmv_alloc(nperms);
+- gsl_eigen_nonsymm_params (1,0,w);
+- gsl_eigen_nonsymmv(&CEXACT.matrix, eval, evec, w);
+- gsl_eigen_nonsymmv_free (w);
+- */
+- gsl_eigen_symmv_workspace* w =  gsl_eigen_symmv_alloc(nperms);
+- gsl_eigen_symmv(&CEXACT.matrix, eval, evec, w);
+- gsl_eigen_symmv_free (w);
+- gsl_eigen_symmv_sort (eval, evec, GSL_EIGEN_SORT_ABS_ASC);
+-
+- {
+-   int i;
+-
+-   printf("#==================================================================\n");
+-   for (i = 0; i < nperms; i++) {
+-     double eval_i = gsl_vector_get (eval, i);
+-     gsl_vector_view evec_i = gsl_matrix_column (evec, i);
+-     printf ("eigenvalue[%u] = %g\n", i, eval_i);
+-     printf ("eigenvector[%u] = \n",i);
+-     gsl_vector_fprintf (stdout,&evec_i.vector, "%10.5f");
+-   }
+-   printf("#==================================================================\n");
+- }
+-
+- gsl_vector_free (eval);
+- gsl_matrix_free (evec);
+-
+-/*
+- gsl_linalg_LU_decomp(&CEXACT.matrix, p, &s);
+- gsl_linalg_LU_invert(&CEXACT, p, &CEINV);
+- gsl_permutation_free(p);
+- gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &CEINV.matrix, &CEXPT.matrix, 0.0, &IDTY.matrix);
+- printf("#==================================================================\n");
+- printf("# Should be inverse of C, assuming it is invertible:\n");
+- for(i=0;i<nperms;i++){
+-   printf("# ");
+-   for(j = 0;j<nperms;j++){
+-     printf("%8.3f ",idty[i][j]);
+-   }
+-   printf("\n");
+- }
+- printf("#==================================================================\n");
+- printf("#==================================================================\n");
+- printf("# Should be normal on identity:\n");
+- for(i=0;i<nperms;i++){
+-   printf("# ");
+-   for(j = 0;j<nperms;j++){
+-     printf("%8.3f ",idty[i][j]);
+-   }
+-   printf("\n");
+- }
+- printf("#==================================================================\n");
+- */
+-
+-    
+-
+- /*
+-  * OK, at this point we have two matrices:  cexact[][] is filled with
+-  * the exact covariance matrix expected for the overlapping permutations.
+-  * cexpt[][] has been filled numerically by generating strings of random
+-  * uints or floats, generating sort index permutations, and
+-  * using them to IDENTICALLY generate an "experimental" version of c[][].
+-  * The two should correspond, in the limit of large tsamples.  IF I
+-  * understand Alhakim, Kawczak and Molchanov, then the way to implement
+-  * the simplest possible chisq test is to evaluate:
+-  *       cexact^-1 cexpt \approx I
+-  * where the diagonal terms should form a vector that is chisq distributed?
+-  * Let's try this...
+-  */
+- 
+- 
+-
+- /*
+-  * Free cexact[][] and cexpt[][]
+-  * Fix this when we're done so we don't leak; for now to much trouble.
+- for(i=0;i<nperms;i++){
+-   free(cexact[i]);
+-   free(cexpt[i]);
+- }
+- free(cexact);
+- free(cexpt);
+-  */
+- 
+- return(0);
+-
+-}
+-
+-void make_cexact()
+-{
+-
+- int i,j,k,ip,t,nop;
+- double fi,fj;
+- /*
+-  * This is the test vector.
+-  */
+- double testv[RGB_OPERM_KMAX*2];  /* easier than malloc etc, but beware length */
+- /*
+-  * pi[] is the permutation index of a sample.  ps[] holds the
+-  * actual sample.
+-  */
+- size_t pi[4096],ps[4096];
+- /*
+-  * We seem to have made a mistake of sorts.  We actually have to sum
+-  * BOTH the forward AND the backward directions.  That means that the
+-  * permutation vector has to be of length 3k-1, with the pi=1 term
+-  * corresponding to the middle.  So for k=2, instead of 0,1,2 we need
+-  * 0 1 2 3 4 and we'll have to do 23, 34 in the leading direction and
+-  * 21, 10 in the trailing direction.
+-  */
+- gsl_permutation **operms;
+-
+- MYDEBUG(D_RGB_OPERM){
+-   printf("#==================================================================\n");
+-   printf("# rgb_operm: Running cexact()\n");
+- }
+-
+- /*
+-  * Test fpipi().  This is probably cruft, actually.
+- MYDEBUG(D_RGB_OPERM){
+-   printf("# rgb_operm: Testing fpipi()\n");
+-   for(i=0;i<nperms;i++){
+-     for(j = 0;j<nperms;j++){
+-       printf("# rgb_operm: fpipi(%u,%u,%u) = %f\n",i,j,nperms,fpipi(i,j,nperms));
+-     }
+-   }
+- }
+- */
+-
+- MYDEBUG(D_RGB_OPERM){
+-   printf("#==================================================================\n");
+-   printf("# rgb_operm: Forming set of %u overlapping permutations\n",noperms);
+-   printf("# rgb_operm: Permutations\n");
+-   printf("# rgb_operm:==============================\n");
+- }
+- operms = (gsl_permutation**) malloc(noperms*sizeof(gsl_permutation*));
+- for(i=0;i<noperms;i++){
+-   operms[i] = gsl_permutation_alloc(3*rgb_operm_k - 2);
+-   /* Must quiet down
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("# rgb_operm: ");
+-   }
+-   */
+-   if(i == 0){
+-     gsl_permutation_init(operms[i]);
+-   } else {
+-     gsl_permutation_memcpy(operms[i],operms[i-1]);
+-     gsl_permutation_next(operms[i]);
+-   }
+-   /*
+-   MYDEBUG(D_RGB_OPERM){
+-     gsl_permutation_fprintf(stdout,operms[i]," %u");
+-     printf("\n");
+-   }
+-   */
+- }
+-
+- /*
+-  * We now form c_exact PRECISELY the same way that we do c_expt[][]
+-  * below, except that instead of pulling random samples of integers
+-  * or floats and averaging over the permutations thus represented,
+-  * we iterate over the complete set of equally weighted permutations
+-  * to get an exact answer.  Note that we have to center on 2k-1 and
+-  * go both forwards and backwards.
+-  */
+- for(t=0;t<noperms;t++){
+-   /*
+-    * To sort into a perm, test vector needs to be double.
+-    */
+-   for(k=0;k<3*rgb_operm_k - 2;k++) testv[k] = (double) operms[t]->data[k];
+-
+-   /* Not cruft, but quiet...
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("#------------------------------------------------------------------\n");
+-     printf("# Generating offset sample permutation pi's\n");
+-   }
+-   */
+-   for(k=0;k<2*rgb_operm_k - 1;k++){
+-     gsl_sort_index((size_t *) ps,&testv[k],1,rgb_operm_k);
+-     pi[k] = piperm((size_t *) ps,rgb_operm_k);
+-
+-     /* Not cruft, but quiet...
+-     MYDEBUG(D_RGB_OPERM){
+-       printf("# %u: ",k);
+-       for(ip=k;ip<rgb_operm_k+k;ip++){
+-         printf("%.1f ",testv[ip]);
+-       }
+-       printf("\n# ");
+-       for(ip=0;ip<rgb_operm_k;ip++){
+-         printf("%u ",ps[ip]);
+-       }
+-       printf(" = %u\n",pi[k]);
+-     }
+-     */
+-
+-   }
+-
+-   /*
+-    * This is the business end of things.  The covariance matrix is the
+-    * the sum of a central function of the permutation indices that yields
+-    * nperms-1/nperms on diagonal, -1/nperms off diagonal, for all the
+-    * possible permutations, for the FIRST permutation in a sample (fi)
+-    * times the sum of the same function over all the overlapping permutations
+-    * drawn from the same sample.  Quite simple, really.
+-    */
+-   for(i=0;i<nperms;i++){
+-     fi = fpipi(i,pi[rgb_operm_k-1],nperms);
+-     for(j=0;j<nperms;j++){
+-       fj = 0.0;
+-       for(k=0;k<rgb_operm_k;k++){
+-         fj += fpipi(j,pi[rgb_operm_k - 1 + k],nperms);
+-         if(k != 0){
+-           fj += fpipi(j,pi[rgb_operm_k - 1 - k],nperms);
+-	 }
+-       }
+-       cexact[i][j] += fi*fj;
+-     }
+-   }
+-
+- }
+-
+- MYDEBUG(D_RGB_OPERM){
+-   printf("# rgb_operm:==============================\n");
+-   printf("# rgb_operm: cexact[][] = \n");
+- }
+- for(i=0;i<nperms;i++){
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("# ");
+-   }
+-   for(j=0;j<nperms;j++){
+-     cexact[i][j] /= noperms;
+-     MYDEBUG(D_RGB_OPERM){
+-       printf("%10.6f  ",cexact[i][j]);
+-     }
+-   }
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("\n");
+-   }
+- }
+-
+- /*
+-  * Free operms[]
+-  */
+- for(i=0;i<noperms;i++){
+-   gsl_permutation_free(operms[i]);
+- }
+- free(operms);
+-
+-}
+-
+-void make_cexpt()
+-{
+-
+- int i,j,k,ip,t;
+- double fi,fj;
+- /*
+-  * This is the test vector.
+-  */
+- double testv[RGB_OPERM_KMAX*2];  /* easier than malloc etc, but beware length */
+- /*
+-  * pi[] is the permutation index of a sample.  ps[] holds the
+-  * actual sample.
+-  */
+- int pi[4096],ps[4096];
+-
+- MYDEBUG(D_RGB_OPERM){
+-   printf("#==================================================================\n");
+-   printf("# rgb_operm: Running cexpt()\n");
+- }
+-
+- /*
+-  * We evaluate cexpt[][] by sampling.  In a nutshell, this involves
+-  *   a) Filling testv[] with 2*rgb_operm_k - 1 random uints or doubles
+-  * It clearly cannot matter which we use, as long as the probability of
+-  * exact duplicates in a sample is very low.
+-  *   b) Using gsl_sort_index the exact same way it was used in make_cexact()
+-  * to generate the pi[] index, using ps[] as scratch space for the sort
+-  * indices.
+-  *   c) Evaluating fi and fj from the SAMPLED result, tsamples times.
+-  *   d) Normalizing.
+-  * Note that this is pretty much identical to the way we formed c_exact[][]
+-  * except that we are determining the relative frequency of each sort order
+-  * permutation 2*rgb_operm_k-1 long.
+-  *
+-  * NOTE WELL!  I honestly think that it is borderline silly to view
+-  * this as a matrix and to go through all of this nonsense.  The theoretical
+-  * c_exact[][] is computed from the observation that all the permutations
+-  * of n objects have equal weight = 1/n!.  Consequently, they should
+-  * individually be binomially distributed, tending to normal with many
+-  * samples.  Collectively they should be distributed like a vector of
+-  * equal binomial probabilities and a p-value should follow either from
+-  * chisq on n!-1 DoF or for that matter a KS test.  I see no way that
+-  * making it into a matrix can increase the sensitivity of the test -- if
+-  * the p-values are well defined in the two cases they can only be equal
+-  * by their very definition.
+-  *
+-  * If you are a statistician reading these words and disagree, please
+-  * communicate with me and explain why I'm wrong.  I'm still very much
+-  * learning statistics and would cherish gentle correction.
+-  */
+- for(t=0;t<tsamples;t++){
+-   /*
+-    * To sort into a perm, test vector needs to be double.
+-    */
+-   for(k=0;k<3*rgb_operm_k - 2;k++) testv[k] = (double) gsl_rng_get(rng);
+-
+-   /* Not cruft, but quiet...
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("#------------------------------------------------------------------\n");
+-     printf("# Generating offset sample permutation pi's\n");
+-   }
+-   */
+-   for(k=0;k<2*rgb_operm_k-1;k++){
+-     gsl_sort_index(ps,&testv[k],1,rgb_operm_k);
+-     pi[k] = piperm(ps,rgb_operm_k);
+-
+-     /* Not cruft, but quiet...
+-     MYDEBUG(D_RGB_OPERM){
+-       printf("# %u: ",k);
+-       for(ip=k;ip<rgb_operm_k+k;ip++){
+-         printf("%.1f ",testv[ip]);
+-       }
+-       printf("\n# ");
+-       for(ip=0;ip<rgb_operm_k;ip++){
+-         printf("%u ",permsample->data[ip]);
+-       }
+-       printf(" = %u\n",pi[k]);
+-     }
+-     */
+-   }
+-
+-   /*
+-    * This is the business end of things.  The covariance matrix is the
+-    * the sum of a central function of the permutation indices that yields
+-    * nperms-1/nperms on diagonal, -1/nperms off diagonal, for all the
+-    * possible permutations, for the FIRST permutation in a sample (fi)
+-    * times the sum of the same function over all the overlapping permutations
+-    * drawn from the same sample.  Quite simple, really.
+-    */
+-   for(i=0;i<nperms;i++){
+-     fi = fpipi(i,pi[rgb_operm_k-1],nperms);
+-     for(j=0;j<nperms;j++){
+-       fj = 0.0;
+-       for(k=0;k<rgb_operm_k;k++){
+-         fj += fpipi(j,pi[rgb_operm_k - 1 + k],nperms);
+-	 if(k != 0){
+-           fj += fpipi(j,pi[rgb_operm_k - 1 - k],nperms);
+-	 }
+-       }
+-       cexpt[i][j] += fi*fj;
+-     }
+-   }
+-
+- }
+-
+- MYDEBUG(D_RGB_OPERM){
+-   printf("# rgb_operm:==============================\n");
+-   printf("# rgb_operm: cexpt[][] = \n");
+- }
+- for(i=0;i<nperms;i++){
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("# ");
+-   }
+-   for(j=0;j<nperms;j++){
+-     cexpt[i][j] /= tsamples;
+-     MYDEBUG(D_RGB_OPERM){
+-       printf("%10.6f  ",cexpt[i][j]);
+-     }
+-   }
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("\n");
+-   }
+- }
+-
+-}
+-
+-uint piperm(size_t *data,int len)
+-{
+-
+- uint i,j,k,max,min;
+- uint pindex,uret,tmp;
+- static gsl_permutation** lookup = 0;
+-
+- /*
+-  * Allocate space for lookup table and fill it.
+-  */
+- if(lookup == 0){
+-   lookup = (gsl_permutation**) malloc(nperms*sizeof(gsl_permutation*));
+-   MYDEBUG(D_RGB_OPERM){
+-     printf("# rgb_operm: Allocating piperm lookup table of perms.\n");
+-   }
+-   for(i=0;i<nperms;i++){
+-        lookup[i] = gsl_permutation_alloc(rgb_operm_k);
+-   }
+-   for(i=0;i<nperms;i++){
+-     if(i == 0){
+-       gsl_permutation_init(lookup[i]);
+-     } else {
+-       gsl_permutation_memcpy(lookup[i],lookup[i-1]);
+-       gsl_permutation_next(lookup[i]);
+-     }
+-   }
+-
+-   /*
+-    * This method yields a mirror symmetry in the permutations top to
+-    * bottom.
+-   for(i=0;i<nperms/2;i++){
+-     if(i == 0){
+-       gsl_permutation_init(lookup[i]);
+-       for(j=0;j<rgb_operm_k;j++){
+-         lookup[nperms-i-1]->data[rgb_operm_k-j-1] = lookup[i]->data[j];
+-       }
+-     } else {
+-       gsl_permutation_memcpy(lookup[i],lookup[i-1]);
+-       gsl_permutation_next(lookup[i]);
+-       for(j=0;j<rgb_operm_k;j++){
+-         lookup[nperms-i-1]->data[rgb_operm_k-j-1] = lookup[i]->data[j];
+-       }
+-     }
+-   }
+-   */
+-   MYDEBUG(D_RGB_OPERM){
+-     for(i=0;i<nperms;i++){
+-       printf("# rgb_operm: %u => ",i);
+-       gsl_permutation_fprintf(stdout,lookup[i]," %u");
+-       printf("\n");
+-     }
+-   }
+-
+- }
+-
+- for(i=0;i<nperms;i++){
+-   if(memcmp(data,lookup[i]->data,len*sizeof(uint))==0){
+-     /* Not cruft, but off:
+-     MYDEBUG(D_RGB_OPERM){
+-       printf("# piperm(): ");
+-       gsl_permutation_fprintf(stdout,lookup[i]," %u");
+-       printf(" = %u\n",i);
+-     }
+-     */
+-     return(i);
+-   }
+- }
+- printf("We'd better not get here...\n");
+-
+- return(0);
+-
+-}
+-
+-double fpipi(int pi1,int pi2,int nkp)
+-{
+-
+- int i;
+- double fret;
+-
+- /*
+-  * compute the k-permutation index from iperm for the window
+-  * at data[offset] of length len.  If it matches pind, return
+-  * the first quantity, otherwise return the second.
+-  */
+- if(pi1 == pi2){
+-
+-   fret = (double) (nkp - 1.0)/nkp;
+-   if(verbose < 0){
+-     printf(" f(%d,%d) = %10.6f\n",pi1,pi2,fret);
+-   }
+-   return(fret);
+-
+- } else {
+-
+-   fret = (double) (-1.0/nkp);
+-   if(verbose < 0){
+-     printf(" f(%d,%d) = %10.6f\n",pi1,pi2,fret);
+-   }
+-   return(fret);
+-
+- }
+-
+-
+-}
+-
+-
+-
+-