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_seq.h"
  11 #include "isl_set.h"
  12 #include "isl_map.h"
  13 #include "isl_map_private.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(struct isl_tab *tab, int offset, int **index)
 210 {
 211         int i, n;
 212         int n_test = tab->n_con - offset;
 213
 214         if (isl_tab_detect_redundant(tab) < 0)
 215                 return -1;
 216
 217         if (!*index)
 218                 *index = isl_alloc_array(tab->mat->ctx, int, n_test);
 219         if (!*index)
 220                 return -1;
 221
 222         for (n = 0, i = 0; i < n_test; ++i) {
 223                 int r;
 224                 r = isl_tab_is_redundant(tab, offset + i);
 225                 if (r < 0)
 226                         return -1;
 227                 if (r)
 228                         continue;
 229                 (*index)[n++] = i;
 230         }
 231
 232         return n;
 233 }
 234
 235 /* basic_map_collect_diff calls add on each of the pieces of
 236  * the set difference between bmap and map until the add method
 237  * return a negative value.
 238  */
 239 struct isl_diff_collector {
 240         int (*add)(struct isl_diff_collector *dc,
 241                     __isl_take isl_basic_map *bmap);
 242 };
 243
 244 /* Compute the set difference between bmap and map and call
 245  * dc->add on each of the piece until this function returns
 246  * a negative value.
 247  * Return 0 on success and -1 on error.  dc->add returning
 248  * a negative value is treated as an error, but the calling
 249  * function can interpret the results based on the state of dc.
 250  *
 251  * Assumes that both bmap and map have known divs.
 252  *
 253  * The difference is computed by a backtracking algorithm.
 254  * Each level corresponds to a basic map in "map".
 255  * When a node in entered for the first time, we check
 256  * if the corresonding basic map intersects the current piece
 257  * of "bmap".  If not, we move to the next level.
 258  * Otherwise, we split the current piece into as many
 259  * pieces as there are non-redundant constraints of the current
 260  * basic map in the intersection.  Each of these pieces is
 261  * handled by a child of the current node.
 262  * In particular, if there are n non-redundant constraints,
 263  * then for each 0 <= i < n, a piece is cut off by adding
 264  * constraints 0 <= j < i and adding the opposite of constraint i.
 265  * If there are no non-redundant constraints, meaning that the current
 266  * piece is a subset of the current basic map, then we simply backtrack.
 267  *
 268  * In the leaves, we check if the remaining piece has any integer points
 269  * and if so, pass it along to dc->add.  As a special case, if nothing
 270  * has been removed when we end up in a leaf, we simply pass along
 271  * the original basic map.
 272  */
 273 static int basic_map_collect_diff(__isl_take isl_basic_map *bmap,
 274         __isl_take isl_map *map, struct isl_diff_collector *dc)
 275 {
 276         int i;
 277         int modified;
 278         int level;
 279         int init;
 280         int empty;
 281         struct isl_tab *tab = NULL;
 282         struct isl_tab_undo **snap = NULL;
 283         int *k = NULL;
 284         int *n = NULL;
 285         int **index = NULL;
 286         int **div_map = NULL;
 287
 288         empty = isl_basic_map_is_empty(bmap);
 289         if (empty) {
 290                 isl_basic_map_free(bmap);
 291                 isl_map_free(map);
 292                 return empty < 0 ? -1 : 0;
 293         }
 294
 295         bmap = isl_basic_map_cow(bmap);
 296         map = isl_map_cow(map);
 297
 298         if (!bmap || !map)
 299                 goto error;
 300
 301         snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
 302         k = isl_alloc_array(map->ctx, int, map->n);
 303         n = isl_alloc_array(map->ctx, int, map->n);
 304         index = isl_calloc_array(map->ctx, int *, map->n);
 305         div_map = isl_calloc_array(map->ctx, int *, map->n);
 306         if (!snap || !k || !n || !index || !div_map)
 307                 goto error;
 308
 309         bmap = isl_basic_map_order_divs(bmap);
 310         map = isl_map_order_divs(map);
 311
 312         tab = isl_tab_from_basic_map(bmap);
 313         if (isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
 314                 goto error;
 315
 316         modified = 0;
 317         level = 0;
 318         init = 1;
 319
 320         while (level >= 0) {
 321                 if (level >= map->n) {
 322                         int empty;
 323                         struct isl_basic_map *bm;
 324                         if (!modified) {
 325                                 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
 326                                         goto error;
 327                                 break;
 328                         }
 329                         bm = isl_basic_map_copy(tab->bmap);
 330                         bm = isl_basic_map_cow(bm);
 331                         bm = isl_basic_map_update_from_tab(bm, tab);
 332                         bm = isl_basic_map_simplify(bm);
 333                         bm = isl_basic_map_finalize(bm);
 334                         empty = isl_basic_map_is_empty(bm);
 335                         if (empty)
 336                                 isl_basic_map_free(bm);
 337                         else if (dc->add(dc, bm) < 0)
 338                                 goto error;
 339                         if (empty < 0)
 340                                 goto error;
 341                         level--;
 342                         init = 0;
 343                         continue;
 344                 }
 345                 if (init) {
 346                         int offset;
 347                         struct isl_tab_undo *snap2;
 348                         snap2 = isl_tab_snap(tab);
 349                         if (tab_add_divs(tab, map->p[level],
 350                                          &div_map[level]) < 0)
 351                                 goto error;
 352                         offset = tab->n_con;
 353                         snap[level] = isl_tab_snap(tab);
 354                         if (tab_freeze_constraints(tab) < 0)
 355                                 goto error;
 356                         if (tab_add_constraints(tab, map->p[level],
 357                                                 div_map[level]) < 0)
 358                                 goto error;
 359                         k[level] = 0;
 360                         n[level] = 0;
 361                         if (tab->empty) {
 362                                 if (isl_tab_rollback(tab, snap2) < 0)
 363                                         goto error;
 364                                 level++;
 365                                 continue;
 366                         }
 367                         modified = 1;
 368                         n[level] = n_non_redundant(tab, offset, &index[level]);
 369                         if (n[level] < 0)
 370                                 goto error;
 371                         if (n[level] == 0) {
 372                                 level--;
 373                                 init = 0;
 374                                 continue;
 375                         }
 376                         if (isl_tab_rollback(tab, snap[level]) < 0)
 377                                 goto error;
 378                         if (tab_add_constraint(tab, map->p[level],
 379                                         div_map[level], index[level][0], 1) < 0)
 380                                 goto error;
 381                         level++;
 382                         continue;
 383                 } else {
 384                         if (k[level] + 1 >= n[level]) {
 385                                 level--;
 386                                 continue;
 387                         }
 388                         if (isl_tab_rollback(tab, snap[level]) < 0)
 389                                 goto error;
 390                         if (tab_add_constraint(tab, map->p[level],
 391                                                 div_map[level],
 392                                                 index[level][k[level]], 0) < 0)
 393                                 goto error;
 394                         snap[level] = isl_tab_snap(tab);
 395                         k[level]++;
 396                         if (tab_add_constraint(tab, map->p[level],
 397                                                 div_map[level],
 398                                                 index[level][k[level]], 1) < 0)
 399                                 goto error;
 400                         level++;
 401                         init = 1;
 402                         continue;
 403                 }
 404         }
 405
 406         isl_tab_free(tab);
 407         free(snap);
 408         free(n);
 409         free(k);
 410         for (i = 0; index && i < map->n; ++i)
 411                 free(index[i]);
 412         free(index);
 413         for (i = 0; div_map && i < map->n; ++i)
 414                 free(div_map[i]);
 415         free(div_map);
 416
 417         isl_basic_map_free(bmap);
 418         isl_map_free(map);
 419
 420         return 0;
 421 error:
 422         isl_tab_free(tab);
 423         free(snap);
 424         free(n);
 425         free(k);
 426         for (i = 0; index && i < map->n; ++i)
 427                 free(index[i]);
 428         free(index);
 429         for (i = 0; div_map && i < map->n; ++i)
 430                 free(div_map[i]);
 431         free(div_map);
 432         isl_basic_map_free(bmap);
 433         isl_map_free(map);
 434         return -1;
 435 }
 436
 437 /* A diff collector that actually collects all parts of the
 438  * set difference in the field diff.
 439  */
 440 struct isl_subtract_diff_collector {
 441         struct isl_diff_collector dc;
 442         struct isl_map *diff;
 443 };
 444
 445 /* isl_subtract_diff_collector callback.
 446  */
 447 static int basic_map_subtract_add(struct isl_diff_collector *dc,
 448                             __isl_take isl_basic_map *bmap)
 449 {
 450         struct isl_subtract_diff_collector *sdc;
 451         sdc = (struct isl_subtract_diff_collector *)dc;
 452
 453         sdc->diff = isl_map_union_disjoint(sdc->diff,
 454                         isl_map_from_basic_map(bmap));
 455
 456         return sdc->diff ? 0 : -1;
 457 }
 458
 459 /* Return the set difference between bmap and map.
 460  */
 461 static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
 462         __isl_take isl_map *map)
 463 {
 464         struct isl_subtract_diff_collector sdc;
 465         sdc.dc.add = &basic_map_subtract_add;
 466         sdc.diff = isl_map_empty_like_basic_map(bmap);
 467         if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
 468                 isl_map_free(sdc.diff);
 469                 sdc.diff = NULL;
 470         }
 471         return sdc.diff;
 472 }
 473
 474 /* Return the set difference between map1 and map2.
 475  * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
 476  */
 477 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
 478 {
 479         int i;
 480         struct isl_map *diff;
 481
 482         if (!map1 || !map2)
 483                 goto error;
 484
 485         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
 486
 487         if (isl_map_is_empty(map2)) {
 488                 isl_map_free(map2);
 489                 return map1;
 490         }
 491
 492         map1 = isl_map_compute_divs(map1);
 493         map2 = isl_map_compute_divs(map2);
 494         if (!map1 || !map2)
 495                 goto error;
 496
 497         map1 = isl_map_remove_empty_parts(map1);
 498         map2 = isl_map_remove_empty_parts(map2);
 499
 500         diff = isl_map_empty_like(map1);
 501         for (i = 0; i < map1->n; ++i) {
 502                 struct isl_map *d;
 503                 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
 504                                        isl_map_copy(map2));
 505                 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
 506                         diff = isl_map_union_disjoint(diff, d);
 507                 else
 508                         diff = isl_map_union(diff, d);
 509         }
 510
 511         isl_map_free(map1);
 512         isl_map_free(map2);
 513
 514         return diff;
 515 error:
 516         isl_map_free(map1);
 517         isl_map_free(map2);
 518         return NULL;
 519 }
 520
 521 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 522 {
 523         return (struct isl_set *)
 524                 isl_map_subtract(
 525                         (struct isl_map *)set1, (struct isl_map *)set2);
 526 }
 527
 528 /* A diff collector that aborts as soon as its add function is called,
 529  * setting empty to 0.
 530  */
 531 struct isl_is_empty_diff_collector {
 532         struct isl_diff_collector dc;
 533         int empty;
 534 };
 535
 536 /* isl_is_empty_diff_collector callback.
 537  */
 538 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
 539                             __isl_take isl_basic_map *bmap)
 540 {
 541         struct isl_is_empty_diff_collector *edc;
 542         edc = (struct isl_is_empty_diff_collector *)dc;
 543
 544         edc->empty = 0;
 545
 546         isl_basic_map_free(bmap);
 547         return -1;
 548 }
 549
 550 /* Check if bmap \ map is empty by computing this set difference
 551  * and breaking off as soon as the difference is known to be non-empty.
 552  */
 553 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
 554         __isl_keep isl_map *map)
 555 {
 556         int r;
 557         struct isl_is_empty_diff_collector edc;
 558
 559         r = isl_basic_map_fast_is_empty(bmap);
 560         if (r)
 561                 return r;
 562
 563         edc.dc.add = &basic_map_is_empty_add;
 564         edc.empty = 1;
 565         r = basic_map_collect_diff(isl_basic_map_copy(bmap),
 566                                    isl_map_copy(map), &edc.dc);
 567         if (!edc.empty)
 568                 return 0;
 569
 570         return r < 0 ? -1 : 1;
 571 }
 572
 573 /* Check if map1 \ map2 is empty by checking if the set difference is empty
 574  * for each of the basic maps in map1.
 575  */
 576 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 577 {
 578         int i;
 579         int is_empty = 1;
 580
 581         if (!map1 || !map2)
 582                 return -1;
 583
 584         for (i = 0; i < map1->n; ++i) {
 585                 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
 586                 if (is_empty < 0 || !is_empty)
 587                          break;
 588         }
 589
 590         return is_empty;
 591 }
 592
 593 /* Return 1 if "bmap" contains a single element.
 594  */
 595 int isl_basic_map_is_singleton(__isl_keep isl_basic_map *bmap)
 596 {
 597         if (!bmap)
 598                 return -1;
 599         if (bmap->n_div)
 600                 return 0;
 601         if (bmap->n_ineq)
 602                 return 0;
 603         return bmap->n_eq == isl_basic_map_total_dim(bmap);
 604 }
 605
 606 /* Return 1 if "map" contains a single element.
 607  */
 608 int isl_map_is_singleton(__isl_keep isl_map *map)
 609 {
 610         if (!map)
 611                 return -1;
 612         if (map->n != 1)
 613                 return 0;
 614
 615         return isl_basic_map_is_singleton(map->p[0]);
 616 }
 617
 618 /* Given a singleton basic map, extract the single element
 619  * as an isl_point.
 620  */
 621 static __isl_give isl_point *singleton_extract_point(
 622         __isl_keep isl_basic_map *bmap)
 623 {
 624         int i, j;
 625         unsigned dim;
 626         struct isl_vec *point;
 627         isl_int m;
 628
 629         if (!bmap)
 630                 return NULL;
 631
 632         dim = isl_basic_map_total_dim(bmap);
 633         isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
 634         point = isl_vec_alloc(bmap->ctx, 1 + dim);
 635         if (!point)
 636                 return NULL;
 637
 638         isl_int_init(m);
 639
 640         isl_int_set_si(point->el[0], 1);
 641         for (j = 0; j < bmap->n_eq; ++j) {
 642                 int s;
 643                 int i = dim - 1 - j;
 644                 isl_assert(bmap->ctx,
 645                     isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
 646                     goto error);
 647                 isl_assert(bmap->ctx,
 648                     isl_int_is_one(bmap->eq[j][1 + i]) ||
 649                     isl_int_is_negone(bmap->eq[j][1 + i]),
 650                     goto error);
 651                 isl_assert(bmap->ctx,
 652                     isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
 653                     goto error);
 654
 655                 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
 656                 isl_int_divexact(m, bmap->eq[j][1 + i], m);
 657                 isl_int_abs(m, m);
 658                 isl_seq_scale(point->el, point->el, m, 1 + i);
 659                 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
 660                 isl_int_neg(m, m);
 661                 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
 662         }
 663
 664         isl_int_clear(m);
 665         return isl_point_alloc(isl_basic_map_get_dim(bmap), point);
 666 error:
 667         isl_int_clear(m);
 668         isl_vec_free(point);
 669         return NULL;
 670 }
 671
 672 /* Return 1 is the singleton map "map1" is a subset of "map2",
 673  * i.e., if the single element of "map1" is also an element of "map2".
 674  */
 675 static int map_is_singleton_subset(__isl_keep isl_map *map1,
 676         __isl_keep isl_map *map2)
 677 {
 678         int i;
 679         int is_subset = 0;
 680         struct isl_point *point;
 681
 682         if (!map1 || !map2)
 683                 return -1;
 684         if (map1->n != 1)
 685                 return -1;
 686
 687         point = singleton_extract_point(map1->p[0]);
 688         if (!point)
 689                 return -1;
 690
 691         for (i = 0; i < map2->n; ++i) {
 692                 is_subset = isl_basic_map_contains_point(map2->p[i], point);
 693                 if (is_subset)
 694                         break;
 695         }
 696
 697         isl_point_free(point);
 698         return is_subset;
 699 }
 700
 701 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
 702 {
 703         int is_subset = 0;
 704         struct isl_map *diff;
 705
 706         if (!map1 || !map2)
 707                 return -1;
 708
 709         if (isl_map_is_empty(map1))
 710                 return 1;
 711
 712         if (isl_map_is_empty(map2))
 713                 return 0;
 714
 715         if (isl_map_fast_is_universe(map2))
 716                 return 1;
 717
 718         map1 = isl_map_compute_divs(isl_map_copy(map1));
 719         map2 = isl_map_compute_divs(isl_map_copy(map2));
 720         if (isl_map_is_singleton(map1)) {
 721                 is_subset = map_is_singleton_subset(map1, map2);
 722                 isl_map_free(map1);
 723                 isl_map_free(map2);
 724                 return is_subset;
 725         }
 726         is_subset = map_diff_is_empty(map1, map2);
 727         isl_map_free(map1);
 728         isl_map_free(map2);
 729
 730         return is_subset;
 731 }
 732
 733 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 734 {
 735         return isl_map_is_subset(
 736                         (struct isl_map *)set1, (struct isl_map *)set2);
 737 }
 738
 739 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
 740 {
 741         int i;
 742         struct isl_subtract_diff_collector sdc;
 743         sdc.dc.add = &basic_map_subtract_add;
 744
 745         if (!map)
 746                 return NULL;
 747         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 748                 return map;
 749         if (map->n <= 1)
 750                 return map;
 751
 752         map = isl_map_compute_divs(map);
 753         map = isl_map_remove_empty_parts(map);
 754
 755         if (!map || map->n <= 1)
 756                 return map;
 757
 758         sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 759
 760         for (i = 1; i < map->n; ++i) {
 761                 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
 762                 struct isl_map *copy = isl_map_copy(sdc.diff);
 763                 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
 764                         isl_map_free(sdc.diff);
 765                         sdc.diff = NULL;
 766                         break;
 767                 }
 768         }
 769
 770         isl_map_free(map);
 771
 772         return sdc.diff;
 773 }
 774
 775 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
 776 {
 777         return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
 778 }
 779
 780 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
 781 {
 782         isl_set *universe;
 783
 784         if (!set)
 785                 return NULL;
 786
 787         universe = isl_set_universe(isl_set_get_dim(set));
 788
 789         return isl_set_subtract(universe, set);
 790 }