isl_map_subtract.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the MIT 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 #include <isl_vec_private.h>
  17
  18 /* Expand the constraint "c" into "v".  The initial "dim" dimensions
  19  * are the same, but "v" may have more divs than "c" and the divs of "c"
  20  * may appear in different positions in "v".
  21  * The number of divs in "c" is given by "n_div" and the mapping
  22  * of divs in "c" to divs in "v" is given by "div_map".
  23  *
  24  * Although it shouldn't happen in practice, it is theoretically
  25  * possible that two or more divs in "c" are mapped to the same div in "v".
  26  * These divs are then necessarily the same, so we simply add their
  27  * coefficients.
  28  */
  29 static void expand_constraint(isl_vec *v, unsigned dim,
  30         isl_int *c, int *div_map, unsigned n_div)
  31 {
  32         int i;
  33
  34         isl_seq_cpy(v->el, c, 1 + dim);
  35         isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
  36
  37         for (i = 0; i < n_div; ++i) {
  38                 int pos = 1 + dim + div_map[i];
  39                 isl_int_add(v->el[pos], v->el[pos], c[1 + dim + i]);
  40         }
  41 }
  42
  43 /* Add all constraints of bmap to tab.  The equalities of bmap
  44  * are added as a pair of inequalities.
  45  */
  46 static int tab_add_constraints(struct isl_tab *tab,
  47         __isl_keep isl_basic_map *bmap, int *div_map)
  48 {
  49         int i;
  50         unsigned dim;
  51         unsigned tab_total;
  52         unsigned bmap_total;
  53         isl_vec *v;
  54
  55         if (!tab || !bmap)
  56                 return -1;
  57
  58         tab_total = isl_basic_map_total_dim(tab->bmap);
  59         bmap_total = isl_basic_map_total_dim(bmap);
  60         dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
  61
  62         if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
  63                 return -1;
  64
  65         v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
  66         if (!v)
  67                 return -1;
  68
  69         for (i = 0; i < bmap->n_eq; ++i) {
  70                 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
  71                 if (isl_tab_add_ineq(tab, v->el) < 0)
  72                         goto error;
  73                 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
  74                 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
  75                 if (isl_tab_add_ineq(tab, v->el) < 0)
  76                         goto error;
  77                 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
  78                 if (tab->empty)
  79                         break;
  80         }
  81
  82         for (i = 0; i < bmap->n_ineq; ++i) {
  83                 expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
  84                 if (isl_tab_add_ineq(tab, v->el) < 0)
  85                         goto error;
  86                 if (tab->empty)
  87                         break;
  88         }
  89
  90         isl_vec_free(v);
  91         return 0;
  92 error:
  93         isl_vec_free(v);
  94         return -1;
  95 }
  96
  97 /* Add a specific constraint of bmap (or its opposite) to tab.
  98  * The position of the constraint is specified by "c", where
  99  * the equalities of bmap are counted twice, once for the inequality
 100  * that is equal to the equality, and once for its negation.
 101  */
 102 static int tab_add_constraint(struct isl_tab *tab,
 103         __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
 104 {
 105         unsigned dim;
 106         unsigned tab_total;
 107         unsigned bmap_total;
 108         isl_vec *v;
 109         int r;
 110
 111         if (!tab || !bmap)
 112                 return -1;
 113
 114         tab_total = isl_basic_map_total_dim(tab->bmap);
 115         bmap_total = isl_basic_map_total_dim(bmap);
 116         dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
 117
 118         v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
 119         if (!v)
 120                 return -1;
 121
 122         if (c < 2 * bmap->n_eq) {
 123                 if ((c % 2) != oppose)
 124                         isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
 125                                         1 + bmap_total);
 126                 if (oppose)
 127                         isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
 128                 expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
 129                 r = isl_tab_add_ineq(tab, v->el);
 130                 if (oppose)
 131                         isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
 132                 if ((c % 2) != oppose)
 133                         isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
 134                                         1 + bmap_total);
 135         } else {
 136                 c -= 2 * bmap->n_eq;
 137                 if (oppose) {
 138                         isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
 139                                         1 + bmap_total);
 140                         isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
 141                 }
 142                 expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
 143                 r = isl_tab_add_ineq(tab, v->el);
 144                 if (oppose) {
 145                         isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
 146                         isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
 147                                         1 + bmap_total);
 148                 }
 149         }
 150
 151         isl_vec_free(v);
 152         return r;
 153 }
 154
 155 static int tab_add_divs(struct isl_tab *tab, __isl_keep isl_basic_map *bmap,
 156         int **div_map)
 157 {
 158         int i, j;
 159         struct isl_vec *vec;
 160         unsigned total;
 161         unsigned dim;
 162
 163         if (!bmap)
 164                 return -1;
 165         if (!bmap->n_div)
 166                 return 0;
 167
 168         if (!*div_map)
 169                 *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
 170         if (!*div_map)
 171                 return -1;
 172
 173         total = isl_basic_map_total_dim(tab->bmap);
 174         dim = total - tab->bmap->n_div;
 175         vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
 176         if (!vec)
 177                 return -1;
 178
 179         for (i = 0; i < bmap->n_div; ++i) {
 180                 isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
 181                 isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
 182                 for (j = 0; j < i; ++j)
 183                         isl_int_set(vec->el[2 + dim + (*div_map)[j]],
 184                                         bmap->div[i][2 + dim + j]);
 185                 for (j = 0; j < tab->bmap->n_div; ++j)
 186                         if (isl_seq_eq(tab->bmap->div[j],
 187                                         vec->el, 2 + dim + tab->bmap->n_div))
 188                                 break;
 189                 (*div_map)[i] = j;
 190                 if (j == tab->bmap->n_div) {
 191                         vec->size = 2 + dim + tab->bmap->n_div;
 192                         if (isl_tab_add_div(tab, vec, NULL, NULL) < 0)
 193                                 goto error;
 194                 }
 195         }
 196
 197         isl_vec_free(vec);
 198
 199         return 0;
 200 error:
 201         isl_vec_free(vec);
 202
 203         return -1;
 204 }
 205
 206 /* Freeze all constraints of tableau tab.
 207  */
 208 static int tab_freeze_constraints(struct isl_tab *tab)
 209 {
 210         int i;
 211
 212         for (i = 0; i < tab->n_con; ++i)
 213                 if (isl_tab_freeze_constraint(tab, i) < 0)
 214                         return -1;
 215
 216         return 0;
 217 }
 218
 219 /* Check for redundant constraints starting at offset.
 220  * Put the indices of the redundant constraints in index
 221  * and return the number of redundant constraints.
 222  */
 223 static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,
 224         int offset, int **index)
 225 {
 226         int i, n;
 227         int n_test = tab->n_con - offset;
 228
 229         if (isl_tab_detect_redundant(tab) < 0)
 230                 return -1;
 231
 232         if (n_test == 0)
 233                 return 0;
 234         if (!*index)
 235                 *index = isl_alloc_array(ctx, int, n_test);
 236         if (!*index)
 237                 return -1;
 238
 239         for (n = 0, i = 0; i < n_test; ++i) {
 240                 int r;
 241                 r = isl_tab_is_redundant(tab, offset + i);
 242                 if (r < 0)
 243                         return -1;
 244                 if (r)
 245                         continue;
 246                 (*index)[n++] = i;
 247         }
 248
 249         return n;
 250 }
 251
 252 /* basic_map_collect_diff calls add on each of the pieces of
 253  * the set difference between bmap and map until the add method
 254  * return a negative value.
 255  */
 256 struct isl_diff_collector {
 257         int (*add)(struct isl_diff_collector *dc,
 258                     __isl_take isl_basic_map *bmap);
 259 };
 260
 261 /* Compute the set difference between bmap and map and call
 262  * dc->add on each of the piece until this function returns
 263  * a negative value.
 264  * Return 0 on success and -1 on error.  dc->add returning
 265  * a negative value is treated as an error, but the calling
 266  * function can interpret the results based on the state of dc.
 267  *
 268  * Assumes that map has known divs.
 269  *
 270  * The difference is computed by a backtracking algorithm.
 271  * Each level corresponds to a basic map in "map".
 272  * When a node in entered for the first time, we check
 273  * if the corresonding basic map intersects the current piece
 274  * of "bmap".  If not, we move to the next level.
 275  * Otherwise, we split the current piece into as many
 276  * pieces as there are non-redundant constraints of the current
 277  * basic map in the intersection.  Each of these pieces is
 278  * handled by a child of the current node.
 279  * In particular, if there are n non-redundant constraints,
 280  * then for each 0 <= i < n, a piece is cut off by adding
 281  * constraints 0 <= j < i and adding the opposite of constraint i.
 282  * If there are no non-redundant constraints, meaning that the current
 283  * piece is a subset of the current basic map, then we simply backtrack.
 284  *
 285  * In the leaves, we check if the remaining piece has any integer points
 286  * and if so, pass it along to dc->add.  As a special case, if nothing
 287  * has been removed when we end up in a leaf, we simply pass along
 288  * the original basic map.
 289  */
 290 static int basic_map_collect_diff(__isl_take isl_basic_map *bmap,
 291         __isl_take isl_map *map, struct isl_diff_collector *dc)
 292 {
 293         int i;
 294         int modified;
 295         int level;
 296         int init;
 297         int empty;
 298         isl_ctx *ctx;
 299         struct isl_tab *tab = NULL;
 300         struct isl_tab_undo **snap = NULL;
 301         int *k = NULL;
 302         int *n = NULL;
 303         int **index = NULL;
 304         int **div_map = NULL;
 305
 306         empty = isl_basic_map_is_empty(bmap);
 307         if (empty) {
 308                 isl_basic_map_free(bmap);
 309                 isl_map_free(map);
 310                 return empty < 0 ? -1 : 0;
 311         }
 312
 313         bmap = isl_basic_map_cow(bmap);
 314         map = isl_map_cow(map);
 315
 316         if (!bmap || !map)
 317                 goto error;
 318
 319         ctx = map->ctx;
 320         snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
 321         k = isl_alloc_array(map->ctx, int, map->n);
 322         n = isl_alloc_array(map->ctx, int, map->n);
 323         index = isl_calloc_array(map->ctx, int *, map->n);
 324         div_map = isl_calloc_array(map->ctx, int *, map->n);
 325         if (!snap || !k || !n || !index || !div_map)
 326                 goto error;
 327
 328         bmap = isl_basic_map_order_divs(bmap);
 329         map = isl_map_order_divs(map);
 330
 331         tab = isl_tab_from_basic_map(bmap, 1);
 332         if (!tab)
 333                 goto error;
 334
 335         modified = 0;
 336         level = 0;
 337         init = 1;
 338
 339         while (level >= 0) {
 340                 if (level >= map->n) {
 341                         int empty;
 342                         struct isl_basic_map *bm;
 343                         if (!modified) {
 344                                 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
 345                                         goto error;
 346                                 break;
 347                         }
 348                         bm = isl_basic_map_copy(tab->bmap);
 349                         bm = isl_basic_map_cow(bm);
 350                         bm = isl_basic_map_update_from_tab(bm, tab);
 351                         bm = isl_basic_map_simplify(bm);
 352                         bm = isl_basic_map_finalize(bm);
 353                         empty = isl_basic_map_is_empty(bm);
 354                         if (empty)
 355                                 isl_basic_map_free(bm);
 356                         else if (dc->add(dc, bm) < 0)
 357                                 goto error;
 358                         if (empty < 0)
 359                                 goto error;
 360                         level--;
 361                         init = 0;
 362                         continue;
 363                 }
 364                 if (init) {
 365                         int offset;
 366                         struct isl_tab_undo *snap2;
 367                         snap2 = isl_tab_snap(tab);
 368                         if (tab_add_divs(tab, map->p[level],
 369                                          &div_map[level]) < 0)
 370                                 goto error;
 371                         offset = tab->n_con;
 372                         snap[level] = isl_tab_snap(tab);
 373                         if (tab_freeze_constraints(tab) < 0)
 374                                 goto error;
 375                         if (tab_add_constraints(tab, map->p[level],
 376                                                 div_map[level]) < 0)
 377                                 goto error;
 378                         k[level] = 0;
 379                         n[level] = 0;
 380                         if (tab->empty) {
 381                                 if (isl_tab_rollback(tab, snap2) < 0)
 382                                         goto error;
 383                                 level++;
 384                                 continue;
 385                         }
 386                         modified = 1;
 387                         n[level] = n_non_redundant(ctx, tab, offset,
 388                                                     &index[level]);
 389                         if (n[level] < 0)
 390                                 goto error;
 391                         if (n[level] == 0) {
 392                                 level--;
 393                                 init = 0;
 394                                 continue;
 395                         }
 396                         if (isl_tab_rollback(tab, snap[level]) < 0)
 397                                 goto error;
 398                         if (tab_add_constraint(tab, map->p[level],
 399                                         div_map[level], index[level][0], 1) < 0)
 400                                 goto error;
 401                         level++;
 402                         continue;
 403                 } else {
 404                         if (k[level] + 1 >= n[level]) {
 405                                 level--;
 406                                 continue;
 407                         }
 408                         if (isl_tab_rollback(tab, snap[level]) < 0)
 409                                 goto error;
 410                         if (tab_add_constraint(tab, map->p[level],
 411                                                 div_map[level],
 412                                                 index[level][k[level]], 0) < 0)
 413                                 goto error;
 414                         snap[level] = isl_tab_snap(tab);
 415                         k[level]++;
 416                         if (tab_add_constraint(tab, map->p[level],
 417                                                 div_map[level],
 418                                                 index[level][k[level]], 1) < 0)
 419                                 goto error;
 420                         level++;
 421                         init = 1;
 422                         continue;
 423                 }
 424         }
 425
 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
 437         isl_basic_map_free(bmap);
 438         isl_map_free(map);
 439
 440         return 0;
 441 error:
 442         isl_tab_free(tab);
 443         free(snap);
 444         free(n);
 445         free(k);
 446         for (i = 0; index && i < map->n; ++i)
 447                 free(index[i]);
 448         free(index);
 449         for (i = 0; div_map && i < map->n; ++i)
 450                 free(div_map[i]);
 451         free(div_map);
 452         isl_basic_map_free(bmap);
 453         isl_map_free(map);
 454         return -1;
 455 }
 456
 457 /* A diff collector that actually collects all parts of the
 458  * set difference in the field diff.
 459  */
 460 struct isl_subtract_diff_collector {
 461         struct isl_diff_collector dc;
 462         struct isl_map *diff;
 463 };
 464
 465 /* isl_subtract_diff_collector callback.
 466  */
 467 static int basic_map_subtract_add(struct isl_diff_collector *dc,
 468                             __isl_take isl_basic_map *bmap)
 469 {
 470         struct isl_subtract_diff_collector *sdc;
 471         sdc = (struct isl_subtract_diff_collector *)dc;
 472
 473         sdc->diff = isl_map_union_disjoint(sdc->diff,
 474                         isl_map_from_basic_map(bmap));
 475
 476         return sdc->diff ? 0 : -1;
 477 }
 478
 479 /* Return the set difference between bmap and map.
 480  */
 481 static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
 482         __isl_take isl_map *map)
 483 {
 484         struct isl_subtract_diff_collector sdc;
 485         sdc.dc.add = &basic_map_subtract_add;
 486         sdc.diff = isl_map_empty_like_basic_map(bmap);
 487         if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
 488                 isl_map_free(sdc.diff);
 489                 sdc.diff = NULL;
 490         }
 491         return sdc.diff;
 492 }
 493
 494 /* Return the set difference between map1 and map2.
 495  * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
 496  *
 497  * If "map1" and "map2" are disjoint, then simply return "map1".
 498  */
 499 static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,
 500         __isl_take isl_map *map2)
 501 {
 502         int i;
 503         int disjoint;
 504         struct isl_map *diff;
 505
 506         if (!map1 || !map2)
 507                 goto error;
 508
 509         isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
 510
 511         disjoint = isl_map_is_disjoint(map1, map2);
 512         if (disjoint < 0)
 513                 goto error;
 514         if (disjoint) {
 515                 isl_map_free(map2);
 516                 return map1;
 517         }
 518
 519         map1 = isl_map_compute_divs(map1);
 520         map2 = isl_map_compute_divs(map2);
 521         if (!map1 || !map2)
 522                 goto error;
 523
 524         map1 = isl_map_remove_empty_parts(map1);
 525         map2 = isl_map_remove_empty_parts(map2);
 526
 527         diff = isl_map_empty_like(map1);
 528         for (i = 0; i < map1->n; ++i) {
 529                 struct isl_map *d;
 530                 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
 531                                        isl_map_copy(map2));
 532                 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
 533                         diff = isl_map_union_disjoint(diff, d);
 534                 else
 535                         diff = isl_map_union(diff, d);
 536         }
 537
 538         isl_map_free(map1);
 539         isl_map_free(map2);
 540
 541         return diff;
 542 error:
 543         isl_map_free(map1);
 544         isl_map_free(map2);
 545         return NULL;
 546 }
 547
 548 __isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
 549         __isl_take isl_map *map2)
 550 {
 551         return isl_map_align_params_map_map_and(map1, map2, &map_subtract);
 552 }
 553
 554 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 555 {
 556         return (struct isl_set *)
 557                 isl_map_subtract(
 558                         (struct isl_map *)set1, (struct isl_map *)set2);
 559 }
 560
 561 /* Remove the elements of "dom" from the domain of "map".
 562  */
 563 static __isl_give isl_map *map_subtract_domain(__isl_take isl_map *map,
 564         __isl_take isl_set *dom)
 565 {
 566         isl_map *ext_dom;
 567
 568         if (!isl_map_compatible_domain(map, dom))
 569                 isl_die(isl_set_get_ctx(dom), isl_error_invalid,
 570                         "incompatible spaces", goto error);
 571
 572         ext_dom = isl_map_universe(isl_map_get_space(map));
 573         ext_dom = isl_map_intersect_domain(ext_dom, dom);
 574         return isl_map_subtract(map, ext_dom);
 575 error:
 576         isl_map_free(map);
 577         isl_set_free(dom);
 578         return NULL;
 579 }
 580
 581 __isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,
 582         __isl_take isl_set *dom)
 583 {
 584         return isl_map_align_params_map_map_and(map, dom, &map_subtract_domain);
 585 }
 586
 587 /* Remove the elements of "dom" from the range of "map".
 588  */
 589 static __isl_give isl_map *map_subtract_range(__isl_take isl_map *map,
 590         __isl_take isl_set *dom)
 591 {
 592         isl_map *ext_dom;
 593
 594         if (!isl_map_compatible_range(map, dom))
 595                 isl_die(isl_set_get_ctx(dom), isl_error_invalid,
 596                         "incompatible spaces", goto error);
 597
 598         ext_dom = isl_map_universe(isl_map_get_space(map));
 599         ext_dom = isl_map_intersect_range(ext_dom, dom);
 600         return isl_map_subtract(map, ext_dom);
 601 error:
 602         isl_map_free(map);
 603         isl_set_free(dom);
 604         return NULL;
 605 }
 606
 607 __isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,
 608         __isl_take isl_set *dom)
 609 {
 610         return isl_map_align_params_map_map_and(map, dom, &map_subtract_range);
 611 }
 612
 613 /* A diff collector that aborts as soon as its add function is called,
 614  * setting empty to 0.
 615  */
 616 struct isl_is_empty_diff_collector {
 617         struct isl_diff_collector dc;
 618         int empty;
 619 };
 620
 621 /* isl_is_empty_diff_collector callback.
 622  */
 623 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
 624                             __isl_take isl_basic_map *bmap)
 625 {
 626         struct isl_is_empty_diff_collector *edc;
 627         edc = (struct isl_is_empty_diff_collector *)dc;
 628
 629         edc->empty = 0;
 630
 631         isl_basic_map_free(bmap);
 632         return -1;
 633 }
 634
 635 /* Check if bmap \ map is empty by computing this set difference
 636  * and breaking off as soon as the difference is known to be non-empty.
 637  */
 638 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
 639         __isl_keep isl_map *map)
 640 {
 641         int r;
 642         struct isl_is_empty_diff_collector edc;
 643
 644         r = isl_basic_map_plain_is_empty(bmap);
 645         if (r)
 646                 return r;
 647
 648         edc.dc.add = &basic_map_is_empty_add;
 649         edc.empty = 1;
 650         r = basic_map_collect_diff(isl_basic_map_copy(bmap),
 651                                    isl_map_copy(map), &edc.dc);
 652         if (!edc.empty)
 653                 return 0;
 654
 655         return r < 0 ? -1 : 1;
 656 }
 657
 658 /* Check if map1 \ map2 is empty by checking if the set difference is empty
 659  * for each of the basic maps in map1.
 660  */
 661 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 662 {
 663         int i;
 664         int is_empty = 1;
 665
 666         if (!map1 || !map2)
 667                 return -1;
 668
 669         for (i = 0; i < map1->n; ++i) {
 670                 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
 671                 if (is_empty < 0 || !is_empty)
 672                          break;
 673         }
 674
 675         return is_empty;
 676 }
 677
 678 /* Return 1 if "bmap" contains a single element.
 679  */
 680 int isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
 681 {
 682         if (!bmap)
 683                 return -1;
 684         if (bmap->n_div)
 685                 return 0;
 686         if (bmap->n_ineq)
 687                 return 0;
 688         return bmap->n_eq == isl_basic_map_total_dim(bmap);
 689 }
 690
 691 /* Return 1 if "map" contains a single element.
 692  */
 693 int isl_map_plain_is_singleton(__isl_keep isl_map *map)
 694 {
 695         if (!map)
 696                 return -1;
 697         if (map->n != 1)
 698                 return 0;
 699
 700         return isl_basic_map_plain_is_singleton(map->p[0]);
 701 }
 702
 703 /* Given a singleton basic map, extract the single element
 704  * as an isl_point.
 705  */
 706 static __isl_give isl_point *singleton_extract_point(
 707         __isl_keep isl_basic_map *bmap)
 708 {
 709         int j;
 710         unsigned dim;
 711         struct isl_vec *point;
 712         isl_int m;
 713
 714         if (!bmap)
 715                 return NULL;
 716
 717         dim = isl_basic_map_total_dim(bmap);
 718         isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
 719         point = isl_vec_alloc(bmap->ctx, 1 + dim);
 720         if (!point)
 721                 return NULL;
 722
 723         isl_int_init(m);
 724
 725         isl_int_set_si(point->el[0], 1);
 726         for (j = 0; j < bmap->n_eq; ++j) {
 727                 int i = dim - 1 - j;
 728                 isl_assert(bmap->ctx,
 729                     isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
 730                     goto error);
 731                 isl_assert(bmap->ctx,
 732                     isl_int_is_one(bmap->eq[j][1 + i]) ||
 733                     isl_int_is_negone(bmap->eq[j][1 + i]),
 734                     goto error);
 735                 isl_assert(bmap->ctx,
 736                     isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
 737                     goto error);
 738
 739                 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
 740                 isl_int_divexact(m, bmap->eq[j][1 + i], m);
 741                 isl_int_abs(m, m);
 742                 isl_seq_scale(point->el, point->el, m, 1 + i);
 743                 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
 744                 isl_int_neg(m, m);
 745                 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
 746         }
 747
 748         isl_int_clear(m);
 749         return isl_point_alloc(isl_basic_map_get_space(bmap), point);
 750 error:
 751         isl_int_clear(m);
 752         isl_vec_free(point);
 753         return NULL;
 754 }
 755
 756 /* Return 1 is the singleton map "map1" is a subset of "map2",
 757  * i.e., if the single element of "map1" is also an element of "map2".
 758  * Assumes "map2" has known divs.
 759  */
 760 static int map_is_singleton_subset(__isl_keep isl_map *map1,
 761         __isl_keep isl_map *map2)
 762 {
 763         int i;
 764         int is_subset = 0;
 765         struct isl_point *point;
 766
 767         if (!map1 || !map2)
 768                 return -1;
 769         if (map1->n != 1)
 770                 return -1;
 771
 772         point = singleton_extract_point(map1->p[0]);
 773         if (!point)
 774                 return -1;
 775
 776         for (i = 0; i < map2->n; ++i) {
 777                 is_subset = isl_basic_map_contains_point(map2->p[i], point);
 778                 if (is_subset)
 779                         break;
 780         }
 781
 782         isl_point_free(point);
 783         return is_subset;
 784 }
 785
 786 static int map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 787 {
 788         int is_subset = 0;
 789         int empty;
 790         int rat1, rat2;
 791
 792         if (!map1 || !map2)
 793                 return -1;
 794
 795         if (!isl_map_has_equal_space(map1, map2))
 796                 return 0;
 797
 798         empty = isl_map_is_empty(map1);
 799         if (empty < 0)
 800                 return -1;
 801         if (empty)
 802                 return 1;
 803
 804         empty = isl_map_is_empty(map2);
 805         if (empty < 0)
 806                 return -1;
 807         if (empty)
 808                 return 0;
 809
 810         rat1 = isl_map_has_rational(map1);
 811         rat2 = isl_map_has_rational(map2);
 812         if (rat1 < 0 || rat2 < 0)
 813                 return -1;
 814         if (rat1 && !rat2)
 815                 return 0;
 816
 817         if (isl_map_plain_is_universe(map2))
 818                 return 1;
 819
 820         map2 = isl_map_compute_divs(isl_map_copy(map2));
 821         if (isl_map_plain_is_singleton(map1)) {
 822                 is_subset = map_is_singleton_subset(map1, map2);
 823                 isl_map_free(map2);
 824                 return is_subset;
 825         }
 826         is_subset = map_diff_is_empty(map1, map2);
 827         isl_map_free(map2);
 828
 829         return is_subset;
 830 }
 831
 832 int isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 833 {
 834         return isl_map_align_params_map_map_and_test(map1, map2,
 835                                                         &map_is_subset);
 836 }
 837
 838 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 839 {
 840         return isl_map_is_subset(
 841                         (struct isl_map *)set1, (struct isl_map *)set2);
 842 }
 843
 844 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
 845 {
 846         int i;
 847         struct isl_subtract_diff_collector sdc;
 848         sdc.dc.add = &basic_map_subtract_add;
 849
 850         if (!map)
 851                 return NULL;
 852         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 853                 return map;
 854         if (map->n <= 1)
 855                 return map;
 856
 857         map = isl_map_compute_divs(map);
 858         map = isl_map_remove_empty_parts(map);
 859
 860         if (!map || map->n <= 1)
 861                 return map;
 862
 863         sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 864
 865         for (i = 1; i < map->n; ++i) {
 866                 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
 867                 struct isl_map *copy = isl_map_copy(sdc.diff);
 868                 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
 869                         isl_map_free(sdc.diff);
 870                         sdc.diff = NULL;
 871                         break;
 872                 }
 873         }
 874
 875         isl_map_free(map);
 876
 877         return sdc.diff;
 878 }
 879
 880 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
 881 {
 882         return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
 883 }
 884
 885 __isl_give isl_map *isl_map_complement(__isl_take isl_map *map)
 886 {
 887         isl_map *universe;
 888
 889         if (!map)
 890                 return NULL;
 891
 892         universe = isl_map_universe(isl_map_get_space(map));
 893
 894         return isl_map_subtract(universe, map);
 895 }
 896
 897 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
 898 {
 899         return isl_map_complement(set);
 900 }