isl_map_subtract.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_map_private.h>
  11 #include <isl/seq.h>
  12 #include <isl/set.h>
  13 #include <isl/map.h>
  14 #include "isl_tab.h"
  15 #include <isl_point_private.h>
  16
  17 static void expand_constraint(isl_vec *v, unsigned dim,
  18         isl_int *c, int *div_map, unsigned n_div)
  19 {
  20         int i;
  21
  22         isl_seq_cpy(v->el, c, 1 + dim);
  23         isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
  24
  25         for (i = 0; i < n_div; ++i)
  26                 isl_int_set(v->el[1 + dim + div_map[i]], c[1 + dim + i]);
  27 }
  28
  29 /* Add all constraints of bmap to tab.  The equalities of bmap
  30  * are added as a pair of inequalities.
  31  */
  32 static int tab_add_constraints(struct isl_tab *tab,
  33         __isl_keep isl_basic_map *bmap, int *div_map)
  34 {
  35         int i;
  36         unsigned dim;
  37         unsigned tab_total;
  38         unsigned bmap_total;
  39         isl_vec *v;
  40
  41         if (!tab || !bmap)
  42                 return -1;
  43
  44         tab_total = isl_basic_map_total_dim(tab->bmap);
  45         bmap_total = isl_basic_map_total_dim(bmap);
  46         dim = isl_dim_total(tab->bmap->dim);
  47
  48         if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
  49                 return -1;
  50
  51         v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
  52         if (!v)
  53                 return -1;
  54
  55         for (i = 0; i < bmap->n_eq; ++i) {
  56                 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
  57                 if (isl_tab_add_ineq(tab, v->el) < 0)
  58                         goto error;
  59                 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
  60                 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
  61                 if (isl_tab_add_ineq(tab, v->el) < 0)
  62                         goto error;
  63                 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
  64                 if (tab->empty)
  65                         break;
  66         }
  67
  68         for (i = 0; i < bmap->n_ineq; ++i) {
  69                 expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
  70                 if (isl_tab_add_ineq(tab, v->el) < 0)
  71                         goto error;
  72                 if (tab->empty)
  73                         break;
  74         }
  75
  76         isl_vec_free(v);
  77         return 0;
  78 error:
  79         isl_vec_free(v);
  80         return -1;
  81 }
  82
  83 /* Add a specific constraint of bmap (or its opposite) to tab.
  84  * The position of the constraint is specified by "c", where
  85  * the equalities of bmap are counted twice, once for the inequality
  86  * that is equal to the equality, and once for its negation.
  87  */
  88 static int tab_add_constraint(struct isl_tab *tab,
  89         __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
  90 {
  91         unsigned dim;
  92         unsigned tab_total;
  93         unsigned bmap_total;
  94         isl_vec *v;
  95         int r;
  96
  97         if (!tab || !bmap)
  98                 return -1;
  99
 100         tab_total = isl_basic_map_total_dim(tab->bmap);
 101         bmap_total = isl_basic_map_total_dim(bmap);
 102         dim = isl_dim_total(tab->bmap->dim);
 103
 104         v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
 105         if (!v)
 106                 return -1;
 107
 108         if (c < 2 * bmap->n_eq) {
 109                 if ((c % 2) != oppose)
 110                         isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
 111                                         1 + bmap_total);
 112                 if (oppose)
 113                         isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
 114                 expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
 115                 r = isl_tab_add_ineq(tab, v->el);
 116                 if (oppose)
 117                         isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
 118                 if ((c % 2) != oppose)
 119                         isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
 120                                         1 + bmap_total);
 121         } else {
 122                 c -= 2 * bmap->n_eq;
 123                 if (oppose) {
 124                         isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
 125                                         1 + bmap_total);
 126                         isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
 127                 }
 128                 expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
 129                 r = isl_tab_add_ineq(tab, v->el);
 130                 if (oppose) {
 131                         isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
 132                         isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
 133                                         1 + bmap_total);
 134                 }
 135         }
 136
 137         isl_vec_free(v);
 138         return r;
 139 }
 140
 141 static int tab_add_divs(struct isl_tab *tab, __isl_keep isl_basic_map *bmap,
 142         int **div_map)
 143 {
 144         int i, j;
 145         struct isl_vec *vec;
 146         unsigned total;
 147         unsigned dim;
 148
 149         if (!bmap)
 150                 return -1;
 151         if (!bmap->n_div)
 152                 return 0;
 153
 154         if (!*div_map)
 155                 *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
 156         if (!*div_map)
 157                 return -1;
 158
 159         total = isl_basic_map_total_dim(tab->bmap);
 160         dim = total - tab->bmap->n_div;
 161         vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
 162         if (!vec)
 163                 return -1;
 164
 165         for (i = 0; i < bmap->n_div; ++i) {
 166                 isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
 167                 isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
 168                 for (j = 0; j < i; ++j)
 169                         isl_int_set(vec->el[2 + dim + (*div_map)[j]],
 170                                         bmap->div[i][2 + dim + j]);
 171                 for (j = 0; j < tab->bmap->n_div; ++j)
 172                         if (isl_seq_eq(tab->bmap->div[j],
 173                                         vec->el, 2 + dim + tab->bmap->n_div))
 174                                 break;
 175                 (*div_map)[i] = j;
 176                 if (j == tab->bmap->n_div) {
 177                         vec->size = 2 + dim + tab->bmap->n_div;
 178                         if (isl_tab_add_div(tab, vec, NULL, NULL) < 0)
 179                                 goto error;
 180                 }
 181         }
 182
 183         isl_vec_free(vec);
 184
 185         return 0;
 186 error:
 187         isl_vec_free(vec);
 188
 189         return -1;
 190 }
 191
 192 /* Freeze all constraints of tableau tab.
 193  */
 194 static int tab_freeze_constraints(struct isl_tab *tab)
 195 {
 196         int i;
 197
 198         for (i = 0; i < tab->n_con; ++i)
 199                 if (isl_tab_freeze_constraint(tab, i) < 0)
 200                         return -1;
 201
 202         return 0;
 203 }
 204
 205 /* Check for redundant constraints starting at offset.
 206  * Put the indices of the redundant constraints in index
 207  * and return the number of redundant constraints.
 208  */
 209 static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,
 210         int offset, int **index)
 211 {
 212         int i, n;
 213         int n_test = tab->n_con - offset;
 214
 215         if (isl_tab_detect_redundant(tab) < 0)
 216                 return -1;
 217
 218         if (!*index)
 219                 *index = isl_alloc_array(ctx, int, n_test);
 220         if (!*index)
 221                 return -1;
 222
 223         for (n = 0, i = 0; i < n_test; ++i) {
 224                 int r;
 225                 r = isl_tab_is_redundant(tab, offset + i);
 226                 if (r < 0)
 227                         return -1;
 228                 if (r)
 229                         continue;
 230                 (*index)[n++] = i;
 231         }
 232
 233         return n;
 234 }
 235
 236 /* basic_map_collect_diff calls add on each of the pieces of
 237  * the set difference between bmap and map until the add method
 238  * return a negative value.
 239  */
 240 struct isl_diff_collector {
 241         int (*add)(struct isl_diff_collector *dc,
 242                     __isl_take isl_basic_map *bmap);
 243 };
 244
 245 /* Compute the set difference between bmap and map and call
 246  * dc->add on each of the piece until this function returns
 247  * a negative value.
 248  * Return 0 on success and -1 on error.  dc->add returning
 249  * a negative value is treated as an error, but the calling
 250  * function can interpret the results based on the state of dc.
 251  *
 252  * Assumes that map has known divs.
 253  *
 254  * The difference is computed by a backtracking algorithm.
 255  * Each level corresponds to a basic map in "map".
 256  * When a node in entered for the first time, we check
 257  * if the corresonding basic map intersects the current piece
 258  * of "bmap".  If not, we move to the next level.
 259  * Otherwise, we split the current piece into as many
 260  * pieces as there are non-redundant constraints of the current
 261  * basic map in the intersection.  Each of these pieces is
 262  * handled by a child of the current node.
 263  * In particular, if there are n non-redundant constraints,
 264  * then for each 0 <= i < n, a piece is cut off by adding
 265  * constraints 0 <= j < i and adding the opposite of constraint i.
 266  * If there are no non-redundant constraints, meaning that the current
 267  * piece is a subset of the current basic map, then we simply backtrack.
 268  *
 269  * In the leaves, we check if the remaining piece has any integer points
 270  * and if so, pass it along to dc->add.  As a special case, if nothing
 271  * has been removed when we end up in a leaf, we simply pass along
 272  * the original basic map.
 273  */
 274 static int basic_map_collect_diff(__isl_take isl_basic_map *bmap,
 275         __isl_take isl_map *map, struct isl_diff_collector *dc)
 276 {
 277         int i;
 278         int modified;
 279         int level;
 280         int init;
 281         int empty;
 282         isl_ctx *ctx;
 283         struct isl_tab *tab = NULL;
 284         struct isl_tab_undo **snap = NULL;
 285         int *k = NULL;
 286         int *n = NULL;
 287         int **index = NULL;
 288         int **div_map = NULL;
 289
 290         empty = isl_basic_map_is_empty(bmap);
 291         if (empty) {
 292                 isl_basic_map_free(bmap);
 293                 isl_map_free(map);
 294                 return empty < 0 ? -1 : 0;
 295         }
 296
 297         bmap = isl_basic_map_cow(bmap);
 298         map = isl_map_cow(map);
 299
 300         if (!bmap || !map)
 301                 goto error;
 302
 303         ctx = map->ctx;
 304         snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
 305         k = isl_alloc_array(map->ctx, int, map->n);
 306         n = isl_alloc_array(map->ctx, int, map->n);
 307         index = isl_calloc_array(map->ctx, int *, map->n);
 308         div_map = isl_calloc_array(map->ctx, int *, map->n);
 309         if (!snap || !k || !n || !index || !div_map)
 310                 goto error;
 311
 312         bmap = isl_basic_map_order_divs(bmap);
 313         map = isl_map_order_divs(map);
 314
 315         tab = isl_tab_from_basic_map(bmap);
 316         if (isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
 317                 goto error;
 318
 319         modified = 0;
 320         level = 0;
 321         init = 1;
 322
 323         while (level >= 0) {
 324                 if (level >= map->n) {
 325                         int empty;
 326                         struct isl_basic_map *bm;
 327                         if (!modified) {
 328                                 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
 329                                         goto error;
 330                                 break;
 331                         }
 332                         bm = isl_basic_map_copy(tab->bmap);
 333                         bm = isl_basic_map_cow(bm);
 334                         bm = isl_basic_map_update_from_tab(bm, tab);
 335                         bm = isl_basic_map_simplify(bm);
 336                         bm = isl_basic_map_finalize(bm);
 337                         empty = isl_basic_map_is_empty(bm);
 338                         if (empty)
 339                                 isl_basic_map_free(bm);
 340                         else if (dc->add(dc, bm) < 0)
 341                                 goto error;
 342                         if (empty < 0)
 343                                 goto error;
 344                         level--;
 345                         init = 0;
 346                         continue;
 347                 }
 348                 if (init) {
 349                         int offset;
 350                         struct isl_tab_undo *snap2;
 351                         snap2 = isl_tab_snap(tab);
 352                         if (tab_add_divs(tab, map->p[level],
 353                                          &div_map[level]) < 0)
 354                                 goto error;
 355                         offset = tab->n_con;
 356                         snap[level] = isl_tab_snap(tab);
 357                         if (tab_freeze_constraints(tab) < 0)
 358                                 goto error;
 359                         if (tab_add_constraints(tab, map->p[level],
 360                                                 div_map[level]) < 0)
 361                                 goto error;
 362                         k[level] = 0;
 363                         n[level] = 0;
 364                         if (tab->empty) {
 365                                 if (isl_tab_rollback(tab, snap2) < 0)
 366                                         goto error;
 367                                 level++;
 368                                 continue;
 369                         }
 370                         modified = 1;
 371                         n[level] = n_non_redundant(ctx, tab, offset,
 372                                                     &index[level]);
 373                         if (n[level] < 0)
 374                                 goto error;
 375                         if (n[level] == 0) {
 376                                 level--;
 377                                 init = 0;
 378                                 continue;
 379                         }
 380                         if (isl_tab_rollback(tab, snap[level]) < 0)
 381                                 goto error;
 382                         if (tab_add_constraint(tab, map->p[level],
 383                                         div_map[level], index[level][0], 1) < 0)
 384                                 goto error;
 385                         level++;
 386                         continue;
 387                 } else {
 388                         if (k[level] + 1 >= n[level]) {
 389                                 level--;
 390                                 continue;
 391                         }
 392                         if (isl_tab_rollback(tab, snap[level]) < 0)
 393                                 goto error;
 394                         if (tab_add_constraint(tab, map->p[level],
 395                                                 div_map[level],
 396                                                 index[level][k[level]], 0) < 0)
 397                                 goto error;
 398                         snap[level] = isl_tab_snap(tab);
 399                         k[level]++;
 400                         if (tab_add_constraint(tab, map->p[level],
 401                                                 div_map[level],
 402                                                 index[level][k[level]], 1) < 0)
 403                                 goto error;
 404                         level++;
 405                         init = 1;
 406                         continue;
 407                 }
 408         }
 409
 410         isl_tab_free(tab);
 411         free(snap);
 412         free(n);
 413         free(k);
 414         for (i = 0; index && i < map->n; ++i)
 415                 free(index[i]);
 416         free(index);
 417         for (i = 0; div_map && i < map->n; ++i)
 418                 free(div_map[i]);
 419         free(div_map);
 420
 421         isl_basic_map_free(bmap);
 422         isl_map_free(map);
 423
 424         return 0;
 425 error:
 426         isl_tab_free(tab);
 427         free(snap);
 428         free(n);
 429         free(k);
 430         for (i = 0; index && i < map->n; ++i)
 431                 free(index[i]);
 432         free(index);
 433         for (i = 0; div_map && i < map->n; ++i)
 434                 free(div_map[i]);
 435         free(div_map);
 436         isl_basic_map_free(bmap);
 437         isl_map_free(map);
 438         return -1;
 439 }
 440
 441 /* A diff collector that actually collects all parts of the
 442  * set difference in the field diff.
 443  */
 444 struct isl_subtract_diff_collector {
 445         struct isl_diff_collector dc;
 446         struct isl_map *diff;
 447 };
 448
 449 /* isl_subtract_diff_collector callback.
 450  */
 451 static int basic_map_subtract_add(struct isl_diff_collector *dc,
 452                             __isl_take isl_basic_map *bmap)
 453 {
 454         struct isl_subtract_diff_collector *sdc;
 455         sdc = (struct isl_subtract_diff_collector *)dc;
 456
 457         sdc->diff = isl_map_union_disjoint(sdc->diff,
 458                         isl_map_from_basic_map(bmap));
 459
 460         return sdc->diff ? 0 : -1;
 461 }
 462
 463 /* Return the set difference between bmap and map.
 464  */
 465 static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
 466         __isl_take isl_map *map)
 467 {
 468         struct isl_subtract_diff_collector sdc;
 469         sdc.dc.add = &basic_map_subtract_add;
 470         sdc.diff = isl_map_empty_like_basic_map(bmap);
 471         if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
 472                 isl_map_free(sdc.diff);
 473                 sdc.diff = NULL;
 474         }
 475         return sdc.diff;
 476 }
 477
 478 /* Return the set difference between map1 and map2.
 479  * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
 480  */
 481 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
 482 {
 483         int i;
 484         struct isl_map *diff;
 485
 486         if (!map1 || !map2)
 487                 goto error;
 488
 489         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
 490
 491         if (isl_map_is_empty(map2)) {
 492                 isl_map_free(map2);
 493                 return map1;
 494         }
 495
 496         map1 = isl_map_compute_divs(map1);
 497         map2 = isl_map_compute_divs(map2);
 498         if (!map1 || !map2)
 499                 goto error;
 500
 501         map1 = isl_map_remove_empty_parts(map1);
 502         map2 = isl_map_remove_empty_parts(map2);
 503
 504         diff = isl_map_empty_like(map1);
 505         for (i = 0; i < map1->n; ++i) {
 506                 struct isl_map *d;
 507                 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
 508                                        isl_map_copy(map2));
 509                 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
 510                         diff = isl_map_union_disjoint(diff, d);
 511                 else
 512                         diff = isl_map_union(diff, d);
 513         }
 514
 515         isl_map_free(map1);
 516         isl_map_free(map2);
 517
 518         return diff;
 519 error:
 520         isl_map_free(map1);
 521         isl_map_free(map2);
 522         return NULL;
 523 }
 524
 525 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 526 {
 527         return (struct isl_set *)
 528                 isl_map_subtract(
 529                         (struct isl_map *)set1, (struct isl_map *)set2);
 530 }
 531
 532 /* A diff collector that aborts as soon as its add function is called,
 533  * setting empty to 0.
 534  */
 535 struct isl_is_empty_diff_collector {
 536         struct isl_diff_collector dc;
 537         int empty;
 538 };
 539
 540 /* isl_is_empty_diff_collector callback.
 541  */
 542 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
 543                             __isl_take isl_basic_map *bmap)
 544 {
 545         struct isl_is_empty_diff_collector *edc;
 546         edc = (struct isl_is_empty_diff_collector *)dc;
 547
 548         edc->empty = 0;
 549
 550         isl_basic_map_free(bmap);
 551         return -1;
 552 }
 553
 554 /* Check if bmap \ map is empty by computing this set difference
 555  * and breaking off as soon as the difference is known to be non-empty.
 556  */
 557 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
 558         __isl_keep isl_map *map)
 559 {
 560         int r;
 561         struct isl_is_empty_diff_collector edc;
 562
 563         r = isl_basic_map_fast_is_empty(bmap);
 564         if (r)
 565                 return r;
 566
 567         edc.dc.add = &basic_map_is_empty_add;
 568         edc.empty = 1;
 569         r = basic_map_collect_diff(isl_basic_map_copy(bmap),
 570                                    isl_map_copy(map), &edc.dc);
 571         if (!edc.empty)
 572                 return 0;
 573
 574         return r < 0 ? -1 : 1;
 575 }
 576
 577 /* Check if map1 \ map2 is empty by checking if the set difference is empty
 578  * for each of the basic maps in map1.
 579  */
 580 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 581 {
 582         int i;
 583         int is_empty = 1;
 584
 585         if (!map1 || !map2)
 586                 return -1;
 587
 588         for (i = 0; i < map1->n; ++i) {
 589                 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
 590                 if (is_empty < 0 || !is_empty)
 591                          break;
 592         }
 593
 594         return is_empty;
 595 }
 596
 597 /* Return 1 if "bmap" contains a single element.
 598  */
 599 int isl_basic_map_fast_is_singleton(__isl_keep isl_basic_map *bmap)
 600 {
 601         if (!bmap)
 602                 return -1;
 603         if (bmap->n_div)
 604                 return 0;
 605         if (bmap->n_ineq)
 606                 return 0;
 607         return bmap->n_eq == isl_basic_map_total_dim(bmap);
 608 }
 609
 610 /* Return 1 if "map" contains a single element.
 611  */
 612 int isl_map_fast_is_singleton(__isl_keep isl_map *map)
 613 {
 614         if (!map)
 615                 return -1;
 616         if (map->n != 1)
 617                 return 0;
 618
 619         return isl_basic_map_fast_is_singleton(map->p[0]);
 620 }
 621
 622 /* Given a singleton basic map, extract the single element
 623  * as an isl_point.
 624  */
 625 static __isl_give isl_point *singleton_extract_point(
 626         __isl_keep isl_basic_map *bmap)
 627 {
 628         int i, j;
 629         unsigned dim;
 630         struct isl_vec *point;
 631         isl_int m;
 632
 633         if (!bmap)
 634                 return NULL;
 635
 636         dim = isl_basic_map_total_dim(bmap);
 637         isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
 638         point = isl_vec_alloc(bmap->ctx, 1 + dim);
 639         if (!point)
 640                 return NULL;
 641
 642         isl_int_init(m);
 643
 644         isl_int_set_si(point->el[0], 1);
 645         for (j = 0; j < bmap->n_eq; ++j) {
 646                 int s;
 647                 int i = dim - 1 - j;
 648                 isl_assert(bmap->ctx,
 649                     isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
 650                     goto error);
 651                 isl_assert(bmap->ctx,
 652                     isl_int_is_one(bmap->eq[j][1 + i]) ||
 653                     isl_int_is_negone(bmap->eq[j][1 + i]),
 654                     goto error);
 655                 isl_assert(bmap->ctx,
 656                     isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
 657                     goto error);
 658
 659                 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
 660                 isl_int_divexact(m, bmap->eq[j][1 + i], m);
 661                 isl_int_abs(m, m);
 662                 isl_seq_scale(point->el, point->el, m, 1 + i);
 663                 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
 664                 isl_int_neg(m, m);
 665                 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
 666         }
 667
 668         isl_int_clear(m);
 669         return isl_point_alloc(isl_basic_map_get_dim(bmap), point);
 670 error:
 671         isl_int_clear(m);
 672         isl_vec_free(point);
 673         return NULL;
 674 }
 675
 676 /* Return 1 is the singleton map "map1" is a subset of "map2",
 677  * i.e., if the single element of "map1" is also an element of "map2".
 678  * Assumes "map2" has known divs.
 679  */
 680 static int map_is_singleton_subset(__isl_keep isl_map *map1,
 681         __isl_keep isl_map *map2)
 682 {
 683         int i;
 684         int is_subset = 0;
 685         struct isl_point *point;
 686
 687         if (!map1 || !map2)
 688                 return -1;
 689         if (map1->n != 1)
 690                 return -1;
 691
 692         point = singleton_extract_point(map1->p[0]);
 693         if (!point)
 694                 return -1;
 695
 696         for (i = 0; i < map2->n; ++i) {
 697                 is_subset = isl_basic_map_contains_point(map2->p[i], point);
 698                 if (is_subset)
 699                         break;
 700         }
 701
 702         isl_point_free(point);
 703         return is_subset;
 704 }
 705
 706 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
 707 {
 708         int is_subset = 0;
 709         struct isl_map *diff;
 710
 711         if (!map1 || !map2)
 712                 return -1;
 713
 714         if (isl_map_is_empty(map1))
 715                 return 1;
 716
 717         if (isl_map_is_empty(map2))
 718                 return 0;
 719
 720         if (isl_map_fast_is_universe(map2))
 721                 return 1;
 722
 723         map2 = isl_map_compute_divs(isl_map_copy(map2));
 724         if (isl_map_fast_is_singleton(map1)) {
 725                 is_subset = map_is_singleton_subset(map1, map2);
 726                 isl_map_free(map2);
 727                 return is_subset;
 728         }
 729         is_subset = map_diff_is_empty(map1, map2);
 730         isl_map_free(map2);
 731
 732         return is_subset;
 733 }
 734
 735 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 736 {
 737         return isl_map_is_subset(
 738                         (struct isl_map *)set1, (struct isl_map *)set2);
 739 }
 740
 741 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
 742 {
 743         int i;
 744         struct isl_subtract_diff_collector sdc;
 745         sdc.dc.add = &basic_map_subtract_add;
 746
 747         if (!map)
 748                 return NULL;
 749         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 750                 return map;
 751         if (map->n <= 1)
 752                 return map;
 753
 754         map = isl_map_compute_divs(map);
 755         map = isl_map_remove_empty_parts(map);
 756
 757         if (!map || map->n <= 1)
 758                 return map;
 759
 760         sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 761
 762         for (i = 1; i < map->n; ++i) {
 763                 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
 764                 struct isl_map *copy = isl_map_copy(sdc.diff);
 765                 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
 766                         isl_map_free(sdc.diff);
 767                         sdc.diff = NULL;
 768                         break;
 769                 }
 770         }
 771
 772         isl_map_free(map);
 773
 774         return sdc.diff;
 775 }
 776
 777 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
 778 {
 779         return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
 780 }
 781
 782 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
 783 {
 784         isl_set *universe;
 785
 786         if (!set)
 787                 return NULL;
 788
 789         universe = isl_set_universe(isl_set_get_dim(set));
 790
 791         return isl_set_subtract(universe, set);
 792 }