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_ctx_private.h>
  11 #include <isl_map_private.h>
  12 #include "isl_sample.h"
  13 #include "isl_sample_piplib.h"
  14 #include <isl/vec.h>
  15 #include <isl/mat.h>
  16 #include <isl/seq.h>
  17 #include "isl_equalities.h"
  18 #include "isl_tab.h"
  19 #include "isl_basis_reduction.h"
  20 #include <isl_factorization.h>
  21 #include <isl_point_private.h>
  22
  23 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
  24 {
  25         struct isl_vec *vec;
  26
  27         vec = isl_vec_alloc(bset->ctx, 0);
  28         isl_basic_set_free(bset);
  29         return vec;
  30 }
  31
  32 /* Construct a zero sample of the same dimension as bset.
  33  * As a special case, if bset is zero-dimensional, this
  34  * function creates a zero-dimensional sample point.
  35  */
  36 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
  37 {
  38         unsigned dim;
  39         struct isl_vec *sample;
  40
  41         dim = isl_basic_set_total_dim(bset);
  42         sample = isl_vec_alloc(bset->ctx, 1 + dim);
  43         if (sample) {
  44                 isl_int_set_si(sample->el[0], 1);
  45                 isl_seq_clr(sample->el + 1, dim);
  46         }
  47         isl_basic_set_free(bset);
  48         return sample;
  49 }
  50
  51 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
  52 {
  53         int i;
  54         isl_int t;
  55         struct isl_vec *sample;
  56
  57         bset = isl_basic_set_simplify(bset);
  58         if (!bset)
  59                 return NULL;
  60         if (isl_basic_set_plain_is_empty(bset))
  61                 return empty_sample(bset);
  62         if (bset->n_eq == 0 && bset->n_ineq == 0)
  63                 return zero_sample(bset);
  64
  65         sample = isl_vec_alloc(bset->ctx, 2);
  66         if (!sample)
  67                 goto error;
  68         if (!bset)
  69                 return NULL;
  70         isl_int_set_si(sample->block.data[0], 1);
  71
  72         if (bset->n_eq > 0) {
  73                 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
  74                 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
  75                 if (isl_int_is_one(bset->eq[0][1]))
  76                         isl_int_neg(sample->el[1], bset->eq[0][0]);
  77                 else {
  78                         isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
  79                                    goto error);
  80                         isl_int_set(sample->el[1], bset->eq[0][0]);
  81                 }
  82                 isl_basic_set_free(bset);
  83                 return sample;
  84         }
  85
  86         isl_int_init(t);
  87         if (isl_int_is_one(bset->ineq[0][1]))
  88                 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
  89         else
  90                 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
  91         for (i = 1; i < bset->n_ineq; ++i) {
  92                 isl_seq_inner_product(sample->block.data,
  93                                         bset->ineq[i], 2, &t);
  94                 if (isl_int_is_neg(t))
  95                         break;
  96         }
  97         isl_int_clear(t);
  98         if (i < bset->n_ineq) {
  99                 isl_vec_free(sample);
 100                 return empty_sample(bset);
 101         }
 102
 103         isl_basic_set_free(bset);
 104         return sample;
 105 error:
 106         isl_basic_set_free(bset);
 107         isl_vec_free(sample);
 108         return NULL;
 109 }
 110
 111 static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
 112 {
 113         int i, j, n;
 114         struct isl_mat *dirs = NULL;
 115         struct isl_mat *bounds = NULL;
 116         unsigned dim;
 117
 118         if (!bset)
 119                 return NULL;
 120
 121         dim = isl_basic_set_n_dim(bset);
 122         bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
 123         if (!bounds)
 124                 return NULL;
 125
 126         isl_int_set_si(bounds->row[0][0], 1);
 127         isl_seq_clr(bounds->row[0]+1, dim);
 128         bounds->n_row = 1;
 129
 130         if (bset->n_ineq == 0)
 131                 return bounds;
 132
 133         dirs = isl_mat_alloc(bset->ctx, dim, dim);
 134         if (!dirs) {
 135                 isl_mat_free(bounds);
 136                 return NULL;
 137         }
 138         isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
 139         isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
 140         for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
 141                 int pos;
 142
 143                 isl_seq_cpy(dirs->row[n], bset->ineq[j]+1, dirs->n_col);
 144
 145                 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
 146                 if (pos < 0)
 147                         continue;
 148                 for (i = 0; i < n; ++i) {
 149                         int pos_i;
 150                         pos_i = isl_seq_first_non_zero(dirs->row[i], dirs->n_col);
 151                         if (pos_i < pos)
 152                                 continue;
 153                         if (pos_i > pos)
 154                                 break;
 155                         isl_seq_elim(dirs->row[n], dirs->row[i], pos,
 156                                         dirs->n_col, NULL);
 157                         pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
 158                         if (pos < 0)
 159                                 break;
 160                 }
 161                 if (pos < 0)
 162                         continue;
 163                 if (i < n) {
 164                         int k;
 165                         isl_int *t = dirs->row[n];
 166                         for (k = n; k > i; --k)
 167                                 dirs->row[k] = dirs->row[k-1];
 168                         dirs->row[i] = t;
 169                 }
 170                 ++n;
 171                 isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
 172         }
 173         isl_mat_free(dirs);
 174         bounds->n_row = 1+n;
 175         return bounds;
 176 }
 177
 178 static void swap_inequality(struct isl_basic_set *bset, int a, int b)
 179 {
 180         isl_int *t = bset->ineq[a];
 181         bset->ineq[a] = bset->ineq[b];
 182         bset->ineq[b] = t;
 183 }
 184
 185 /* Skew into positive orthant and project out lineality space.
 186  *
 187  * We perform a unimodular transformation that turns a selected
 188  * maximal set of linearly independent bounds into constraints
 189  * on the first dimensions that impose that these first dimensions
 190  * are non-negative.  In particular, the constraint matrix is lower
 191  * triangular with positive entries on the diagonal and negative
 192  * entries below.
 193  * If "bset" has a lineality space then these constraints (and therefore
 194  * all constraints in bset) only involve the first dimensions.
 195  * The remaining dimensions then do not appear in any constraints and
 196  * we can select any value for them, say zero.  We therefore project
 197  * out this final dimensions and plug in the value zero later.  This
 198  * is accomplished by simply dropping the final columns of
 199  * the unimodular transformation.
 200  */
 201 static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
 202         struct isl_basic_set *bset, struct isl_mat **T)
 203 {
 204         struct isl_mat *U = NULL;
 205         struct isl_mat *bounds = NULL;
 206         int i, j;
 207         unsigned old_dim, new_dim;
 208
 209         *T = NULL;
 210         if (!bset)
 211                 return NULL;
 212
 213         isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
 214         isl_assert(bset->ctx, bset->n_div == 0, goto error);
 215         isl_assert(bset->ctx, bset->n_eq == 0, goto error);
 216
 217         old_dim = isl_basic_set_n_dim(bset);
 218         /* Try to move (multiples of) unit rows up. */
 219         for (i = 0, j = 0; i < bset->n_ineq; ++i) {
 220                 int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
 221                 if (pos < 0)
 222                         continue;
 223                 if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
 224                                                 old_dim-pos-1) >= 0)
 225                         continue;
 226                 if (i != j)
 227                         swap_inequality(bset, i, j);
 228                 ++j;
 229         }
 230         bounds = independent_bounds(bset);
 231         if (!bounds)
 232                 goto error;
 233         new_dim = bounds->n_row - 1;
 234         bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
 235         if (!bounds)
 236                 goto error;
 237         U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
 238         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 239         if (!bset)
 240                 goto error;
 241         *T = U;
 242         isl_mat_free(bounds);
 243         return bset;
 244 error:
 245         isl_mat_free(bounds);
 246         isl_mat_free(U);
 247         isl_basic_set_free(bset);
 248         return NULL;
 249 }
 250
 251 /* Find a sample integer point, if any, in bset, which is known
 252  * to have equalities.  If bset contains no integer points, then
 253  * return a zero-length vector.
 254  * We simply remove the known equalities, compute a sample
 255  * in the resulting bset, using the specified recurse function,
 256  * and then transform the sample back to the original space.
 257  */
 258 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
 259         struct isl_vec *(*recurse)(struct isl_basic_set *))
 260 {
 261         struct isl_mat *T;
 262         struct isl_vec *sample;
 263
 264         if (!bset)
 265                 return NULL;
 266
 267         bset = isl_basic_set_remove_equalities(bset, &T, NULL);
 268         sample = recurse(bset);
 269         if (!sample || sample->size == 0)
 270                 isl_mat_free(T);
 271         else
 272                 sample = isl_mat_vec_product(T, sample);
 273         return sample;
 274 }
 275
 276 /* Return a matrix containing the equalities of the tableau
 277  * in constraint form.  The tableau is assumed to have
 278  * an associated bset that has been kept up-to-date.
 279  */
 280 static struct isl_mat *tab_equalities(struct isl_tab *tab)
 281 {
 282         int i, j;
 283         int n_eq;
 284         struct isl_mat *eq;
 285         struct isl_basic_set *bset;
 286
 287         if (!tab)
 288                 return NULL;
 289
 290         bset = isl_tab_peek_bset(tab);
 291         isl_assert(tab->mat->ctx, bset, return NULL);
 292
 293         n_eq = tab->n_var - tab->n_col + tab->n_dead;
 294         if (tab->empty || n_eq == 0)
 295                 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
 296         if (n_eq == tab->n_var)
 297                 return isl_mat_identity(tab->mat->ctx, tab->n_var);
 298
 299         eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
 300         if (!eq)
 301                 return NULL;
 302         for (i = 0, j = 0; i < tab->n_con; ++i) {
 303                 if (tab->con[i].is_row)
 304                         continue;
 305                 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
 306                         continue;
 307                 if (i < bset->n_eq)
 308                         isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
 309                 else
 310                         isl_seq_cpy(eq->row[j],
 311                                     bset->ineq[i - bset->n_eq] + 1, tab->n_var);
 312                 ++j;
 313         }
 314         isl_assert(bset->ctx, j == n_eq, goto error);
 315         return eq;
 316 error:
 317         isl_mat_free(eq);
 318         return NULL;
 319 }
 320
 321 /* Compute and return an initial basis for the bounded tableau "tab".
 322  *
 323  * If the tableau is either full-dimensional or zero-dimensional,
 324  * the we simply return an identity matrix.
 325  * Otherwise, we construct a basis whose first directions correspond
 326  * to equalities.
 327  */
 328 static struct isl_mat *initial_basis(struct isl_tab *tab)
 329 {
 330         int n_eq;
 331         struct isl_mat *eq;
 332         struct isl_mat *Q;
 333
 334         tab->n_unbounded = 0;
 335         tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
 336         if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
 337                 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
 338
 339         eq = tab_equalities(tab);
 340         eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
 341         if (!eq)
 342                 return NULL;
 343         isl_mat_free(eq);
 344
 345         Q = isl_mat_lin_to_aff(Q);
 346         return Q;
 347 }
 348
 349 /* Given a tableau representing a set, find and return
 350  * an integer point in the set, if there is any.
 351  *
 352  * We perform a depth first search
 353  * for an integer point, by scanning all possible values in the range
 354  * attained by a basis vector, where an initial basis may have been set
 355  * by the calling function.  Otherwise an initial basis that exploits
 356  * the equalities in the tableau is created.
 357  * tab->n_zero is currently ignored and is clobbered by this function.
 358  *
 359  * The tableau is allowed to have unbounded direction, but then
 360  * the calling function needs to set an initial basis, with the
 361  * unbounded directions last and with tab->n_unbounded set
 362  * to the number of unbounded directions.
 363  * Furthermore, the calling functions needs to add shifted copies
 364  * of all constraints involving unbounded directions to ensure
 365  * that any feasible rational value in these directions can be rounded
 366  * up to yield a feasible integer value.
 367  * In particular, let B define the given basis x' = B x
 368  * and let T be the inverse of B, i.e., X = T x'.
 369  * Let a x + c >= 0 be a constraint of the set represented by the tableau,
 370  * or a T x' + c >= 0 in terms of the given basis.  Assume that
 371  * the bounded directions have an integer value, then we can safely
 372  * round up the values for the unbounded directions if we make sure
 373  * that x' not only satisfies the original constraint, but also
 374  * the constraint "a T x' + c + s >= 0" with s the sum of all
 375  * negative values in the last n_unbounded entries of "a T".
 376  * The calling function therefore needs to add the constraint
 377  * a x + c + s >= 0.  The current function then scans the first
 378  * directions for an integer value and once those have been found,
 379  * it can compute "T ceil(B x)" to yield an integer point in the set.
 380  * Note that during the search, the first rows of B may be changed
 381  * by a basis reduction, but the last n_unbounded rows of B remain
 382  * unaltered and are also not mixed into the first rows.
 383  *
 384  * The search is implemented iteratively.  "level" identifies the current
 385  * basis vector.  "init" is true if we want the first value at the current
 386  * level and false if we want the next value.
 387  *
 388  * The initial basis is the identity matrix.  If the range in some direction
 389  * contains more than one integer value, we perform basis reduction based
 390  * on the value of ctx->opt->gbr
 391  *      - ISL_GBR_NEVER:        never perform basis reduction
 392  *      - ISL_GBR_ONCE:         only perform basis reduction the first
 393  *                              time such a range is encountered
 394  *      - ISL_GBR_ALWAYS:       always perform basis reduction when
 395  *                              such a range is encountered
 396  *
 397  * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
 398  * reduction computation to return early.  That is, as soon as it
 399  * finds a reasonable first direction.
 400  */
 401 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
 402 {
 403         unsigned dim;
 404         unsigned gbr;
 405         struct isl_ctx *ctx;
 406         struct isl_vec *sample;
 407         struct isl_vec *min;
 408         struct isl_vec *max;
 409         enum isl_lp_result res;
 410         int level;
 411         int init;
 412         int reduced;
 413         struct isl_tab_undo **snap;
 414
 415         if (!tab)
 416                 return NULL;
 417         if (tab->empty)
 418                 return isl_vec_alloc(tab->mat->ctx, 0);
 419
 420         if (!tab->basis)
 421                 tab->basis = initial_basis(tab);
 422         if (!tab->basis)
 423                 return NULL;
 424         isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
 425                     return NULL);
 426         isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
 427                     return NULL);
 428
 429         ctx = tab->mat->ctx;
 430         dim = tab->n_var;
 431         gbr = ctx->opt->gbr;
 432
 433         if (tab->n_unbounded == tab->n_var) {
 434                 sample = isl_tab_get_sample_value(tab);
 435                 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
 436                 sample = isl_vec_ceil(sample);
 437                 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
 438                                                         sample);
 439                 return sample;
 440         }
 441
 442         if (isl_tab_extend_cons(tab, dim + 1) < 0)
 443                 return NULL;
 444
 445         min = isl_vec_alloc(ctx, dim);
 446         max = isl_vec_alloc(ctx, dim);
 447         snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
 448
 449         if (!min || !max || !snap)
 450                 goto error;
 451
 452         level = 0;
 453         init = 1;
 454         reduced = 0;
 455
 456         while (level >= 0) {
 457                 int empty = 0;
 458                 if (init) {
 459                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 460                                     ctx->one, &min->el[level], NULL, 0);
 461                         if (res == isl_lp_empty)
 462                                 empty = 1;
 463                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 464                         if (res == isl_lp_error)
 465                                 goto error;
 466                         if (!empty && isl_tab_sample_is_integer(tab))
 467                                 break;
 468                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 469                                     tab->basis->row[1 + level] + 1, dim);
 470                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 471                                     ctx->one, &max->el[level], NULL, 0);
 472                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 473                                     tab->basis->row[1 + level] + 1, dim);
 474                         isl_int_neg(max->el[level], max->el[level]);
 475                         if (res == isl_lp_empty)
 476                                 empty = 1;
 477                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 478                         if (res == isl_lp_error)
 479                                 goto error;
 480                         if (!empty && isl_tab_sample_is_integer(tab))
 481                                 break;
 482                         if (!empty && !reduced &&
 483                             ctx->opt->gbr != ISL_GBR_NEVER &&
 484                             isl_int_lt(min->el[level], max->el[level])) {
 485                                 unsigned gbr_only_first;
 486                                 if (ctx->opt->gbr == ISL_GBR_ONCE)
 487                                         ctx->opt->gbr = ISL_GBR_NEVER;
 488                                 tab->n_zero = level;
 489                                 gbr_only_first = ctx->opt->gbr_only_first;
 490                                 ctx->opt->gbr_only_first =
 491                                         ctx->opt->gbr == ISL_GBR_ALWAYS;
 492                                 tab = isl_tab_compute_reduced_basis(tab);
 493                                 ctx->opt->gbr_only_first = gbr_only_first;
 494                                 if (!tab || !tab->basis)
 495                                         goto error;
 496                                 reduced = 1;
 497                                 continue;
 498                         }
 499                         reduced = 0;
 500                         snap[level] = isl_tab_snap(tab);
 501                 } else
 502                         isl_int_add_ui(min->el[level], min->el[level], 1);
 503
 504                 if (empty || isl_int_gt(min->el[level], max->el[level])) {
 505                         level--;
 506                         init = 0;
 507                         if (level >= 0)
 508                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 509                                         goto error;
 510                         continue;
 511                 }
 512                 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
 513                 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
 514                         goto error;
 515                 isl_int_set_si(tab->basis->row[1 + level][0], 0);
 516                 if (level + tab->n_unbounded < dim - 1) {
 517                         ++level;
 518                         init = 1;
 519                         continue;
 520                 }
 521                 break;
 522         }
 523
 524         if (level >= 0) {
 525                 sample = isl_tab_get_sample_value(tab);
 526                 if (!sample)
 527                         goto error;
 528                 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
 529                         sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
 530                                                      sample);
 531                         sample = isl_vec_ceil(sample);
 532                         sample = isl_mat_vec_inverse_product(
 533                                         isl_mat_copy(tab->basis), sample);
 534                 }
 535         } else
 536                 sample = isl_vec_alloc(ctx, 0);
 537
 538         ctx->opt->gbr = gbr;
 539         isl_vec_free(min);
 540         isl_vec_free(max);
 541         free(snap);
 542         return sample;
 543 error:
 544         ctx->opt->gbr = gbr;
 545         isl_vec_free(min);
 546         isl_vec_free(max);
 547         free(snap);
 548         return NULL;
 549 }
 550
 551 static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
 552
 553 /* Compute a sample point of the given basic set, based on the given,
 554  * non-trivial factorization.
 555  */
 556 static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
 557         __isl_take isl_factorizer *f)
 558 {
 559         int i, n;
 560         isl_vec *sample = NULL;
 561         isl_ctx *ctx;
 562         unsigned nparam;
 563         unsigned nvar;
 564
 565         ctx = isl_basic_set_get_ctx(bset);
 566         if (!ctx)
 567                 goto error;
 568
 569         nparam = isl_basic_set_dim(bset, isl_dim_param);
 570         nvar = isl_basic_set_dim(bset, isl_dim_set);
 571
 572         sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
 573         if (!sample)
 574                 goto error;
 575         isl_int_set_si(sample->el[0], 1);
 576
 577         bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
 578
 579         for (i = 0, n = 0; i < f->n_group; ++i) {
 580                 isl_basic_set *bset_i;
 581                 isl_vec *sample_i;
 582
 583                 bset_i = isl_basic_set_copy(bset);
 584                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
 585                             nparam + n + f->len[i], nvar - n - f->len[i]);
 586                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
 587                             nparam, n);
 588                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
 589                             n + f->len[i], nvar - n - f->len[i]);
 590                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
 591
 592                 sample_i = sample_bounded(bset_i);
 593                 if (!sample_i)
 594                         goto error;
 595                 if (sample_i->size == 0) {
 596                         isl_basic_set_free(bset);
 597                         isl_factorizer_free(f);
 598                         isl_vec_free(sample);
 599                         return sample_i;
 600                 }
 601                 isl_seq_cpy(sample->el + 1 + nparam + n,
 602                             sample_i->el + 1, f->len[i]);
 603                 isl_vec_free(sample_i);
 604
 605                 n += f->len[i];
 606         }
 607
 608         f->morph = isl_morph_inverse(f->morph);
 609         sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
 610
 611         isl_basic_set_free(bset);
 612         isl_factorizer_free(f);
 613         return sample;
 614 error:
 615         isl_basic_set_free(bset);
 616         isl_factorizer_free(f);
 617         isl_vec_free(sample);
 618         return NULL;
 619 }
 620
 621 /* Given a basic set that is known to be bounded, find and return
 622  * an integer point in the basic set, if there is any.
 623  *
 624  * After handling some trivial cases, we construct a tableau
 625  * and then use isl_tab_sample to find a sample, passing it
 626  * the identity matrix as initial basis.
 627  */
 628 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
 629 {
 630         unsigned dim;
 631         struct isl_ctx *ctx;
 632         struct isl_vec *sample;
 633         struct isl_tab *tab = NULL;
 634         isl_factorizer *f;
 635
 636         if (!bset)
 637                 return NULL;
 638
 639         if (isl_basic_set_plain_is_empty(bset))
 640                 return empty_sample(bset);
 641
 642         dim = isl_basic_set_total_dim(bset);
 643         if (dim == 0)
 644                 return zero_sample(bset);
 645         if (dim == 1)
 646                 return interval_sample(bset);
 647         if (bset->n_eq > 0)
 648                 return sample_eq(bset, sample_bounded);
 649
 650         f = isl_basic_set_factorizer(bset);
 651         if (!f)
 652                 goto error;
 653         if (f->n_group != 0)
 654                 return factored_sample(bset, f);
 655         isl_factorizer_free(f);
 656
 657         ctx = bset->ctx;
 658
 659         tab = isl_tab_from_basic_set(bset);
 660         if (tab && tab->empty) {
 661                 isl_tab_free(tab);
 662                 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
 663                 sample = isl_vec_alloc(bset->ctx, 0);
 664                 isl_basic_set_free(bset);
 665                 return sample;
 666         }
 667
 668         if (isl_tab_track_bset(tab, isl_basic_set_copy(bset)) < 0)
 669                 goto error;
 670         if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
 671                 if (isl_tab_detect_implicit_equalities(tab) < 0)
 672                         goto error;
 673
 674         sample = isl_tab_sample(tab);
 675         if (!sample)
 676                 goto error;
 677
 678         if (sample->size > 0) {
 679                 isl_vec_free(bset->sample);
 680                 bset->sample = isl_vec_copy(sample);
 681         }
 682
 683         isl_basic_set_free(bset);
 684         isl_tab_free(tab);
 685         return sample;
 686 error:
 687         isl_basic_set_free(bset);
 688         isl_tab_free(tab);
 689         return NULL;
 690 }
 691
 692 /* Given a basic set "bset" and a value "sample" for the first coordinates
 693  * of bset, plug in these values and drop the corresponding coordinates.
 694  *
 695  * We do this by computing the preimage of the transformation
 696  *
 697  *           [ 1 0 ]
 698  *      x =  [ s 0 ] x'
 699  *           [ 0 I ]
 700  *
 701  * where [1 s] is the sample value and I is the identity matrix of the
 702  * appropriate dimension.
 703  */
 704 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
 705         struct isl_vec *sample)
 706 {
 707         int i;
 708         unsigned total;
 709         struct isl_mat *T;
 710
 711         if (!bset || !sample)
 712                 goto error;
 713
 714         total = isl_basic_set_total_dim(bset);
 715         T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
 716         if (!T)
 717                 goto error;
 718
 719         for (i = 0; i < sample->size; ++i) {
 720                 isl_int_set(T->row[i][0], sample->el[i]);
 721                 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
 722         }
 723         for (i = 0; i < T->n_col - 1; ++i) {
 724                 isl_seq_clr(T->row[sample->size + i], T->n_col);
 725                 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
 726         }
 727         isl_vec_free(sample);
 728
 729         bset = isl_basic_set_preimage(bset, T);
 730         return bset;
 731 error:
 732         isl_basic_set_free(bset);
 733         isl_vec_free(sample);
 734         return NULL;
 735 }
 736
 737 /* Given a basic set "bset", return any (possibly non-integer) point
 738  * in the basic set.
 739  */
 740 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
 741 {
 742         struct isl_tab *tab;
 743         struct isl_vec *sample;
 744
 745         if (!bset)
 746                 return NULL;
 747
 748         tab = isl_tab_from_basic_set(bset);
 749         sample = isl_tab_get_sample_value(tab);
 750         isl_tab_free(tab);
 751
 752         isl_basic_set_free(bset);
 753
 754         return sample;
 755 }
 756
 757 /* Given a linear cone "cone" and a rational point "vec",
 758  * construct a polyhedron with shifted copies of the constraints in "cone",
 759  * i.e., a polyhedron with "cone" as its recession cone, such that each
 760  * point x in this polyhedron is such that the unit box positioned at x
 761  * lies entirely inside the affine cone 'vec + cone'.
 762  * Any rational point in this polyhedron may therefore be rounded up
 763  * to yield an integer point that lies inside said affine cone.
 764  *
 765  * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
 766  * point "vec" by v/d.
 767  * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
 768  * by <a_i, x> - b/d >= 0.
 769  * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
 770  * We prefer this polyhedron over the actual affine cone because it doesn't
 771  * require a scaling of the constraints.
 772  * If each of the vertices of the unit cube positioned at x lies inside
 773  * this polyhedron, then the whole unit cube at x lies inside the affine cone.
 774  * We therefore impose that x' = x + \sum e_i, for any selection of unit
 775  * vectors lies inside the polyhedron, i.e.,
 776  *
 777  *      <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
 778  *
 779  * The most stringent of these constraints is the one that selects
 780  * all negative a_i, so the polyhedron we are looking for has constraints
 781  *
 782  *      <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
 783  *
 784  * Note that if cone were known to have only non-negative rays
 785  * (which can be accomplished by a unimodular transformation),
 786  * then we would only have to check the points x' = x + e_i
 787  * and we only have to add the smallest negative a_i (if any)
 788  * instead of the sum of all negative a_i.
 789  */
 790 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
 791         struct isl_vec *vec)
 792 {
 793         int i, j, k;
 794         unsigned total;
 795
 796         struct isl_basic_set *shift = NULL;
 797
 798         if (!cone || !vec)
 799                 goto error;
 800
 801         isl_assert(cone->ctx, cone->n_eq == 0, goto error);
 802
 803         total = isl_basic_set_total_dim(cone);
 804
 805         shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
 806                                         0, 0, cone->n_ineq);
 807
 808         for (i = 0; i < cone->n_ineq; ++i) {
 809                 k = isl_basic_set_alloc_inequality(shift);
 810                 if (k < 0)
 811                         goto error;
 812                 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
 813                 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
 814                                       &shift->ineq[k][0]);
 815                 isl_int_cdiv_q(shift->ineq[k][0],
 816                                shift->ineq[k][0], vec->el[0]);
 817                 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
 818                 for (j = 0; j < total; ++j) {
 819                         if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
 820                                 continue;
 821                         isl_int_add(shift->ineq[k][0],
 822                                     shift->ineq[k][0], shift->ineq[k][1 + j]);
 823                 }
 824         }
 825
 826         isl_basic_set_free(cone);
 827         isl_vec_free(vec);
 828
 829         return isl_basic_set_finalize(shift);
 830 error:
 831         isl_basic_set_free(shift);
 832         isl_basic_set_free(cone);
 833         isl_vec_free(vec);
 834         return NULL;
 835 }
 836
 837 /* Given a rational point vec in a (transformed) basic set,
 838  * such that cone is the recession cone of the original basic set,
 839  * "round up" the rational point to an integer point.
 840  *
 841  * We first check if the rational point just happens to be integer.
 842  * If not, we transform the cone in the same way as the basic set,
 843  * pick a point x in this cone shifted to the rational point such that
 844  * the whole unit cube at x is also inside this affine cone.
 845  * Then we simply round up the coordinates of x and return the
 846  * resulting integer point.
 847  */
 848 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
 849         struct isl_basic_set *cone, struct isl_mat *U)
 850 {
 851         unsigned total;
 852
 853         if (!vec || !cone || !U)
 854                 goto error;
 855
 856         isl_assert(vec->ctx, vec->size != 0, goto error);
 857         if (isl_int_is_one(vec->el[0])) {
 858                 isl_mat_free(U);
 859                 isl_basic_set_free(cone);
 860                 return vec;
 861         }
 862
 863         total = isl_basic_set_total_dim(cone);
 864         cone = isl_basic_set_preimage(cone, U);
 865         cone = isl_basic_set_remove_dims(cone, isl_dim_set,
 866                                          0, total - (vec->size - 1));
 867
 868         cone = shift_cone(cone, vec);
 869
 870         vec = rational_sample(cone);
 871         vec = isl_vec_ceil(vec);
 872         return vec;
 873 error:
 874         isl_mat_free(U);
 875         isl_vec_free(vec);
 876         isl_basic_set_free(cone);
 877         return NULL;
 878 }
 879
 880 /* Concatenate two integer vectors, i.e., two vectors with denominator
 881  * (stored in element 0) equal to 1.
 882  */
 883 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
 884 {
 885         struct isl_vec *vec;
 886
 887         if (!vec1 || !vec2)
 888                 goto error;
 889         isl_assert(vec1->ctx, vec1->size > 0, goto error);
 890         isl_assert(vec2->ctx, vec2->size > 0, goto error);
 891         isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
 892         isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
 893
 894         vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
 895         if (!vec)
 896                 goto error;
 897
 898         isl_seq_cpy(vec->el, vec1->el, vec1->size);
 899         isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
 900
 901         isl_vec_free(vec1);
 902         isl_vec_free(vec2);
 903
 904         return vec;
 905 error:
 906         isl_vec_free(vec1);
 907         isl_vec_free(vec2);
 908         return NULL;
 909 }
 910
 911 /* Give a basic set "bset" with recession cone "cone", compute and
 912  * return an integer point in bset, if any.
 913  *
 914  * If the recession cone is full-dimensional, then we know that
 915  * bset contains an infinite number of integer points and it is
 916  * fairly easy to pick one of them.
 917  * If the recession cone is not full-dimensional, then we first
 918  * transform bset such that the bounded directions appear as
 919  * the first dimensions of the transformed basic set.
 920  * We do this by using a unimodular transformation that transforms
 921  * the equalities in the recession cone to equalities on the first
 922  * dimensions.
 923  *
 924  * The transformed set is then projected onto its bounded dimensions.
 925  * Note that to compute this projection, we can simply drop all constraints
 926  * involving any of the unbounded dimensions since these constraints
 927  * cannot be combined to produce a constraint on the bounded dimensions.
 928  * To see this, assume that there is such a combination of constraints
 929  * that produces a constraint on the bounded dimensions.  This means
 930  * that some combination of the unbounded dimensions has both an upper
 931  * bound and a lower bound in terms of the bounded dimensions, but then
 932  * this combination would be a bounded direction too and would have been
 933  * transformed into a bounded dimensions.
 934  *
 935  * We then compute a sample value in the bounded dimensions.
 936  * If no such value can be found, then the original set did not contain
 937  * any integer points and we are done.
 938  * Otherwise, we plug in the value we found in the bounded dimensions,
 939  * project out these bounded dimensions and end up with a set with
 940  * a full-dimensional recession cone.
 941  * A sample point in this set is computed by "rounding up" any
 942  * rational point in the set.
 943  *
 944  * The sample points in the bounded and unbounded dimensions are
 945  * then combined into a single sample point and transformed back
 946  * to the original space.
 947  */
 948 __isl_give isl_vec *isl_basic_set_sample_with_cone(
 949         __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
 950 {
 951         unsigned total;
 952         unsigned cone_dim;
 953         struct isl_mat *M, *U;
 954         struct isl_vec *sample;
 955         struct isl_vec *cone_sample;
 956         struct isl_ctx *ctx;
 957         struct isl_basic_set *bounded;
 958
 959         if (!bset || !cone)
 960                 goto error;
 961
 962         ctx = bset->ctx;
 963         total = isl_basic_set_total_dim(cone);
 964         cone_dim = total - cone->n_eq;
 965
 966         M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
 967         M = isl_mat_left_hermite(M, 0, &U, NULL);
 968         if (!M)
 969                 goto error;
 970         isl_mat_free(M);
 971
 972         U = isl_mat_lin_to_aff(U);
 973         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 974
 975         bounded = isl_basic_set_copy(bset);
 976         bounded = isl_basic_set_drop_constraints_involving(bounded,
 977                                                    total - cone_dim, cone_dim);
 978         bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
 979         sample = sample_bounded(bounded);
 980         if (!sample || sample->size == 0) {
 981                 isl_basic_set_free(bset);
 982                 isl_basic_set_free(cone);
 983                 isl_mat_free(U);
 984                 return sample;
 985         }
 986         bset = plug_in(bset, isl_vec_copy(sample));
 987         cone_sample = rational_sample(bset);
 988         cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
 989         sample = vec_concat(sample, cone_sample);
 990         sample = isl_mat_vec_product(U, sample);
 991         return sample;
 992 error:
 993         isl_basic_set_free(cone);
 994         isl_basic_set_free(bset);
 995         return NULL;
 996 }
 997
 998 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
 999 {
1000         int i;
1001
1002         isl_int_set_si(*s, 0);
1003
1004         for (i = 0; i < v->size; ++i)
1005                 if (isl_int_is_neg(v->el[i]))
1006                         isl_int_add(*s, *s, v->el[i]);
1007 }
1008
1009 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
1010  * to the recession cone and the inverse of a new basis U = inv(B),
1011  * with the unbounded directions in B last,
1012  * add constraints to "tab" that ensure any rational value
1013  * in the unbounded directions can be rounded up to an integer value.
1014  *
1015  * The new basis is given by x' = B x, i.e., x = U x'.
1016  * For any rational value of the last tab->n_unbounded coordinates
1017  * in the update tableau, the value that is obtained by rounding
1018  * up this value should be contained in the original tableau.
1019  * For any constraint "a x + c >= 0", we therefore need to add
1020  * a constraint "a x + c + s >= 0", with s the sum of all negative
1021  * entries in the last elements of "a U".
1022  *
1023  * Since we are not interested in the first entries of any of the "a U",
1024  * we first drop the columns of U that correpond to bounded directions.
1025  */
1026 static int tab_shift_cone(struct isl_tab *tab,
1027         struct isl_tab *tab_cone, struct isl_mat *U)
1028 {
1029         int i;
1030         isl_int v;
1031         struct isl_basic_set *bset = NULL;
1032
1033         if (tab && tab->n_unbounded == 0) {
1034                 isl_mat_free(U);
1035                 return 0;
1036         }
1037         isl_int_init(v);
1038         if (!tab || !tab_cone || !U)
1039                 goto error;
1040         bset = isl_tab_peek_bset(tab_cone);
1041         U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1042         for (i = 0; i < bset->n_ineq; ++i) {
1043                 int ok;
1044                 struct isl_vec *row = NULL;
1045                 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1046                         continue;
1047                 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1048                 if (!row)
1049                         goto error;
1050                 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1051                 row = isl_vec_mat_product(row, isl_mat_copy(U));
1052                 if (!row)
1053                         goto error;
1054                 vec_sum_of_neg(row, &v);
1055                 isl_vec_free(row);
1056                 if (isl_int_is_zero(v))
1057                         continue;
1058                 tab = isl_tab_extend(tab, 1);
1059                 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1060                 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1061                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1062                 if (!ok)
1063                         goto error;
1064         }
1065
1066         isl_mat_free(U);
1067         isl_int_clear(v);
1068         return 0;
1069 error:
1070         isl_mat_free(U);
1071         isl_int_clear(v);
1072         return -1;
1073 }
1074
1075 /* Compute and return an initial basis for the possibly
1076  * unbounded tableau "tab".  "tab_cone" is a tableau
1077  * for the corresponding recession cone.
1078  * Additionally, add constraints to "tab" that ensure
1079  * that any rational value for the unbounded directions
1080  * can be rounded up to an integer value.
1081  *
1082  * If the tableau is bounded, i.e., if the recession cone
1083  * is zero-dimensional, then we just use inital_basis.
1084  * Otherwise, we construct a basis whose first directions
1085  * correspond to equalities, followed by bounded directions,
1086  * i.e., equalities in the recession cone.
1087  * The remaining directions are then unbounded.
1088  */
1089 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1090         struct isl_tab *tab_cone)
1091 {
1092         struct isl_mat *eq;
1093         struct isl_mat *cone_eq;
1094         struct isl_mat *U, *Q;
1095
1096         if (!tab || !tab_cone)
1097                 return -1;
1098
1099         if (tab_cone->n_col == tab_cone->n_dead) {
1100                 tab->basis = initial_basis(tab);
1101                 return tab->basis ? 0 : -1;
1102         }
1103
1104         eq = tab_equalities(tab);
1105         if (!eq)
1106                 return -1;
1107         tab->n_zero = eq->n_row;
1108         cone_eq = tab_equalities(tab_cone);
1109         eq = isl_mat_concat(eq, cone_eq);
1110         if (!eq)
1111                 return -1;
1112         tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1113         eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1114         if (!eq)
1115                 return -1;
1116         isl_mat_free(eq);
1117         tab->basis = isl_mat_lin_to_aff(Q);
1118         if (tab_shift_cone(tab, tab_cone, U) < 0)
1119                 return -1;
1120         if (!tab->basis)
1121                 return -1;
1122         return 0;
1123 }
1124
1125 /* Compute and return a sample point in bset using generalized basis
1126  * reduction.  We first check if the input set has a non-trivial
1127  * recession cone.  If so, we perform some extra preprocessing in
1128  * sample_with_cone.  Otherwise, we directly perform generalized basis
1129  * reduction.
1130  */
1131 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1132 {
1133         unsigned dim;
1134         struct isl_basic_set *cone;
1135
1136         dim = isl_basic_set_total_dim(bset);
1137
1138         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1139         if (!cone)
1140                 goto error;
1141
1142         if (cone->n_eq < dim)
1143                 return isl_basic_set_sample_with_cone(bset, cone);
1144
1145         isl_basic_set_free(cone);
1146         return sample_bounded(bset);
1147 error:
1148         isl_basic_set_free(bset);
1149         return NULL;
1150 }
1151
1152 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
1153 {
1154         struct isl_mat *T;
1155         struct isl_ctx *ctx;
1156         struct isl_vec *sample;
1157
1158         bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
1159         if (!bset)
1160                 return NULL;
1161
1162         ctx = bset->ctx;
1163         sample = isl_pip_basic_set_sample(bset);
1164
1165         if (sample && sample->size != 0)
1166                 sample = isl_mat_vec_product(T, sample);
1167         else
1168                 isl_mat_free(T);
1169
1170         return sample;
1171 }
1172
1173 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1174 {
1175         struct isl_ctx *ctx;
1176         unsigned dim;
1177         if (!bset)
1178                 return NULL;
1179
1180         ctx = bset->ctx;
1181         if (isl_basic_set_plain_is_empty(bset))
1182                 return empty_sample(bset);
1183
1184         dim = isl_basic_set_n_dim(bset);
1185         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1186         isl_assert(ctx, bset->n_div == 0, goto error);
1187
1188         if (bset->sample && bset->sample->size == 1 + dim) {
1189                 int contains = isl_basic_set_contains(bset, bset->sample);
1190                 if (contains < 0)
1191                         goto error;
1192                 if (contains) {
1193                         struct isl_vec *sample = isl_vec_copy(bset->sample);
1194                         isl_basic_set_free(bset);
1195                         return sample;
1196                 }
1197         }
1198         isl_vec_free(bset->sample);
1199         bset->sample = NULL;
1200
1201         if (bset->n_eq > 0)
1202                 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1203                                                : isl_basic_set_sample_vec);
1204         if (dim == 0)
1205                 return zero_sample(bset);
1206         if (dim == 1)
1207                 return interval_sample(bset);
1208
1209         switch (bset->ctx->opt->ilp_solver) {
1210         case ISL_ILP_PIP:
1211                 return pip_sample(bset);
1212         case ISL_ILP_GBR:
1213                 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1214         }
1215         isl_assert(bset->ctx, 0, );
1216 error:
1217         isl_basic_set_free(bset);
1218         return NULL;
1219 }
1220
1221 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1222 {
1223         return basic_set_sample(bset, 0);
1224 }
1225
1226 /* Compute an integer sample in "bset", where the caller guarantees
1227  * that "bset" is bounded.
1228  */
1229 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1230 {
1231         return basic_set_sample(bset, 1);
1232 }
1233
1234 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1235 {
1236         int i;
1237         int k;
1238         struct isl_basic_set *bset = NULL;
1239         struct isl_ctx *ctx;
1240         unsigned dim;
1241
1242         if (!vec)
1243                 return NULL;
1244         ctx = vec->ctx;
1245         isl_assert(ctx, vec->size != 0, goto error);
1246
1247         bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1248         if (!bset)
1249                 goto error;
1250         dim = isl_basic_set_n_dim(bset);
1251         for (i = dim - 1; i >= 0; --i) {
1252                 k = isl_basic_set_alloc_equality(bset);
1253                 if (k < 0)
1254                         goto error;
1255                 isl_seq_clr(bset->eq[k], 1 + dim);
1256                 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1257                 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1258         }
1259         bset->sample = vec;
1260
1261         return bset;
1262 error:
1263         isl_basic_set_free(bset);
1264         isl_vec_free(vec);
1265         return NULL;
1266 }
1267
1268 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1269 {
1270         struct isl_basic_set *bset;
1271         struct isl_vec *sample_vec;
1272
1273         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1274         sample_vec = isl_basic_set_sample_vec(bset);
1275         if (!sample_vec)
1276                 goto error;
1277         if (sample_vec->size == 0) {
1278                 struct isl_basic_map *sample;
1279                 sample = isl_basic_map_empty_like(bmap);
1280                 isl_vec_free(sample_vec);
1281                 isl_basic_map_free(bmap);
1282                 return sample;
1283         }
1284         bset = isl_basic_set_from_vec(sample_vec);
1285         return isl_basic_map_overlying_set(bset, bmap);
1286 error:
1287         isl_basic_map_free(bmap);
1288         return NULL;
1289 }
1290
1291 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1292 {
1293         int i;
1294         isl_basic_map *sample = NULL;
1295
1296         if (!map)
1297                 goto error;
1298
1299         for (i = 0; i < map->n; ++i) {
1300                 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1301                 if (!sample)
1302                         goto error;
1303                 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1304                         break;
1305                 isl_basic_map_free(sample);
1306         }
1307         if (i == map->n)
1308                 sample = isl_basic_map_empty_like_map(map);
1309         isl_map_free(map);
1310         return sample;
1311 error:
1312         isl_map_free(map);
1313         return NULL;
1314 }
1315
1316 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1317 {
1318         return (isl_basic_set *) isl_map_sample((isl_map *)set);
1319 }
1320
1321 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1322 {
1323         isl_vec *vec;
1324         isl_space *dim;
1325
1326         dim = isl_basic_set_get_space(bset);
1327         bset = isl_basic_set_underlying_set(bset);
1328         vec = isl_basic_set_sample_vec(bset);
1329
1330         return isl_point_alloc(dim, vec);
1331 }
1332
1333 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1334 {
1335         int i;
1336         isl_point *pnt;
1337
1338         if (!set)
1339                 return NULL;
1340
1341         for (i = 0; i < set->n; ++i) {
1342                 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1343                 if (!pnt)
1344                         goto error;
1345                 if (!isl_point_is_void(pnt))
1346                         break;
1347                 isl_point_free(pnt);
1348         }
1349         if (i == set->n)
1350                 pnt = isl_point_void(isl_set_get_space(set));
1351
1352         isl_set_free(set);
1353         return pnt;
1354 error:
1355         isl_set_free(set);
1356         return NULL;
1357 }