topcom.c

   1 #include <assert.h>
   2 #include <barvinok/util.h>
   3 #include <barvinok/options.h>
   4 #include <unistd.h>
   5 #include "polysign.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 i, ix, j;
 168     int nbV = bit_vector_count(domain->domain.F, domain->F_len);
 169     unsigned cols = vertices->Domain->NbColumns;
 170     unsigned rows = vertices->Domain->NbRows;
 171     Matrix *Constraints = Matrix_Alloc(nbV * rows + C->NbConstraints, cols);
 172
 173     for (i = 0, j = 0, ix = 0, bx = MSB;
 174             vertices;
 175             vertices = vertices->next, ++i) {
 176         if ((domain->domain.F[ix] & bx) == bx)
 177             Vector_Copy(vertices->Domain->p[0],
 178                         Constraints->p[(j++)*rows], rows * cols);
 179         NEXT(ix, bx);
 180     }
 181     Vector_Copy(C->Constraint[0], Constraints->p[j*rows], C->NbConstraints * cols);
 182     domain->domain.Domain = Constraints2Polyhedron(Constraints, MaxRays);
 183     Matrix_Free(Constraints);
 184 }
 185
 186 static void add_domain(struct domain **domains, struct domain *domain,
 187                        Param_Vertices *vertices, Polyhedron *C,
 188                        struct barvinok_options *options)
 189 {
 190     options->stats->topcom_chambers++;
 191
 192     for (; *domains; domains = (struct domain **)&(*domains)->domain.next) {
 193         int i;
 194         for (i = 0; i < (*domains)->F_len; ++i)
 195             if (((*domains)->domain.F[i] & domain->domain.F[i])
 196                         != domain->domain.F[i])
 197                 break;
 198         if (i < (*domains)->F_len)
 199             continue;
 200         for (; i < domain->F_len; ++i)
 201             if (domain->domain.F[i])
 202                 break;
 203         if (i >= domain->F_len) {
 204             Param_Domain_Free(&domain->domain);
 205             return;
 206         }
 207     }
 208     options->stats->topcom_distinct_chambers++;
 209     compute_domain(domain, vertices, C, options->MaxRays);
 210     *domains = domain;
 211 }
 212
 213 #define INT_BITS (sizeof(unsigned) * 8)
 214
 215 /* Remove any empty or lower-dimensional chamber.  The latter
 216  * lie on the boundary of the context and are facets of other chambers.
 217  *
 218  * While we are examining each chamber, also extend the F vector
 219  * of each chamber to the maximum.
 220  */
 221 static void remove_empty_chambers(Param_Domain **PD, unsigned vertex_words)
 222 {
 223     while (*PD) {
 224         int remove = 0;
 225         int i;
 226
 227         if ((*PD)->Domain->NbEq > 0)
 228             remove = 1;
 229         else {
 230             POL_ENSURE_FACETS((*PD)->Domain);
 231             if ((*PD)->Domain->NbEq > 0)
 232                 remove = 1;
 233         }
 234         if (remove) {
 235             Param_Domain *D = *PD;
 236             *PD = (*PD)->next;
 237             D->next = NULL;
 238             Param_Domain_Free(D);
 239             continue;
 240         }
 241         if ((i = ((struct domain*)(*PD))->F_len) < vertex_words)
 242             (*PD)->F = realloc((*PD)->F, vertex_words * sizeof(unsigned));
 243         for (; i < vertex_words; ++i)
 244             (*PD)->F[i] = 0;
 245         PD = &(*PD)->next;
 246     }
 247 }
 248
 249 static Param_Polyhedron *points2triangs(Matrix *K, Polyhedron *P, Polyhedron *C,
 250                                         struct barvinok_options *options)
 251 {
 252     int in, out;
 253     int i, j;
 254     pid_t child;
 255     FILE *fin, *fout;
 256     int d = K->NbRows;
 257     int words = (d+INT_BITS-1)/INT_BITS;
 258     Param_Vertices *vertices = NULL;
 259     struct domain *domains = NULL;
 260     int vertex_words = 1;
 261     Param_Polyhedron *PP = ALLOC(Param_Polyhedron);
 262     unsigned MaxRays = options->MaxRays;
 263
 264     PP->nbV = 0;
 265     PP->Constraints = Polyhedron2Constraints(P);
 266     /* We need the exact facets, because we may make some of them open later */
 267     POL_UNSET(options->MaxRays, POL_INTEGER);
 268
 269     run_points2triangs(&child, &in, &out);
 270
 271     fin = fdopen(in, "w");
 272     fprintf(fin, "[\n");
 273     for (i = 0; i < K->NbRows; ++i) {
 274         fprintf(fin, "[");
 275         for (j = 0; j < K->NbColumns; ++j)
 276             value_print(fin, P_VALUE_FMT, K->p[i][j]);
 277         fprintf(fin, "]");
 278     }
 279     fprintf(fin, "]\n");
 280     fclose(fin);
 281
 282     fout = fdopen(out, "r");
 283     while (fscanf(fout, "T[%d]:={", &i) == 1) {
 284         struct domain *domain = ALLOC(struct domain);
 285         memset(domain, 0, sizeof(*domain));
 286         domain->domain.F = calloc(vertex_words, sizeof(unsigned));
 287         domain->F_len = vertex_words;
 288
 289         while (fgetc(fout) == '{') {    /* '{' or closing '}' */
 290             int c;
 291             unsigned *F = calloc(words, sizeof(unsigned));
 292
 293             for (j = 0; j < K->NbColumns; ++j) {
 294                 unsigned v, shift;
 295                 fscanf(fout, "%d", &v);
 296                 shift = INT_BITS - (v % INT_BITS) - 1;
 297                 F[v / INT_BITS] |= 1u << shift;
 298                 fgetc(fout); /* , or } */
 299             }
 300             if (!domain->F_len)
 301                 free(F);
 302             else if (add_vertex_to_domain(&vertices, words, F, PP->Constraints,
 303                                           d, C->Dimension,
 304                                           domain, options->MaxRays))
 305                 ++PP->nbV;
 306             if ((c = fgetc(fout)) != ',')       /* , or } */
 307                 ungetc(c, fout);
 308         }
 309         if (domain->F_len)
 310             vertex_words = domain->F_len;
 311         fgetc(fout); /* ; */
 312         fgetc(fout); /* \n */
 313         if (bit_vector_count(domain->domain.F, domain->F_len) > 0)
 314             add_domain(&domains, domain, vertices, C, options);
 315         else {
 316             options->stats->topcom_empty_chambers++;
 317             Param_Domain_Free(&domain->domain);
 318         }
 319     }
 320     fclose(fout);
 321
 322     PP->V = vertices;
 323     PP->D = &domains->domain;
 324
 325     remove_empty_chambers(&PP->D, vertex_words);
 326
 327     options->MaxRays = MaxRays;
 328
 329     return PP;
 330 }
 331
 332 /* Assumes M is of full row rank */
 333 static Matrix *null_space(Matrix *M)
 334 {
 335     Matrix *H, *Q, *U;
 336     Matrix *N;
 337     int i;
 338
 339     left_hermite(M, &H, &Q, &U);
 340     N = Matrix_Alloc(M->NbColumns, M->NbColumns - M->NbRows);
 341     for (i = 0; i < N->NbRows; ++i)
 342         Vector_Copy(U->p[i] + M->NbRows, N->p[i], N->NbColumns);
 343     Matrix_Free(H);
 344     Matrix_Free(Q);
 345     Matrix_Free(U);
 346     return N;
 347 }
 348
 349 static void SwapColumns(Value **V, int n, int i, int j)
 350 {
 351     int r;
 352
 353     for (r = 0; r < n; ++r)
 354         value_swap(V[r][i], V[r][j]);
 355 }
 356
 357 /* C is assumed to be the "true" context, i.e., it has been intersected
 358  * with the projection of P onto the parameter space.
 359  * Furthermore, P and C are assumed to be full-dimensional.
 360  */
 361 Param_Polyhedron *TC_P2PP(Polyhedron *P, Polyhedron *C,
 362                           struct barvinok_options *options)
 363 {
 364     unsigned nparam = C->Dimension;
 365     unsigned nvar = P->Dimension - C->Dimension;
 366     int i, j;
 367     Matrix *H;
 368     Matrix *A;
 369     Matrix *K;
 370     int rows;
 371     Param_Polyhedron *PP;
 372
 373     assert(C->NbEq == 0);
 374
 375     H = standard_constraints(P, nparam, &rows, NULL);
 376
 377     A = Matrix_Alloc(rows, nvar+rows);
 378     for (i = nvar; i < H->NbRows; ++i) {
 379         Vector_Oppose(H->p[i], A->p[i-nvar], H->NbColumns);
 380         value_set_si(A->p[i-nvar][i], 1);
 381     }
 382     for (i = 0, j = H->NbRows-nvar; i < nvar; ++i) {
 383         if (First_Non_Zero(H->p[i], i) == -1)
 384             continue;
 385         Vector_Oppose(H->p[i], A->p[j], H->NbColumns);
 386         value_set_si(A->p[j][j+nvar], 1);
 387         SwapColumns(A->p, A->NbRows, j+nvar, i);
 388         ++j;
 389     }
 390     K = null_space(A);
 391     Matrix_Free(A);
 392     /* Ignore extra constraints */
 393     K->NbRows = H->NbRows;
 394     Matrix_Free(H);
 395     PP = points2triangs(K, P, C, options);
 396     Matrix_Free(K);
 397     return PP;
 398 }