isl_sample.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include "isl_sample.h"
  11 #include "isl_sample_piplib.h"
  12 #include "isl_vec.h"
  13 #include "isl_mat.h"
  14 #include "isl_seq.h"
  15 #include "isl_map_private.h"
  16 #include "isl_equalities.h"
  17 #include "isl_tab.h"
  18 #include "isl_basis_reduction.h"
  19 #include <isl_point_private.h>
  20
  21 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
  22 {
  23         struct isl_vec *vec;
  24
  25         vec = isl_vec_alloc(bset->ctx, 0);
  26         isl_basic_set_free(bset);
  27         return vec;
  28 }
  29
  30 /* Construct a zero sample of the same dimension as bset.
  31  * As a special case, if bset is zero-dimensional, this
  32  * function creates a zero-dimensional sample point.
  33  */
  34 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
  35 {
  36         unsigned dim;
  37         struct isl_vec *sample;
  38
  39         dim = isl_basic_set_total_dim(bset);
  40         sample = isl_vec_alloc(bset->ctx, 1 + dim);
  41         if (sample) {
  42                 isl_int_set_si(sample->el[0], 1);
  43                 isl_seq_clr(sample->el + 1, dim);
  44         }
  45         isl_basic_set_free(bset);
  46         return sample;
  47 }
  48
  49 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
  50 {
  51         int i;
  52         isl_int t;
  53         struct isl_vec *sample;
  54
  55         bset = isl_basic_set_simplify(bset);
  56         if (!bset)
  57                 return NULL;
  58         if (isl_basic_set_fast_is_empty(bset))
  59                 return empty_sample(bset);
  60         if (bset->n_eq == 0 && bset->n_ineq == 0)
  61                 return zero_sample(bset);
  62
  63         sample = isl_vec_alloc(bset->ctx, 2);
  64         if (!sample)
  65                 goto error;
  66         if (!bset)
  67                 return NULL;
  68         isl_int_set_si(sample->block.data[0], 1);
  69
  70         if (bset->n_eq > 0) {
  71                 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
  72                 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
  73                 if (isl_int_is_one(bset->eq[0][1]))
  74                         isl_int_neg(sample->el[1], bset->eq[0][0]);
  75                 else {
  76                         isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
  77                                    goto error);
  78                         isl_int_set(sample->el[1], bset->eq[0][0]);
  79                 }
  80                 isl_basic_set_free(bset);
  81                 return sample;
  82         }
  83
  84         isl_int_init(t);
  85         if (isl_int_is_one(bset->ineq[0][1]))
  86                 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
  87         else
  88                 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
  89         for (i = 1; i < bset->n_ineq; ++i) {
  90                 isl_seq_inner_product(sample->block.data,
  91                                         bset->ineq[i], 2, &t);
  92                 if (isl_int_is_neg(t))
  93                         break;
  94         }
  95         isl_int_clear(t);
  96         if (i < bset->n_ineq) {
  97                 isl_vec_free(sample);
  98                 return empty_sample(bset);
  99         }
 100
 101         isl_basic_set_free(bset);
 102         return sample;
 103 error:
 104         isl_basic_set_free(bset);
 105         isl_vec_free(sample);
 106         return NULL;
 107 }
 108
 109 static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
 110 {
 111         int i, j, n;
 112         struct isl_mat *dirs = NULL;
 113         struct isl_mat *bounds = NULL;
 114         unsigned dim;
 115
 116         if (!bset)
 117                 return NULL;
 118
 119         dim = isl_basic_set_n_dim(bset);
 120         bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
 121         if (!bounds)
 122                 return NULL;
 123
 124         isl_int_set_si(bounds->row[0][0], 1);
 125         isl_seq_clr(bounds->row[0]+1, dim);
 126         bounds->n_row = 1;
 127
 128         if (bset->n_ineq == 0)
 129                 return bounds;
 130
 131         dirs = isl_mat_alloc(bset->ctx, dim, dim);
 132         if (!dirs) {
 133                 isl_mat_free(bounds);
 134                 return NULL;
 135         }
 136         isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
 137         isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
 138         for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
 139                 int pos;
 140
 141                 isl_seq_cpy(dirs->row[n], bset->ineq[j]+1, dirs->n_col);
 142
 143                 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
 144                 if (pos < 0)
 145                         continue;
 146                 for (i = 0; i < n; ++i) {
 147                         int pos_i;
 148                         pos_i = isl_seq_first_non_zero(dirs->row[i], dirs->n_col);
 149                         if (pos_i < pos)
 150                                 continue;
 151                         if (pos_i > pos)
 152                                 break;
 153                         isl_seq_elim(dirs->row[n], dirs->row[i], pos,
 154                                         dirs->n_col, NULL);
 155                         pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
 156                         if (pos < 0)
 157                                 break;
 158                 }
 159                 if (pos < 0)
 160                         continue;
 161                 if (i < n) {
 162                         int k;
 163                         isl_int *t = dirs->row[n];
 164                         for (k = n; k > i; --k)
 165                                 dirs->row[k] = dirs->row[k-1];
 166                         dirs->row[i] = t;
 167                 }
 168                 ++n;
 169                 isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
 170         }
 171         isl_mat_free(dirs);
 172         bounds->n_row = 1+n;
 173         return bounds;
 174 }
 175
 176 static void swap_inequality(struct isl_basic_set *bset, int a, int b)
 177 {
 178         isl_int *t = bset->ineq[a];
 179         bset->ineq[a] = bset->ineq[b];
 180         bset->ineq[b] = t;
 181 }
 182
 183 /* Skew into positive orthant and project out lineality space.
 184  *
 185  * We perform a unimodular transformation that turns a selected
 186  * maximal set of linearly independent bounds into constraints
 187  * on the first dimensions that impose that these first dimensions
 188  * are non-negative.  In particular, the constraint matrix is lower
 189  * triangular with positive entries on the diagonal and negative
 190  * entries below.
 191  * If "bset" has a lineality space then these constraints (and therefore
 192  * all constraints in bset) only involve the first dimensions.
 193  * The remaining dimensions then do not appear in any constraints and
 194  * we can select any value for them, say zero.  We therefore project
 195  * out this final dimensions and plug in the value zero later.  This
 196  * is accomplished by simply dropping the final columns of
 197  * the unimodular transformation.
 198  */
 199 static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
 200         struct isl_basic_set *bset, struct isl_mat **T)
 201 {
 202         struct isl_mat *U = NULL;
 203         struct isl_mat *bounds = NULL;
 204         int i, j;
 205         unsigned old_dim, new_dim;
 206
 207         *T = NULL;
 208         if (!bset)
 209                 return NULL;
 210
 211         isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
 212         isl_assert(bset->ctx, bset->n_div == 0, goto error);
 213         isl_assert(bset->ctx, bset->n_eq == 0, goto error);
 214
 215         old_dim = isl_basic_set_n_dim(bset);
 216         /* Try to move (multiples of) unit rows up. */
 217         for (i = 0, j = 0; i < bset->n_ineq; ++i) {
 218                 int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
 219                 if (pos < 0)
 220                         continue;
 221                 if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
 222                                                 old_dim-pos-1) >= 0)
 223                         continue;
 224                 if (i != j)
 225                         swap_inequality(bset, i, j);
 226                 ++j;
 227         }
 228         bounds = independent_bounds(bset);
 229         if (!bounds)
 230                 goto error;
 231         new_dim = bounds->n_row - 1;
 232         bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
 233         if (!bounds)
 234                 goto error;
 235         U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
 236         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 237         if (!bset)
 238                 goto error;
 239         *T = U;
 240         isl_mat_free(bounds);
 241         return bset;
 242 error:
 243         isl_mat_free(bounds);
 244         isl_mat_free(U);
 245         isl_basic_set_free(bset);
 246         return NULL;
 247 }
 248
 249 /* Find a sample integer point, if any, in bset, which is known
 250  * to have equalities.  If bset contains no integer points, then
 251  * return a zero-length vector.
 252  * We simply remove the known equalities, compute a sample
 253  * in the resulting bset, using the specified recurse function,
 254  * and then transform the sample back to the original space.
 255  */
 256 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
 257         struct isl_vec *(*recurse)(struct isl_basic_set *))
 258 {
 259         struct isl_mat *T;
 260         struct isl_vec *sample;
 261
 262         if (!bset)
 263                 return NULL;
 264
 265         bset = isl_basic_set_remove_equalities(bset, &T, NULL);
 266         sample = recurse(bset);
 267         if (!sample || sample->size == 0)
 268                 isl_mat_free(T);
 269         else
 270                 sample = isl_mat_vec_product(T, sample);
 271         return sample;
 272 }
 273
 274 /* Return a matrix containing the equalities of the tableau
 275  * in constraint form.  The tableau is assumed to have
 276  * an associated bset that has been kept up-to-date.
 277  */
 278 static struct isl_mat *tab_equalities(struct isl_tab *tab)
 279 {
 280         int i, j;
 281         int n_eq;
 282         struct isl_mat *eq;
 283         struct isl_basic_set *bset;
 284
 285         if (!tab)
 286                 return NULL;
 287
 288         bset = isl_tab_peek_bset(tab);
 289         isl_assert(tab->mat->ctx, bset, return NULL);
 290
 291         n_eq = tab->n_var - tab->n_col + tab->n_dead;
 292         if (tab->empty || n_eq == 0)
 293                 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
 294         if (n_eq == tab->n_var)
 295                 return isl_mat_identity(tab->mat->ctx, tab->n_var);
 296
 297         eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
 298         if (!eq)
 299                 return NULL;
 300         for (i = 0, j = 0; i < tab->n_con; ++i) {
 301                 if (tab->con[i].is_row)
 302                         continue;
 303                 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
 304                         continue;
 305                 if (i < bset->n_eq)
 306                         isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
 307                 else
 308                         isl_seq_cpy(eq->row[j],
 309                                     bset->ineq[i - bset->n_eq] + 1, tab->n_var);
 310                 ++j;
 311         }
 312         isl_assert(bset->ctx, j == n_eq, goto error);
 313         return eq;
 314 error:
 315         isl_mat_free(eq);
 316         return NULL;
 317 }
 318
 319 /* Compute and return an initial basis for the bounded tableau "tab".
 320  *
 321  * If the tableau is either full-dimensional or zero-dimensional,
 322  * the we simply return an identity matrix.
 323  * Otherwise, we construct a basis whose first directions correspond
 324  * to equalities.
 325  */
 326 static struct isl_mat *initial_basis(struct isl_tab *tab)
 327 {
 328         int n_eq;
 329         struct isl_mat *eq;
 330         struct isl_mat *Q;
 331
 332         tab->n_unbounded = 0;
 333         tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
 334         if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
 335                 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
 336
 337         eq = tab_equalities(tab);
 338         eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
 339         if (!eq)
 340                 return NULL;
 341         isl_mat_free(eq);
 342
 343         Q = isl_mat_lin_to_aff(Q);
 344         return Q;
 345 }
 346
 347 /* Given a tableau representing a set, find and return
 348  * an integer point in the set, if there is any.
 349  *
 350  * We perform a depth first search
 351  * for an integer point, by scanning all possible values in the range
 352  * attained by a basis vector, where an initial basis may have been set
 353  * by the calling function.  Otherwise an initial basis that exploits
 354  * the equalities in the tableau is created.
 355  * tab->n_zero is currently ignored and is clobbered by this function.
 356  *
 357  * The tableau is allowed to have unbounded direction, but then
 358  * the calling function needs to set an initial basis, with the
 359  * unbounded directions last and with tab->n_unbounded set
 360  * to the number of unbounded directions.
 361  * Furthermore, the calling functions needs to add shifted copies
 362  * of all constraints involving unbounded directions to ensure
 363  * that any feasible rational value in these directions can be rounded
 364  * up to yield a feasible integer value.
 365  * In particular, let B define the given basis x' = B x
 366  * and let T be the inverse of B, i.e., X = T x'.
 367  * Let a x + c >= 0 be a constraint of the set represented by the tableau,
 368  * or a T x' + c >= 0 in terms of the given basis.  Assume that
 369  * the bounded directions have an integer value, then we can safely
 370  * round up the values for the unbounded directions if we make sure
 371  * that x' not only satisfies the original constraint, but also
 372  * the constraint "a T x' + c + s >= 0" with s the sum of all
 373  * negative values in the last n_unbounded entries of "a T".
 374  * The calling function therefore needs to add the constraint
 375  * a x + c + s >= 0.  The current function then scans the first
 376  * directions for an integer value and once those have been found,
 377  * it can compute "T ceil(B x)" to yield an integer point in the set.
 378  * Note that during the search, the first rows of B may be changed
 379  * by a basis reduction, but the last n_unbounded rows of B remain
 380  * unaltered and are also not mixed into the first rows.
 381  *
 382  * The search is implemented iteratively.  "level" identifies the current
 383  * basis vector.  "init" is true if we want the first value at the current
 384  * level and false if we want the next value.
 385  *
 386  * The initial basis is the identity matrix.  If the range in some direction
 387  * contains more than one integer value, we perform basis reduction based
 388  * on the value of ctx->opt->gbr
 389  *      - ISL_GBR_NEVER:        never perform basis reduction
 390  *      - ISL_GBR_ONCE:         only perform basis reduction the first
 391  *                              time such a range is encountered
 392  *      - ISL_GBR_ALWAYS:       always perform basis reduction when
 393  *                              such a range is encountered
 394  *
 395  * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
 396  * reduction computation to return early.  That is, as soon as it
 397  * finds a reasonable first direction.
 398  */
 399 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
 400 {
 401         unsigned dim;
 402         unsigned gbr;
 403         struct isl_ctx *ctx;
 404         struct isl_vec *sample;
 405         struct isl_vec *min;
 406         struct isl_vec *max;
 407         enum isl_lp_result res;
 408         int level;
 409         int init;
 410         int reduced;
 411         struct isl_tab_undo **snap;
 412
 413         if (!tab)
 414                 return NULL;
 415         if (tab->empty)
 416                 return isl_vec_alloc(tab->mat->ctx, 0);
 417
 418         if (!tab->basis)
 419                 tab->basis = initial_basis(tab);
 420         if (!tab->basis)
 421                 return NULL;
 422         isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
 423                     return NULL);
 424         isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
 425                     return NULL);
 426
 427         ctx = tab->mat->ctx;
 428         dim = tab->n_var;
 429         gbr = ctx->opt->gbr;
 430
 431         if (tab->n_unbounded == tab->n_var) {
 432                 sample = isl_tab_get_sample_value(tab);
 433                 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
 434                 sample = isl_vec_ceil(sample);
 435                 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
 436                                                         sample);
 437                 return sample;
 438         }
 439
 440         if (isl_tab_extend_cons(tab, dim + 1) < 0)
 441                 return NULL;
 442
 443         min = isl_vec_alloc(ctx, dim);
 444         max = isl_vec_alloc(ctx, dim);
 445         snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
 446
 447         if (!min || !max || !snap)
 448                 goto error;
 449
 450         level = 0;
 451         init = 1;
 452         reduced = 0;
 453
 454         while (level >= 0) {
 455                 int empty = 0;
 456                 if (init) {
 457                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 458                                     ctx->one, &min->el[level], NULL, 0);
 459                         if (res == isl_lp_empty)
 460                                 empty = 1;
 461                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 462                         if (res == isl_lp_error)
 463                                 goto error;
 464                         if (!empty && isl_tab_sample_is_integer(tab))
 465                                 break;
 466                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 467                                     tab->basis->row[1 + level] + 1, dim);
 468                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 469                                     ctx->one, &max->el[level], NULL, 0);
 470                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 471                                     tab->basis->row[1 + level] + 1, dim);
 472                         isl_int_neg(max->el[level], max->el[level]);
 473                         if (res == isl_lp_empty)
 474                                 empty = 1;
 475                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 476                         if (res == isl_lp_error)
 477                                 goto error;
 478                         if (!empty && isl_tab_sample_is_integer(tab))
 479                                 break;
 480                         if (!empty && !reduced &&
 481                             ctx->opt->gbr != ISL_GBR_NEVER &&
 482                             isl_int_lt(min->el[level], max->el[level])) {
 483                                 unsigned gbr_only_first;
 484                                 if (ctx->opt->gbr == ISL_GBR_ONCE)
 485                                         ctx->opt->gbr = ISL_GBR_NEVER;
 486                                 tab->n_zero = level;
 487                                 gbr_only_first = ctx->opt->gbr_only_first;
 488                                 ctx->opt->gbr_only_first =
 489                                         ctx->opt->gbr == ISL_GBR_ALWAYS;
 490                                 tab = isl_tab_compute_reduced_basis(tab);
 491                                 ctx->opt->gbr_only_first = gbr_only_first;
 492                                 if (!tab || !tab->basis)
 493                                         goto error;
 494                                 reduced = 1;
 495                                 continue;
 496                         }
 497                         reduced = 0;
 498                         snap[level] = isl_tab_snap(tab);
 499                 } else
 500                         isl_int_add_ui(min->el[level], min->el[level], 1);
 501
 502                 if (empty || isl_int_gt(min->el[level], max->el[level])) {
 503                         level--;
 504                         init = 0;
 505                         if (level >= 0)
 506                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 507                                         goto error;
 508                         continue;
 509                 }
 510                 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
 511                 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
 512                         goto error;
 513                 isl_int_set_si(tab->basis->row[1 + level][0], 0);
 514                 if (level + tab->n_unbounded < dim - 1) {
 515                         ++level;
 516                         init = 1;
 517                         continue;
 518                 }
 519                 break;
 520         }
 521
 522         if (level >= 0) {
 523                 sample = isl_tab_get_sample_value(tab);
 524                 if (!sample)
 525                         goto error;
 526                 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
 527                         sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
 528                                                      sample);
 529                         sample = isl_vec_ceil(sample);
 530                         sample = isl_mat_vec_inverse_product(
 531                                         isl_mat_copy(tab->basis), sample);
 532                 }
 533         } else
 534                 sample = isl_vec_alloc(ctx, 0);
 535
 536         ctx->opt->gbr = gbr;
 537         isl_vec_free(min);
 538         isl_vec_free(max);
 539         free(snap);
 540         return sample;
 541 error:
 542         ctx->opt->gbr = gbr;
 543         isl_vec_free(min);
 544         isl_vec_free(max);
 545         free(snap);
 546         return NULL;
 547 }
 548
 549 /* Given a basic set that is known to be bounded, find and return
 550  * an integer point in the basic set, if there is any.
 551  *
 552  * After handling some trivial cases, we construct a tableau
 553  * and then use isl_tab_sample to find a sample, passing it
 554  * the identity matrix as initial basis.
 555  */
 556 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
 557 {
 558         unsigned dim;
 559         struct isl_ctx *ctx;
 560         struct isl_vec *sample;
 561         struct isl_tab *tab = NULL;
 562
 563         if (!bset)
 564                 return NULL;
 565
 566         if (isl_basic_set_fast_is_empty(bset))
 567                 return empty_sample(bset);
 568
 569         dim = isl_basic_set_total_dim(bset);
 570         if (dim == 0)
 571                 return zero_sample(bset);
 572         if (dim == 1)
 573                 return interval_sample(bset);
 574         if (bset->n_eq > 0)
 575                 return sample_eq(bset, sample_bounded);
 576
 577         ctx = bset->ctx;
 578
 579         tab = isl_tab_from_basic_set(bset);
 580         if (tab && tab->empty) {
 581                 isl_tab_free(tab);
 582                 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
 583                 sample = isl_vec_alloc(bset->ctx, 0);
 584                 isl_basic_set_free(bset);
 585                 return sample;
 586         }
 587
 588         if (isl_tab_track_bset(tab, isl_basic_set_copy(bset)) < 0)
 589                 goto error;
 590         if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
 591                 if (isl_tab_detect_implicit_equalities(tab) < 0)
 592                         goto error;
 593
 594         sample = isl_tab_sample(tab);
 595         if (!sample)
 596                 goto error;
 597
 598         if (sample->size > 0) {
 599                 isl_vec_free(bset->sample);
 600                 bset->sample = isl_vec_copy(sample);
 601         }
 602
 603         isl_basic_set_free(bset);
 604         isl_tab_free(tab);
 605         return sample;
 606 error:
 607         isl_basic_set_free(bset);
 608         isl_tab_free(tab);
 609         return NULL;
 610 }
 611
 612 /* Given a basic set "bset" and a value "sample" for the first coordinates
 613  * of bset, plug in these values and drop the corresponding coordinates.
 614  *
 615  * We do this by computing the preimage of the transformation
 616  *
 617  *           [ 1 0 ]
 618  *      x =  [ s 0 ] x'
 619  *           [ 0 I ]
 620  *
 621  * where [1 s] is the sample value and I is the identity matrix of the
 622  * appropriate dimension.
 623  */
 624 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
 625         struct isl_vec *sample)
 626 {
 627         int i;
 628         unsigned total;
 629         struct isl_mat *T;
 630
 631         if (!bset || !sample)
 632                 goto error;
 633
 634         total = isl_basic_set_total_dim(bset);
 635         T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
 636         if (!T)
 637                 goto error;
 638
 639         for (i = 0; i < sample->size; ++i) {
 640                 isl_int_set(T->row[i][0], sample->el[i]);
 641                 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
 642         }
 643         for (i = 0; i < T->n_col - 1; ++i) {
 644                 isl_seq_clr(T->row[sample->size + i], T->n_col);
 645                 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
 646         }
 647         isl_vec_free(sample);
 648
 649         bset = isl_basic_set_preimage(bset, T);
 650         return bset;
 651 error:
 652         isl_basic_set_free(bset);
 653         isl_vec_free(sample);
 654         return NULL;
 655 }
 656
 657 /* Given a basic set "bset", return any (possibly non-integer) point
 658  * in the basic set.
 659  */
 660 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
 661 {
 662         struct isl_tab *tab;
 663         struct isl_vec *sample;
 664
 665         if (!bset)
 666                 return NULL;
 667
 668         tab = isl_tab_from_basic_set(bset);
 669         sample = isl_tab_get_sample_value(tab);
 670         isl_tab_free(tab);
 671
 672         isl_basic_set_free(bset);
 673
 674         return sample;
 675 }
 676
 677 /* Given a linear cone "cone" and a rational point "vec",
 678  * construct a polyhedron with shifted copies of the constraints in "cone",
 679  * i.e., a polyhedron with "cone" as its recession cone, such that each
 680  * point x in this polyhedron is such that the unit box positioned at x
 681  * lies entirely inside the affine cone 'vec + cone'.
 682  * Any rational point in this polyhedron may therefore be rounded up
 683  * to yield an integer point that lies inside said affine cone.
 684  *
 685  * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
 686  * point "vec" by v/d.
 687  * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
 688  * by <a_i, x> - b/d >= 0.
 689  * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
 690  * We prefer this polyhedron over the actual affine cone because it doesn't
 691  * require a scaling of the constraints.
 692  * If each of the vertices of the unit cube positioned at x lies inside
 693  * this polyhedron, then the whole unit cube at x lies inside the affine cone.
 694  * We therefore impose that x' = x + \sum e_i, for any selection of unit
 695  * vectors lies inside the polyhedron, i.e.,
 696  *
 697  *      <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
 698  *
 699  * The most stringent of these constraints is the one that selects
 700  * all negative a_i, so the polyhedron we are looking for has constraints
 701  *
 702  *      <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
 703  *
 704  * Note that if cone were known to have only non-negative rays
 705  * (which can be accomplished by a unimodular transformation),
 706  * then we would only have to check the points x' = x + e_i
 707  * and we only have to add the smallest negative a_i (if any)
 708  * instead of the sum of all negative a_i.
 709  */
 710 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
 711         struct isl_vec *vec)
 712 {
 713         int i, j, k;
 714         unsigned total;
 715
 716         struct isl_basic_set *shift = NULL;
 717
 718         if (!cone || !vec)
 719                 goto error;
 720
 721         isl_assert(cone->ctx, cone->n_eq == 0, goto error);
 722
 723         total = isl_basic_set_total_dim(cone);
 724
 725         shift = isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone),
 726                                         0, 0, cone->n_ineq);
 727
 728         for (i = 0; i < cone->n_ineq; ++i) {
 729                 k = isl_basic_set_alloc_inequality(shift);
 730                 if (k < 0)
 731                         goto error;
 732                 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
 733                 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
 734                                       &shift->ineq[k][0]);
 735                 isl_int_cdiv_q(shift->ineq[k][0],
 736                                shift->ineq[k][0], vec->el[0]);
 737                 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
 738                 for (j = 0; j < total; ++j) {
 739                         if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
 740                                 continue;
 741                         isl_int_add(shift->ineq[k][0],
 742                                     shift->ineq[k][0], shift->ineq[k][1 + j]);
 743                 }
 744         }
 745
 746         isl_basic_set_free(cone);
 747         isl_vec_free(vec);
 748
 749         return isl_basic_set_finalize(shift);
 750 error:
 751         isl_basic_set_free(shift);
 752         isl_basic_set_free(cone);
 753         isl_vec_free(vec);
 754         return NULL;
 755 }
 756
 757 /* Given a rational point vec in a (transformed) basic set,
 758  * such that cone is the recession cone of the original basic set,
 759  * "round up" the rational point to an integer point.
 760  *
 761  * We first check if the rational point just happens to be integer.
 762  * If not, we transform the cone in the same way as the basic set,
 763  * pick a point x in this cone shifted to the rational point such that
 764  * the whole unit cube at x is also inside this affine cone.
 765  * Then we simply round up the coordinates of x and return the
 766  * resulting integer point.
 767  */
 768 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
 769         struct isl_basic_set *cone, struct isl_mat *U)
 770 {
 771         unsigned total;
 772
 773         if (!vec || !cone || !U)
 774                 goto error;
 775
 776         isl_assert(vec->ctx, vec->size != 0, goto error);
 777         if (isl_int_is_one(vec->el[0])) {
 778                 isl_mat_free(U);
 779                 isl_basic_set_free(cone);
 780                 return vec;
 781         }
 782
 783         total = isl_basic_set_total_dim(cone);
 784         cone = isl_basic_set_preimage(cone, U);
 785         cone = isl_basic_set_remove_dims(cone, 0, total - (vec->size - 1));
 786
 787         cone = shift_cone(cone, vec);
 788
 789         vec = rational_sample(cone);
 790         vec = isl_vec_ceil(vec);
 791         return vec;
 792 error:
 793         isl_mat_free(U);
 794         isl_vec_free(vec);
 795         isl_basic_set_free(cone);
 796         return NULL;
 797 }
 798
 799 /* Concatenate two integer vectors, i.e., two vectors with denominator
 800  * (stored in element 0) equal to 1.
 801  */
 802 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
 803 {
 804         struct isl_vec *vec;
 805
 806         if (!vec1 || !vec2)
 807                 goto error;
 808         isl_assert(vec1->ctx, vec1->size > 0, goto error);
 809         isl_assert(vec2->ctx, vec2->size > 0, goto error);
 810         isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
 811         isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
 812
 813         vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
 814         if (!vec)
 815                 goto error;
 816
 817         isl_seq_cpy(vec->el, vec1->el, vec1->size);
 818         isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
 819
 820         isl_vec_free(vec1);
 821         isl_vec_free(vec2);
 822
 823         return vec;
 824 error:
 825         isl_vec_free(vec1);
 826         isl_vec_free(vec2);
 827         return NULL;
 828 }
 829
 830 /* Drop all constraints in bset that involve any of the dimensions
 831  * first to first+n-1.
 832  */
 833 static struct isl_basic_set *drop_constraints_involving
 834         (struct isl_basic_set *bset, unsigned first, unsigned n)
 835 {
 836         int i;
 837
 838         bset = isl_basic_set_cow(bset);
 839
 840         if (!bset)
 841                 return NULL;
 842
 843         for (i = bset->n_ineq - 1; i >= 0; --i) {
 844                 if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
 845                         continue;
 846                 isl_basic_set_drop_inequality(bset, i);
 847         }
 848
 849         return bset;
 850 }
 851
 852 /* Give a basic set "bset" with recession cone "cone", compute and
 853  * return an integer point in bset, if any.
 854  *
 855  * If the recession cone is full-dimensional, then we know that
 856  * bset contains an infinite number of integer points and it is
 857  * fairly easy to pick one of them.
 858  * If the recession cone is not full-dimensional, then we first
 859  * transform bset such that the bounded directions appear as
 860  * the first dimensions of the transformed basic set.
 861  * We do this by using a unimodular transformation that transforms
 862  * the equalities in the recession cone to equalities on the first
 863  * dimensions.
 864  *
 865  * The transformed set is then projected onto its bounded dimensions.
 866  * Note that to compute this projection, we can simply drop all constraints
 867  * involving any of the unbounded dimensions since these constraints
 868  * cannot be combined to produce a constraint on the bounded dimensions.
 869  * To see this, assume that there is such a combination of constraints
 870  * that produces a constraint on the bounded dimensions.  This means
 871  * that some combination of the unbounded dimensions has both an upper
 872  * bound and a lower bound in terms of the bounded dimensions, but then
 873  * this combination would be a bounded direction too and would have been
 874  * transformed into a bounded dimensions.
 875  *
 876  * We then compute a sample value in the bounded dimensions.
 877  * If no such value can be found, then the original set did not contain
 878  * any integer points and we are done.
 879  * Otherwise, we plug in the value we found in the bounded dimensions,
 880  * project out these bounded dimensions and end up with a set with
 881  * a full-dimensional recession cone.
 882  * A sample point in this set is computed by "rounding up" any
 883  * rational point in the set.
 884  *
 885  * The sample points in the bounded and unbounded dimensions are
 886  * then combined into a single sample point and transformed back
 887  * to the original space.
 888  */
 889 __isl_give isl_vec *isl_basic_set_sample_with_cone(
 890         __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
 891 {
 892         unsigned total;
 893         unsigned cone_dim;
 894         struct isl_mat *M, *U;
 895         struct isl_vec *sample;
 896         struct isl_vec *cone_sample;
 897         struct isl_ctx *ctx;
 898         struct isl_basic_set *bounded;
 899
 900         if (!bset || !cone)
 901                 goto error;
 902
 903         ctx = bset->ctx;
 904         total = isl_basic_set_total_dim(cone);
 905         cone_dim = total - cone->n_eq;
 906
 907         M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
 908         M = isl_mat_left_hermite(M, 0, &U, NULL);
 909         if (!M)
 910                 goto error;
 911         isl_mat_free(M);
 912
 913         U = isl_mat_lin_to_aff(U);
 914         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 915
 916         bounded = isl_basic_set_copy(bset);
 917         bounded = drop_constraints_involving(bounded, total - cone_dim, cone_dim);
 918         bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
 919         sample = sample_bounded(bounded);
 920         if (!sample || sample->size == 0) {
 921                 isl_basic_set_free(bset);
 922                 isl_basic_set_free(cone);
 923                 isl_mat_free(U);
 924                 return sample;
 925         }
 926         bset = plug_in(bset, isl_vec_copy(sample));
 927         cone_sample = rational_sample(bset);
 928         cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
 929         sample = vec_concat(sample, cone_sample);
 930         sample = isl_mat_vec_product(U, sample);
 931         return sample;
 932 error:
 933         isl_basic_set_free(cone);
 934         isl_basic_set_free(bset);
 935         return NULL;
 936 }
 937
 938 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
 939 {
 940         int i;
 941
 942         isl_int_set_si(*s, 0);
 943
 944         for (i = 0; i < v->size; ++i)
 945                 if (isl_int_is_neg(v->el[i]))
 946                         isl_int_add(*s, *s, v->el[i]);
 947 }
 948
 949 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
 950  * to the recession cone and the inverse of a new basis U = inv(B),
 951  * with the unbounded directions in B last,
 952  * add constraints to "tab" that ensure any rational value
 953  * in the unbounded directions can be rounded up to an integer value.
 954  *
 955  * The new basis is given by x' = B x, i.e., x = U x'.
 956  * For any rational value of the last tab->n_unbounded coordinates
 957  * in the update tableau, the value that is obtained by rounding
 958  * up this value should be contained in the original tableau.
 959  * For any constraint "a x + c >= 0", we therefore need to add
 960  * a constraint "a x + c + s >= 0", with s the sum of all negative
 961  * entries in the last elements of "a U".
 962  *
 963  * Since we are not interested in the first entries of any of the "a U",
 964  * we first drop the columns of U that correpond to bounded directions.
 965  */
 966 static int tab_shift_cone(struct isl_tab *tab,
 967         struct isl_tab *tab_cone, struct isl_mat *U)
 968 {
 969         int i;
 970         isl_int v;
 971         struct isl_basic_set *bset = NULL;
 972
 973         if (tab && tab->n_unbounded == 0) {
 974                 isl_mat_free(U);
 975                 return 0;
 976         }
 977         isl_int_init(v);
 978         if (!tab || !tab_cone || !U)
 979                 goto error;
 980         bset = isl_tab_peek_bset(tab_cone);
 981         U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
 982         for (i = 0; i < bset->n_ineq; ++i) {
 983                 int ok;
 984                 struct isl_vec *row = NULL;
 985                 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
 986                         continue;
 987                 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
 988                 if (!row)
 989                         goto error;
 990                 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
 991                 row = isl_vec_mat_product(row, isl_mat_copy(U));
 992                 if (!row)
 993                         goto error;
 994                 vec_sum_of_neg(row, &v);
 995                 isl_vec_free(row);
 996                 if (isl_int_is_zero(v))
 997                         continue;
 998                 tab = isl_tab_extend(tab, 1);
 999                 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1000                 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1001                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1002                 if (!ok)
1003                         goto error;
1004         }
1005
1006         isl_mat_free(U);
1007         isl_int_clear(v);
1008         return 0;
1009 error:
1010         isl_mat_free(U);
1011         isl_int_clear(v);
1012         return -1;
1013 }
1014
1015 /* Compute and return an initial basis for the possibly
1016  * unbounded tableau "tab".  "tab_cone" is a tableau
1017  * for the corresponding recession cone.
1018  * Additionally, add constraints to "tab" that ensure
1019  * that any rational value for the unbounded directions
1020  * can be rounded up to an integer value.
1021  *
1022  * If the tableau is bounded, i.e., if the recession cone
1023  * is zero-dimensional, then we just use inital_basis.
1024  * Otherwise, we construct a basis whose first directions
1025  * correspond to equalities, followed by bounded directions,
1026  * i.e., equalities in the recession cone.
1027  * The remaining directions are then unbounded.
1028  */
1029 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1030         struct isl_tab *tab_cone)
1031 {
1032         struct isl_mat *eq;
1033         struct isl_mat *cone_eq;
1034         struct isl_mat *U, *Q;
1035
1036         if (!tab || !tab_cone)
1037                 return -1;
1038
1039         if (tab_cone->n_col == tab_cone->n_dead) {
1040                 tab->basis = initial_basis(tab);
1041                 return tab->basis ? 0 : -1;
1042         }
1043
1044         eq = tab_equalities(tab);
1045         if (!eq)
1046                 return -1;
1047         tab->n_zero = eq->n_row;
1048         cone_eq = tab_equalities(tab_cone);
1049         eq = isl_mat_concat(eq, cone_eq);
1050         if (!eq)
1051                 return -1;
1052         tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1053         eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1054         if (!eq)
1055                 return -1;
1056         isl_mat_free(eq);
1057         tab->basis = isl_mat_lin_to_aff(Q);
1058         if (tab_shift_cone(tab, tab_cone, U) < 0)
1059                 return -1;
1060         if (!tab->basis)
1061                 return -1;
1062         return 0;
1063 }
1064
1065 /* Compute and return a sample point in bset using generalized basis
1066  * reduction.  We first check if the input set has a non-trivial
1067  * recession cone.  If so, we perform some extra preprocessing in
1068  * sample_with_cone.  Otherwise, we directly perform generalized basis
1069  * reduction.
1070  */
1071 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1072 {
1073         unsigned dim;
1074         struct isl_basic_set *cone;
1075
1076         dim = isl_basic_set_total_dim(bset);
1077
1078         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1079         if (!cone)
1080                 goto error;
1081
1082         if (cone->n_eq < dim)
1083                 return isl_basic_set_sample_with_cone(bset, cone);
1084
1085         isl_basic_set_free(cone);
1086         return sample_bounded(bset);
1087 error:
1088         isl_basic_set_free(bset);
1089         return NULL;
1090 }
1091
1092 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
1093 {
1094         struct isl_mat *T;
1095         struct isl_ctx *ctx;
1096         struct isl_vec *sample;
1097
1098         bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
1099         if (!bset)
1100                 return NULL;
1101
1102         ctx = bset->ctx;
1103         sample = isl_pip_basic_set_sample(bset);
1104
1105         if (sample && sample->size != 0)
1106                 sample = isl_mat_vec_product(T, sample);
1107         else
1108                 isl_mat_free(T);
1109
1110         return sample;
1111 }
1112
1113 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1114 {
1115         struct isl_ctx *ctx;
1116         unsigned dim;
1117         if (!bset)
1118                 return NULL;
1119
1120         ctx = bset->ctx;
1121         if (isl_basic_set_fast_is_empty(bset))
1122                 return empty_sample(bset);
1123
1124         dim = isl_basic_set_n_dim(bset);
1125         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1126         isl_assert(ctx, bset->n_div == 0, goto error);
1127
1128         if (bset->sample && bset->sample->size == 1 + dim) {
1129                 int contains = isl_basic_set_contains(bset, bset->sample);
1130                 if (contains < 0)
1131                         goto error;
1132                 if (contains) {
1133                         struct isl_vec *sample = isl_vec_copy(bset->sample);
1134                         isl_basic_set_free(bset);
1135                         return sample;
1136                 }
1137         }
1138         isl_vec_free(bset->sample);
1139         bset->sample = NULL;
1140
1141         if (bset->n_eq > 0)
1142                 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1143                                                : isl_basic_set_sample_vec);
1144         if (dim == 0)
1145                 return zero_sample(bset);
1146         if (dim == 1)
1147                 return interval_sample(bset);
1148
1149         switch (bset->ctx->opt->ilp_solver) {
1150         case ISL_ILP_PIP:
1151                 return pip_sample(bset);
1152         case ISL_ILP_GBR:
1153                 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1154         }
1155         isl_assert(bset->ctx, 0, );
1156 error:
1157         isl_basic_set_free(bset);
1158         return NULL;
1159 }
1160
1161 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1162 {
1163         return basic_set_sample(bset, 0);
1164 }
1165
1166 /* Compute an integer sample in "bset", where the caller guarantees
1167  * that "bset" is bounded.
1168  */
1169 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1170 {
1171         return basic_set_sample(bset, 1);
1172 }
1173
1174 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1175 {
1176         int i;
1177         int k;
1178         struct isl_basic_set *bset = NULL;
1179         struct isl_ctx *ctx;
1180         unsigned dim;
1181
1182         if (!vec)
1183                 return NULL;
1184         ctx = vec->ctx;
1185         isl_assert(ctx, vec->size != 0, goto error);
1186
1187         bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1188         if (!bset)
1189                 goto error;
1190         dim = isl_basic_set_n_dim(bset);
1191         for (i = dim - 1; i >= 0; --i) {
1192                 k = isl_basic_set_alloc_equality(bset);
1193                 if (k < 0)
1194                         goto error;
1195                 isl_seq_clr(bset->eq[k], 1 + dim);
1196                 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1197                 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1198         }
1199         bset->sample = vec;
1200
1201         return bset;
1202 error:
1203         isl_basic_set_free(bset);
1204         isl_vec_free(vec);
1205         return NULL;
1206 }
1207
1208 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1209 {
1210         struct isl_basic_set *bset;
1211         struct isl_vec *sample_vec;
1212
1213         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1214         sample_vec = isl_basic_set_sample_vec(bset);
1215         if (!sample_vec)
1216                 goto error;
1217         if (sample_vec->size == 0) {
1218                 struct isl_basic_map *sample;
1219                 sample = isl_basic_map_empty_like(bmap);
1220                 isl_vec_free(sample_vec);
1221                 isl_basic_map_free(bmap);
1222                 return sample;
1223         }
1224         bset = isl_basic_set_from_vec(sample_vec);
1225         return isl_basic_map_overlying_set(bset, bmap);
1226 error:
1227         isl_basic_map_free(bmap);
1228         return NULL;
1229 }
1230
1231 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1232 {
1233         int i;
1234         isl_basic_map *sample = NULL;
1235
1236         if (!map)
1237                 goto error;
1238
1239         for (i = 0; i < map->n; ++i) {
1240                 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1241                 if (!sample)
1242                         goto error;
1243                 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1244                         break;
1245                 isl_basic_map_free(sample);
1246         }
1247         if (i == map->n)
1248                 sample = isl_basic_map_empty_like_map(map);
1249         isl_map_free(map);
1250         return sample;
1251 error:
1252         isl_map_free(map);
1253         return NULL;
1254 }
1255
1256 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1257 {
1258         return (isl_basic_set *) isl_map_sample((isl_map *)set);
1259 }
1260
1261 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1262 {
1263         isl_vec *vec;
1264         isl_dim *dim;
1265
1266         dim = isl_basic_set_get_dim(bset);
1267         bset = isl_basic_set_underlying_set(bset);
1268         vec = isl_basic_set_sample_vec(bset);
1269
1270         return isl_point_alloc(dim, vec);
1271 }
1272
1273 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1274 {
1275         int i;
1276         isl_point *pnt;
1277
1278         if (!set)
1279                 return NULL;
1280
1281         for (i = 0; i < set->n; ++i) {
1282                 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1283                 if (!pnt)
1284                         goto error;
1285                 if (!isl_point_is_void(pnt))
1286                         break;
1287                 isl_point_free(pnt);
1288         }
1289         if (i == set->n)
1290                 pnt = isl_point_void(isl_set_get_dim(set));
1291
1292         isl_set_free(set);
1293         return pnt;
1294 error:
1295         isl_set_free(set);
1296         return NULL;
1297 }