topcom.c

   1 #include <barvinok/util.h>
   2 #include <barvinok/options.h>
   3 #include <unistd.h>
   4 #include "topcom.h"
   5 #include "config.h"
   6
   7 #define ALLOC(type) (type*)malloc(sizeof(type))
   8
   9 void run_points2triangs(pid_t *child, int *in, int *out)
  10 {
  11     int in_fd[2], out_fd[2];
  12
  13     if (pipe(in_fd))
  14         assert(0);
  15     if (pipe(out_fd))
  16         assert(0);
  17     *child = fork();
  18     assert(*child >= 0);
  19     if (!*child) {
  20         int rc;
  21
  22         dup2(in_fd[0], 0);
  23         dup2(out_fd[1], 1);
  24         close(in_fd[0]);
  25         close(out_fd[1]);
  26         close(in_fd[1]);
  27         close(out_fd[0]);
  28
  29         rc = execl(POINTS2TRIANGS_PATH, "points2triangs", "--regular", NULL);
  30         assert(0);
  31     }
  32     close(in_fd[0]);
  33     close(out_fd[1]);
  34     *in = in_fd[1];
  35     *out = out_fd[0];
  36 }
  37
  38 struct domain {
  39     Param_Domain    domain;
  40     int             F_len;
  41 };
  42
  43 static Param_Vertices *construct_vertex(unsigned *vertex_facets,
  44                                        Matrix *Constraints,
  45                                        int d, unsigned nparam, unsigned MaxRays)
  46 {
  47     unsigned nvar = Constraints->NbColumns-2 - nparam;
  48     Matrix *A = Matrix_Alloc(nvar+1, nvar+1);
  49     Matrix *inv = Matrix_Alloc(nvar+1, nvar+1);
  50     Matrix *B = Matrix_Alloc(nvar, nparam+2);
  51     Matrix *V = Matrix_Alloc(nvar, nparam+2);
  52     Matrix *Domain = Matrix_Alloc(d-nvar, nparam+2);
  53     Polyhedron *AD;
  54     unsigned bx;
  55     int i, j, ix;
  56     int ok;
  57     Param_Vertices *vertex;
  58
  59     for (j = 0, i = 0, ix = 0, bx = MSB; i < d; ++i) {
  60         if ((vertex_facets[ix] & bx) == bx) {
  61             Vector_Copy(Constraints->p[i]+1, A->p[j], nvar);
  62             Vector_Oppose(Constraints->p[i]+1+nvar, B->p[j++], nparam+1);
  63         }
  64         NEXT(ix, bx);
  65     }
  66     assert(j == nvar);
  67     value_set_si(A->p[nvar][nvar], 1);
  68     ok = Matrix_Inverse(A, inv);
  69     assert(ok);
  70     Matrix_Free(A);
  71     inv->NbRows = nvar;
  72     inv->NbColumns = nvar;
  73     Matrix_Product(inv, B, V);
  74     Matrix_Free(B);
  75     for (i = 0; i < nvar; ++i) {
  76         value_assign(V->p[i][nparam+1], inv->p[nvar][nvar]);
  77         Vector_Normalize(V->p[i], V->NbColumns);
  78     }
  79     Matrix_Free(inv);
  80     for (j = 0, i = 0, ix = 0, bx = MSB; i < d; ++i) {
  81         if ((vertex_facets[ix] & bx) == bx) {
  82             NEXT(ix, bx);
  83             continue;
  84         }
  85         Param_Inner_Product(Constraints->p[i], V, Domain->p[j]);
  86         if (First_Non_Zero(Domain->p[j]+1, nparam+1) == -1)
  87             vertex_facets[ix] |= bx;
  88         else
  89             value_set_si(Domain->p[j++][0], 1);
  90         NEXT(ix, bx);
  91     }
  92     Domain->NbRows = j;
  93     A = Matrix_Copy(Domain);
  94     AD = Constraints2Polyhedron(A, MaxRays);
  95     Matrix_Free(A);
  96     POL_ENSURE_VERTICES(AD);
  97     /* A vertex with a lower-dimensional activity domain
  98      * saturates more facets than derived above and is actually
  99      * the superimposition of two or more vertices.
 100      * We therefore discard the domain and (ultimately)
 101      * the chamber containing it.
 102      * We keep the vertex, though, since it may reappear
 103      * in other chambers, which will then likewise be discarded.
 104      * The same holds if the activity domain is empty.
 105      */
 106     if (AD->NbEq > 0) {
 107         Matrix_Free(Domain);
 108         Domain = NULL;
 109     }
 110     Polyhedron_Free(AD);
 111     vertex = calloc(1, sizeof(Param_Vertices));
 112     vertex->Facets = vertex_facets;
 113     vertex->Vertex = V;
 114     vertex->Domain = Domain;
 115     return vertex;
 116 }
 117
 118 static int add_vertex_to_domain(Param_Vertices **vertices, int words,
 119                                 unsigned *vertex_facets,
 120                                 Matrix *Constraints, int d, unsigned nparam,
 121                                 struct domain *domain,
 122                                 unsigned MaxRays)
 123 {
 124     Param_Vertices *vertex;
 125     unsigned vbx;
 126     int vi, vix;
 127
 128     for (vi = 0, vix = 0, vbx = MSB;
 129             *vertices;
 130             vertices = &(*vertices)->next, ++vi) {
 131         int i;
 132         for (i = 0; i < words; ++i)
 133             if (((*vertices)->Facets[i] & vertex_facets[i]) != vertex_facets[i])
 134                 break;
 135         if (i >= words) {
 136             if (!(*vertices)->Domain)
 137                 domain->F_len = 0;
 138             else
 139                 domain->domain.F[vix] |= vbx;
 140             free(vertex_facets);
 141             return 0;
 142         }
 143         NEXT(vix, vbx);
 144     }
 145     if (domain->F_len <= vix) {
 146         domain->F_len++;
 147         domain->domain.F = realloc(domain->domain.F,
 148                                    domain->F_len * sizeof(unsigned));
 149         domain->domain.F[domain->F_len-1] = 0;
 150     }
 151     vertex = construct_vertex(vertex_facets, Constraints, d, nparam, MaxRays);
 152     if (!vertex->Domain)
 153         domain->F_len = 0;
 154     else
 155         domain->domain.F[vix] |= vbx;
 156     vertex->next = *vertices;
 157     *vertices = vertex;
 158     return 1;
 159 }
 160
 161 static int bit_count(unsigned *F, int F_len)
 162 {
 163     int i;
 164     int count = 0;
 165
 166     for (i = 0; i < F_len; ++i) {
 167         unsigned v = F[i];
 168         while (v) {
 169             v &= v-1;
 170             ++count;
 171         }
 172     }
 173     return count;
 174 }
 175
 176 static void compute_domain(struct domain *domain, Param_Vertices *vertices,
 177                            Polyhedron *C, unsigned MaxRays)
 178 {
 179     unsigned bx;
 180     int i, ix, j;
 181     int nbV = bit_count(domain->domain.F, domain->F_len);
 182     unsigned cols = vertices->Domain->NbColumns;
 183     unsigned rows = vertices->Domain->NbRows;
 184     Matrix *Constraints = Matrix_Alloc(nbV * rows + C->NbConstraints, cols);
 185
 186     for (i = 0, j = 0, ix = 0, bx = MSB;
 187             vertices;
 188             vertices = vertices->next, ++i) {
 189         if ((domain->domain.F[ix] & bx) == bx)
 190             Vector_Copy(vertices->Domain->p[0],
 191                         Constraints->p[(j++)*rows], rows * cols);
 192         NEXT(ix, bx);
 193     }
 194     Vector_Copy(C->Constraint[0], Constraints->p[j*rows], C->NbConstraints * cols);
 195     domain->domain.Domain = Constraints2Polyhedron(Constraints, MaxRays);
 196     Matrix_Free(Constraints);
 197 }
 198
 199 static void add_domain(struct domain **domains, struct domain *domain,
 200                        Param_Vertices *vertices, Polyhedron *C,
 201                        struct barvinok_options *options)
 202 {
 203     options->stats->topcom_chambers++;
 204
 205     for (; *domains; domains = (struct domain **)&(*domains)->domain.next) {
 206         int i;
 207         for (i = 0; i < (*domains)->F_len; ++i)
 208             if (((*domains)->domain.F[i] & domain->domain.F[i])
 209                         != domain->domain.F[i])
 210                 break;
 211         if (i < (*domains)->F_len)
 212             continue;
 213         for (; i < domain->F_len; ++i)
 214             if (domain->domain.F[i])
 215                 break;
 216         if (i >= domain->F_len) {
 217             Param_Domain_Free(&domain->domain);
 218             return;
 219         }
 220     }
 221     options->stats->topcom_distinct_chambers++;
 222     compute_domain(domain, vertices, C, options->MaxRays);
 223     *domains = domain;
 224 }
 225
 226 #define INT_BITS (sizeof(unsigned) * 8)
 227
 228 /* Remove any empty or lower-dimensional chamber.  The latter
 229  * lie on the boundary of the context and are facets of other chambers.
 230  *
 231  * While we are examining each chamber, also extend the F vector
 232  * of each chamber to the maximum.
 233  */
 234 static void remove_empty_chambers(Param_Domain **PD, unsigned vertex_words)
 235 {
 236     while (*PD) {
 237         int remove = 0;
 238         int i;
 239
 240         if ((*PD)->Domain->NbEq > 0)
 241             remove = 1;
 242         else {
 243             POL_ENSURE_FACETS((*PD)->Domain);
 244             if ((*PD)->Domain->NbEq > 0)
 245                 remove = 1;
 246         }
 247         if (remove) {
 248             Param_Domain *D = *PD;
 249             *PD = (*PD)->next;
 250             D->next = NULL;
 251             Param_Domain_Free(D);
 252             continue;
 253         }
 254         if ((i = ((struct domain*)(*PD))->F_len) < vertex_words)
 255             (*PD)->F = realloc((*PD)->F, vertex_words * sizeof(unsigned));
 256         for (; i < vertex_words; ++i)
 257             (*PD)->F[i] = 0;
 258         PD = &(*PD)->next;
 259     }
 260 }
 261
 262 static Param_Polyhedron *points2triangs(Matrix *K, Polyhedron *P, Polyhedron *C,
 263                                         struct barvinok_options *options)
 264 {
 265     int in, out;
 266     int i, j;
 267     pid_t child;
 268     FILE *fin, *fout;
 269     int d = K->NbRows;
 270     int words = (d+INT_BITS-1)/INT_BITS;
 271     Param_Vertices *vertices = NULL;
 272     struct domain *domains = NULL;
 273     int vertex_words = 1;
 274     Param_Polyhedron *PP = ALLOC(Param_Polyhedron);
 275     unsigned MaxRays = options->MaxRays;
 276
 277     PP->nbV = 0;
 278     PP->Constraints = Polyhedron2Constraints(P);
 279     /* We need the exact facets, because we may make some of them open later */
 280     POL_UNSET(options->MaxRays, POL_INTEGER);
 281
 282     run_points2triangs(&child, &in, &out);
 283
 284     fin = fdopen(in, "w");
 285     fprintf(fin, "[\n");
 286     for (i = 0; i < K->NbRows; ++i) {
 287         fprintf(fin, "[");
 288         for (j = 0; j < K->NbColumns; ++j)
 289             value_print(fin, P_VALUE_FMT, K->p[i][j]);
 290         fprintf(fin, "]");
 291     }
 292     fprintf(fin, "]\n");
 293     fclose(fin);
 294
 295     fout = fdopen(out, "r");
 296     while (fscanf(fout, "T[%d]:={", &i) == 1) {
 297         struct domain *domain = ALLOC(struct domain);
 298         memset(domain, 0, sizeof(*domain));
 299         domain->domain.F = calloc(vertex_words, sizeof(unsigned));
 300         domain->F_len = vertex_words;
 301
 302         while (fgetc(fout) == '{') {    /* '{' or closing '}' */
 303             int c;
 304             unsigned *F = calloc(words, sizeof(unsigned));
 305
 306             for (j = 0; j < K->NbColumns; ++j) {
 307                 unsigned v, shift;
 308                 fscanf(fout, "%d", &v);
 309                 shift = INT_BITS - (v % INT_BITS) - 1;
 310                 F[v / INT_BITS] |= 1u << shift;
 311                 fgetc(fout); /* , or } */
 312             }
 313             if (!domain->F_len)
 314                 free(F);
 315             else if (add_vertex_to_domain(&vertices, words, F, PP->Constraints,
 316                                           d, C->Dimension,
 317                                           domain, options->MaxRays))
 318                 ++PP->nbV;
 319             if ((c = fgetc(fout)) != ',')       /* , or } */
 320                 ungetc(c, fout);
 321         }
 322         if (domain->F_len)
 323             vertex_words = domain->F_len;
 324         fgetc(fout); /* ; */
 325         fgetc(fout); /* \n */
 326         if (bit_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 static int is_unit_row(Value *row, int pos, int len)
 371 {
 372     if (!value_one_p(row[pos]) && !value_mone_p(row[pos]))
 373         return 0;
 374     return First_Non_Zero(row+pos+1, len-(pos+1)) == -1;
 375 }
 376
 377 /* C is assumed to be the "true" context, i.e., it has been intersected
 378  * with the projection of P onto the parameter space.
 379  * Furthermore, P and C are assumed to be full-dimensional.
 380  */
 381 Param_Polyhedron *TC_P2PP(Polyhedron *P, Polyhedron *C,
 382                           struct barvinok_options *options)
 383 {
 384     unsigned nparam = C->Dimension;
 385     unsigned nvar = P->Dimension - C->Dimension;
 386     Matrix *M;
 387     int i, j, d;
 388     Matrix *H, *U, *Q;
 389     Matrix *A;
 390     Matrix *K;
 391     int rows;
 392     Param_Polyhedron *PP;
 393
 394     assert(P->NbEq == 0);
 395     assert(C->NbEq == 0);
 396     /* move constraints only involving parameters down
 397      * and move unit vectors (if there are any) to the right place.
 398      */
 399     for (d = 0, j = P->NbConstraints; d < j; ++d) {
 400         int index;
 401         index = First_Non_Zero(P->Constraint[d]+1, nvar);
 402         if (index != -1) {
 403             if (index != d &&
 404                 is_unit_row(P->Constraint[d]+1, index, nvar)) {
 405                 Vector_Exchange(P->Constraint[d], P->Constraint[index],
 406                                 P->Dimension+2);
 407                 if (index > d)
 408                     --d;
 409             }
 410             continue;
 411         }
 412         while (d < --j && First_Non_Zero(P->Constraint[j]+1, nvar) == -1)
 413             ;
 414         if (d >= j)
 415             break;
 416         Vector_Exchange(P->Constraint[d], P->Constraint[j], P->Dimension+2);
 417     }
 418     M = Matrix_Alloc(d+nvar, nvar);
 419     for (j = 0; j < d; ++j)
 420         Vector_Copy(P->Constraint[j]+1, M->p[j], nvar);
 421
 422     neg_left_hermite(M, &H, &Q, &U);
 423     Matrix_Free(M);
 424     Matrix_Free(Q);
 425     Matrix_Free(U);
 426     H->NbRows -= nvar;
 427
 428     /* Rearrange rows such that top of H is lower diagonal and
 429      * add extra unit vector rows that are positive linear
 430      * combinations of two or more of the top rows.
 431      */
 432     for (i = 0; i < H->NbColumns; ++i) {
 433         for (j = i; j < H->NbRows; ++j)
 434             if (value_notzero_p(H->p[j][i]))
 435                 break;
 436         if (j != i) {
 437             Vector_Exchange(P->Constraint[i], P->Constraint[j], P->Dimension+2);
 438             Vector_Exchange(H->p[i], H->p[j], H->NbColumns);
 439         }
 440         if (First_Non_Zero(H->p[i], i) != -1)
 441             value_set_si(H->p[H->NbRows++][i], 1);
 442     }
 443
 444     rows = H->NbRows-nvar;
 445     A = Matrix_Alloc(rows, nvar+rows);
 446     for (i = nvar; i < d; ++i) {
 447         Vector_Oppose(H->p[i], A->p[i-nvar], H->NbColumns);
 448         value_set_si(A->p[i-nvar][i], 1);
 449     }
 450     for (; i < H->NbRows; ++i) {
 451         j = First_Non_Zero(H->p[i], nvar);
 452         assert(j != -1);
 453         Vector_Oppose(H->p[j], A->p[i-nvar], H->NbColumns);
 454         value_set_si(A->p[i-nvar][i], 1);
 455         SwapColumns(A->p, A->NbRows, i, j);
 456     }
 457     Matrix_Free(H);
 458     K = null_space(A);
 459     Matrix_Free(A);
 460     /* Ignore extra constraints */
 461     K->NbRows = d;
 462     PP = points2triangs(K, P, C, options);
 463     Matrix_Free(K);
 464     return PP;
 465 }