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         tab->n_unbounded = 0;
 329         tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
 330         if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
 331                 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
 332
 333         eq = tab_equalities(tab);
 334         eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
 335         if (!eq)
 336                 return NULL;
 337         isl_mat_free(eq);
 338
 339         Q = isl_mat_lin_to_aff(Q);
 340         return Q;
 341 }
 342
 343 /* Given a tableau representing a set, find and return
 344  * an integer point in the set, if there is any.
 345  *
 346  * We perform a depth first search
 347  * for an integer point, by scanning all possible values in the range
 348  * attained by a basis vector, where an initial basis may have been set
 349  * by the calling function.  Otherwise an initial basis that exploits
 350  * the equalities in the tableau is created.
 351  * tab->n_zero is currently ignored and is clobbered by this function.
 352  *
 353  * The tableau is allowed to have unbounded direction, but then
 354  * the calling function needs to set an initial basis, with the
 355  * unbounded directions last and with tab->n_unbounded set
 356  * to the number of unbounded directions.
 357  * Furthermore, the calling functions needs to add shifted copies
 358  * of all constraints involving unbounded directions to ensure
 359  * that any feasible rational value in these directions can be rounded
 360  * up to yield a feasible integer value.
 361  * In particular, let B define the given basis x' = B x
 362  * and let T be the inverse of B, i.e., X = T x'.
 363  * Let a x + c >= 0 be a constraint of the set represented by the tableau,
 364  * or a T x' + c >= 0 in terms of the given basis.  Assume that
 365  * the bounded directions have an integer value, then we can safely
 366  * round up the values for the unbounded directions if we make sure
 367  * that x' not only satisfies the original constraint, but also
 368  * the constraint "a T x' + c + s >= 0" with s the sum of all
 369  * negative values in the last n_unbounded entries of "a T".
 370  * The calling function therefore needs to add the constraint
 371  * a x + c + s >= 0.  The current function then scans the first
 372  * directions for an integer value and once those have been found,
 373  * it can compute "T ceil(B x)" to yield an integer point in the set.
 374  * Note that during the search, the first rows of B may be changed
 375  * by a basis reduction, but the last n_unbounded rows of B remain
 376  * unaltered and are also not mixed into the first rows.
 377  *
 378  * The search is implemented iteratively.  "level" identifies the current
 379  * basis vector.  "init" is true if we want the first value at the current
 380  * level and false if we want the next value.
 381  *
 382  * The initial basis is the identity matrix.  If the range in some direction
 383  * contains more than one integer value, we perform basis reduction based
 384  * on the value of ctx->opt->gbr
 385  *      - ISL_GBR_NEVER:        never perform basis reduction
 386  *      - ISL_GBR_ONCE:         only perform basis reduction the first
 387  *                              time such a range is encountered
 388  *      - ISL_GBR_ALWAYS:       always perform basis reduction when
 389  *                              such a range is encountered
 390  *
 391  * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
 392  * reduction computation to return early.  That is, as soon as it
 393  * finds a reasonable first direction.
 394  */
 395 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
 396 {
 397         unsigned dim;
 398         unsigned gbr;
 399         struct isl_ctx *ctx;
 400         struct isl_vec *sample;
 401         struct isl_vec *min;
 402         struct isl_vec *max;
 403         enum isl_lp_result res;
 404         int level;
 405         int init;
 406         int reduced;
 407         struct isl_tab_undo **snap;
 408
 409         if (!tab)
 410                 return NULL;
 411         if (tab->empty)
 412                 return isl_vec_alloc(tab->mat->ctx, 0);
 413
 414         if (!tab->basis)
 415                 tab->basis = initial_basis(tab);
 416         if (!tab->basis)
 417                 return NULL;
 418         isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
 419                     return NULL);
 420         isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
 421                     return NULL);
 422
 423         ctx = tab->mat->ctx;
 424         dim = tab->n_var;
 425         gbr = ctx->opt->gbr;
 426
 427         if (tab->n_unbounded == tab->n_var) {
 428                 sample = isl_tab_get_sample_value(tab);
 429                 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
 430                 sample = isl_vec_ceil(sample);
 431                 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
 432                                                         sample);
 433                 return sample;
 434         }
 435
 436         if (isl_tab_extend_cons(tab, dim + 1) < 0)
 437                 return NULL;
 438
 439         min = isl_vec_alloc(ctx, dim);
 440         max = isl_vec_alloc(ctx, dim);
 441         snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
 442
 443         if (!min || !max || !snap)
 444                 goto error;
 445
 446         level = 0;
 447         init = 1;
 448         reduced = 0;
 449
 450         while (level >= 0) {
 451                 int empty = 0;
 452                 if (init) {
 453                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 454                                     ctx->one, &min->el[level], NULL, 0);
 455                         if (res == isl_lp_empty)
 456                                 empty = 1;
 457                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 458                         if (res == isl_lp_error)
 459                                 goto error;
 460                         if (!empty && isl_tab_sample_is_integer(tab))
 461                                 break;
 462                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 463                                     tab->basis->row[1 + level] + 1, dim);
 464                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 465                                     ctx->one, &max->el[level], NULL, 0);
 466                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 467                                     tab->basis->row[1 + level] + 1, dim);
 468                         isl_int_neg(max->el[level], max->el[level]);
 469                         if (res == isl_lp_empty)
 470                                 empty = 1;
 471                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 472                         if (res == isl_lp_error)
 473                                 goto error;
 474                         if (!empty && isl_tab_sample_is_integer(tab))
 475                                 break;
 476                         if (!empty && !reduced &&
 477                             ctx->opt->gbr != ISL_GBR_NEVER &&
 478                             isl_int_lt(min->el[level], max->el[level])) {
 479                                 unsigned gbr_only_first;
 480                                 if (ctx->opt->gbr == ISL_GBR_ONCE)
 481                                         ctx->opt->gbr = ISL_GBR_NEVER;
 482                                 tab->n_zero = level;
 483                                 gbr_only_first = ctx->opt->gbr_only_first;
 484                                 ctx->opt->gbr_only_first =
 485                                         ctx->opt->gbr == ISL_GBR_ALWAYS;
 486                                 tab = isl_tab_compute_reduced_basis(tab);
 487                                 ctx->opt->gbr_only_first = gbr_only_first;
 488                                 if (!tab || !tab->basis)
 489                                         goto error;
 490                                 reduced = 1;
 491                                 continue;
 492                         }
 493                         reduced = 0;
 494                         snap[level] = isl_tab_snap(tab);
 495                 } else
 496                         isl_int_add_ui(min->el[level], min->el[level], 1);
 497
 498                 if (empty || isl_int_gt(min->el[level], max->el[level])) {
 499                         level--;
 500                         init = 0;
 501                         if (level >= 0)
 502                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 503                                         goto error;
 504                         continue;
 505                 }
 506                 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
 507                 tab = isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]);
 508                 isl_int_set_si(tab->basis->row[1 + level][0], 0);
 509                 if (level + tab->n_unbounded < dim - 1) {
 510                         ++level;
 511                         init = 1;
 512                         continue;
 513                 }
 514                 break;
 515         }
 516
 517         if (level >= 0) {
 518                 sample = isl_tab_get_sample_value(tab);
 519                 if (!sample)
 520                         goto error;
 521                 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
 522                         sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
 523                                                      sample);
 524                         sample = isl_vec_ceil(sample);
 525                         sample = isl_mat_vec_inverse_product(
 526                                         isl_mat_copy(tab->basis), sample);
 527                 }
 528         } else
 529                 sample = isl_vec_alloc(ctx, 0);
 530
 531         ctx->opt->gbr = gbr;
 532         isl_vec_free(min);
 533         isl_vec_free(max);
 534         free(snap);
 535         return sample;
 536 error:
 537         ctx->opt->gbr = gbr;
 538         isl_vec_free(min);
 539         isl_vec_free(max);
 540         free(snap);
 541         return NULL;
 542 }
 543
 544 /* Given a basic set that is known to be bounded, find and return
 545  * an integer point in the basic set, if there is any.
 546  *
 547  * After handling some trivial cases, we construct a tableau
 548  * and then use isl_tab_sample to find a sample, passing it
 549  * the identity matrix as initial basis.
 550  */
 551 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
 552 {
 553         unsigned dim;
 554         struct isl_ctx *ctx;
 555         struct isl_vec *sample;
 556         struct isl_tab *tab = NULL;
 557
 558         if (!bset)
 559                 return NULL;
 560
 561         if (isl_basic_set_fast_is_empty(bset))
 562                 return empty_sample(bset);
 563
 564         dim = isl_basic_set_total_dim(bset);
 565         if (dim == 0)
 566                 return zero_sample(bset);
 567         if (dim == 1)
 568                 return interval_sample(bset);
 569         if (bset->n_eq > 0)
 570                 return sample_eq(bset, sample_bounded);
 571
 572         ctx = bset->ctx;
 573
 574         tab = isl_tab_from_basic_set(bset);
 575         if (tab && tab->empty) {
 576                 isl_tab_free(tab);
 577                 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
 578                 sample = isl_vec_alloc(bset->ctx, 0);
 579                 isl_basic_set_free(bset);
 580                 return sample;
 581         }
 582
 583         if (isl_tab_track_bset(tab, isl_basic_set_copy(bset)) < 0)
 584                 goto error;
 585         if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
 586                 tab = isl_tab_detect_implicit_equalities(tab);
 587         if (!tab)
 588                 goto error;
 589
 590         sample = isl_tab_sample(tab);
 591         if (!sample)
 592                 goto error;
 593
 594         if (sample->size > 0) {
 595                 isl_vec_free(bset->sample);
 596                 bset->sample = isl_vec_copy(sample);
 597         }
 598
 599         isl_basic_set_free(bset);
 600         isl_tab_free(tab);
 601         return sample;
 602 error:
 603         isl_basic_set_free(bset);
 604         isl_tab_free(tab);
 605         return NULL;
 606 }
 607
 608 /* Given a basic set "bset" and a value "sample" for the first coordinates
 609  * of bset, plug in these values and drop the corresponding coordinates.
 610  *
 611  * We do this by computing the preimage of the transformation
 612  *
 613  *           [ 1 0 ]
 614  *      x =  [ s 0 ] x'
 615  *           [ 0 I ]
 616  *
 617  * where [1 s] is the sample value and I is the identity matrix of the
 618  * appropriate dimension.
 619  */
 620 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
 621         struct isl_vec *sample)
 622 {
 623         int i;
 624         unsigned total;
 625         struct isl_mat *T;
 626
 627         if (!bset || !sample)
 628                 goto error;
 629
 630         total = isl_basic_set_total_dim(bset);
 631         T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
 632         if (!T)
 633                 goto error;
 634
 635         for (i = 0; i < sample->size; ++i) {
 636                 isl_int_set(T->row[i][0], sample->el[i]);
 637                 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
 638         }
 639         for (i = 0; i < T->n_col - 1; ++i) {
 640                 isl_seq_clr(T->row[sample->size + i], T->n_col);
 641                 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
 642         }
 643         isl_vec_free(sample);
 644
 645         bset = isl_basic_set_preimage(bset, T);
 646         return bset;
 647 error:
 648         isl_basic_set_free(bset);
 649         isl_vec_free(sample);
 650         return NULL;
 651 }
 652
 653 /* Given a basic set "bset", return any (possibly non-integer) point
 654  * in the basic set.
 655  */
 656 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
 657 {
 658         struct isl_tab *tab;
 659         struct isl_vec *sample;
 660
 661         if (!bset)
 662                 return NULL;
 663
 664         tab = isl_tab_from_basic_set(bset);
 665         sample = isl_tab_get_sample_value(tab);
 666         isl_tab_free(tab);
 667
 668         isl_basic_set_free(bset);
 669
 670         return sample;
 671 }
 672
 673 /* Given a linear cone "cone" and a rational point "vec",
 674  * construct a polyhedron with shifted copies of the constraints in "cone",
 675  * i.e., a polyhedron with "cone" as its recession cone, such that each
 676  * point x in this polyhedron is such that the unit box positioned at x
 677  * lies entirely inside the affine cone 'vec + cone'.
 678  * Any rational point in this polyhedron may therefore be rounded up
 679  * to yield an integer point that lies inside said affine cone.
 680  *
 681  * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
 682  * point "vec" by v/d.
 683  * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
 684  * by <a_i, x> - b/d >= 0.
 685  * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
 686  * We prefer this polyhedron over the actual affine cone because it doesn't
 687  * require a scaling of the constraints.
 688  * If each of the vertices of the unit cube positioned at x lies inside
 689  * this polyhedron, then the whole unit cube at x lies inside the affine cone.
 690  * We therefore impose that x' = x + \sum e_i, for any selection of unit
 691  * vectors lies inside the polyhedron, i.e.,
 692  *
 693  *      <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
 694  *
 695  * The most stringent of these constraints is the one that selects
 696  * all negative a_i, so the polyhedron we are looking for has constraints
 697  *
 698  *      <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
 699  *
 700  * Note that if cone were known to have only non-negative rays
 701  * (which can be accomplished by a unimodular transformation),
 702  * then we would only have to check the points x' = x + e_i
 703  * and we only have to add the smallest negative a_i (if any)
 704  * instead of the sum of all negative a_i.
 705  */
 706 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
 707         struct isl_vec *vec)
 708 {
 709         int i, j, k;
 710         unsigned total;
 711
 712         struct isl_basic_set *shift = NULL;
 713
 714         if (!cone || !vec)
 715                 goto error;
 716
 717         isl_assert(cone->ctx, cone->n_eq == 0, goto error);
 718
 719         total = isl_basic_set_total_dim(cone);
 720
 721         shift = isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone),
 722                                         0, 0, cone->n_ineq);
 723
 724         for (i = 0; i < cone->n_ineq; ++i) {
 725                 k = isl_basic_set_alloc_inequality(shift);
 726                 if (k < 0)
 727                         goto error;
 728                 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
 729                 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
 730                                       &shift->ineq[k][0]);
 731                 isl_int_cdiv_q(shift->ineq[k][0],
 732                                shift->ineq[k][0], vec->el[0]);
 733                 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
 734                 for (j = 0; j < total; ++j) {
 735                         if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
 736                                 continue;
 737                         isl_int_add(shift->ineq[k][0],
 738                                     shift->ineq[k][0], shift->ineq[k][1 + j]);
 739                 }
 740         }
 741
 742         isl_basic_set_free(cone);
 743         isl_vec_free(vec);
 744
 745         return isl_basic_set_finalize(shift);
 746 error:
 747         isl_basic_set_free(shift);
 748         isl_basic_set_free(cone);
 749         isl_vec_free(vec);
 750         return NULL;
 751 }
 752
 753 /* Given a rational point vec in a (transformed) basic set,
 754  * such that cone is the recession cone of the original basic set,
 755  * "round up" the rational point to an integer point.
 756  *
 757  * We first check if the rational point just happens to be integer.
 758  * If not, we transform the cone in the same way as the basic set,
 759  * pick a point x in this cone shifted to the rational point such that
 760  * the whole unit cube at x is also inside this affine cone.
 761  * Then we simply round up the coordinates of x and return the
 762  * resulting integer point.
 763  */
 764 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
 765         struct isl_basic_set *cone, struct isl_mat *U)
 766 {
 767         unsigned total;
 768
 769         if (!vec || !cone || !U)
 770                 goto error;
 771
 772         isl_assert(vec->ctx, vec->size != 0, goto error);
 773         if (isl_int_is_one(vec->el[0])) {
 774                 isl_mat_free(U);
 775                 isl_basic_set_free(cone);
 776                 return vec;
 777         }
 778
 779         total = isl_basic_set_total_dim(cone);
 780         cone = isl_basic_set_preimage(cone, U);
 781         cone = isl_basic_set_remove_dims(cone, 0, total - (vec->size - 1));
 782
 783         cone = shift_cone(cone, vec);
 784
 785         vec = rational_sample(cone);
 786         vec = isl_vec_ceil(vec);
 787         return vec;
 788 error:
 789         isl_mat_free(U);
 790         isl_vec_free(vec);
 791         isl_basic_set_free(cone);
 792         return NULL;
 793 }
 794
 795 /* Concatenate two integer vectors, i.e., two vectors with denominator
 796  * (stored in element 0) equal to 1.
 797  */
 798 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
 799 {
 800         struct isl_vec *vec;
 801
 802         if (!vec1 || !vec2)
 803                 goto error;
 804         isl_assert(vec1->ctx, vec1->size > 0, goto error);
 805         isl_assert(vec2->ctx, vec2->size > 0, goto error);
 806         isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
 807         isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
 808
 809         vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
 810         if (!vec)
 811                 goto error;
 812
 813         isl_seq_cpy(vec->el, vec1->el, vec1->size);
 814         isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
 815
 816         isl_vec_free(vec1);
 817         isl_vec_free(vec2);
 818
 819         return vec;
 820 error:
 821         isl_vec_free(vec1);
 822         isl_vec_free(vec2);
 823         return NULL;
 824 }
 825
 826 /* Drop all constraints in bset that involve any of the dimensions
 827  * first to first+n-1.
 828  */
 829 static struct isl_basic_set *drop_constraints_involving
 830         (struct isl_basic_set *bset, unsigned first, unsigned n)
 831 {
 832         int i;
 833
 834         if (!bset)
 835                 return NULL;
 836
 837         bset = isl_basic_set_cow(bset);
 838
 839         for (i = bset->n_ineq - 1; i >= 0; --i) {
 840                 if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
 841                         continue;
 842                 isl_basic_set_drop_inequality(bset, i);
 843         }
 844
 845         return bset;
 846 }
 847
 848 /* Give a basic set "bset" with recession cone "cone", compute and
 849  * return an integer point in bset, if any.
 850  *
 851  * If the recession cone is full-dimensional, then we know that
 852  * bset contains an infinite number of integer points and it is
 853  * fairly easy to pick one of them.
 854  * If the recession cone is not full-dimensional, then we first
 855  * transform bset such that the bounded directions appear as
 856  * the first dimensions of the transformed basic set.
 857  * We do this by using a unimodular transformation that transforms
 858  * the equalities in the recession cone to equalities on the first
 859  * dimensions.
 860  *
 861  * The transformed set is then projected onto its bounded dimensions.
 862  * Note that to compute this projection, we can simply drop all constraints
 863  * involving any of the unbounded dimensions since these constraints
 864  * cannot be combined to produce a constraint on the bounded dimensions.
 865  * To see this, assume that there is such a combination of constraints
 866  * that produces a constraint on the bounded dimensions.  This means
 867  * that some combination of the unbounded dimensions has both an upper
 868  * bound and a lower bound in terms of the bounded dimensions, but then
 869  * this combination would be a bounded direction too and would have been
 870  * transformed into a bounded dimensions.
 871  *
 872  * We then compute a sample value in the bounded dimensions.
 873  * If no such value can be found, then the original set did not contain
 874  * any integer points and we are done.
 875  * Otherwise, we plug in the value we found in the bounded dimensions,
 876  * project out these bounded dimensions and end up with a set with
 877  * a full-dimensional recession cone.
 878  * A sample point in this set is computed by "rounding up" any
 879  * rational point in the set.
 880  *
 881  * The sample points in the bounded and unbounded dimensions are
 882  * then combined into a single sample point and transformed back
 883  * to the original space.
 884  */
 885 __isl_give isl_vec *isl_basic_set_sample_with_cone(
 886         __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
 887 {
 888         unsigned total;
 889         unsigned cone_dim;
 890         struct isl_mat *M, *U;
 891         struct isl_vec *sample;
 892         struct isl_vec *cone_sample;
 893         struct isl_ctx *ctx;
 894         struct isl_basic_set *bounded;
 895
 896         if (!bset || !cone)
 897                 goto error;
 898
 899         ctx = bset->ctx;
 900         total = isl_basic_set_total_dim(cone);
 901         cone_dim = total - cone->n_eq;
 902
 903         M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
 904         M = isl_mat_left_hermite(M, 0, &U, NULL);
 905         if (!M)
 906                 goto error;
 907         isl_mat_free(M);
 908
 909         U = isl_mat_lin_to_aff(U);
 910         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 911
 912         bounded = isl_basic_set_copy(bset);
 913         bounded = drop_constraints_involving(bounded, total - cone_dim, cone_dim);
 914         bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
 915         sample = sample_bounded(bounded);
 916         if (!sample || sample->size == 0) {
 917                 isl_basic_set_free(bset);
 918                 isl_basic_set_free(cone);
 919                 isl_mat_free(U);
 920                 return sample;
 921         }
 922         bset = plug_in(bset, isl_vec_copy(sample));
 923         cone_sample = rational_sample(bset);
 924         cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
 925         sample = vec_concat(sample, cone_sample);
 926         sample = isl_mat_vec_product(U, sample);
 927         return sample;
 928 error:
 929         isl_basic_set_free(cone);
 930         isl_basic_set_free(bset);
 931         return NULL;
 932 }
 933
 934 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
 935 {
 936         int i;
 937
 938         isl_int_set_si(*s, 0);
 939
 940         for (i = 0; i < v->size; ++i)
 941                 if (isl_int_is_neg(v->el[i]))
 942                         isl_int_add(*s, *s, v->el[i]);
 943 }
 944
 945 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
 946  * to the recession cone and the inverse of a new basis U = inv(B),
 947  * with the unbounded directions in B last,
 948  * add constraints to "tab" that ensure any rational value
 949  * in the unbounded directions can be rounded up to an integer value.
 950  *
 951  * The new basis is given by x' = B x, i.e., x = U x'.
 952  * For any rational value of the last tab->n_unbounded coordinates
 953  * in the update tableau, the value that is obtained by rounding
 954  * up this value should be contained in the original tableau.
 955  * For any constraint "a x + c >= 0", we therefore need to add
 956  * a constraint "a x + c + s >= 0", with s the sum of all negative
 957  * entries in the last elements of "a U".
 958  *
 959  * Since we are not interested in the first entries of any of the "a U",
 960  * we first drop the columns of U that correpond to bounded directions.
 961  */
 962 static int tab_shift_cone(struct isl_tab *tab,
 963         struct isl_tab *tab_cone, struct isl_mat *U)
 964 {
 965         int i;
 966         isl_int v;
 967         struct isl_basic_set *bset = NULL;
 968
 969         if (tab && tab->n_unbounded == 0) {
 970                 isl_mat_free(U);
 971                 return 0;
 972         }
 973         isl_int_init(v);
 974         if (!tab || !tab_cone || !U)
 975                 goto error;
 976         bset = isl_tab_peek_bset(tab_cone);
 977         U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
 978         for (i = 0; i < bset->n_ineq; ++i) {
 979                 int ok;
 980                 struct isl_vec *row = NULL;
 981                 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
 982                         continue;
 983                 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
 984                 if (!row)
 985                         goto error;
 986                 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
 987                 row = isl_vec_mat_product(row, isl_mat_copy(U));
 988                 if (!row)
 989                         goto error;
 990                 vec_sum_of_neg(row, &v);
 991                 isl_vec_free(row);
 992                 if (isl_int_is_zero(v))
 993                         continue;
 994                 tab = isl_tab_extend(tab, 1);
 995                 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
 996                 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
 997                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
 998                 if (!ok)
 999                         goto error;
1000         }
1001
1002         isl_mat_free(U);
1003         isl_int_clear(v);
1004         return 0;
1005 error:
1006         isl_mat_free(U);
1007         isl_int_clear(v);
1008         return -1;
1009 }
1010
1011 /* Compute and return an initial basis for the possibly
1012  * unbounded tableau "tab".  "tab_cone" is a tableau
1013  * for the corresponding recession cone.
1014  * Additionally, add constraints to "tab" that ensure
1015  * that any rational value for the unbounded directions
1016  * can be rounded up to an integer value.
1017  *
1018  * If the tableau is bounded, i.e., if the recession cone
1019  * is zero-dimensional, then we just use inital_basis.
1020  * Otherwise, we construct a basis whose first directions
1021  * correspond to equalities, followed by bounded directions,
1022  * i.e., equalities in the recession cone.
1023  * The remaining directions are then unbounded.
1024  */
1025 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1026         struct isl_tab *tab_cone)
1027 {
1028         struct isl_mat *eq;
1029         struct isl_mat *cone_eq;
1030         struct isl_mat *U, *Q;
1031
1032         if (!tab || !tab_cone)
1033                 return -1;
1034
1035         if (tab_cone->n_col == tab_cone->n_dead) {
1036                 tab->basis = initial_basis(tab);
1037                 return tab->basis ? 0 : -1;
1038         }
1039
1040         eq = tab_equalities(tab);
1041         if (!eq)
1042                 return -1;
1043         tab->n_zero = eq->n_row;
1044         cone_eq = tab_equalities(tab_cone);
1045         eq = isl_mat_concat(eq, cone_eq);
1046         if (!eq)
1047                 return -1;
1048         tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1049         eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1050         if (!eq)
1051                 return -1;
1052         isl_mat_free(eq);
1053         tab->basis = isl_mat_lin_to_aff(Q);
1054         if (tab_shift_cone(tab, tab_cone, U) < 0)
1055                 return -1;
1056         if (!tab->basis)
1057                 return -1;
1058         return 0;
1059 }
1060
1061 /* Compute and return a sample point in bset using generalized basis
1062  * reduction.  We first check if the input set has a non-trivial
1063  * recession cone.  If so, we perform some extra preprocessing in
1064  * sample_with_cone.  Otherwise, we directly perform generalized basis
1065  * reduction.
1066  */
1067 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1068 {
1069         unsigned dim;
1070         struct isl_basic_set *cone;
1071
1072         dim = isl_basic_set_total_dim(bset);
1073
1074         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1075
1076         if (cone->n_eq < dim)
1077                 return isl_basic_set_sample_with_cone(bset, cone);
1078
1079         isl_basic_set_free(cone);
1080         return sample_bounded(bset);
1081 }
1082
1083 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
1084 {
1085         struct isl_mat *T;
1086         struct isl_ctx *ctx;
1087         struct isl_vec *sample;
1088
1089         bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
1090         if (!bset)
1091                 return NULL;
1092
1093         ctx = bset->ctx;
1094         sample = isl_pip_basic_set_sample(bset);
1095
1096         if (sample && sample->size != 0)
1097                 sample = isl_mat_vec_product(T, sample);
1098         else
1099                 isl_mat_free(T);
1100
1101         return sample;
1102 }
1103
1104 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1105 {
1106         struct isl_ctx *ctx;
1107         unsigned dim;
1108         if (!bset)
1109                 return NULL;
1110
1111         ctx = bset->ctx;
1112         if (isl_basic_set_fast_is_empty(bset))
1113                 return empty_sample(bset);
1114
1115         dim = isl_basic_set_n_dim(bset);
1116         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1117         isl_assert(ctx, bset->n_div == 0, goto error);
1118
1119         if (bset->sample && bset->sample->size == 1 + dim) {
1120                 int contains = isl_basic_set_contains(bset, bset->sample);
1121                 if (contains < 0)
1122                         goto error;
1123                 if (contains) {
1124                         struct isl_vec *sample = isl_vec_copy(bset->sample);
1125                         isl_basic_set_free(bset);
1126                         return sample;
1127                 }
1128         }
1129         isl_vec_free(bset->sample);
1130         bset->sample = NULL;
1131
1132         if (bset->n_eq > 0)
1133                 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1134                                                : isl_basic_set_sample_vec);
1135         if (dim == 0)
1136                 return zero_sample(bset);
1137         if (dim == 1)
1138                 return interval_sample(bset);
1139
1140         switch (bset->ctx->opt->ilp_solver) {
1141         case ISL_ILP_PIP:
1142                 return pip_sample(bset);
1143         case ISL_ILP_GBR:
1144                 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1145         }
1146         isl_assert(bset->ctx, 0, );
1147 error:
1148         isl_basic_set_free(bset);
1149         return NULL;
1150 }
1151
1152 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1153 {
1154         return basic_set_sample(bset, 0);
1155 }
1156
1157 /* Compute an integer sample in "bset", where the caller guarantees
1158  * that "bset" is bounded.
1159  */
1160 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1161 {
1162         return basic_set_sample(bset, 1);
1163 }
1164
1165 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1166 {
1167         int i;
1168         int k;
1169         struct isl_basic_set *bset = NULL;
1170         struct isl_ctx *ctx;
1171         unsigned dim;
1172
1173         if (!vec)
1174                 return NULL;
1175         ctx = vec->ctx;
1176         isl_assert(ctx, vec->size != 0, goto error);
1177
1178         bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1179         if (!bset)
1180                 goto error;
1181         dim = isl_basic_set_n_dim(bset);
1182         for (i = dim - 1; i >= 0; --i) {
1183                 k = isl_basic_set_alloc_equality(bset);
1184                 if (k < 0)
1185                         goto error;
1186                 isl_seq_clr(bset->eq[k], 1 + dim);
1187                 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1188                 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1189         }
1190         bset->sample = vec;
1191
1192         return bset;
1193 error:
1194         isl_basic_set_free(bset);
1195         isl_vec_free(vec);
1196         return NULL;
1197 }
1198
1199 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1200 {
1201         struct isl_basic_set *bset;
1202         struct isl_vec *sample_vec;
1203
1204         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1205         sample_vec = isl_basic_set_sample_vec(bset);
1206         if (!sample_vec)
1207                 goto error;
1208         if (sample_vec->size == 0) {
1209                 struct isl_basic_map *sample;
1210                 sample = isl_basic_map_empty_like(bmap);
1211                 isl_vec_free(sample_vec);
1212                 isl_basic_map_free(bmap);
1213                 return sample;
1214         }
1215         bset = isl_basic_set_from_vec(sample_vec);
1216         return isl_basic_map_overlying_set(bset, bmap);
1217 error:
1218         isl_basic_map_free(bmap);
1219         return NULL;
1220 }
1221
1222 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1223 {
1224         int i;
1225         isl_basic_map *sample = NULL;
1226
1227         if (!map)
1228                 goto error;
1229
1230         for (i = 0; i < map->n; ++i) {
1231                 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1232                 if (!sample)
1233                         goto error;
1234                 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1235                         break;
1236                 isl_basic_map_free(sample);
1237         }
1238         if (i == map->n)
1239                 sample = isl_basic_map_empty_like_map(map);
1240         isl_map_free(map);
1241         return sample;
1242 error:
1243         isl_map_free(map);
1244         return NULL;
1245 }
1246
1247 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1248 {
1249         return (isl_basic_set *) isl_map_sample((isl_map *)set);
1250 }
1251
1252 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1253 {
1254         isl_vec *vec;
1255         isl_dim *dim;
1256
1257         dim = isl_basic_set_get_dim(bset);
1258         bset = isl_basic_set_underlying_set(bset);
1259         vec = isl_basic_set_sample_vec(bset);
1260
1261         return isl_point_alloc(dim, vec);
1262 }
1263
1264 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1265 {
1266         int i;
1267         isl_point *pnt;
1268
1269         if (!set)
1270                 return NULL;
1271
1272         for (i = 0; i < set->n; ++i) {
1273                 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1274                 if (!pnt)
1275                         goto error;
1276                 if (!isl_point_is_void(pnt))
1277                         break;
1278                 isl_point_free(pnt);
1279         }
1280         if (i == set->n)
1281                 pnt = isl_point_void(isl_set_get_dim(set));
1282
1283         isl_set_free(set);
1284         return pnt;
1285 error:
1286         isl_set_free(set);
1287         return NULL;
1288 }