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 #include <isl_options_private.h>
  23
  24 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
  25 {
  26         struct isl_vec *vec;
  27
  28         vec = isl_vec_alloc(bset->ctx, 0);
  29         isl_basic_set_free(bset);
  30         return vec;
  31 }
  32
  33 /* Construct a zero sample of the same dimension as bset.
  34  * As a special case, if bset is zero-dimensional, this
  35  * function creates a zero-dimensional sample point.
  36  */
  37 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
  38 {
  39         unsigned dim;
  40         struct isl_vec *sample;
  41
  42         dim = isl_basic_set_total_dim(bset);
  43         sample = isl_vec_alloc(bset->ctx, 1 + dim);
  44         if (sample) {
  45                 isl_int_set_si(sample->el[0], 1);
  46                 isl_seq_clr(sample->el + 1, dim);
  47         }
  48         isl_basic_set_free(bset);
  49         return sample;
  50 }
  51
  52 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
  53 {
  54         int i;
  55         isl_int t;
  56         struct isl_vec *sample;
  57
  58         bset = isl_basic_set_simplify(bset);
  59         if (!bset)
  60                 return NULL;
  61         if (isl_basic_set_plain_is_empty(bset))
  62                 return empty_sample(bset);
  63         if (bset->n_eq == 0 && bset->n_ineq == 0)
  64                 return zero_sample(bset);
  65
  66         sample = isl_vec_alloc(bset->ctx, 2);
  67         if (!sample)
  68                 goto error;
  69         if (!bset)
  70                 return NULL;
  71         isl_int_set_si(sample->block.data[0], 1);
  72
  73         if (bset->n_eq > 0) {
  74                 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
  75                 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
  76                 if (isl_int_is_one(bset->eq[0][1]))
  77                         isl_int_neg(sample->el[1], bset->eq[0][0]);
  78                 else {
  79                         isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
  80                                    goto error);
  81                         isl_int_set(sample->el[1], bset->eq[0][0]);
  82                 }
  83                 isl_basic_set_free(bset);
  84                 return sample;
  85         }
  86
  87         isl_int_init(t);
  88         if (isl_int_is_one(bset->ineq[0][1]))
  89                 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
  90         else
  91                 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
  92         for (i = 1; i < bset->n_ineq; ++i) {
  93                 isl_seq_inner_product(sample->block.data,
  94                                         bset->ineq[i], 2, &t);
  95                 if (isl_int_is_neg(t))
  96                         break;
  97         }
  98         isl_int_clear(t);
  99         if (i < bset->n_ineq) {
 100                 isl_vec_free(sample);
 101                 return empty_sample(bset);
 102         }
 103
 104         isl_basic_set_free(bset);
 105         return sample;
 106 error:
 107         isl_basic_set_free(bset);
 108         isl_vec_free(sample);
 109         return NULL;
 110 }
 111
 112 static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
 113 {
 114         int i, j, n;
 115         struct isl_mat *dirs = NULL;
 116         struct isl_mat *bounds = NULL;
 117         unsigned dim;
 118
 119         if (!bset)
 120                 return NULL;
 121
 122         dim = isl_basic_set_n_dim(bset);
 123         bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
 124         if (!bounds)
 125                 return NULL;
 126
 127         isl_int_set_si(bounds->row[0][0], 1);
 128         isl_seq_clr(bounds->row[0]+1, dim);
 129         bounds->n_row = 1;
 130
 131         if (bset->n_ineq == 0)
 132                 return bounds;
 133
 134         dirs = isl_mat_alloc(bset->ctx, dim, dim);
 135         if (!dirs) {
 136                 isl_mat_free(bounds);
 137                 return NULL;
 138         }
 139         isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
 140         isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
 141         for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
 142                 int pos;
 143
 144                 isl_seq_cpy(dirs->row[n], bset->ineq[j]+1, dirs->n_col);
 145
 146                 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
 147                 if (pos < 0)
 148                         continue;
 149                 for (i = 0; i < n; ++i) {
 150                         int pos_i;
 151                         pos_i = isl_seq_first_non_zero(dirs->row[i], dirs->n_col);
 152                         if (pos_i < pos)
 153                                 continue;
 154                         if (pos_i > pos)
 155                                 break;
 156                         isl_seq_elim(dirs->row[n], dirs->row[i], pos,
 157                                         dirs->n_col, NULL);
 158                         pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
 159                         if (pos < 0)
 160                                 break;
 161                 }
 162                 if (pos < 0)
 163                         continue;
 164                 if (i < n) {
 165                         int k;
 166                         isl_int *t = dirs->row[n];
 167                         for (k = n; k > i; --k)
 168                                 dirs->row[k] = dirs->row[k-1];
 169                         dirs->row[i] = t;
 170                 }
 171                 ++n;
 172                 isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
 173         }
 174         isl_mat_free(dirs);
 175         bounds->n_row = 1+n;
 176         return bounds;
 177 }
 178
 179 static void swap_inequality(struct isl_basic_set *bset, int a, int b)
 180 {
 181         isl_int *t = bset->ineq[a];
 182         bset->ineq[a] = bset->ineq[b];
 183         bset->ineq[b] = t;
 184 }
 185
 186 /* Skew into positive orthant and project out lineality space.
 187  *
 188  * We perform a unimodular transformation that turns a selected
 189  * maximal set of linearly independent bounds into constraints
 190  * on the first dimensions that impose that these first dimensions
 191  * are non-negative.  In particular, the constraint matrix is lower
 192  * triangular with positive entries on the diagonal and negative
 193  * entries below.
 194  * If "bset" has a lineality space then these constraints (and therefore
 195  * all constraints in bset) only involve the first dimensions.
 196  * The remaining dimensions then do not appear in any constraints and
 197  * we can select any value for them, say zero.  We therefore project
 198  * out this final dimensions and plug in the value zero later.  This
 199  * is accomplished by simply dropping the final columns of
 200  * the unimodular transformation.
 201  */
 202 static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
 203         struct isl_basic_set *bset, struct isl_mat **T)
 204 {
 205         struct isl_mat *U = NULL;
 206         struct isl_mat *bounds = NULL;
 207         int i, j;
 208         unsigned old_dim, new_dim;
 209
 210         *T = NULL;
 211         if (!bset)
 212                 return NULL;
 213
 214         isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
 215         isl_assert(bset->ctx, bset->n_div == 0, goto error);
 216         isl_assert(bset->ctx, bset->n_eq == 0, goto error);
 217
 218         old_dim = isl_basic_set_n_dim(bset);
 219         /* Try to move (multiples of) unit rows up. */
 220         for (i = 0, j = 0; i < bset->n_ineq; ++i) {
 221                 int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
 222                 if (pos < 0)
 223                         continue;
 224                 if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
 225                                                 old_dim-pos-1) >= 0)
 226                         continue;
 227                 if (i != j)
 228                         swap_inequality(bset, i, j);
 229                 ++j;
 230         }
 231         bounds = independent_bounds(bset);
 232         if (!bounds)
 233                 goto error;
 234         new_dim = bounds->n_row - 1;
 235         bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
 236         if (!bounds)
 237                 goto error;
 238         U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
 239         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 240         if (!bset)
 241                 goto error;
 242         *T = U;
 243         isl_mat_free(bounds);
 244         return bset;
 245 error:
 246         isl_mat_free(bounds);
 247         isl_mat_free(U);
 248         isl_basic_set_free(bset);
 249         return NULL;
 250 }
 251
 252 /* Find a sample integer point, if any, in bset, which is known
 253  * to have equalities.  If bset contains no integer points, then
 254  * return a zero-length vector.
 255  * We simply remove the known equalities, compute a sample
 256  * in the resulting bset, using the specified recurse function,
 257  * and then transform the sample back to the original space.
 258  */
 259 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
 260         struct isl_vec *(*recurse)(struct isl_basic_set *))
 261 {
 262         struct isl_mat *T;
 263         struct isl_vec *sample;
 264
 265         if (!bset)
 266                 return NULL;
 267
 268         bset = isl_basic_set_remove_equalities(bset, &T, NULL);
 269         sample = recurse(bset);
 270         if (!sample || sample->size == 0)
 271                 isl_mat_free(T);
 272         else
 273                 sample = isl_mat_vec_product(T, sample);
 274         return sample;
 275 }
 276
 277 /* Return a matrix containing the equalities of the tableau
 278  * in constraint form.  The tableau is assumed to have
 279  * an associated bset that has been kept up-to-date.
 280  */
 281 static struct isl_mat *tab_equalities(struct isl_tab *tab)
 282 {
 283         int i, j;
 284         int n_eq;
 285         struct isl_mat *eq;
 286         struct isl_basic_set *bset;
 287
 288         if (!tab)
 289                 return NULL;
 290
 291         bset = isl_tab_peek_bset(tab);
 292         isl_assert(tab->mat->ctx, bset, return NULL);
 293
 294         n_eq = tab->n_var - tab->n_col + tab->n_dead;
 295         if (tab->empty || n_eq == 0)
 296                 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
 297         if (n_eq == tab->n_var)
 298                 return isl_mat_identity(tab->mat->ctx, tab->n_var);
 299
 300         eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
 301         if (!eq)
 302                 return NULL;
 303         for (i = 0, j = 0; i < tab->n_con; ++i) {
 304                 if (tab->con[i].is_row)
 305                         continue;
 306                 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
 307                         continue;
 308                 if (i < bset->n_eq)
 309                         isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
 310                 else
 311                         isl_seq_cpy(eq->row[j],
 312                                     bset->ineq[i - bset->n_eq] + 1, tab->n_var);
 313                 ++j;
 314         }
 315         isl_assert(bset->ctx, j == n_eq, goto error);
 316         return eq;
 317 error:
 318         isl_mat_free(eq);
 319         return NULL;
 320 }
 321
 322 /* Compute and return an initial basis for the bounded tableau "tab".
 323  *
 324  * If the tableau is either full-dimensional or zero-dimensional,
 325  * the we simply return an identity matrix.
 326  * Otherwise, we construct a basis whose first directions correspond
 327  * to equalities.
 328  */
 329 static struct isl_mat *initial_basis(struct isl_tab *tab)
 330 {
 331         int n_eq;
 332         struct isl_mat *eq;
 333         struct isl_mat *Q;
 334
 335         tab->n_unbounded = 0;
 336         tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
 337         if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
 338                 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
 339
 340         eq = tab_equalities(tab);
 341         eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
 342         if (!eq)
 343                 return NULL;
 344         isl_mat_free(eq);
 345
 346         Q = isl_mat_lin_to_aff(Q);
 347         return Q;
 348 }
 349
 350 /* Given a tableau representing a set, find and return
 351  * an integer point in the set, if there is any.
 352  *
 353  * We perform a depth first search
 354  * for an integer point, by scanning all possible values in the range
 355  * attained by a basis vector, where an initial basis may have been set
 356  * by the calling function.  Otherwise an initial basis that exploits
 357  * the equalities in the tableau is created.
 358  * tab->n_zero is currently ignored and is clobbered by this function.
 359  *
 360  * The tableau is allowed to have unbounded direction, but then
 361  * the calling function needs to set an initial basis, with the
 362  * unbounded directions last and with tab->n_unbounded set
 363  * to the number of unbounded directions.
 364  * Furthermore, the calling functions needs to add shifted copies
 365  * of all constraints involving unbounded directions to ensure
 366  * that any feasible rational value in these directions can be rounded
 367  * up to yield a feasible integer value.
 368  * In particular, let B define the given basis x' = B x
 369  * and let T be the inverse of B, i.e., X = T x'.
 370  * Let a x + c >= 0 be a constraint of the set represented by the tableau,
 371  * or a T x' + c >= 0 in terms of the given basis.  Assume that
 372  * the bounded directions have an integer value, then we can safely
 373  * round up the values for the unbounded directions if we make sure
 374  * that x' not only satisfies the original constraint, but also
 375  * the constraint "a T x' + c + s >= 0" with s the sum of all
 376  * negative values in the last n_unbounded entries of "a T".
 377  * The calling function therefore needs to add the constraint
 378  * a x + c + s >= 0.  The current function then scans the first
 379  * directions for an integer value and once those have been found,
 380  * it can compute "T ceil(B x)" to yield an integer point in the set.
 381  * Note that during the search, the first rows of B may be changed
 382  * by a basis reduction, but the last n_unbounded rows of B remain
 383  * unaltered and are also not mixed into the first rows.
 384  *
 385  * The search is implemented iteratively.  "level" identifies the current
 386  * basis vector.  "init" is true if we want the first value at the current
 387  * level and false if we want the next value.
 388  *
 389  * The initial basis is the identity matrix.  If the range in some direction
 390  * contains more than one integer value, we perform basis reduction based
 391  * on the value of ctx->opt->gbr
 392  *      - ISL_GBR_NEVER:        never perform basis reduction
 393  *      - ISL_GBR_ONCE:         only perform basis reduction the first
 394  *                              time such a range is encountered
 395  *      - ISL_GBR_ALWAYS:       always perform basis reduction when
 396  *                              such a range is encountered
 397  *
 398  * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
 399  * reduction computation to return early.  That is, as soon as it
 400  * finds a reasonable first direction.
 401  */
 402 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
 403 {
 404         unsigned dim;
 405         unsigned gbr;
 406         struct isl_ctx *ctx;
 407         struct isl_vec *sample;
 408         struct isl_vec *min;
 409         struct isl_vec *max;
 410         enum isl_lp_result res;
 411         int level;
 412         int init;
 413         int reduced;
 414         struct isl_tab_undo **snap;
 415
 416         if (!tab)
 417                 return NULL;
 418         if (tab->empty)
 419                 return isl_vec_alloc(tab->mat->ctx, 0);
 420
 421         if (!tab->basis)
 422                 tab->basis = initial_basis(tab);
 423         if (!tab->basis)
 424                 return NULL;
 425         isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
 426                     return NULL);
 427         isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
 428                     return NULL);
 429
 430         ctx = tab->mat->ctx;
 431         dim = tab->n_var;
 432         gbr = ctx->opt->gbr;
 433
 434         if (tab->n_unbounded == tab->n_var) {
 435                 sample = isl_tab_get_sample_value(tab);
 436                 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
 437                 sample = isl_vec_ceil(sample);
 438                 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
 439                                                         sample);
 440                 return sample;
 441         }
 442
 443         if (isl_tab_extend_cons(tab, dim + 1) < 0)
 444                 return NULL;
 445
 446         min = isl_vec_alloc(ctx, dim);
 447         max = isl_vec_alloc(ctx, dim);
 448         snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
 449
 450         if (!min || !max || !snap)
 451                 goto error;
 452
 453         level = 0;
 454         init = 1;
 455         reduced = 0;
 456
 457         while (level >= 0) {
 458                 int empty = 0;
 459                 if (init) {
 460                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 461                                     ctx->one, &min->el[level], NULL, 0);
 462                         if (res == isl_lp_empty)
 463                                 empty = 1;
 464                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 465                         if (res == isl_lp_error)
 466                                 goto error;
 467                         if (!empty && isl_tab_sample_is_integer(tab))
 468                                 break;
 469                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 470                                     tab->basis->row[1 + level] + 1, dim);
 471                         res = isl_tab_min(tab, tab->basis->row[1 + level],
 472                                     ctx->one, &max->el[level], NULL, 0);
 473                         isl_seq_neg(tab->basis->row[1 + level] + 1,
 474                                     tab->basis->row[1 + level] + 1, dim);
 475                         isl_int_neg(max->el[level], max->el[level]);
 476                         if (res == isl_lp_empty)
 477                                 empty = 1;
 478                         isl_assert(ctx, res != isl_lp_unbounded, goto error);
 479                         if (res == isl_lp_error)
 480                                 goto error;
 481                         if (!empty && isl_tab_sample_is_integer(tab))
 482                                 break;
 483                         if (!empty && !reduced &&
 484                             ctx->opt->gbr != ISL_GBR_NEVER &&
 485                             isl_int_lt(min->el[level], max->el[level])) {
 486                                 unsigned gbr_only_first;
 487                                 if (ctx->opt->gbr == ISL_GBR_ONCE)
 488                                         ctx->opt->gbr = ISL_GBR_NEVER;
 489                                 tab->n_zero = level;
 490                                 gbr_only_first = ctx->opt->gbr_only_first;
 491                                 ctx->opt->gbr_only_first =
 492                                         ctx->opt->gbr == ISL_GBR_ALWAYS;
 493                                 tab = isl_tab_compute_reduced_basis(tab);
 494                                 ctx->opt->gbr_only_first = gbr_only_first;
 495                                 if (!tab || !tab->basis)
 496                                         goto error;
 497                                 reduced = 1;
 498                                 continue;
 499                         }
 500                         reduced = 0;
 501                         snap[level] = isl_tab_snap(tab);
 502                 } else
 503                         isl_int_add_ui(min->el[level], min->el[level], 1);
 504
 505                 if (empty || isl_int_gt(min->el[level], max->el[level])) {
 506                         level--;
 507                         init = 0;
 508                         if (level >= 0)
 509                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 510                                         goto error;
 511                         continue;
 512                 }
 513                 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
 514                 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
 515                         goto error;
 516                 isl_int_set_si(tab->basis->row[1 + level][0], 0);
 517                 if (level + tab->n_unbounded < dim - 1) {
 518                         ++level;
 519                         init = 1;
 520                         continue;
 521                 }
 522                 break;
 523         }
 524
 525         if (level >= 0) {
 526                 sample = isl_tab_get_sample_value(tab);
 527                 if (!sample)
 528                         goto error;
 529                 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
 530                         sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
 531                                                      sample);
 532                         sample = isl_vec_ceil(sample);
 533                         sample = isl_mat_vec_inverse_product(
 534                                         isl_mat_copy(tab->basis), sample);
 535                 }
 536         } else
 537                 sample = isl_vec_alloc(ctx, 0);
 538
 539         ctx->opt->gbr = gbr;
 540         isl_vec_free(min);
 541         isl_vec_free(max);
 542         free(snap);
 543         return sample;
 544 error:
 545         ctx->opt->gbr = gbr;
 546         isl_vec_free(min);
 547         isl_vec_free(max);
 548         free(snap);
 549         return NULL;
 550 }
 551
 552 static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
 553
 554 /* Compute a sample point of the given basic set, based on the given,
 555  * non-trivial factorization.
 556  */
 557 static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
 558         __isl_take isl_factorizer *f)
 559 {
 560         int i, n;
 561         isl_vec *sample = NULL;
 562         isl_ctx *ctx;
 563         unsigned nparam;
 564         unsigned nvar;
 565
 566         ctx = isl_basic_set_get_ctx(bset);
 567         if (!ctx)
 568                 goto error;
 569
 570         nparam = isl_basic_set_dim(bset, isl_dim_param);
 571         nvar = isl_basic_set_dim(bset, isl_dim_set);
 572
 573         sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
 574         if (!sample)
 575                 goto error;
 576         isl_int_set_si(sample->el[0], 1);
 577
 578         bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
 579
 580         for (i = 0, n = 0; i < f->n_group; ++i) {
 581                 isl_basic_set *bset_i;
 582                 isl_vec *sample_i;
 583
 584                 bset_i = isl_basic_set_copy(bset);
 585                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
 586                             nparam + n + f->len[i], nvar - n - f->len[i]);
 587                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
 588                             nparam, n);
 589                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
 590                             n + f->len[i], nvar - n - f->len[i]);
 591                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
 592
 593                 sample_i = sample_bounded(bset_i);
 594                 if (!sample_i)
 595                         goto error;
 596                 if (sample_i->size == 0) {
 597                         isl_basic_set_free(bset);
 598                         isl_factorizer_free(f);
 599                         isl_vec_free(sample);
 600                         return sample_i;
 601                 }
 602                 isl_seq_cpy(sample->el + 1 + nparam + n,
 603                             sample_i->el + 1, f->len[i]);
 604                 isl_vec_free(sample_i);
 605
 606                 n += f->len[i];
 607         }
 608
 609         f->morph = isl_morph_inverse(f->morph);
 610         sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
 611
 612         isl_basic_set_free(bset);
 613         isl_factorizer_free(f);
 614         return sample;
 615 error:
 616         isl_basic_set_free(bset);
 617         isl_factorizer_free(f);
 618         isl_vec_free(sample);
 619         return NULL;
 620 }
 621
 622 /* Given a basic set that is known to be bounded, find and return
 623  * an integer point in the basic set, if there is any.
 624  *
 625  * After handling some trivial cases, we construct a tableau
 626  * and then use isl_tab_sample to find a sample, passing it
 627  * the identity matrix as initial basis.
 628  */
 629 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
 630 {
 631         unsigned dim;
 632         struct isl_ctx *ctx;
 633         struct isl_vec *sample;
 634         struct isl_tab *tab = NULL;
 635         isl_factorizer *f;
 636
 637         if (!bset)
 638                 return NULL;
 639
 640         if (isl_basic_set_plain_is_empty(bset))
 641                 return empty_sample(bset);
 642
 643         dim = isl_basic_set_total_dim(bset);
 644         if (dim == 0)
 645                 return zero_sample(bset);
 646         if (dim == 1)
 647                 return interval_sample(bset);
 648         if (bset->n_eq > 0)
 649                 return sample_eq(bset, sample_bounded);
 650
 651         f = isl_basic_set_factorizer(bset);
 652         if (!f)
 653                 goto error;
 654         if (f->n_group != 0)
 655                 return factored_sample(bset, f);
 656         isl_factorizer_free(f);
 657
 658         ctx = bset->ctx;
 659
 660         tab = isl_tab_from_basic_set(bset, 1);
 661         if (tab && tab->empty) {
 662                 isl_tab_free(tab);
 663                 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
 664                 sample = isl_vec_alloc(bset->ctx, 0);
 665                 isl_basic_set_free(bset);
 666                 return sample;
 667         }
 668
 669         if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
 670                 if (isl_tab_detect_implicit_equalities(tab) < 0)
 671                         goto error;
 672
 673         sample = isl_tab_sample(tab);
 674         if (!sample)
 675                 goto error;
 676
 677         if (sample->size > 0) {
 678                 isl_vec_free(bset->sample);
 679                 bset->sample = isl_vec_copy(sample);
 680         }
 681
 682         isl_basic_set_free(bset);
 683         isl_tab_free(tab);
 684         return sample;
 685 error:
 686         isl_basic_set_free(bset);
 687         isl_tab_free(tab);
 688         return NULL;
 689 }
 690
 691 /* Given a basic set "bset" and a value "sample" for the first coordinates
 692  * of bset, plug in these values and drop the corresponding coordinates.
 693  *
 694  * We do this by computing the preimage of the transformation
 695  *
 696  *           [ 1 0 ]
 697  *      x =  [ s 0 ] x'
 698  *           [ 0 I ]
 699  *
 700  * where [1 s] is the sample value and I is the identity matrix of the
 701  * appropriate dimension.
 702  */
 703 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
 704         struct isl_vec *sample)
 705 {
 706         int i;
 707         unsigned total;
 708         struct isl_mat *T;
 709
 710         if (!bset || !sample)
 711                 goto error;
 712
 713         total = isl_basic_set_total_dim(bset);
 714         T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
 715         if (!T)
 716                 goto error;
 717
 718         for (i = 0; i < sample->size; ++i) {
 719                 isl_int_set(T->row[i][0], sample->el[i]);
 720                 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
 721         }
 722         for (i = 0; i < T->n_col - 1; ++i) {
 723                 isl_seq_clr(T->row[sample->size + i], T->n_col);
 724                 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
 725         }
 726         isl_vec_free(sample);
 727
 728         bset = isl_basic_set_preimage(bset, T);
 729         return bset;
 730 error:
 731         isl_basic_set_free(bset);
 732         isl_vec_free(sample);
 733         return NULL;
 734 }
 735
 736 /* Given a basic set "bset", return any (possibly non-integer) point
 737  * in the basic set.
 738  */
 739 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
 740 {
 741         struct isl_tab *tab;
 742         struct isl_vec *sample;
 743
 744         if (!bset)
 745                 return NULL;
 746
 747         tab = isl_tab_from_basic_set(bset, 0);
 748         sample = isl_tab_get_sample_value(tab);
 749         isl_tab_free(tab);
 750
 751         isl_basic_set_free(bset);
 752
 753         return sample;
 754 }
 755
 756 /* Given a linear cone "cone" and a rational point "vec",
 757  * construct a polyhedron with shifted copies of the constraints in "cone",
 758  * i.e., a polyhedron with "cone" as its recession cone, such that each
 759  * point x in this polyhedron is such that the unit box positioned at x
 760  * lies entirely inside the affine cone 'vec + cone'.
 761  * Any rational point in this polyhedron may therefore be rounded up
 762  * to yield an integer point that lies inside said affine cone.
 763  *
 764  * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
 765  * point "vec" by v/d.
 766  * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
 767  * by <a_i, x> - b/d >= 0.
 768  * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
 769  * We prefer this polyhedron over the actual affine cone because it doesn't
 770  * require a scaling of the constraints.
 771  * If each of the vertices of the unit cube positioned at x lies inside
 772  * this polyhedron, then the whole unit cube at x lies inside the affine cone.
 773  * We therefore impose that x' = x + \sum e_i, for any selection of unit
 774  * vectors lies inside the polyhedron, i.e.,
 775  *
 776  *      <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
 777  *
 778  * The most stringent of these constraints is the one that selects
 779  * all negative a_i, so the polyhedron we are looking for has constraints
 780  *
 781  *      <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
 782  *
 783  * Note that if cone were known to have only non-negative rays
 784  * (which can be accomplished by a unimodular transformation),
 785  * then we would only have to check the points x' = x + e_i
 786  * and we only have to add the smallest negative a_i (if any)
 787  * instead of the sum of all negative a_i.
 788  */
 789 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
 790         struct isl_vec *vec)
 791 {
 792         int i, j, k;
 793         unsigned total;
 794
 795         struct isl_basic_set *shift = NULL;
 796
 797         if (!cone || !vec)
 798                 goto error;
 799
 800         isl_assert(cone->ctx, cone->n_eq == 0, goto error);
 801
 802         total = isl_basic_set_total_dim(cone);
 803
 804         shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
 805                                         0, 0, cone->n_ineq);
 806
 807         for (i = 0; i < cone->n_ineq; ++i) {
 808                 k = isl_basic_set_alloc_inequality(shift);
 809                 if (k < 0)
 810                         goto error;
 811                 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
 812                 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
 813                                       &shift->ineq[k][0]);
 814                 isl_int_cdiv_q(shift->ineq[k][0],
 815                                shift->ineq[k][0], vec->el[0]);
 816                 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
 817                 for (j = 0; j < total; ++j) {
 818                         if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
 819                                 continue;
 820                         isl_int_add(shift->ineq[k][0],
 821                                     shift->ineq[k][0], shift->ineq[k][1 + j]);
 822                 }
 823         }
 824
 825         isl_basic_set_free(cone);
 826         isl_vec_free(vec);
 827
 828         return isl_basic_set_finalize(shift);
 829 error:
 830         isl_basic_set_free(shift);
 831         isl_basic_set_free(cone);
 832         isl_vec_free(vec);
 833         return NULL;
 834 }
 835
 836 /* Given a rational point vec in a (transformed) basic set,
 837  * such that cone is the recession cone of the original basic set,
 838  * "round up" the rational point to an integer point.
 839  *
 840  * We first check if the rational point just happens to be integer.
 841  * If not, we transform the cone in the same way as the basic set,
 842  * pick a point x in this cone shifted to the rational point such that
 843  * the whole unit cube at x is also inside this affine cone.
 844  * Then we simply round up the coordinates of x and return the
 845  * resulting integer point.
 846  */
 847 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
 848         struct isl_basic_set *cone, struct isl_mat *U)
 849 {
 850         unsigned total;
 851
 852         if (!vec || !cone || !U)
 853                 goto error;
 854
 855         isl_assert(vec->ctx, vec->size != 0, goto error);
 856         if (isl_int_is_one(vec->el[0])) {
 857                 isl_mat_free(U);
 858                 isl_basic_set_free(cone);
 859                 return vec;
 860         }
 861
 862         total = isl_basic_set_total_dim(cone);
 863         cone = isl_basic_set_preimage(cone, U);
 864         cone = isl_basic_set_remove_dims(cone, isl_dim_set,
 865                                          0, total - (vec->size - 1));
 866
 867         cone = shift_cone(cone, vec);
 868
 869         vec = rational_sample(cone);
 870         vec = isl_vec_ceil(vec);
 871         return vec;
 872 error:
 873         isl_mat_free(U);
 874         isl_vec_free(vec);
 875         isl_basic_set_free(cone);
 876         return NULL;
 877 }
 878
 879 /* Concatenate two integer vectors, i.e., two vectors with denominator
 880  * (stored in element 0) equal to 1.
 881  */
 882 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
 883 {
 884         struct isl_vec *vec;
 885
 886         if (!vec1 || !vec2)
 887                 goto error;
 888         isl_assert(vec1->ctx, vec1->size > 0, goto error);
 889         isl_assert(vec2->ctx, vec2->size > 0, goto error);
 890         isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
 891         isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
 892
 893         vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
 894         if (!vec)
 895                 goto error;
 896
 897         isl_seq_cpy(vec->el, vec1->el, vec1->size);
 898         isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
 899
 900         isl_vec_free(vec1);
 901         isl_vec_free(vec2);
 902
 903         return vec;
 904 error:
 905         isl_vec_free(vec1);
 906         isl_vec_free(vec2);
 907         return NULL;
 908 }
 909
 910 /* Give a basic set "bset" with recession cone "cone", compute and
 911  * return an integer point in bset, if any.
 912  *
 913  * If the recession cone is full-dimensional, then we know that
 914  * bset contains an infinite number of integer points and it is
 915  * fairly easy to pick one of them.
 916  * If the recession cone is not full-dimensional, then we first
 917  * transform bset such that the bounded directions appear as
 918  * the first dimensions of the transformed basic set.
 919  * We do this by using a unimodular transformation that transforms
 920  * the equalities in the recession cone to equalities on the first
 921  * dimensions.
 922  *
 923  * The transformed set is then projected onto its bounded dimensions.
 924  * Note that to compute this projection, we can simply drop all constraints
 925  * involving any of the unbounded dimensions since these constraints
 926  * cannot be combined to produce a constraint on the bounded dimensions.
 927  * To see this, assume that there is such a combination of constraints
 928  * that produces a constraint on the bounded dimensions.  This means
 929  * that some combination of the unbounded dimensions has both an upper
 930  * bound and a lower bound in terms of the bounded dimensions, but then
 931  * this combination would be a bounded direction too and would have been
 932  * transformed into a bounded dimensions.
 933  *
 934  * We then compute a sample value in the bounded dimensions.
 935  * If no such value can be found, then the original set did not contain
 936  * any integer points and we are done.
 937  * Otherwise, we plug in the value we found in the bounded dimensions,
 938  * project out these bounded dimensions and end up with a set with
 939  * a full-dimensional recession cone.
 940  * A sample point in this set is computed by "rounding up" any
 941  * rational point in the set.
 942  *
 943  * The sample points in the bounded and unbounded dimensions are
 944  * then combined into a single sample point and transformed back
 945  * to the original space.
 946  */
 947 __isl_give isl_vec *isl_basic_set_sample_with_cone(
 948         __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
 949 {
 950         unsigned total;
 951         unsigned cone_dim;
 952         struct isl_mat *M, *U;
 953         struct isl_vec *sample;
 954         struct isl_vec *cone_sample;
 955         struct isl_ctx *ctx;
 956         struct isl_basic_set *bounded;
 957
 958         if (!bset || !cone)
 959                 goto error;
 960
 961         ctx = bset->ctx;
 962         total = isl_basic_set_total_dim(cone);
 963         cone_dim = total - cone->n_eq;
 964
 965         M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
 966         M = isl_mat_left_hermite(M, 0, &U, NULL);
 967         if (!M)
 968                 goto error;
 969         isl_mat_free(M);
 970
 971         U = isl_mat_lin_to_aff(U);
 972         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 973
 974         bounded = isl_basic_set_copy(bset);
 975         bounded = isl_basic_set_drop_constraints_involving(bounded,
 976                                                    total - cone_dim, cone_dim);
 977         bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
 978         sample = sample_bounded(bounded);
 979         if (!sample || sample->size == 0) {
 980                 isl_basic_set_free(bset);
 981                 isl_basic_set_free(cone);
 982                 isl_mat_free(U);
 983                 return sample;
 984         }
 985         bset = plug_in(bset, isl_vec_copy(sample));
 986         cone_sample = rational_sample(bset);
 987         cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
 988         sample = vec_concat(sample, cone_sample);
 989         sample = isl_mat_vec_product(U, sample);
 990         return sample;
 991 error:
 992         isl_basic_set_free(cone);
 993         isl_basic_set_free(bset);
 994         return NULL;
 995 }
 996
 997 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
 998 {
 999         int i;
1000
1001         isl_int_set_si(*s, 0);
1002
1003         for (i = 0; i < v->size; ++i)
1004                 if (isl_int_is_neg(v->el[i]))
1005                         isl_int_add(*s, *s, v->el[i]);
1006 }
1007
1008 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
1009  * to the recession cone and the inverse of a new basis U = inv(B),
1010  * with the unbounded directions in B last,
1011  * add constraints to "tab" that ensure any rational value
1012  * in the unbounded directions can be rounded up to an integer value.
1013  *
1014  * The new basis is given by x' = B x, i.e., x = U x'.
1015  * For any rational value of the last tab->n_unbounded coordinates
1016  * in the update tableau, the value that is obtained by rounding
1017  * up this value should be contained in the original tableau.
1018  * For any constraint "a x + c >= 0", we therefore need to add
1019  * a constraint "a x + c + s >= 0", with s the sum of all negative
1020  * entries in the last elements of "a U".
1021  *
1022  * Since we are not interested in the first entries of any of the "a U",
1023  * we first drop the columns of U that correpond to bounded directions.
1024  */
1025 static int tab_shift_cone(struct isl_tab *tab,
1026         struct isl_tab *tab_cone, struct isl_mat *U)
1027 {
1028         int i;
1029         isl_int v;
1030         struct isl_basic_set *bset = NULL;
1031
1032         if (tab && tab->n_unbounded == 0) {
1033                 isl_mat_free(U);
1034                 return 0;
1035         }
1036         isl_int_init(v);
1037         if (!tab || !tab_cone || !U)
1038                 goto error;
1039         bset = isl_tab_peek_bset(tab_cone);
1040         U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1041         for (i = 0; i < bset->n_ineq; ++i) {
1042                 int ok;
1043                 struct isl_vec *row = NULL;
1044                 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1045                         continue;
1046                 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1047                 if (!row)
1048                         goto error;
1049                 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1050                 row = isl_vec_mat_product(row, isl_mat_copy(U));
1051                 if (!row)
1052                         goto error;
1053                 vec_sum_of_neg(row, &v);
1054                 isl_vec_free(row);
1055                 if (isl_int_is_zero(v))
1056                         continue;
1057                 tab = isl_tab_extend(tab, 1);
1058                 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1059                 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1060                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1061                 if (!ok)
1062                         goto error;
1063         }
1064
1065         isl_mat_free(U);
1066         isl_int_clear(v);
1067         return 0;
1068 error:
1069         isl_mat_free(U);
1070         isl_int_clear(v);
1071         return -1;
1072 }
1073
1074 /* Compute and return an initial basis for the possibly
1075  * unbounded tableau "tab".  "tab_cone" is a tableau
1076  * for the corresponding recession cone.
1077  * Additionally, add constraints to "tab" that ensure
1078  * that any rational value for the unbounded directions
1079  * can be rounded up to an integer value.
1080  *
1081  * If the tableau is bounded, i.e., if the recession cone
1082  * is zero-dimensional, then we just use inital_basis.
1083  * Otherwise, we construct a basis whose first directions
1084  * correspond to equalities, followed by bounded directions,
1085  * i.e., equalities in the recession cone.
1086  * The remaining directions are then unbounded.
1087  */
1088 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1089         struct isl_tab *tab_cone)
1090 {
1091         struct isl_mat *eq;
1092         struct isl_mat *cone_eq;
1093         struct isl_mat *U, *Q;
1094
1095         if (!tab || !tab_cone)
1096                 return -1;
1097
1098         if (tab_cone->n_col == tab_cone->n_dead) {
1099                 tab->basis = initial_basis(tab);
1100                 return tab->basis ? 0 : -1;
1101         }
1102
1103         eq = tab_equalities(tab);
1104         if (!eq)
1105                 return -1;
1106         tab->n_zero = eq->n_row;
1107         cone_eq = tab_equalities(tab_cone);
1108         eq = isl_mat_concat(eq, cone_eq);
1109         if (!eq)
1110                 return -1;
1111         tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1112         eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1113         if (!eq)
1114                 return -1;
1115         isl_mat_free(eq);
1116         tab->basis = isl_mat_lin_to_aff(Q);
1117         if (tab_shift_cone(tab, tab_cone, U) < 0)
1118                 return -1;
1119         if (!tab->basis)
1120                 return -1;
1121         return 0;
1122 }
1123
1124 /* Compute and return a sample point in bset using generalized basis
1125  * reduction.  We first check if the input set has a non-trivial
1126  * recession cone.  If so, we perform some extra preprocessing in
1127  * sample_with_cone.  Otherwise, we directly perform generalized basis
1128  * reduction.
1129  */
1130 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1131 {
1132         unsigned dim;
1133         struct isl_basic_set *cone;
1134
1135         dim = isl_basic_set_total_dim(bset);
1136
1137         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1138         if (!cone)
1139                 goto error;
1140
1141         if (cone->n_eq < dim)
1142                 return isl_basic_set_sample_with_cone(bset, cone);
1143
1144         isl_basic_set_free(cone);
1145         return sample_bounded(bset);
1146 error:
1147         isl_basic_set_free(bset);
1148         return NULL;
1149 }
1150
1151 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
1152 {
1153         struct isl_mat *T;
1154         struct isl_ctx *ctx;
1155         struct isl_vec *sample;
1156
1157         bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
1158         if (!bset)
1159                 return NULL;
1160
1161         ctx = bset->ctx;
1162         sample = isl_pip_basic_set_sample(bset);
1163
1164         if (sample && sample->size != 0)
1165                 sample = isl_mat_vec_product(T, sample);
1166         else
1167                 isl_mat_free(T);
1168
1169         return sample;
1170 }
1171
1172 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1173 {
1174         struct isl_ctx *ctx;
1175         unsigned dim;
1176         if (!bset)
1177                 return NULL;
1178
1179         ctx = bset->ctx;
1180         if (isl_basic_set_plain_is_empty(bset))
1181                 return empty_sample(bset);
1182
1183         dim = isl_basic_set_n_dim(bset);
1184         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1185         isl_assert(ctx, bset->n_div == 0, goto error);
1186
1187         if (bset->sample && bset->sample->size == 1 + dim) {
1188                 int contains = isl_basic_set_contains(bset, bset->sample);
1189                 if (contains < 0)
1190                         goto error;
1191                 if (contains) {
1192                         struct isl_vec *sample = isl_vec_copy(bset->sample);
1193                         isl_basic_set_free(bset);
1194                         return sample;
1195                 }
1196         }
1197         isl_vec_free(bset->sample);
1198         bset->sample = NULL;
1199
1200         if (bset->n_eq > 0)
1201                 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1202                                                : isl_basic_set_sample_vec);
1203         if (dim == 0)
1204                 return zero_sample(bset);
1205         if (dim == 1)
1206                 return interval_sample(bset);
1207
1208         switch (bset->ctx->opt->ilp_solver) {
1209         case ISL_ILP_PIP:
1210                 return pip_sample(bset);
1211         case ISL_ILP_GBR:
1212                 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1213         }
1214         isl_assert(bset->ctx, 0, );
1215 error:
1216         isl_basic_set_free(bset);
1217         return NULL;
1218 }
1219
1220 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1221 {
1222         return basic_set_sample(bset, 0);
1223 }
1224
1225 /* Compute an integer sample in "bset", where the caller guarantees
1226  * that "bset" is bounded.
1227  */
1228 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1229 {
1230         return basic_set_sample(bset, 1);
1231 }
1232
1233 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1234 {
1235         int i;
1236         int k;
1237         struct isl_basic_set *bset = NULL;
1238         struct isl_ctx *ctx;
1239         unsigned dim;
1240
1241         if (!vec)
1242                 return NULL;
1243         ctx = vec->ctx;
1244         isl_assert(ctx, vec->size != 0, goto error);
1245
1246         bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1247         if (!bset)
1248                 goto error;
1249         dim = isl_basic_set_n_dim(bset);
1250         for (i = dim - 1; i >= 0; --i) {
1251                 k = isl_basic_set_alloc_equality(bset);
1252                 if (k < 0)
1253                         goto error;
1254                 isl_seq_clr(bset->eq[k], 1 + dim);
1255                 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1256                 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1257         }
1258         bset->sample = vec;
1259
1260         return bset;
1261 error:
1262         isl_basic_set_free(bset);
1263         isl_vec_free(vec);
1264         return NULL;
1265 }
1266
1267 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1268 {
1269         struct isl_basic_set *bset;
1270         struct isl_vec *sample_vec;
1271
1272         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1273         sample_vec = isl_basic_set_sample_vec(bset);
1274         if (!sample_vec)
1275                 goto error;
1276         if (sample_vec->size == 0) {
1277                 struct isl_basic_map *sample;
1278                 sample = isl_basic_map_empty_like(bmap);
1279                 isl_vec_free(sample_vec);
1280                 isl_basic_map_free(bmap);
1281                 return sample;
1282         }
1283         bset = isl_basic_set_from_vec(sample_vec);
1284         return isl_basic_map_overlying_set(bset, bmap);
1285 error:
1286         isl_basic_map_free(bmap);
1287         return NULL;
1288 }
1289
1290 __isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1291 {
1292         return isl_basic_map_sample(bset);
1293 }
1294
1295 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1296 {
1297         int i;
1298         isl_basic_map *sample = NULL;
1299
1300         if (!map)
1301                 goto error;
1302
1303         for (i = 0; i < map->n; ++i) {
1304                 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1305                 if (!sample)
1306                         goto error;
1307                 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1308                         break;
1309                 isl_basic_map_free(sample);
1310         }
1311         if (i == map->n)
1312                 sample = isl_basic_map_empty_like_map(map);
1313         isl_map_free(map);
1314         return sample;
1315 error:
1316         isl_map_free(map);
1317         return NULL;
1318 }
1319
1320 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1321 {
1322         return (isl_basic_set *) isl_map_sample((isl_map *)set);
1323 }
1324
1325 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1326 {
1327         isl_vec *vec;
1328         isl_space *dim;
1329
1330         dim = isl_basic_set_get_space(bset);
1331         bset = isl_basic_set_underlying_set(bset);
1332         vec = isl_basic_set_sample_vec(bset);
1333
1334         return isl_point_alloc(dim, vec);
1335 }
1336
1337 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1338 {
1339         int i;
1340         isl_point *pnt;
1341
1342         if (!set)
1343                 return NULL;
1344
1345         for (i = 0; i < set->n; ++i) {
1346                 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1347                 if (!pnt)
1348                         goto error;
1349                 if (!isl_point_is_void(pnt))
1350                         break;
1351                 isl_point_free(pnt);
1352         }
1353         if (i == set->n)
1354                 pnt = isl_point_void(isl_set_get_space(set));
1355
1356         isl_set_free(set);
1357         return pnt;
1358 error:
1359         isl_set_free(set);
1360         return NULL;
1361 }