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