barvinok_enumerate.cc

   1 #include <assert.h>
   2 #include <unistd.h>
   3 #include <stdlib.h>
   4 #include <isl_set_polylib.h>
   5 #include <barvinok/evalue.h>
   6 #include <barvinok/util.h>
   7 #include <barvinok/barvinok.h>
   8 #include "barvinok_enumerate_options.h"
   9 #include "verify.h"
  10 #include "verif_ehrhart.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 int 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_int v, n, d;
  42         isl_qpolynomial *cnt = NULL;
  43         int pa = vpe->vpd.options->barvinok->approx->approximation;
  44         int cst;
  45         int ok;
  46         FILE *out = vpe->vpd.options->print_all ? stdout : stderr;
  47
  48         vpe->vpd.n--;
  49
  50         isl_int_init(v);
  51         isl_int_init(n);
  52         isl_int_init(d);
  53         set = isl_set_copy(vpe->set);
  54         nparam = isl_set_dim(set, isl_dim_param);
  55         for (i = 0; i < nparam; ++i) {
  56                 isl_point_get_coordinate(pnt, isl_dim_param, i, &v);
  57                 set = isl_set_fix(set, isl_dim_param, i, v);
  58         }
  59
  60         if (isl_set_count(set, &v) < 0)
  61                 goto error;
  62
  63         cnt = isl_pw_qpolynomial_eval(isl_pw_qpolynomial_copy(vpe->pwqp),
  64                                         isl_point_copy(pnt));
  65
  66         cst = isl_qpolynomial_is_cst(cnt, &n, &d);
  67         if (cst != 1)
  68                 goto error;
  69
  70         if (pa == BV_APPROX_SIGN_LOWER)
  71                 isl_int_cdiv_q(n, n, d);
  72         else if (pa == BV_APPROX_SIGN_UPPER)
  73                 isl_int_fdiv_q(n, n, d);
  74         else
  75                 isl_int_tdiv_q(n, n, d);
  76
  77         if (pa == BV_APPROX_SIGN_APPROX)
  78                 /* just accept everything */
  79                 ok = 1;
  80         else if (pa == BV_APPROX_SIGN_LOWER)
  81                 ok = isl_int_le(n, v);
  82         else if (pa == BV_APPROX_SIGN_UPPER)
  83                 ok = isl_int_ge(n, v);
  84         else
  85                 ok = isl_int_eq(n, v);
  86
  87         if (vpe->vpd.options->print_all || !ok) {
  88                 fprintf(out, "EP(");
  89                 for (i = 0; i < nparam; ++i) {
  90                         if (i)
  91                                 fprintf(out, ", ");
  92                         isl_point_get_coordinate(pnt, isl_dim_param, i, &d);
  93                         isl_int_print(out, d, 0);
  94                 }
  95                 fprintf(out, ") = ");
  96                 isl_int_print(out, n, 0);
  97                 fprintf(out, ", count = ");
  98                 isl_int_print(out, v, 0);
  99                 if (ok)
 100                         fprintf(out, ". OK\n");
 101                 else
 102                         fprintf(out, ". NOT OK\n");
 103         } else if ((vpe->vpd.n % vpe->vpd.s) == 0) {
 104                 printf("o");
 105                 fflush(stdout);
 106         }
 107
 108         if (0) {
 109 error:
 110                 ok = 0;
 111         }
 112         isl_set_free(set);
 113         isl_qpolynomial_free(cnt);
 114         isl_int_clear(v);
 115         isl_int_clear(n);
 116         isl_int_clear(d);
 117         isl_point_free(pnt);
 118
 119         if (!ok)
 120                 vpe->vpd.error = 1;
 121
 122         if (vpe->vpd.options->continue_on_error)
 123                 ok = 1;
 124
 125         return (vpe->vpd.n >= 1 && ok) ? 0 : -1;
 126 }
 127
 128 static int verify_isl(Polyhedron *P, Polyhedron *C,
 129                 evalue *EP, const struct verify_options *options)
 130 {
 131         struct verify_point_enum vpe = { { options } };
 132         int i;
 133         isl_ctx *ctx = isl_ctx_alloc();
 134         isl_space *dim;
 135         isl_set *set;
 136         isl_set *set_C;
 137         int r;
 138
 139         dim = isl_space_set_alloc(ctx, C->Dimension, P->Dimension - C->Dimension);
 140         for (i = 0; i < C->Dimension; ++i)
 141                 dim = isl_space_set_dim_name(dim, isl_dim_param, i, options->params[i]);
 142         set = isl_set_new_from_polylib(P, isl_space_copy(dim));
 143         dim = isl_space_params(dim);
 144         set_C = isl_set_new_from_polylib(C, dim);
 145         set_C = isl_set_intersect_params(isl_set_copy(set), set_C);
 146         set_C = isl_set_params(set_C);
 147
 148         set_C = verify_context_set_bounds(set_C, options);
 149
 150         r = verify_point_data_init(&vpe.vpd, set_C);
 151
 152         vpe.set = set;
 153         vpe.pwqp = isl_pw_qpolynomial_from_evalue(isl_set_get_space(set_C), EP);
 154         if (r == 0)
 155                 isl_set_foreach_point(set_C, verify_point, &vpe);
 156         if (vpe.vpd.error)
 157                 r = -1;
 158
 159         isl_pw_qpolynomial_free(vpe.pwqp);
 160         isl_set_free(set);
 161         isl_set_free(set_C);
 162
 163         isl_ctx_free(ctx);
 164
 165         verify_point_data_fini(&vpe.vpd);
 166
 167         return r;
 168 }
 169
 170 static int verify(Polyhedron *P, Polyhedron *C, evalue *EP, skewed_gen_fun *gf,
 171                    struct enumerate_options *options)
 172 {
 173     Polyhedron *CS, *S;
 174     Vector *p;
 175     int result = 0;
 176
 177     if (!options->series || options->function)
 178         return verify_isl(P, C, EP, options->verify);
 179
 180     CS = check_poly_context_scan(P, &C, C->Dimension, options->verify);
 181
 182     p = Vector_Alloc(P->Dimension+2);
 183     value_set_si(p->p[P->Dimension+1], 1);
 184
 185     /* S = scanning list of polyhedra */
 186     S = Polyhedron_Scan(P, C, options->verify->barvinok->MaxRays);
 187
 188     check_poly_init(C, options->verify);
 189
 190     /******* CHECK NOW *********/
 191     if (S) {
 192         if (!options->series || options->function) {
 193             if (!check_poly_EP(S, CS, EP, 0, C->Dimension, 0, p->p,
 194                                 options->verify))
 195                 result = -1;
 196         } else {
 197             if (!check_poly_gf(S, CS, gf, 0, C->Dimension, 0, p->p,
 198                                 options->verify))
 199                 result = -1;
 200         }
 201         Domain_Free(S);
 202     }
 203
 204     if (result == -1)
 205         fprintf(stderr,"Check failed !\n");
 206
 207     if (!options->verify->print_all)
 208         printf( "\n" );
 209
 210     Vector_Free(p);
 211     if (CS) {
 212         Domain_Free(CS);
 213         Domain_Free(C);
 214     }
 215
 216     return result;
 217 }
 218
 219 /* frees M and Minv */
 220 static void apply_transformation(Polyhedron **P, Polyhedron **C,
 221                                  bool free_P, bool free_C,
 222                                  Matrix *M, Matrix *Minv, Matrix **inv,
 223                                  barvinok_options *options)
 224 {
 225     Polyhedron *T;
 226     Matrix *M2;
 227
 228     M2 = align_matrix(M, (*P)->Dimension + 1);
 229     T = *P;
 230     *P = Polyhedron_Preimage(*P, M2, options->MaxRays);
 231     if (free_P)
 232         Polyhedron_Free(T);
 233     Matrix_Free(M2);
 234
 235     T = *C;
 236     *C = Polyhedron_Preimage(*C, M, options->MaxRays);
 237     if (free_C)
 238         Polyhedron_Free(T);
 239
 240     Matrix_Free(M);
 241
 242     if (*inv) {
 243         Matrix *T = *inv;
 244         *inv = Matrix_Alloc(Minv->NbRows, T->NbColumns);
 245         Matrix_Product(Minv, T, *inv);
 246         Matrix_Free(T);
 247         Matrix_Free(Minv);
 248     } else
 249         *inv = Minv;
 250 }
 251
 252 /* Since we have "compressed" the parameters (in case there were
 253  * any equalities), the result is independent of the coordinates in the
 254  * coordinate subspace spanned by the lines.  We can therefore assume
 255  * these coordinates are zero and compute the inverse image of the map
 256  * from a lower dimensional space that adds zeros in the appropriate
 257  * places.
 258  */
 259 static void remove_lines(Polyhedron *C, Matrix **M, Matrix **Minv)
 260 {
 261     Matrix *L = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 262     for (int r = 0; r < C->NbBid; ++r)
 263         Vector_Copy(C->Ray[r]+1, L->p[r], C->Dimension);
 264     unimodular_complete(L, C->NbBid);
 265     assert(value_one_p(L->p[C->Dimension][C->Dimension]));
 266     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 267     Matrix_Transposition(L);
 268     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 269
 270     *M = Matrix_Alloc(C->Dimension+1, C->Dimension-C->NbBid+1);
 271     for (int i = 0; i < C->Dimension+1; ++i)
 272         Vector_Copy(L->p[i]+C->NbBid, (*M)->p[i], C->Dimension-C->NbBid+1);
 273
 274     Matrix *Linv = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 275     int ok = Matrix_Inverse(L, Linv);
 276     assert(ok);
 277     Matrix_Free(L);
 278
 279     *Minv = Matrix_Alloc(C->Dimension-C->NbBid+1, C->Dimension+1);
 280     for (int i = C->NbBid; i < C->Dimension+1; ++i)
 281         Vector_AntiScale(Linv->p[i], (*Minv)->p[i-C->NbBid],
 282                          Linv->p[C->Dimension][C->Dimension], C->Dimension+1);
 283     Matrix_Free(Linv);
 284 }
 285
 286 static skewed_gen_fun *series(Polyhedron *P, Polyhedron* C,
 287                                 barvinok_options *options)
 288 {
 289     Polyhedron *C1, *C2;
 290     gen_fun *gf;
 291     Matrix *inv = NULL;
 292     Matrix *eq = NULL;
 293     Matrix *div = NULL;
 294     Polyhedron *PT = P;
 295
 296     /* Compute true context */
 297     C1 = Polyhedron_Project(P, C->Dimension);
 298     C2 = DomainIntersection(C, C1, options->MaxRays);
 299     Polyhedron_Free(C1);
 300
 301     POL_ENSURE_VERTICES(C2);
 302     if (C2->NbBid != 0) {
 303         Polyhedron *T;
 304         Matrix *M, *Minv, *M2;
 305         Matrix *CP;
 306         if (C2->NbEq || P->NbEq) {
 307             /* We remove all equalities to be sure all lines are unit vectors */
 308             Polyhedron *CT = C2;
 309             remove_all_equalities(&PT, &CT, &CP, NULL, C2->Dimension,
 310                                   options->MaxRays);
 311             if (CT != C2) {
 312                 Polyhedron_Free(C2);
 313                 C2 = CT;
 314             }
 315             if (CP) {
 316                 inv = left_inverse(CP, &eq);
 317                 Matrix_Free(CP);
 318
 319                 int d = 0;
 320                 Value tmp;
 321                 value_init(tmp);
 322                 div = Matrix_Alloc(inv->NbRows-1, inv->NbColumns+1);
 323                 for (int i = 0; i < inv->NbRows-1; ++i) {
 324                     Vector_Gcd(inv->p[i], inv->NbColumns, &tmp);
 325                     if (mpz_divisible_p(tmp,
 326                                         inv->p[inv->NbRows-1][inv->NbColumns-1]))
 327                         continue;
 328                     Vector_Copy(inv->p[i], div->p[d], inv->NbColumns);
 329                     value_assign(div->p[d][inv->NbColumns],
 330                                  inv->p[inv->NbRows-1][inv->NbColumns-1]);
 331                     ++d;
 332                 }
 333                 value_clear(tmp);
 334
 335                 if (!d) {
 336                     Matrix_Free(div);
 337                     div = NULL;
 338                 } else
 339                     div->NbRows = d;
 340             }
 341         }
 342         POL_ENSURE_VERTICES(C2);
 343
 344         if (C2->NbBid) {
 345             Matrix *M, *Minv;
 346             remove_lines(C2, &M, &Minv);
 347             apply_transformation(&PT, &C2, PT != P, C2 != C, M, Minv, &inv,
 348                                  options);
 349         }
 350     }
 351     POL_ENSURE_VERTICES(C2);
 352     if (!Polyhedron_has_revlex_positive_rays(C2, C2->Dimension)) {
 353         Polyhedron *T;
 354         Matrix *Constraints;
 355         Matrix *H, *Q, *U;
 356         Constraints = Matrix_Alloc(C2->NbConstraints, C2->Dimension+1);
 357         for (int i = 0; i < C2->NbConstraints; ++i)
 358             Vector_Copy(C2->Constraint[i]+1, Constraints->p[i], C2->Dimension);
 359         left_hermite(Constraints, &H, &Q, &U);
 360         Matrix_Free(Constraints);
 361         /* flip rows of Q */
 362         for (int i = 0; i < C2->Dimension/2; ++i)
 363             Vector_Exchange(Q->p[i], Q->p[C2->Dimension-1-i], C2->Dimension);
 364         Matrix_Free(H);
 365         Matrix_Free(U);
 366         Matrix *M = Matrix_Alloc(C2->Dimension+1, C2->Dimension+1);
 367         U = Matrix_Copy(Q);
 368         int ok = Matrix_Inverse(U, M);
 369         assert(ok);
 370         Matrix_Free(U);
 371
 372         apply_transformation(&PT, &C2, PT != P, C2 != C, M, Q, &inv, options);
 373     }
 374     gf = barvinok_series_with_options(PT, C2, options);
 375     Polyhedron_Free(C2);
 376     if (PT != P)
 377         Polyhedron_Free(PT);
 378     return new skewed_gen_fun(gf, inv, eq, div);
 379 }
 380
 381 int main(int argc, char **argv)
 382 {
 383     Polyhedron *A, *C;
 384     Matrix *M;
 385     evalue *EP = NULL;
 386     skewed_gen_fun *gf = NULL;
 387     const char **param_name;
 388     int print_solution = 1;
 389     int result = 0;
 390     struct enumerate_options *options = enumerate_options_new_with_defaults();
 391
 392     argc = enumerate_options_parse(options, argc, argv, ISL_ARG_ALL);
 393
 394     M = Matrix_Read();
 395     assert(M);
 396     A = Constraints2Polyhedron(M, options->verify->barvinok->MaxRays);
 397     Matrix_Free(M);
 398     M = Matrix_Read();
 399     assert(M);
 400     C = Constraints2Polyhedron(M, options->verify->barvinok->MaxRays);
 401     Matrix_Free(M);
 402     assert(A->Dimension >= C->Dimension);
 403     param_name = Read_ParamNames(stdin, C->Dimension);
 404
 405     if (options->verify->verify) {
 406         verify_options_set_range(options->verify, A->Dimension);
 407         if (!options->verify->barvinok->verbose)
 408             print_solution = 0;
 409     }
 410
 411     if (print_solution && options->verify->barvinok->verbose) {
 412         Polyhedron_Print(stdout, P_VALUE_FMT, A);
 413         Polyhedron_Print(stdout, P_VALUE_FMT, C);
 414     }
 415
 416     if (options->series) {
 417         gf = series(A, C, options->verify->barvinok);
 418         if (print_solution) {
 419             gf->print(cout, C->Dimension, param_name);
 420             puts("");
 421         }
 422         if (options->function) {
 423             EP = *gf;
 424             if (print_solution)
 425                 print_evalue(stdout, EP, param_name);
 426         }
 427     } else {
 428         EP = barvinok_enumerate_with_options(A, C, options->verify->barvinok);
 429         assert(EP);
 430         if (evalue_convert(EP, options->convert, options->verify->barvinok->verbose,
 431                            C->Dimension, param_name))
 432             print_solution = 0;
 433         if (options->size)
 434             printf("\nSize: %zd\n", evalue_size(EP));
 435         if (print_solution)
 436             print_evalue(stdout, EP, param_name);
 437     }
 438
 439     if (options->verify->verify) {
 440         options->verify->params = param_name;
 441         result = verify(A, C, EP, gf, options);
 442     }
 443
 444     if (gf)
 445         delete gf;
 446     if (EP)
 447         evalue_free(EP);
 448
 449     if (options->verify->barvinok->print_stats)
 450         barvinok_stats_print(options->verify->barvinok->stats, stdout);
 451
 452     Free_ParamNames(param_name, C->Dimension);
 453     Polyhedron_Free(A);
 454     Polyhedron_Free(C);
 455     enumerate_options_free(options);
 456     return result;
 457 }