barvinok_enumerate.cc

   1 #include <assert.h>
   2 #include <unistd.h>
   3 #include <stdlib.h>
   4 #include <gmp.h>
   5 #include <isl/ctx.h>
   6 #include <isl/val.h>
   7 #include <isl/space.h>
   8 #include <isl/point.h>
   9 #include <isl/set.h>
  10 #include <isl/polynomial.h>
  11 #include <isl/printer.h>
  12 #include <isl_set_polylib.h>
  13 #include <barvinok/evalue.h>
  14 #include <barvinok/util.h>
  15 #include <barvinok/barvinok.h>
  16 #include "barvinok_enumerate_options.h"
  17 #include "verify.h"
  18 #include "verify_series.h"
  19 #include "remove_equalities.h"
  20 #include "evalue_convert.h"
  21 #include "conversion.h"
  22 #include "skewed_genfun.h"
  23
  24 #undef CS   /* for Solaris 10 */
  25
  26 using std::cout;
  27 using std::endl;
  28
  29 /* The input of this example program is the same as that of testehrhart
  30  * in the PolyLib distribution, i.e., a polytope in combined
  31  * data and parameter space, a context polytope in parameter space
  32  * and (optionally) the names of the parameters.
  33  * Both polytopes are in PolyLib notation.
  34  */
  35
  36 struct verify_point_enum {
  37         struct verify_point_data vpd;
  38         isl_set *set;
  39         isl_pw_qpolynomial *pwqp;
  40 };
  41
  42 static isl_stat verify_point(__isl_take isl_point *pnt, void *user)
  43 {
  44         struct verify_point_enum *vpe = (struct verify_point_enum *) user;
  45         isl_set *set;
  46         int i;
  47         unsigned nparam;
  48         isl_val *v, *n, *t;
  49         int pa = vpe->vpd.options->barvinok->approx->approximation;
  50         int ok;
  51         FILE *out = vpe->vpd.options->print_all ? stdout : stderr;
  52
  53         vpe->vpd.n--;
  54
  55         set = isl_set_copy(vpe->set);
  56         nparam = isl_set_dim(set, isl_dim_param);
  57         for (i = 0; i < nparam; ++i) {
  58                 v = isl_point_get_coordinate_val(pnt, isl_dim_param, i);
  59                 set = isl_set_fix_val(set, isl_dim_param, i, v);
  60         }
  61
  62         v = isl_set_count_val(set);
  63
  64         n = isl_pw_qpolynomial_eval(isl_pw_qpolynomial_copy(vpe->pwqp),
  65                                         isl_point_copy(pnt));
  66
  67         if (pa == BV_APPROX_SIGN_LOWER)
  68                 n = isl_val_ceil(n);
  69         else if (pa == BV_APPROX_SIGN_UPPER)
  70                 n = isl_val_floor(n);
  71         else
  72                 n = isl_val_trunc(n);
  73
  74         if (pa == BV_APPROX_SIGN_APPROX)
  75                 /* just accept everything */
  76                 ok = 1;
  77         else if (pa == BV_APPROX_SIGN_LOWER)
  78                 ok = isl_val_le(n, v);
  79         else if (pa == BV_APPROX_SIGN_UPPER)
  80                 ok = isl_val_ge(n, v);
  81         else
  82                 ok = isl_val_eq(n, v);
  83
  84         if (vpe->vpd.options->print_all || !ok) {
  85                 isl_ctx *ctx = isl_point_get_ctx(pnt);
  86                 isl_printer *p;
  87                 p = isl_printer_to_file(ctx, out);
  88                 p = isl_printer_print_str(p, "EP(");
  89                 for (i = 0; i < nparam; ++i) {
  90                         if (i)
  91                                 p = isl_printer_print_str(p, ", ");
  92                         t = isl_point_get_coordinate_val(pnt, isl_dim_param, i);
  93                         p = isl_printer_print_val(p, t);
  94                         isl_val_free(t);
  95                 }
  96                 p = isl_printer_print_str(p, ") = ");
  97                 p = isl_printer_print_val(p, n);
  98                 p = isl_printer_print_str(p, ", count = ");
  99                 p = isl_printer_print_val(p, v);
 100                 if (ok)
 101                         p = isl_printer_print_str(p, ". OK");
 102                 else
 103                         p = isl_printer_print_str(p, ". NOT OK");
 104                 p = isl_printer_end_line(p);
 105                 isl_printer_free(p);
 106         } else if ((vpe->vpd.n % vpe->vpd.s) == 0) {
 107                 printf("o");
 108                 fflush(stdout);
 109         }
 110
 111         isl_set_free(set);
 112         isl_val_free(v);
 113         isl_val_free(n);
 114         isl_point_free(pnt);
 115
 116         if (!ok)
 117                 vpe->vpd.error = 1;
 118
 119         if (vpe->vpd.options->continue_on_error)
 120                 ok = 1;
 121
 122         return (vpe->vpd.n >= 1 && ok) ? isl_stat_ok : isl_stat_error;
 123 }
 124
 125 static int verify_isl(Polyhedron *P, Polyhedron *C,
 126                 evalue *EP, const struct verify_options *options)
 127 {
 128         struct verify_point_enum vpe = { { options } };
 129         int i;
 130         isl_ctx *ctx = isl_ctx_alloc();
 131         isl_space *dim;
 132         isl_set *set;
 133         isl_set *set_C;
 134         int r;
 135
 136         dim = isl_space_set_alloc(ctx, C->Dimension, P->Dimension - C->Dimension);
 137         for (i = 0; i < C->Dimension; ++i)
 138                 dim = isl_space_set_dim_name(dim, isl_dim_param, i, options->params[i]);
 139         set = isl_set_new_from_polylib(P, isl_space_copy(dim));
 140         dim = isl_space_params(dim);
 141         set_C = isl_set_new_from_polylib(C, dim);
 142         set_C = isl_set_intersect_params(isl_set_copy(set), set_C);
 143         set_C = isl_set_params(set_C);
 144
 145         set_C = verify_context_set_bounds(set_C, options);
 146
 147         r = verify_point_data_init(&vpe.vpd, set_C);
 148
 149         vpe.set = set;
 150         vpe.pwqp = isl_pw_qpolynomial_from_evalue(isl_set_get_space(set_C), EP);
 151         if (r == 0)
 152                 isl_set_foreach_point(set_C, verify_point, &vpe);
 153         if (vpe.vpd.error)
 154                 r = -1;
 155
 156         isl_pw_qpolynomial_free(vpe.pwqp);
 157         isl_set_free(set);
 158         isl_set_free(set_C);
 159
 160         isl_ctx_free(ctx);
 161
 162         verify_point_data_fini(&vpe.vpd);
 163
 164         return r;
 165 }
 166
 167 static int verify(Polyhedron *P, Polyhedron *C, evalue *EP, skewed_gen_fun *gf,
 168                    struct enumerate_options *options)
 169 {
 170     Polyhedron *CS, *S;
 171     Vector *p;
 172     int result = 0;
 173
 174     if (!options->series || options->function)
 175         return verify_isl(P, C, EP, options->verify);
 176
 177     CS = check_poly_context_scan(P, &C, C->Dimension, options->verify);
 178
 179     p = Vector_Alloc(P->Dimension+2);
 180     value_set_si(p->p[P->Dimension+1], 1);
 181
 182     /* S = scanning list of polyhedra */
 183     S = Polyhedron_Scan(P, C, options->verify->barvinok->MaxRays);
 184
 185     check_poly_init(C, options->verify);
 186
 187     /******* CHECK NOW *********/
 188     if (S) {
 189         if (!check_poly_gf(S, CS, gf, 0, C->Dimension, 0, p->p,
 190                             options->verify))
 191             result = -1;
 192         Domain_Free(S);
 193     }
 194
 195     if (result == -1)
 196         fprintf(stderr,"Check failed !\n");
 197
 198     if (!options->verify->print_all)
 199         printf( "\n" );
 200
 201     Vector_Free(p);
 202     if (CS) {
 203         Domain_Free(CS);
 204         Domain_Free(C);
 205     }
 206
 207     return result;
 208 }
 209
 210 /* frees M and Minv */
 211 static void apply_transformation(Polyhedron **P, Polyhedron **C,
 212                                  bool free_P, bool free_C,
 213                                  Matrix *M, Matrix *Minv, Matrix **inv,
 214                                  barvinok_options *options)
 215 {
 216     Polyhedron *T;
 217     Matrix *M2;
 218
 219     M2 = align_matrix(M, (*P)->Dimension + 1);
 220     T = *P;
 221     *P = Polyhedron_Preimage(*P, M2, options->MaxRays);
 222     if (free_P)
 223         Polyhedron_Free(T);
 224     Matrix_Free(M2);
 225
 226     T = *C;
 227     *C = Polyhedron_Preimage(*C, M, options->MaxRays);
 228     if (free_C)
 229         Polyhedron_Free(T);
 230
 231     Matrix_Free(M);
 232
 233     if (*inv) {
 234         Matrix *T = *inv;
 235         *inv = Matrix_Alloc(Minv->NbRows, T->NbColumns);
 236         Matrix_Product(Minv, T, *inv);
 237         Matrix_Free(T);
 238         Matrix_Free(Minv);
 239     } else
 240         *inv = Minv;
 241 }
 242
 243 /* Since we have "compressed" the parameters (in case there were
 244  * any equalities), the result is independent of the coordinates in the
 245  * coordinate subspace spanned by the lines.  We can therefore assume
 246  * these coordinates are zero and compute the inverse image of the map
 247  * from a lower dimensional space that adds zeros in the appropriate
 248  * places.
 249  */
 250 static void remove_lines(Polyhedron *C, Matrix **M, Matrix **Minv)
 251 {
 252     Matrix *L = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 253     for (int r = 0; r < C->NbBid; ++r)
 254         Vector_Copy(C->Ray[r]+1, L->p[r], C->Dimension);
 255     unimodular_complete(L, C->NbBid);
 256     assert(value_one_p(L->p[C->Dimension][C->Dimension]));
 257     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 258     Matrix_Transposition(L);
 259     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 260
 261     *M = Matrix_Alloc(C->Dimension+1, C->Dimension-C->NbBid+1);
 262     for (int i = 0; i < C->Dimension+1; ++i)
 263         Vector_Copy(L->p[i]+C->NbBid, (*M)->p[i], C->Dimension-C->NbBid+1);
 264
 265     Matrix *Linv = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 266     int ok = Matrix_Inverse(L, Linv);
 267     assert(ok);
 268     Matrix_Free(L);
 269
 270     *Minv = Matrix_Alloc(C->Dimension-C->NbBid+1, C->Dimension+1);
 271     for (int i = C->NbBid; i < C->Dimension+1; ++i)
 272         Vector_AntiScale(Linv->p[i], (*Minv)->p[i-C->NbBid],
 273                          Linv->p[C->Dimension][C->Dimension], C->Dimension+1);
 274     Matrix_Free(Linv);
 275 }
 276
 277 static skewed_gen_fun *series(Polyhedron *P, Polyhedron* C,
 278                                 barvinok_options *options)
 279 {
 280     Polyhedron *C1, *C2;
 281     gen_fun *gf;
 282     Matrix *inv = NULL;
 283     Matrix *eq = NULL;
 284     Matrix *div = NULL;
 285     Polyhedron *PT = P;
 286
 287     /* Compute true context */
 288     C1 = Polyhedron_Project(P, C->Dimension);
 289     C2 = DomainIntersection(C, C1, options->MaxRays);
 290     Polyhedron_Free(C1);
 291
 292     POL_ENSURE_VERTICES(C2);
 293     if (C2->NbBid != 0) {
 294         Matrix *CP;
 295         if (C2->NbEq || P->NbEq) {
 296             /* We remove all equalities to be sure all lines are unit vectors */
 297             Polyhedron *CT = C2;
 298             remove_all_equalities(&PT, &CT, &CP, NULL, C2->Dimension,
 299                                   options->MaxRays);
 300             if (CT != C2) {
 301                 Polyhedron_Free(C2);
 302                 C2 = CT;
 303             }
 304             if (CP) {
 305                 inv = left_inverse(CP, &eq);
 306                 Matrix_Free(CP);
 307
 308                 int d = 0;
 309                 Value tmp;
 310                 value_init(tmp);
 311                 div = Matrix_Alloc(inv->NbRows-1, inv->NbColumns+1);
 312                 for (int i = 0; i < inv->NbRows-1; ++i) {
 313                     Vector_Gcd(inv->p[i], inv->NbColumns, &tmp);
 314                     if (mpz_divisible_p(tmp,
 315                                         inv->p[inv->NbRows-1][inv->NbColumns-1]))
 316                         continue;
 317                     Vector_Copy(inv->p[i], div->p[d], inv->NbColumns);
 318                     value_assign(div->p[d][inv->NbColumns],
 319                                  inv->p[inv->NbRows-1][inv->NbColumns-1]);
 320                     ++d;
 321                 }
 322                 value_clear(tmp);
 323
 324                 if (!d) {
 325                     Matrix_Free(div);
 326                     div = NULL;
 327                 } else
 328                     div->NbRows = d;
 329             }
 330         }
 331         POL_ENSURE_VERTICES(C2);
 332
 333         if (C2->NbBid) {
 334             Matrix *M, *Minv;
 335             remove_lines(C2, &M, &Minv);
 336             apply_transformation(&PT, &C2, PT != P, C2 != C, M, Minv, &inv,
 337                                  options);
 338         }
 339     }
 340     POL_ENSURE_VERTICES(C2);
 341     if (!Polyhedron_has_revlex_positive_rays(C2, C2->Dimension)) {
 342         Matrix *Constraints;
 343         Matrix *H, *Q, *U;
 344         Constraints = Matrix_Alloc(C2->NbConstraints, C2->Dimension+1);
 345         for (int i = 0; i < C2->NbConstraints; ++i)
 346             Vector_Copy(C2->Constraint[i]+1, Constraints->p[i], C2->Dimension);
 347         left_hermite(Constraints, &H, &Q, &U);
 348         Matrix_Free(Constraints);
 349         /* flip rows of Q */
 350         for (int i = 0; i < C2->Dimension/2; ++i)
 351             Vector_Exchange(Q->p[i], Q->p[C2->Dimension-1-i], C2->Dimension);
 352         Matrix_Free(H);
 353         Matrix_Free(U);
 354         Matrix *M = Matrix_Alloc(C2->Dimension+1, C2->Dimension+1);
 355         U = Matrix_Copy(Q);
 356         int ok = Matrix_Inverse(U, M);
 357         assert(ok);
 358         Matrix_Free(U);
 359
 360         apply_transformation(&PT, &C2, PT != P, C2 != C, M, Q, &inv, options);
 361     }
 362     gf = barvinok_series_with_options(PT, C2, options);
 363     Polyhedron_Free(C2);
 364     if (PT != P)
 365         Polyhedron_Free(PT);
 366     return new skewed_gen_fun(gf, inv, eq, div);
 367 }
 368
 369 int main(int argc, char **argv)
 370 {
 371     Polyhedron *A, *C;
 372     Matrix *M;
 373     evalue *EP = NULL;
 374     skewed_gen_fun *gf = NULL;
 375     const char **param_name;
 376     int print_solution = 1;
 377     int result = 0;
 378     struct enumerate_options *options = enumerate_options_new_with_defaults();
 379
 380     argc = enumerate_options_parse(options, argc, argv, ISL_ARG_ALL);
 381
 382     M = Matrix_Read();
 383     assert(M);
 384     A = Constraints2Polyhedron(M, options->verify->barvinok->MaxRays);
 385     Matrix_Free(M);
 386     M = Matrix_Read();
 387     assert(M);
 388     C = Constraints2Polyhedron(M, options->verify->barvinok->MaxRays);
 389     Matrix_Free(M);
 390     assert(A->Dimension >= C->Dimension);
 391     param_name = Read_ParamNames(stdin, C->Dimension);
 392
 393     if (options->verify->verify) {
 394         verify_options_set_range(options->verify, A->Dimension);
 395         if (!options->verify->barvinok->verbose)
 396             print_solution = 0;
 397     }
 398
 399     if (print_solution && options->verify->barvinok->verbose) {
 400         Polyhedron_Print(stdout, P_VALUE_FMT, A);
 401         Polyhedron_Print(stdout, P_VALUE_FMT, C);
 402     }
 403
 404     if (options->series) {
 405         gf = series(A, C, options->verify->barvinok);
 406         if (print_solution) {
 407             gf->print(cout, C->Dimension, param_name);
 408             puts("");
 409         }
 410         if (options->function) {
 411             EP = *gf;
 412             if (print_solution)
 413                 print_evalue(stdout, EP, param_name);
 414         }
 415     } else {
 416         EP = barvinok_enumerate_with_options(A, C, options->verify->barvinok);
 417         assert(EP);
 418         if (evalue_convert(EP, options->convert, options->verify->barvinok->verbose,
 419                            C->Dimension, param_name))
 420             print_solution = 0;
 421         if (options->size)
 422             printf("\nSize: %zd\n", evalue_size(EP));
 423         if (print_solution)
 424             print_evalue(stdout, EP, param_name);
 425     }
 426
 427     if (options->verify->verify) {
 428         options->verify->params = param_name;
 429         result = verify(A, C, EP, gf, options);
 430     }
 431
 432     if (gf)
 433         delete gf;
 434     if (EP)
 435         evalue_free(EP);
 436
 437     if (options->verify->barvinok->print_stats)
 438         barvinok_stats_print(options->verify->barvinok->stats, stdout);
 439
 440     Free_ParamNames(param_name, C->Dimension);
 441     Polyhedron_Free(A);
 442     Polyhedron_Free(C);
 443     enumerate_options_free(options);
 444     return result;
 445 }