barvinok_enumerate.cc

   1 #include <assert.h>
   2 #include <unistd.h>
   3 #include <stdlib.h>
   4 #include <gmp.h>
   5 #include <isl_set_polylib.h>
   6 #include <barvinok/evalue.h>
   7 #include <barvinok/util.h>
   8 #include <barvinok/barvinok.h>
   9 #include "barvinok_enumerate_options.h"
  10 #include "verify.h"
  11 #include "verify_series.h"
  12 #include "remove_equalities.h"
  13 #include "evalue_convert.h"
  14 #include "conversion.h"
  15 #include "skewed_genfun.h"
  16
  17 #undef CS   /* for Solaris 10 */
  18
  19 using std::cout;
  20 using std::endl;
  21
  22 /* The input of this example program is the same as that of testehrhart
  23  * in the PolyLib distribution, i.e., a polytope in combined
  24  * data and parameter space, a context polytope in parameter space
  25  * and (optionally) the names of the parameters.
  26  * Both polytopes are in PolyLib notation.
  27  */
  28
  29 struct verify_point_enum {
  30         struct verify_point_data vpd;
  31         isl_set *set;
  32         isl_pw_qpolynomial *pwqp;
  33 };
  34
  35 static isl_stat verify_point(__isl_take isl_point *pnt, void *user)
  36 {
  37         struct verify_point_enum *vpe = (struct verify_point_enum *) user;
  38         isl_set *set;
  39         int i;
  40         unsigned nparam;
  41         isl_val *v, *n, *t;
  42         int pa = vpe->vpd.options->barvinok->approx->approximation;
  43         int ok;
  44         FILE *out = vpe->vpd.options->print_all ? stdout : stderr;
  45
  46         vpe->vpd.n--;
  47
  48         set = isl_set_copy(vpe->set);
  49         nparam = isl_set_dim(set, isl_dim_param);
  50         for (i = 0; i < nparam; ++i) {
  51                 v = isl_point_get_coordinate_val(pnt, isl_dim_param, i);
  52                 set = isl_set_fix_val(set, isl_dim_param, i, v);
  53         }
  54
  55         v = isl_set_count_val(set);
  56
  57         n = isl_pw_qpolynomial_eval(isl_pw_qpolynomial_copy(vpe->pwqp),
  58                                         isl_point_copy(pnt));
  59
  60         if (pa == BV_APPROX_SIGN_LOWER)
  61                 n = isl_val_ceil(n);
  62         else if (pa == BV_APPROX_SIGN_UPPER)
  63                 n = isl_val_floor(n);
  64         else
  65                 n = isl_val_trunc(n);
  66
  67         if (pa == BV_APPROX_SIGN_APPROX)
  68                 /* just accept everything */
  69                 ok = 1;
  70         else if (pa == BV_APPROX_SIGN_LOWER)
  71                 ok = isl_val_le(n, v);
  72         else if (pa == BV_APPROX_SIGN_UPPER)
  73                 ok = isl_val_ge(n, v);
  74         else
  75                 ok = isl_val_eq(n, v);
  76
  77         if (vpe->vpd.options->print_all || !ok) {
  78                 isl_ctx *ctx = isl_point_get_ctx(pnt);
  79                 isl_printer *p;
  80                 p = isl_printer_to_file(ctx, out);
  81                 p = isl_printer_print_str(p, "EP(");
  82                 for (i = 0; i < nparam; ++i) {
  83                         if (i)
  84                                 p = isl_printer_print_str(p, ", ");
  85                         t = isl_point_get_coordinate_val(pnt, isl_dim_param, i);
  86                         p = isl_printer_print_val(p, t);
  87                         isl_val_free(t);
  88                 }
  89                 p = isl_printer_print_str(p, ") = ");
  90                 p = isl_printer_print_val(p, n);
  91                 p = isl_printer_print_str(p, ", count = ");
  92                 p = isl_printer_print_val(p, v);
  93                 if (ok)
  94                         p = isl_printer_print_str(p, ". OK");
  95                 else
  96                         p = isl_printer_print_str(p, ". NOT OK");
  97                 p = isl_printer_end_line(p);
  98                 isl_printer_free(p);
  99         } else if ((vpe->vpd.n % vpe->vpd.s) == 0) {
 100                 printf("o");
 101                 fflush(stdout);
 102         }
 103
 104         isl_set_free(set);
 105         isl_val_free(v);
 106         isl_val_free(n);
 107         isl_point_free(pnt);
 108
 109         if (!ok)
 110                 vpe->vpd.error = 1;
 111
 112         if (vpe->vpd.options->continue_on_error)
 113                 ok = 1;
 114
 115         return (vpe->vpd.n >= 1 && ok) ? isl_stat_ok : isl_stat_error;
 116 }
 117
 118 static int verify_isl(Polyhedron *P, Polyhedron *C,
 119                 evalue *EP, const struct verify_options *options)
 120 {
 121         struct verify_point_enum vpe = { { options } };
 122         int i;
 123         isl_ctx *ctx = isl_ctx_alloc();
 124         isl_space *dim;
 125         isl_set *set;
 126         isl_set *set_C;
 127         int r;
 128
 129         dim = isl_space_set_alloc(ctx, C->Dimension, P->Dimension - C->Dimension);
 130         for (i = 0; i < C->Dimension; ++i)
 131                 dim = isl_space_set_dim_name(dim, isl_dim_param, i, options->params[i]);
 132         set = isl_set_new_from_polylib(P, isl_space_copy(dim));
 133         dim = isl_space_params(dim);
 134         set_C = isl_set_new_from_polylib(C, dim);
 135         set_C = isl_set_intersect_params(isl_set_copy(set), set_C);
 136         set_C = isl_set_params(set_C);
 137
 138         set_C = verify_context_set_bounds(set_C, options);
 139
 140         r = verify_point_data_init(&vpe.vpd, set_C);
 141
 142         vpe.set = set;
 143         vpe.pwqp = isl_pw_qpolynomial_from_evalue(isl_set_get_space(set_C), EP);
 144         if (r == 0)
 145                 isl_set_foreach_point(set_C, verify_point, &vpe);
 146         if (vpe.vpd.error)
 147                 r = -1;
 148
 149         isl_pw_qpolynomial_free(vpe.pwqp);
 150         isl_set_free(set);
 151         isl_set_free(set_C);
 152
 153         isl_ctx_free(ctx);
 154
 155         verify_point_data_fini(&vpe.vpd);
 156
 157         return r;
 158 }
 159
 160 static int verify(Polyhedron *P, Polyhedron *C, evalue *EP, skewed_gen_fun *gf,
 161                    struct enumerate_options *options)
 162 {
 163     Polyhedron *CS, *S;
 164     Vector *p;
 165     int result = 0;
 166
 167     if (!options->series || options->function)
 168         return verify_isl(P, C, EP, options->verify);
 169
 170     CS = check_poly_context_scan(P, &C, C->Dimension, options->verify);
 171
 172     p = Vector_Alloc(P->Dimension+2);
 173     value_set_si(p->p[P->Dimension+1], 1);
 174
 175     /* S = scanning list of polyhedra */
 176     S = Polyhedron_Scan(P, C, options->verify->barvinok->MaxRays);
 177
 178     check_poly_init(C, options->verify);
 179
 180     /******* CHECK NOW *********/
 181     if (S) {
 182         if (!check_poly_gf(S, CS, gf, 0, C->Dimension, 0, p->p,
 183                             options->verify))
 184             result = -1;
 185         Domain_Free(S);
 186     }
 187
 188     if (result == -1)
 189         fprintf(stderr,"Check failed !\n");
 190
 191     if (!options->verify->print_all)
 192         printf( "\n" );
 193
 194     Vector_Free(p);
 195     if (CS) {
 196         Domain_Free(CS);
 197         Domain_Free(C);
 198     }
 199
 200     return result;
 201 }
 202
 203 /* frees M and Minv */
 204 static void apply_transformation(Polyhedron **P, Polyhedron **C,
 205                                  bool free_P, bool free_C,
 206                                  Matrix *M, Matrix *Minv, Matrix **inv,
 207                                  barvinok_options *options)
 208 {
 209     Polyhedron *T;
 210     Matrix *M2;
 211
 212     M2 = align_matrix(M, (*P)->Dimension + 1);
 213     T = *P;
 214     *P = Polyhedron_Preimage(*P, M2, options->MaxRays);
 215     if (free_P)
 216         Polyhedron_Free(T);
 217     Matrix_Free(M2);
 218
 219     T = *C;
 220     *C = Polyhedron_Preimage(*C, M, options->MaxRays);
 221     if (free_C)
 222         Polyhedron_Free(T);
 223
 224     Matrix_Free(M);
 225
 226     if (*inv) {
 227         Matrix *T = *inv;
 228         *inv = Matrix_Alloc(Minv->NbRows, T->NbColumns);
 229         Matrix_Product(Minv, T, *inv);
 230         Matrix_Free(T);
 231         Matrix_Free(Minv);
 232     } else
 233         *inv = Minv;
 234 }
 235
 236 /* Since we have "compressed" the parameters (in case there were
 237  * any equalities), the result is independent of the coordinates in the
 238  * coordinate subspace spanned by the lines.  We can therefore assume
 239  * these coordinates are zero and compute the inverse image of the map
 240  * from a lower dimensional space that adds zeros in the appropriate
 241  * places.
 242  */
 243 static void remove_lines(Polyhedron *C, Matrix **M, Matrix **Minv)
 244 {
 245     Matrix *L = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 246     for (int r = 0; r < C->NbBid; ++r)
 247         Vector_Copy(C->Ray[r]+1, L->p[r], C->Dimension);
 248     unimodular_complete(L, C->NbBid);
 249     assert(value_one_p(L->p[C->Dimension][C->Dimension]));
 250     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 251     Matrix_Transposition(L);
 252     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 253
 254     *M = Matrix_Alloc(C->Dimension+1, C->Dimension-C->NbBid+1);
 255     for (int i = 0; i < C->Dimension+1; ++i)
 256         Vector_Copy(L->p[i]+C->NbBid, (*M)->p[i], C->Dimension-C->NbBid+1);
 257
 258     Matrix *Linv = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 259     int ok = Matrix_Inverse(L, Linv);
 260     assert(ok);
 261     Matrix_Free(L);
 262
 263     *Minv = Matrix_Alloc(C->Dimension-C->NbBid+1, C->Dimension+1);
 264     for (int i = C->NbBid; i < C->Dimension+1; ++i)
 265         Vector_AntiScale(Linv->p[i], (*Minv)->p[i-C->NbBid],
 266                          Linv->p[C->Dimension][C->Dimension], C->Dimension+1);
 267     Matrix_Free(Linv);
 268 }
 269
 270 static skewed_gen_fun *series(Polyhedron *P, Polyhedron* C,
 271                                 barvinok_options *options)
 272 {
 273     Polyhedron *C1, *C2;
 274     gen_fun *gf;
 275     Matrix *inv = NULL;
 276     Matrix *eq = NULL;
 277     Matrix *div = NULL;
 278     Polyhedron *PT = P;
 279
 280     /* Compute true context */
 281     C1 = Polyhedron_Project(P, C->Dimension);
 282     C2 = DomainIntersection(C, C1, options->MaxRays);
 283     Polyhedron_Free(C1);
 284
 285     POL_ENSURE_VERTICES(C2);
 286     if (C2->NbBid != 0) {
 287         Matrix *CP;
 288         if (C2->NbEq || P->NbEq) {
 289             /* We remove all equalities to be sure all lines are unit vectors */
 290             Polyhedron *CT = C2;
 291             remove_all_equalities(&PT, &CT, &CP, NULL, C2->Dimension,
 292                                   options->MaxRays);
 293             if (CT != C2) {
 294                 Polyhedron_Free(C2);
 295                 C2 = CT;
 296             }
 297             if (CP) {
 298                 inv = left_inverse(CP, &eq);
 299                 Matrix_Free(CP);
 300
 301                 int d = 0;
 302                 Value tmp;
 303                 value_init(tmp);
 304                 div = Matrix_Alloc(inv->NbRows-1, inv->NbColumns+1);
 305                 for (int i = 0; i < inv->NbRows-1; ++i) {
 306                     Vector_Gcd(inv->p[i], inv->NbColumns, &tmp);
 307                     if (mpz_divisible_p(tmp,
 308                                         inv->p[inv->NbRows-1][inv->NbColumns-1]))
 309                         continue;
 310                     Vector_Copy(inv->p[i], div->p[d], inv->NbColumns);
 311                     value_assign(div->p[d][inv->NbColumns],
 312                                  inv->p[inv->NbRows-1][inv->NbColumns-1]);
 313                     ++d;
 314                 }
 315                 value_clear(tmp);
 316
 317                 if (!d) {
 318                     Matrix_Free(div);
 319                     div = NULL;
 320                 } else
 321                     div->NbRows = d;
 322             }
 323         }
 324         POL_ENSURE_VERTICES(C2);
 325
 326         if (C2->NbBid) {
 327             Matrix *M, *Minv;
 328             remove_lines(C2, &M, &Minv);
 329             apply_transformation(&PT, &C2, PT != P, C2 != C, M, Minv, &inv,
 330                                  options);
 331         }
 332     }
 333     POL_ENSURE_VERTICES(C2);
 334     if (!Polyhedron_has_revlex_positive_rays(C2, C2->Dimension)) {
 335         Matrix *Constraints;
 336         Matrix *H, *Q, *U;
 337         Constraints = Matrix_Alloc(C2->NbConstraints, C2->Dimension+1);
 338         for (int i = 0; i < C2->NbConstraints; ++i)
 339             Vector_Copy(C2->Constraint[i]+1, Constraints->p[i], C2->Dimension);
 340         left_hermite(Constraints, &H, &Q, &U);
 341         Matrix_Free(Constraints);
 342         /* flip rows of Q */
 343         for (int i = 0; i < C2->Dimension/2; ++i)
 344             Vector_Exchange(Q->p[i], Q->p[C2->Dimension-1-i], C2->Dimension);
 345         Matrix_Free(H);
 346         Matrix_Free(U);
 347         Matrix *M = Matrix_Alloc(C2->Dimension+1, C2->Dimension+1);
 348         U = Matrix_Copy(Q);
 349         int ok = Matrix_Inverse(U, M);
 350         assert(ok);
 351         Matrix_Free(U);
 352
 353         apply_transformation(&PT, &C2, PT != P, C2 != C, M, Q, &inv, options);
 354     }
 355     gf = barvinok_series_with_options(PT, C2, options);
 356     Polyhedron_Free(C2);
 357     if (PT != P)
 358         Polyhedron_Free(PT);
 359     return new skewed_gen_fun(gf, inv, eq, div);
 360 }
 361
 362 int main(int argc, char **argv)
 363 {
 364     Polyhedron *A, *C;
 365     Matrix *M;
 366     evalue *EP = NULL;
 367     skewed_gen_fun *gf = NULL;
 368     const char **param_name;
 369     int print_solution = 1;
 370     int result = 0;
 371     struct enumerate_options *options = enumerate_options_new_with_defaults();
 372
 373     argc = enumerate_options_parse(options, argc, argv, ISL_ARG_ALL);
 374
 375     M = Matrix_Read();
 376     assert(M);
 377     A = Constraints2Polyhedron(M, options->verify->barvinok->MaxRays);
 378     Matrix_Free(M);
 379     M = Matrix_Read();
 380     assert(M);
 381     C = Constraints2Polyhedron(M, options->verify->barvinok->MaxRays);
 382     Matrix_Free(M);
 383     assert(A->Dimension >= C->Dimension);
 384     param_name = Read_ParamNames(stdin, C->Dimension);
 385
 386     if (options->verify->verify) {
 387         verify_options_set_range(options->verify, A->Dimension);
 388         if (!options->verify->barvinok->verbose)
 389             print_solution = 0;
 390     }
 391
 392     if (print_solution && options->verify->barvinok->verbose) {
 393         Polyhedron_Print(stdout, P_VALUE_FMT, A);
 394         Polyhedron_Print(stdout, P_VALUE_FMT, C);
 395     }
 396
 397     if (options->series) {
 398         gf = series(A, C, options->verify->barvinok);
 399         if (print_solution) {
 400             gf->print(cout, C->Dimension, param_name);
 401             puts("");
 402         }
 403         if (options->function) {
 404             EP = *gf;
 405             if (print_solution)
 406                 print_evalue(stdout, EP, param_name);
 407         }
 408     } else {
 409         EP = barvinok_enumerate_with_options(A, C, options->verify->barvinok);
 410         assert(EP);
 411         if (evalue_convert(EP, options->convert, options->verify->barvinok->verbose,
 412                            C->Dimension, param_name))
 413             print_solution = 0;
 414         if (options->size)
 415             printf("\nSize: %zd\n", evalue_size(EP));
 416         if (print_solution)
 417             print_evalue(stdout, EP, param_name);
 418     }
 419
 420     if (options->verify->verify) {
 421         options->verify->params = param_name;
 422         result = verify(A, C, EP, gf, options);
 423     }
 424
 425     if (gf)
 426         delete gf;
 427     if (EP)
 428         evalue_free(EP);
 429
 430     if (options->verify->barvinok->print_stats)
 431         barvinok_stats_print(options->verify->barvinok->stats, stdout);
 432
 433     Free_ParamNames(param_name, C->Dimension);
 434     Polyhedron_Free(A);
 435     Polyhedron_Free(C);
 436     enumerate_options_free(options);
 437     return result;
 438 }