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, 1);
 316
 317         modified = 0;
 318         level = 0;
 319         init = 1;
 320
 321         while (level >= 0) {
 322                 if (level >= map->n) {
 323                         int empty;
 324                         struct isl_basic_map *bm;
 325                         if (!modified) {
 326                                 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
 327                                         goto error;
 328                                 break;
 329                         }
 330                         bm = isl_basic_map_copy(tab->bmap);
 331                         bm = isl_basic_map_cow(bm);
 332                         bm = isl_basic_map_update_from_tab(bm, tab);
 333                         bm = isl_basic_map_simplify(bm);
 334                         bm = isl_basic_map_finalize(bm);
 335                         empty = isl_basic_map_is_empty(bm);
 336                         if (empty)
 337                                 isl_basic_map_free(bm);
 338                         else if (dc->add(dc, bm) < 0)
 339                                 goto error;
 340                         if (empty < 0)
 341                                 goto error;
 342                         level--;
 343                         init = 0;
 344                         continue;
 345                 }
 346                 if (init) {
 347                         int offset;
 348                         struct isl_tab_undo *snap2;
 349                         snap2 = isl_tab_snap(tab);
 350                         if (tab_add_divs(tab, map->p[level],
 351                                          &div_map[level]) < 0)
 352                                 goto error;
 353                         offset = tab->n_con;
 354                         snap[level] = isl_tab_snap(tab);
 355                         if (tab_freeze_constraints(tab) < 0)
 356                                 goto error;
 357                         if (tab_add_constraints(tab, map->p[level],
 358                                                 div_map[level]) < 0)
 359                                 goto error;
 360                         k[level] = 0;
 361                         n[level] = 0;
 362                         if (tab->empty) {
 363                                 if (isl_tab_rollback(tab, snap2) < 0)
 364                                         goto error;
 365                                 level++;
 366                                 continue;
 367                         }
 368                         modified = 1;
 369                         n[level] = n_non_redundant(ctx, tab, offset,
 370                                                     &index[level]);
 371                         if (n[level] < 0)
 372                                 goto error;
 373                         if (n[level] == 0) {
 374                                 level--;
 375                                 init = 0;
 376                                 continue;
 377                         }
 378                         if (isl_tab_rollback(tab, snap[level]) < 0)
 379                                 goto error;
 380                         if (tab_add_constraint(tab, map->p[level],
 381                                         div_map[level], index[level][0], 1) < 0)
 382                                 goto error;
 383                         level++;
 384                         continue;
 385                 } else {
 386                         if (k[level] + 1 >= n[level]) {
 387                                 level--;
 388                                 continue;
 389                         }
 390                         if (isl_tab_rollback(tab, snap[level]) < 0)
 391                                 goto error;
 392                         if (tab_add_constraint(tab, map->p[level],
 393                                                 div_map[level],
 394                                                 index[level][k[level]], 0) < 0)
 395                                 goto error;
 396                         snap[level] = isl_tab_snap(tab);
 397                         k[level]++;
 398                         if (tab_add_constraint(tab, map->p[level],
 399                                                 div_map[level],
 400                                                 index[level][k[level]], 1) < 0)
 401                                 goto error;
 402                         level++;
 403                         init = 1;
 404                         continue;
 405                 }
 406         }
 407
 408         isl_tab_free(tab);
 409         free(snap);
 410         free(n);
 411         free(k);
 412         for (i = 0; index && i < map->n; ++i)
 413                 free(index[i]);
 414         free(index);
 415         for (i = 0; div_map && i < map->n; ++i)
 416                 free(div_map[i]);
 417         free(div_map);
 418
 419         isl_basic_map_free(bmap);
 420         isl_map_free(map);
 421
 422         return 0;
 423 error:
 424         isl_tab_free(tab);
 425         free(snap);
 426         free(n);
 427         free(k);
 428         for (i = 0; index && i < map->n; ++i)
 429                 free(index[i]);
 430         free(index);
 431         for (i = 0; div_map && i < map->n; ++i)
 432                 free(div_map[i]);
 433         free(div_map);
 434         isl_basic_map_free(bmap);
 435         isl_map_free(map);
 436         return -1;
 437 }
 438
 439 /* A diff collector that actually collects all parts of the
 440  * set difference in the field diff.
 441  */
 442 struct isl_subtract_diff_collector {
 443         struct isl_diff_collector dc;
 444         struct isl_map *diff;
 445 };
 446
 447 /* isl_subtract_diff_collector callback.
 448  */
 449 static int basic_map_subtract_add(struct isl_diff_collector *dc,
 450                             __isl_take isl_basic_map *bmap)
 451 {
 452         struct isl_subtract_diff_collector *sdc;
 453         sdc = (struct isl_subtract_diff_collector *)dc;
 454
 455         sdc->diff = isl_map_union_disjoint(sdc->diff,
 456                         isl_map_from_basic_map(bmap));
 457
 458         return sdc->diff ? 0 : -1;
 459 }
 460
 461 /* Return the set difference between bmap and map.
 462  */
 463 static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
 464         __isl_take isl_map *map)
 465 {
 466         struct isl_subtract_diff_collector sdc;
 467         sdc.dc.add = &basic_map_subtract_add;
 468         sdc.diff = isl_map_empty_like_basic_map(bmap);
 469         if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
 470                 isl_map_free(sdc.diff);
 471                 sdc.diff = NULL;
 472         }
 473         return sdc.diff;
 474 }
 475
 476 /* Return the set difference between map1 and map2.
 477  * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
 478  */
 479 static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,
 480         __isl_take isl_map *map2)
 481 {
 482         int i;
 483         struct isl_map *diff;
 484
 485         if (!map1 || !map2)
 486                 goto error;
 487
 488         isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
 489
 490         if (isl_map_is_empty(map2)) {
 491                 isl_map_free(map2);
 492                 return map1;
 493         }
 494
 495         map1 = isl_map_compute_divs(map1);
 496         map2 = isl_map_compute_divs(map2);
 497         if (!map1 || !map2)
 498                 goto error;
 499
 500         map1 = isl_map_remove_empty_parts(map1);
 501         map2 = isl_map_remove_empty_parts(map2);
 502
 503         diff = isl_map_empty_like(map1);
 504         for (i = 0; i < map1->n; ++i) {
 505                 struct isl_map *d;
 506                 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
 507                                        isl_map_copy(map2));
 508                 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
 509                         diff = isl_map_union_disjoint(diff, d);
 510                 else
 511                         diff = isl_map_union(diff, d);
 512         }
 513
 514         isl_map_free(map1);
 515         isl_map_free(map2);
 516
 517         return diff;
 518 error:
 519         isl_map_free(map1);
 520         isl_map_free(map2);
 521         return NULL;
 522 }
 523
 524 __isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
 525         __isl_take isl_map *map2)
 526 {
 527         return isl_map_align_params_map_map_and(map1, map2, &map_subtract);
 528 }
 529
 530 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 531 {
 532         return (struct isl_set *)
 533                 isl_map_subtract(
 534                         (struct isl_map *)set1, (struct isl_map *)set2);
 535 }
 536
 537 /* Remove the elements of "dom" from the domain of "map".
 538  */
 539 static __isl_give isl_map *map_subtract_domain(__isl_take isl_map *map,
 540         __isl_take isl_set *dom)
 541 {
 542         isl_map *ext_dom;
 543
 544         if (!isl_map_compatible_domain(map, dom))
 545                 isl_die(isl_set_get_ctx(dom), isl_error_invalid,
 546                         "incompatible spaces", goto error);
 547
 548         ext_dom = isl_map_universe(isl_map_get_space(map));
 549         ext_dom = isl_map_intersect_domain(ext_dom, dom);
 550         return isl_map_subtract(map, ext_dom);
 551 error:
 552         isl_map_free(map);
 553         isl_set_free(dom);
 554         return NULL;
 555 }
 556
 557 __isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,
 558         __isl_take isl_set *dom)
 559 {
 560         return isl_map_align_params_map_map_and(map, dom, &map_subtract_domain);
 561 }
 562
 563 /* Remove the elements of "dom" from the range of "map".
 564  */
 565 static __isl_give isl_map *map_subtract_range(__isl_take isl_map *map,
 566         __isl_take isl_set *dom)
 567 {
 568         isl_map *ext_dom;
 569
 570         if (!isl_map_compatible_range(map, dom))
 571                 isl_die(isl_set_get_ctx(dom), isl_error_invalid,
 572                         "incompatible spaces", goto error);
 573
 574         ext_dom = isl_map_universe(isl_map_get_space(map));
 575         ext_dom = isl_map_intersect_range(ext_dom, dom);
 576         return isl_map_subtract(map, ext_dom);
 577 error:
 578         isl_map_free(map);
 579         isl_set_free(dom);
 580         return NULL;
 581 }
 582
 583 __isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,
 584         __isl_take isl_set *dom)
 585 {
 586         return isl_map_align_params_map_map_and(map, dom, &map_subtract_range);
 587 }
 588
 589 /* A diff collector that aborts as soon as its add function is called,
 590  * setting empty to 0.
 591  */
 592 struct isl_is_empty_diff_collector {
 593         struct isl_diff_collector dc;
 594         int empty;
 595 };
 596
 597 /* isl_is_empty_diff_collector callback.
 598  */
 599 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
 600                             __isl_take isl_basic_map *bmap)
 601 {
 602         struct isl_is_empty_diff_collector *edc;
 603         edc = (struct isl_is_empty_diff_collector *)dc;
 604
 605         edc->empty = 0;
 606
 607         isl_basic_map_free(bmap);
 608         return -1;
 609 }
 610
 611 /* Check if bmap \ map is empty by computing this set difference
 612  * and breaking off as soon as the difference is known to be non-empty.
 613  */
 614 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
 615         __isl_keep isl_map *map)
 616 {
 617         int r;
 618         struct isl_is_empty_diff_collector edc;
 619
 620         r = isl_basic_map_plain_is_empty(bmap);
 621         if (r)
 622                 return r;
 623
 624         edc.dc.add = &basic_map_is_empty_add;
 625         edc.empty = 1;
 626         r = basic_map_collect_diff(isl_basic_map_copy(bmap),
 627                                    isl_map_copy(map), &edc.dc);
 628         if (!edc.empty)
 629                 return 0;
 630
 631         return r < 0 ? -1 : 1;
 632 }
 633
 634 /* Check if map1 \ map2 is empty by checking if the set difference is empty
 635  * for each of the basic maps in map1.
 636  */
 637 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 638 {
 639         int i;
 640         int is_empty = 1;
 641
 642         if (!map1 || !map2)
 643                 return -1;
 644
 645         for (i = 0; i < map1->n; ++i) {
 646                 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
 647                 if (is_empty < 0 || !is_empty)
 648                          break;
 649         }
 650
 651         return is_empty;
 652 }
 653
 654 /* Return 1 if "bmap" contains a single element.
 655  */
 656 int isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
 657 {
 658         if (!bmap)
 659                 return -1;
 660         if (bmap->n_div)
 661                 return 0;
 662         if (bmap->n_ineq)
 663                 return 0;
 664         return bmap->n_eq == isl_basic_map_total_dim(bmap);
 665 }
 666
 667 /* Return 1 if "map" contains a single element.
 668  */
 669 int isl_map_plain_is_singleton(__isl_keep isl_map *map)
 670 {
 671         if (!map)
 672                 return -1;
 673         if (map->n != 1)
 674                 return 0;
 675
 676         return isl_basic_map_plain_is_singleton(map->p[0]);
 677 }
 678
 679 /* Given a singleton basic map, extract the single element
 680  * as an isl_point.
 681  */
 682 static __isl_give isl_point *singleton_extract_point(
 683         __isl_keep isl_basic_map *bmap)
 684 {
 685         int j;
 686         unsigned dim;
 687         struct isl_vec *point;
 688         isl_int m;
 689
 690         if (!bmap)
 691                 return NULL;
 692
 693         dim = isl_basic_map_total_dim(bmap);
 694         isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
 695         point = isl_vec_alloc(bmap->ctx, 1 + dim);
 696         if (!point)
 697                 return NULL;
 698
 699         isl_int_init(m);
 700
 701         isl_int_set_si(point->el[0], 1);
 702         for (j = 0; j < bmap->n_eq; ++j) {
 703                 int i = dim - 1 - j;
 704                 isl_assert(bmap->ctx,
 705                     isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
 706                     goto error);
 707                 isl_assert(bmap->ctx,
 708                     isl_int_is_one(bmap->eq[j][1 + i]) ||
 709                     isl_int_is_negone(bmap->eq[j][1 + i]),
 710                     goto error);
 711                 isl_assert(bmap->ctx,
 712                     isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
 713                     goto error);
 714
 715                 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
 716                 isl_int_divexact(m, bmap->eq[j][1 + i], m);
 717                 isl_int_abs(m, m);
 718                 isl_seq_scale(point->el, point->el, m, 1 + i);
 719                 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
 720                 isl_int_neg(m, m);
 721                 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
 722         }
 723
 724         isl_int_clear(m);
 725         return isl_point_alloc(isl_basic_map_get_space(bmap), point);
 726 error:
 727         isl_int_clear(m);
 728         isl_vec_free(point);
 729         return NULL;
 730 }
 731
 732 /* Return 1 is the singleton map "map1" is a subset of "map2",
 733  * i.e., if the single element of "map1" is also an element of "map2".
 734  * Assumes "map2" has known divs.
 735  */
 736 static int map_is_singleton_subset(__isl_keep isl_map *map1,
 737         __isl_keep isl_map *map2)
 738 {
 739         int i;
 740         int is_subset = 0;
 741         struct isl_point *point;
 742
 743         if (!map1 || !map2)
 744                 return -1;
 745         if (map1->n != 1)
 746                 return -1;
 747
 748         point = singleton_extract_point(map1->p[0]);
 749         if (!point)
 750                 return -1;
 751
 752         for (i = 0; i < map2->n; ++i) {
 753                 is_subset = isl_basic_map_contains_point(map2->p[i], point);
 754                 if (is_subset)
 755                         break;
 756         }
 757
 758         isl_point_free(point);
 759         return is_subset;
 760 }
 761
 762 static int map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 763 {
 764         int is_subset = 0;
 765
 766         if (!map1 || !map2)
 767                 return -1;
 768
 769         if (!isl_map_has_equal_space(map1, map2))
 770                 return 0;
 771
 772         if (isl_map_is_empty(map1))
 773                 return 1;
 774
 775         if (isl_map_is_empty(map2))
 776                 return 0;
 777
 778         if (isl_map_plain_is_universe(map2))
 779                 return 1;
 780
 781         map2 = isl_map_compute_divs(isl_map_copy(map2));
 782         if (isl_map_plain_is_singleton(map1)) {
 783                 is_subset = map_is_singleton_subset(map1, map2);
 784                 isl_map_free(map2);
 785                 return is_subset;
 786         }
 787         is_subset = map_diff_is_empty(map1, map2);
 788         isl_map_free(map2);
 789
 790         return is_subset;
 791 }
 792
 793 int isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 794 {
 795         return isl_map_align_params_map_map_and_test(map1, map2,
 796                                                         &map_is_subset);
 797 }
 798
 799 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 800 {
 801         return isl_map_is_subset(
 802                         (struct isl_map *)set1, (struct isl_map *)set2);
 803 }
 804
 805 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
 806 {
 807         int i;
 808         struct isl_subtract_diff_collector sdc;
 809         sdc.dc.add = &basic_map_subtract_add;
 810
 811         if (!map)
 812                 return NULL;
 813         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 814                 return map;
 815         if (map->n <= 1)
 816                 return map;
 817
 818         map = isl_map_compute_divs(map);
 819         map = isl_map_remove_empty_parts(map);
 820
 821         if (!map || map->n <= 1)
 822                 return map;
 823
 824         sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 825
 826         for (i = 1; i < map->n; ++i) {
 827                 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
 828                 struct isl_map *copy = isl_map_copy(sdc.diff);
 829                 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
 830                         isl_map_free(sdc.diff);
 831                         sdc.diff = NULL;
 832                         break;
 833                 }
 834         }
 835
 836         isl_map_free(map);
 837
 838         return sdc.diff;
 839 }
 840
 841 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
 842 {
 843         return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
 844 }
 845
 846 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
 847 {
 848         isl_set *universe;
 849
 850         if (!set)
 851                 return NULL;
 852
 853         universe = isl_set_universe(isl_set_get_space(set));
 854
 855         return isl_set_subtract(universe, set);
 856 }