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_space_dim(tab->bmap->dim, isl_dim_all);
  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_space_dim(tab->bmap->dim, isl_dim_all);
 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 static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,
 482         __isl_take isl_map *map2)
 483 {
 484         int i;
 485         struct isl_map *diff;
 486
 487         if (!map1 || !map2)
 488                 goto error;
 489
 490         isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
 491
 492         if (isl_map_is_empty(map2)) {
 493                 isl_map_free(map2);
 494                 return map1;
 495         }
 496
 497         map1 = isl_map_compute_divs(map1);
 498         map2 = isl_map_compute_divs(map2);
 499         if (!map1 || !map2)
 500                 goto error;
 501
 502         map1 = isl_map_remove_empty_parts(map1);
 503         map2 = isl_map_remove_empty_parts(map2);
 504
 505         diff = isl_map_empty_like(map1);
 506         for (i = 0; i < map1->n; ++i) {
 507                 struct isl_map *d;
 508                 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
 509                                        isl_map_copy(map2));
 510                 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
 511                         diff = isl_map_union_disjoint(diff, d);
 512                 else
 513                         diff = isl_map_union(diff, d);
 514         }
 515
 516         isl_map_free(map1);
 517         isl_map_free(map2);
 518
 519         return diff;
 520 error:
 521         isl_map_free(map1);
 522         isl_map_free(map2);
 523         return NULL;
 524 }
 525
 526 __isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
 527         __isl_take isl_map *map2)
 528 {
 529         return isl_map_align_params_map_map_and(map1, map2, &map_subtract);
 530 }
 531
 532 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 533 {
 534         return (struct isl_set *)
 535                 isl_map_subtract(
 536                         (struct isl_map *)set1, (struct isl_map *)set2);
 537 }
 538
 539 /* A diff collector that aborts as soon as its add function is called,
 540  * setting empty to 0.
 541  */
 542 struct isl_is_empty_diff_collector {
 543         struct isl_diff_collector dc;
 544         int empty;
 545 };
 546
 547 /* isl_is_empty_diff_collector callback.
 548  */
 549 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
 550                             __isl_take isl_basic_map *bmap)
 551 {
 552         struct isl_is_empty_diff_collector *edc;
 553         edc = (struct isl_is_empty_diff_collector *)dc;
 554
 555         edc->empty = 0;
 556
 557         isl_basic_map_free(bmap);
 558         return -1;
 559 }
 560
 561 /* Check if bmap \ map is empty by computing this set difference
 562  * and breaking off as soon as the difference is known to be non-empty.
 563  */
 564 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
 565         __isl_keep isl_map *map)
 566 {
 567         int r;
 568         struct isl_is_empty_diff_collector edc;
 569
 570         r = isl_basic_map_plain_is_empty(bmap);
 571         if (r)
 572                 return r;
 573
 574         edc.dc.add = &basic_map_is_empty_add;
 575         edc.empty = 1;
 576         r = basic_map_collect_diff(isl_basic_map_copy(bmap),
 577                                    isl_map_copy(map), &edc.dc);
 578         if (!edc.empty)
 579                 return 0;
 580
 581         return r < 0 ? -1 : 1;
 582 }
 583
 584 /* Check if map1 \ map2 is empty by checking if the set difference is empty
 585  * for each of the basic maps in map1.
 586  */
 587 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 588 {
 589         int i;
 590         int is_empty = 1;
 591
 592         if (!map1 || !map2)
 593                 return -1;
 594
 595         for (i = 0; i < map1->n; ++i) {
 596                 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
 597                 if (is_empty < 0 || !is_empty)
 598                          break;
 599         }
 600
 601         return is_empty;
 602 }
 603
 604 /* Return 1 if "bmap" contains a single element.
 605  */
 606 int isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
 607 {
 608         if (!bmap)
 609                 return -1;
 610         if (bmap->n_div)
 611                 return 0;
 612         if (bmap->n_ineq)
 613                 return 0;
 614         return bmap->n_eq == isl_basic_map_total_dim(bmap);
 615 }
 616
 617 /* Return 1 if "map" contains a single element.
 618  */
 619 int isl_map_plain_is_singleton(__isl_keep isl_map *map)
 620 {
 621         if (!map)
 622                 return -1;
 623         if (map->n != 1)
 624                 return 0;
 625
 626         return isl_basic_map_plain_is_singleton(map->p[0]);
 627 }
 628
 629 /* Given a singleton basic map, extract the single element
 630  * as an isl_point.
 631  */
 632 static __isl_give isl_point *singleton_extract_point(
 633         __isl_keep isl_basic_map *bmap)
 634 {
 635         int j;
 636         unsigned dim;
 637         struct isl_vec *point;
 638         isl_int m;
 639
 640         if (!bmap)
 641                 return NULL;
 642
 643         dim = isl_basic_map_total_dim(bmap);
 644         isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
 645         point = isl_vec_alloc(bmap->ctx, 1 + dim);
 646         if (!point)
 647                 return NULL;
 648
 649         isl_int_init(m);
 650
 651         isl_int_set_si(point->el[0], 1);
 652         for (j = 0; j < bmap->n_eq; ++j) {
 653                 int i = dim - 1 - j;
 654                 isl_assert(bmap->ctx,
 655                     isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
 656                     goto error);
 657                 isl_assert(bmap->ctx,
 658                     isl_int_is_one(bmap->eq[j][1 + i]) ||
 659                     isl_int_is_negone(bmap->eq[j][1 + i]),
 660                     goto error);
 661                 isl_assert(bmap->ctx,
 662                     isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
 663                     goto error);
 664
 665                 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
 666                 isl_int_divexact(m, bmap->eq[j][1 + i], m);
 667                 isl_int_abs(m, m);
 668                 isl_seq_scale(point->el, point->el, m, 1 + i);
 669                 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
 670                 isl_int_neg(m, m);
 671                 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
 672         }
 673
 674         isl_int_clear(m);
 675         return isl_point_alloc(isl_basic_map_get_space(bmap), point);
 676 error:
 677         isl_int_clear(m);
 678         isl_vec_free(point);
 679         return NULL;
 680 }
 681
 682 /* Return 1 is the singleton map "map1" is a subset of "map2",
 683  * i.e., if the single element of "map1" is also an element of "map2".
 684  * Assumes "map2" has known divs.
 685  */
 686 static int map_is_singleton_subset(__isl_keep isl_map *map1,
 687         __isl_keep isl_map *map2)
 688 {
 689         int i;
 690         int is_subset = 0;
 691         struct isl_point *point;
 692
 693         if (!map1 || !map2)
 694                 return -1;
 695         if (map1->n != 1)
 696                 return -1;
 697
 698         point = singleton_extract_point(map1->p[0]);
 699         if (!point)
 700                 return -1;
 701
 702         for (i = 0; i < map2->n; ++i) {
 703                 is_subset = isl_basic_map_contains_point(map2->p[i], point);
 704                 if (is_subset)
 705                         break;
 706         }
 707
 708         isl_point_free(point);
 709         return is_subset;
 710 }
 711
 712 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
 713 {
 714         int is_subset = 0;
 715
 716         if (!map1 || !map2)
 717                 return -1;
 718
 719         if (!isl_map_has_equal_space(map1, map2))
 720                 return 0;
 721
 722         if (isl_map_is_empty(map1))
 723                 return 1;
 724
 725         if (isl_map_is_empty(map2))
 726                 return 0;
 727
 728         if (isl_map_plain_is_universe(map2))
 729                 return 1;
 730
 731         map2 = isl_map_compute_divs(isl_map_copy(map2));
 732         if (isl_map_plain_is_singleton(map1)) {
 733                 is_subset = map_is_singleton_subset(map1, map2);
 734                 isl_map_free(map2);
 735                 return is_subset;
 736         }
 737         is_subset = map_diff_is_empty(map1, map2);
 738         isl_map_free(map2);
 739
 740         return is_subset;
 741 }
 742
 743 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 744 {
 745         return isl_map_is_subset(
 746                         (struct isl_map *)set1, (struct isl_map *)set2);
 747 }
 748
 749 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
 750 {
 751         int i;
 752         struct isl_subtract_diff_collector sdc;
 753         sdc.dc.add = &basic_map_subtract_add;
 754
 755         if (!map)
 756                 return NULL;
 757         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 758                 return map;
 759         if (map->n <= 1)
 760                 return map;
 761
 762         map = isl_map_compute_divs(map);
 763         map = isl_map_remove_empty_parts(map);
 764
 765         if (!map || map->n <= 1)
 766                 return map;
 767
 768         sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 769
 770         for (i = 1; i < map->n; ++i) {
 771                 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
 772                 struct isl_map *copy = isl_map_copy(sdc.diff);
 773                 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
 774                         isl_map_free(sdc.diff);
 775                         sdc.diff = NULL;
 776                         break;
 777                 }
 778         }
 779
 780         isl_map_free(map);
 781
 782         return sdc.diff;
 783 }
 784
 785 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
 786 {
 787         return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
 788 }
 789
 790 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
 791 {
 792         isl_set *universe;
 793
 794         if (!set)
 795                 return NULL;
 796
 797         universe = isl_set_universe(isl_set_get_space(set));
 798
 799         return isl_set_subtract(universe, set);
 800 }