topcom.c

   1 #include <assert.h>
   2 #include <barvinok/util.h>
   3 #include <barvinok/options.h>
   4 #include <unistd.h>
   5 #include "normalization.h"
   6 #include "topcom.h"
   7 #include "config.h"
   8
   9 #define ALLOC(type) (type*)malloc(sizeof(type))
  10
  11 void run_points2triangs(pid_t *child, int *in, int *out)
  12 {
  13     int in_fd[2], out_fd[2];
  14
  15     if (pipe(in_fd))
  16         assert(0);
  17     if (pipe(out_fd))
  18         assert(0);
  19     *child = fork();
  20     assert(*child >= 0);
  21     if (!*child) {
  22         int rc;
  23
  24         dup2(in_fd[0], 0);
  25         dup2(out_fd[1], 1);
  26         close(in_fd[0]);
  27         close(out_fd[1]);
  28         close(in_fd[1]);
  29         close(out_fd[0]);
  30
  31         rc = execl(POINTS2TRIANGS_PATH, "points2triangs", "--regular", NULL);
  32         assert(0);
  33     }
  34     close(in_fd[0]);
  35     close(out_fd[1]);
  36     *in = in_fd[1];
  37     *out = out_fd[0];
  38 }
  39
  40 struct domain {
  41     Param_Domain    domain;
  42     int             F_len;
  43 };
  44
  45 static Param_Vertices *construct_vertex(unsigned *vertex_facets,
  46                                        Matrix *Constraints,
  47                                        int d, unsigned nparam, unsigned MaxRays)
  48 {
  49     unsigned nvar = Constraints->NbColumns-2 - nparam;
  50     Matrix *A = Matrix_Alloc(nvar+1, nvar+1);
  51     Matrix *inv = Matrix_Alloc(nvar+1, nvar+1);
  52     Matrix *B = Matrix_Alloc(nvar, nparam+2);
  53     Matrix *V = Matrix_Alloc(nvar, nparam+2);
  54     Matrix *Domain = Matrix_Alloc(d-nvar, nparam+2);
  55     Polyhedron *AD;
  56     unsigned bx;
  57     int i, j, ix;
  58     int ok;
  59     Param_Vertices *vertex;
  60
  61     for (j = 0, i = 0, ix = 0, bx = MSB; i < d; ++i) {
  62         if ((vertex_facets[ix] & bx) == bx) {
  63             Vector_Copy(Constraints->p[i]+1, A->p[j], nvar);
  64             Vector_Oppose(Constraints->p[i]+1+nvar, B->p[j++], nparam+1);
  65         }
  66         NEXT(ix, bx);
  67     }
  68     assert(j == nvar);
  69     value_set_si(A->p[nvar][nvar], 1);
  70     ok = Matrix_Inverse(A, inv);
  71     assert(ok);
  72     Matrix_Free(A);
  73     inv->NbRows = nvar;
  74     inv->NbColumns = nvar;
  75     Matrix_Product(inv, B, V);
  76     Matrix_Free(B);
  77     for (i = 0; i < nvar; ++i) {
  78         value_assign(V->p[i][nparam+1], inv->p[nvar][nvar]);
  79         Vector_Normalize(V->p[i], V->NbColumns);
  80     }
  81     Matrix_Free(inv);
  82     for (j = 0, i = 0, ix = 0, bx = MSB; i < d; ++i) {
  83         if ((vertex_facets[ix] & bx) == bx) {
  84             NEXT(ix, bx);
  85             continue;
  86         }
  87         Param_Inner_Product(Constraints->p[i], V, Domain->p[j]);
  88         if (First_Non_Zero(Domain->p[j]+1, nparam+1) == -1)
  89             vertex_facets[ix] |= bx;
  90         else
  91             value_set_si(Domain->p[j++][0], 1);
  92         NEXT(ix, bx);
  93     }
  94     Domain->NbRows = j;
  95     A = Matrix_Copy(Domain);
  96     AD = Constraints2Polyhedron(A, MaxRays);
  97     Matrix_Free(A);
  98     POL_ENSURE_VERTICES(AD);
  99     /* A vertex with a lower-dimensional activity domain
 100      * saturates more facets than derived above and is actually
 101      * the superimposition of two or more vertices.
 102      * We therefore discard the domain and (ultimately)
 103      * the chamber containing it.
 104      * We keep the vertex, though, since it may reappear
 105      * in other chambers, which will then likewise be discarded.
 106      * The same holds if the activity domain is empty.
 107      */
 108     if (AD->NbEq > 0) {
 109         Matrix_Free(Domain);
 110         Domain = NULL;
 111     }
 112     Polyhedron_Free(AD);
 113     vertex = calloc(1, sizeof(Param_Vertices));
 114     vertex->Facets = vertex_facets;
 115     vertex->Vertex = V;
 116     vertex->Domain = Domain;
 117     return vertex;
 118 }
 119
 120 static int add_vertex_to_domain(Param_Vertices **vertices, int words,
 121                                 unsigned *vertex_facets,
 122                                 Matrix *Constraints, int d, unsigned nparam,
 123                                 struct domain *domain,
 124                                 unsigned MaxRays)
 125 {
 126     Param_Vertices *vertex;
 127     unsigned vbx;
 128     int vi, vix;
 129
 130     for (vi = 0, vix = 0, vbx = MSB;
 131             *vertices;
 132             vertices = &(*vertices)->next, ++vi) {
 133         int i;
 134         for (i = 0; i < words; ++i)
 135             if (((*vertices)->Facets[i] & vertex_facets[i]) != vertex_facets[i])
 136                 break;
 137         if (i >= words) {
 138             if (!(*vertices)->Domain)
 139                 domain->F_len = 0;
 140             else
 141                 domain->domain.F[vix] |= vbx;
 142             free(vertex_facets);
 143             return 0;
 144         }
 145         NEXT(vix, vbx);
 146     }
 147     if (domain->F_len <= vix) {
 148         domain->F_len++;
 149         domain->domain.F = realloc(domain->domain.F,
 150                                    domain->F_len * sizeof(unsigned));
 151         domain->domain.F[domain->F_len-1] = 0;
 152     }
 153     vertex = construct_vertex(vertex_facets, Constraints, d, nparam, MaxRays);
 154     if (!vertex->Domain)
 155         domain->F_len = 0;
 156     else
 157         domain->domain.F[vix] |= vbx;
 158     vertex->next = *vertices;
 159     *vertices = vertex;
 160     return 1;
 161 }
 162
 163 static void compute_domain(struct domain *domain, Param_Vertices *vertices,
 164                            Polyhedron *C, unsigned MaxRays)
 165 {
 166     unsigned bx;
 167     int ix, j;
 168     int nbV = bit_vector_count(domain->domain.F, domain->F_len);
 169     unsigned cols;
 170     unsigned rows;
 171     Matrix *Constraints;
 172
 173     for (ix = 0, bx = MSB; !vertices->Domain; vertices = vertices->next)
 174         NEXT(ix, bx);
 175
 176     cols = vertices->Domain->NbColumns;
 177     rows = vertices->Domain->NbRows;
 178     Constraints = Matrix_Alloc(nbV * rows + C->NbConstraints, cols);
 179
 180     for (j = 0; vertices; vertices = vertices->next) {
 181         if ((domain->domain.F[ix] & bx) == bx)
 182             Vector_Copy(vertices->Domain->p[0],
 183                         Constraints->p[(j++)*rows], rows * cols);
 184         NEXT(ix, bx);
 185     }
 186     Vector_Copy(C->Constraint[0], Constraints->p[j*rows], C->NbConstraints * cols);
 187     domain->domain.Domain = Constraints2Polyhedron(Constraints, MaxRays);
 188     Matrix_Free(Constraints);
 189 }
 190
 191 static void add_domain(struct domain **domains, struct domain *domain,
 192                        Param_Vertices *vertices, Polyhedron *C,
 193                        struct barvinok_options *options)
 194 {
 195     options->stats->topcom_chambers++;
 196
 197     for (; *domains; domains = (struct domain **)&(*domains)->domain.next) {
 198         int i;
 199         for (i = 0; i < (*domains)->F_len; ++i)
 200             if (((*domains)->domain.F[i] & domain->domain.F[i])
 201                         != domain->domain.F[i])
 202                 break;
 203         if (i < (*domains)->F_len)
 204             continue;
 205         for (; i < domain->F_len; ++i)
 206             if (domain->domain.F[i])
 207                 break;
 208         if (i >= domain->F_len) {
 209             Param_Domain_Free(&domain->domain);
 210             return;
 211         }
 212     }
 213     options->stats->topcom_distinct_chambers++;
 214     compute_domain(domain, vertices, C, options->MaxRays);
 215     *domains = domain;
 216 }
 217
 218 #define INT_BITS (sizeof(unsigned) * 8)
 219
 220 /* Remove any empty or lower-dimensional chamber.  The latter
 221  * lie on the boundary of the context and are facets of other chambers.
 222  *
 223  * While we are examining each chamber, also extend the F vector
 224  * of each chamber to the maximum.
 225  */
 226 static void remove_empty_chambers(Param_Domain **PD, unsigned vertex_words)
 227 {
 228     while (*PD) {
 229         int remove = 0;
 230         int i;
 231
 232         if ((*PD)->Domain->NbEq > 0)
 233             remove = 1;
 234         else {
 235             POL_ENSURE_FACETS((*PD)->Domain);
 236             if ((*PD)->Domain->NbEq > 0)
 237                 remove = 1;
 238         }
 239         if (remove) {
 240             Param_Domain *D = *PD;
 241             *PD = (*PD)->next;
 242             D->next = NULL;
 243             Param_Domain_Free(D);
 244             continue;
 245         }
 246         if ((i = ((struct domain*)(*PD))->F_len) < vertex_words)
 247             (*PD)->F = realloc((*PD)->F, vertex_words * sizeof(unsigned));
 248         for (; i < vertex_words; ++i)
 249             (*PD)->F[i] = 0;
 250         PD = &(*PD)->next;
 251     }
 252 }
 253
 254 static Param_Polyhedron *points2triangs(Matrix *K, Polyhedron *P, Polyhedron *C,
 255                                         struct barvinok_options *options)
 256 {
 257     int in, out;
 258     int i, j;
 259     pid_t child;
 260     FILE *fin, *fout;
 261     int d = K->NbRows;
 262     int words = (d+INT_BITS-1)/INT_BITS;
 263     Param_Vertices *vertices = NULL;
 264     struct domain *domains = NULL;
 265     int vertex_words = 1;
 266     Param_Polyhedron *PP = ALLOC(Param_Polyhedron);
 267     unsigned MaxRays = options->MaxRays;
 268
 269     PP->Rays = NULL;
 270     PP->nbV = 0;
 271     PP->Constraints = Polyhedron2Constraints(P);
 272     /* We need the exact facets, because we may make some of them open later */
 273     POL_UNSET(options->MaxRays, POL_INTEGER);
 274
 275     run_points2triangs(&child, &in, &out);
 276
 277     fin = fdopen(in, "w");
 278     fprintf(fin, "[\n");
 279     for (i = 0; i < K->NbRows; ++i) {
 280         fprintf(fin, "[");
 281         for (j = 0; j < K->NbColumns; ++j)
 282             value_print(fin, P_VALUE_FMT, K->p[i][j]);
 283         fprintf(fin, "]");
 284     }
 285     fprintf(fin, "]\n");
 286     fclose(fin);
 287
 288     fout = fdopen(out, "r");
 289     while (fscanf(fout, "T[%d]:=", &i) == 1) {
 290         int a, b, c;
 291         struct domain *domain = ALLOC(struct domain);
 292         memset(domain, 0, sizeof(*domain));
 293         domain->domain.F = calloc(vertex_words, sizeof(unsigned));
 294         domain->F_len = vertex_words;
 295
 296         c = fgetc(fout);
 297         if (c == '[')
 298                 fscanf(fout, "%d,%d:{", &a, &b);
 299
 300         while (fgetc(fout) == '{') {    /* '{' or closing '}' */
 301             int c;
 302             unsigned *F = calloc(words, sizeof(unsigned));
 303
 304             for (j = 0; j < K->NbColumns; ++j) {
 305                 unsigned v, shift;
 306                 fscanf(fout, "%d", &v);
 307                 shift = INT_BITS - (v % INT_BITS) - 1;
 308                 F[v / INT_BITS] |= 1u << shift;
 309                 fgetc(fout); /* , or } */
 310             }
 311             if (!domain->F_len)
 312                 free(F);
 313             else if (add_vertex_to_domain(&vertices, words, F, PP->Constraints,
 314                                           d, C->Dimension,
 315                                           domain, options->MaxRays))
 316                 ++PP->nbV;
 317             if ((c = fgetc(fout)) != ',')       /* , or } */
 318                 ungetc(c, fout);
 319         }
 320         if (domain->F_len)
 321             vertex_words = domain->F_len;
 322         if (c == '[')
 323                 fgetc(fout); /* ] */
 324         fgetc(fout); /* ; */
 325         fgetc(fout); /* \n */
 326         if (bit_vector_count(domain->domain.F, domain->F_len) > 0)
 327             add_domain(&domains, domain, vertices, C, options);
 328         else {
 329             options->stats->topcom_empty_chambers++;
 330             Param_Domain_Free(&domain->domain);
 331         }
 332     }
 333     fclose(fout);
 334
 335     PP->V = vertices;
 336     PP->D = &domains->domain;
 337
 338     remove_empty_chambers(&PP->D, vertex_words);
 339
 340     options->MaxRays = MaxRays;
 341
 342     return PP;
 343 }
 344
 345 /* Assumes M is of full row rank */
 346 static Matrix *null_space(Matrix *M)
 347 {
 348     Matrix *H, *Q, *U;
 349     Matrix *N;
 350     int i;
 351
 352     left_hermite(M, &H, &Q, &U);
 353     N = Matrix_Alloc(M->NbColumns, M->NbColumns - M->NbRows);
 354     for (i = 0; i < N->NbRows; ++i)
 355         Vector_Copy(U->p[i] + M->NbRows, N->p[i], N->NbColumns);
 356     Matrix_Free(H);
 357     Matrix_Free(Q);
 358     Matrix_Free(U);
 359     return N;
 360 }
 361
 362 static void SwapColumns(Value **V, int n, int i, int j)
 363 {
 364     int r;
 365
 366     for (r = 0; r < n; ++r)
 367         value_swap(V[r][i], V[r][j]);
 368 }
 369
 370 /* C is assumed to be the "true" context, i.e., it has been intersected
 371  * with the projection of P onto the parameter space.
 372  * Furthermore, P and C are assumed to be full-dimensional.
 373  */
 374 Param_Polyhedron *TC_P2PP(Polyhedron *P, Polyhedron *C,
 375                           struct barvinok_options *options)
 376 {
 377     unsigned nparam = C->Dimension;
 378     unsigned nvar = P->Dimension - C->Dimension;
 379     int i, j;
 380     Matrix *H;
 381     Matrix *A;
 382     Matrix *K;
 383     int rows;
 384     Param_Polyhedron *PP;
 385     Matrix M;
 386
 387     assert(C->NbEq == 0);
 388
 389     Polyhedron_Matrix_View(P, &M, P->NbConstraints);
 390     H = standard_constraints(&M, nparam, &rows, NULL);
 391
 392     A = Matrix_Alloc(rows, nvar+rows);
 393     for (i = nvar; i < H->NbRows; ++i) {
 394         Vector_Oppose(H->p[i], A->p[i-nvar], H->NbColumns);
 395         value_set_si(A->p[i-nvar][i], 1);
 396     }
 397     for (i = 0, j = H->NbRows-nvar; i < nvar; ++i) {
 398         if (First_Non_Zero(H->p[i], i) == -1)
 399             continue;
 400         Vector_Oppose(H->p[i], A->p[j], H->NbColumns);
 401         value_set_si(A->p[j][j+nvar], 1);
 402         SwapColumns(A->p, A->NbRows, j+nvar, i);
 403         ++j;
 404     }
 405     K = null_space(A);
 406     Matrix_Free(A);
 407     /* Ignore extra constraints */
 408     K->NbRows = H->NbRows;
 409     Matrix_Free(H);
 410     PP = points2triangs(K, P, C, options);
 411     Matrix_Free(K);
 412     return PP;
 413 }