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
  17 /* Expand the constraint "c" into "v".  The initial "dim" dimensions
  18  * are the same, but "v" may have more divs than "c" and the divs of "c"
  19  * may appear in different positions in "v".
  20  * The number of divs in "c" is given by "n_div" and the mapping
  21  * of divs in "c" to divs in "v" is given by "div_map".
  22  *
  23  * Although it shouldn't happen in practice, it is theoretically
  24  * possible that two or more divs in "c" are mapped to the same div in "v".
  25  * These divs are then necessarily the same, so we simply add their
  26  * coefficients.
  27  */
  28 static void expand_constraint(isl_vec *v, unsigned dim,
  29         isl_int *c, int *div_map, unsigned n_div)
  30 {
  31         int i;
  32
  33         isl_seq_cpy(v->el, c, 1 + dim);
  34         isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
  35
  36         for (i = 0; i < n_div; ++i) {
  37                 int pos = 1 + dim + div_map[i];
  38                 isl_int_add(v->el[pos], v->el[pos], c[1 + dim + i]);
  39         }
  40 }
  41
  42 /* Add all constraints of bmap to tab.  The equalities of bmap
  43  * are added as a pair of inequalities.
  44  */
  45 static int tab_add_constraints(struct isl_tab *tab,
  46         __isl_keep isl_basic_map *bmap, int *div_map)
  47 {
  48         int i;
  49         unsigned dim;
  50         unsigned tab_total;
  51         unsigned bmap_total;
  52         isl_vec *v;
  53
  54         if (!tab || !bmap)
  55                 return -1;
  56
  57         tab_total = isl_basic_map_total_dim(tab->bmap);
  58         bmap_total = isl_basic_map_total_dim(bmap);
  59         dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
  60
  61         if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
  62                 return -1;
  63
  64         v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
  65         if (!v)
  66                 return -1;
  67
  68         for (i = 0; i < bmap->n_eq; ++i) {
  69                 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
  70                 if (isl_tab_add_ineq(tab, v->el) < 0)
  71                         goto error;
  72                 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
  73                 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
  74                 if (isl_tab_add_ineq(tab, v->el) < 0)
  75                         goto error;
  76                 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
  77                 if (tab->empty)
  78                         break;
  79         }
  80
  81         for (i = 0; i < bmap->n_ineq; ++i) {
  82                 expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
  83                 if (isl_tab_add_ineq(tab, v->el) < 0)
  84                         goto error;
  85                 if (tab->empty)
  86                         break;
  87         }
  88
  89         isl_vec_free(v);
  90         return 0;
  91 error:
  92         isl_vec_free(v);
  93         return -1;
  94 }
  95
  96 /* Add a specific constraint of bmap (or its opposite) to tab.
  97  * The position of the constraint is specified by "c", where
  98  * the equalities of bmap are counted twice, once for the inequality
  99  * that is equal to the equality, and once for its negation.
 100  */
 101 static int tab_add_constraint(struct isl_tab *tab,
 102         __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
 103 {
 104         unsigned dim;
 105         unsigned tab_total;
 106         unsigned bmap_total;
 107         isl_vec *v;
 108         int r;
 109
 110         if (!tab || !bmap)
 111                 return -1;
 112
 113         tab_total = isl_basic_map_total_dim(tab->bmap);
 114         bmap_total = isl_basic_map_total_dim(bmap);
 115         dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
 116
 117         v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
 118         if (!v)
 119                 return -1;
 120
 121         if (c < 2 * bmap->n_eq) {
 122                 if ((c % 2) != oppose)
 123                         isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
 124                                         1 + bmap_total);
 125                 if (oppose)
 126                         isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
 127                 expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
 128                 r = isl_tab_add_ineq(tab, v->el);
 129                 if (oppose)
 130                         isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
 131                 if ((c % 2) != oppose)
 132                         isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
 133                                         1 + bmap_total);
 134         } else {
 135                 c -= 2 * bmap->n_eq;
 136                 if (oppose) {
 137                         isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
 138                                         1 + bmap_total);
 139                         isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
 140                 }
 141                 expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
 142                 r = isl_tab_add_ineq(tab, v->el);
 143                 if (oppose) {
 144                         isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
 145                         isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
 146                                         1 + bmap_total);
 147                 }
 148         }
 149
 150         isl_vec_free(v);
 151         return r;
 152 }
 153
 154 static int tab_add_divs(struct isl_tab *tab, __isl_keep isl_basic_map *bmap,
 155         int **div_map)
 156 {
 157         int i, j;
 158         struct isl_vec *vec;
 159         unsigned total;
 160         unsigned dim;
 161
 162         if (!bmap)
 163                 return -1;
 164         if (!bmap->n_div)
 165                 return 0;
 166
 167         if (!*div_map)
 168                 *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
 169         if (!*div_map)
 170                 return -1;
 171
 172         total = isl_basic_map_total_dim(tab->bmap);
 173         dim = total - tab->bmap->n_div;
 174         vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
 175         if (!vec)
 176                 return -1;
 177
 178         for (i = 0; i < bmap->n_div; ++i) {
 179                 isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
 180                 isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
 181                 for (j = 0; j < i; ++j)
 182                         isl_int_set(vec->el[2 + dim + (*div_map)[j]],
 183                                         bmap->div[i][2 + dim + j]);
 184                 for (j = 0; j < tab->bmap->n_div; ++j)
 185                         if (isl_seq_eq(tab->bmap->div[j],
 186                                         vec->el, 2 + dim + tab->bmap->n_div))
 187                                 break;
 188                 (*div_map)[i] = j;
 189                 if (j == tab->bmap->n_div) {
 190                         vec->size = 2 + dim + tab->bmap->n_div;
 191                         if (isl_tab_add_div(tab, vec, NULL, NULL) < 0)
 192                                 goto error;
 193                 }
 194         }
 195
 196         isl_vec_free(vec);
 197
 198         return 0;
 199 error:
 200         isl_vec_free(vec);
 201
 202         return -1;
 203 }
 204
 205 /* Freeze all constraints of tableau tab.
 206  */
 207 static int tab_freeze_constraints(struct isl_tab *tab)
 208 {
 209         int i;
 210
 211         for (i = 0; i < tab->n_con; ++i)
 212                 if (isl_tab_freeze_constraint(tab, i) < 0)
 213                         return -1;
 214
 215         return 0;
 216 }
 217
 218 /* Check for redundant constraints starting at offset.
 219  * Put the indices of the redundant constraints in index
 220  * and return the number of redundant constraints.
 221  */
 222 static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,
 223         int offset, int **index)
 224 {
 225         int i, n;
 226         int n_test = tab->n_con - offset;
 227
 228         if (isl_tab_detect_redundant(tab) < 0)
 229                 return -1;
 230
 231         if (n_test == 0)
 232                 return 0;
 233         if (!*index)
 234                 *index = isl_alloc_array(ctx, int, n_test);
 235         if (!*index)
 236                 return -1;
 237
 238         for (n = 0, i = 0; i < n_test; ++i) {
 239                 int r;
 240                 r = isl_tab_is_redundant(tab, offset + i);
 241                 if (r < 0)
 242                         return -1;
 243                 if (r)
 244                         continue;
 245                 (*index)[n++] = i;
 246         }
 247
 248         return n;
 249 }
 250
 251 /* basic_map_collect_diff calls add on each of the pieces of
 252  * the set difference between bmap and map until the add method
 253  * return a negative value.
 254  */
 255 struct isl_diff_collector {
 256         int (*add)(struct isl_diff_collector *dc,
 257                     __isl_take isl_basic_map *bmap);
 258 };
 259
 260 /* Compute the set difference between bmap and map and call
 261  * dc->add on each of the piece until this function returns
 262  * a negative value.
 263  * Return 0 on success and -1 on error.  dc->add returning
 264  * a negative value is treated as an error, but the calling
 265  * function can interpret the results based on the state of dc.
 266  *
 267  * Assumes that map has known divs.
 268  *
 269  * The difference is computed by a backtracking algorithm.
 270  * Each level corresponds to a basic map in "map".
 271  * When a node in entered for the first time, we check
 272  * if the corresonding basic map intersects the current piece
 273  * of "bmap".  If not, we move to the next level.
 274  * Otherwise, we split the current piece into as many
 275  * pieces as there are non-redundant constraints of the current
 276  * basic map in the intersection.  Each of these pieces is
 277  * handled by a child of the current node.
 278  * In particular, if there are n non-redundant constraints,
 279  * then for each 0 <= i < n, a piece is cut off by adding
 280  * constraints 0 <= j < i and adding the opposite of constraint i.
 281  * If there are no non-redundant constraints, meaning that the current
 282  * piece is a subset of the current basic map, then we simply backtrack.
 283  *
 284  * In the leaves, we check if the remaining piece has any integer points
 285  * and if so, pass it along to dc->add.  As a special case, if nothing
 286  * has been removed when we end up in a leaf, we simply pass along
 287  * the original basic map.
 288  */
 289 static int basic_map_collect_diff(__isl_take isl_basic_map *bmap,
 290         __isl_take isl_map *map, struct isl_diff_collector *dc)
 291 {
 292         int i;
 293         int modified;
 294         int level;
 295         int init;
 296         int empty;
 297         isl_ctx *ctx;
 298         struct isl_tab *tab = NULL;
 299         struct isl_tab_undo **snap = NULL;
 300         int *k = NULL;
 301         int *n = NULL;
 302         int **index = NULL;
 303         int **div_map = NULL;
 304
 305         empty = isl_basic_map_is_empty(bmap);
 306         if (empty) {
 307                 isl_basic_map_free(bmap);
 308                 isl_map_free(map);
 309                 return empty < 0 ? -1 : 0;
 310         }
 311
 312         bmap = isl_basic_map_cow(bmap);
 313         map = isl_map_cow(map);
 314
 315         if (!bmap || !map)
 316                 goto error;
 317
 318         ctx = map->ctx;
 319         snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
 320         k = isl_alloc_array(map->ctx, int, map->n);
 321         n = isl_alloc_array(map->ctx, int, map->n);
 322         index = isl_calloc_array(map->ctx, int *, map->n);
 323         div_map = isl_calloc_array(map->ctx, int *, map->n);
 324         if (!snap || !k || !n || !index || !div_map)
 325                 goto error;
 326
 327         bmap = isl_basic_map_order_divs(bmap);
 328         map = isl_map_order_divs(map);
 329
 330         tab = isl_tab_from_basic_map(bmap, 1);
 331         if (!tab)
 332                 goto error;
 333
 334         modified = 0;
 335         level = 0;
 336         init = 1;
 337
 338         while (level >= 0) {
 339                 if (level >= map->n) {
 340                         int empty;
 341                         struct isl_basic_map *bm;
 342                         if (!modified) {
 343                                 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
 344                                         goto error;
 345                                 break;
 346                         }
 347                         bm = isl_basic_map_copy(tab->bmap);
 348                         bm = isl_basic_map_cow(bm);
 349                         bm = isl_basic_map_update_from_tab(bm, tab);
 350                         bm = isl_basic_map_simplify(bm);
 351                         bm = isl_basic_map_finalize(bm);
 352                         empty = isl_basic_map_is_empty(bm);
 353                         if (empty)
 354                                 isl_basic_map_free(bm);
 355                         else if (dc->add(dc, bm) < 0)
 356                                 goto error;
 357                         if (empty < 0)
 358                                 goto error;
 359                         level--;
 360                         init = 0;
 361                         continue;
 362                 }
 363                 if (init) {
 364                         int offset;
 365                         struct isl_tab_undo *snap2;
 366                         snap2 = isl_tab_snap(tab);
 367                         if (tab_add_divs(tab, map->p[level],
 368                                          &div_map[level]) < 0)
 369                                 goto error;
 370                         offset = tab->n_con;
 371                         snap[level] = isl_tab_snap(tab);
 372                         if (tab_freeze_constraints(tab) < 0)
 373                                 goto error;
 374                         if (tab_add_constraints(tab, map->p[level],
 375                                                 div_map[level]) < 0)
 376                                 goto error;
 377                         k[level] = 0;
 378                         n[level] = 0;
 379                         if (tab->empty) {
 380                                 if (isl_tab_rollback(tab, snap2) < 0)
 381                                         goto error;
 382                                 level++;
 383                                 continue;
 384                         }
 385                         modified = 1;
 386                         n[level] = n_non_redundant(ctx, tab, offset,
 387                                                     &index[level]);
 388                         if (n[level] < 0)
 389                                 goto error;
 390                         if (n[level] == 0) {
 391                                 level--;
 392                                 init = 0;
 393                                 continue;
 394                         }
 395                         if (isl_tab_rollback(tab, snap[level]) < 0)
 396                                 goto error;
 397                         if (tab_add_constraint(tab, map->p[level],
 398                                         div_map[level], index[level][0], 1) < 0)
 399                                 goto error;
 400                         level++;
 401                         continue;
 402                 } else {
 403                         if (k[level] + 1 >= n[level]) {
 404                                 level--;
 405                                 continue;
 406                         }
 407                         if (isl_tab_rollback(tab, snap[level]) < 0)
 408                                 goto error;
 409                         if (tab_add_constraint(tab, map->p[level],
 410                                                 div_map[level],
 411                                                 index[level][k[level]], 0) < 0)
 412                                 goto error;
 413                         snap[level] = isl_tab_snap(tab);
 414                         k[level]++;
 415                         if (tab_add_constraint(tab, map->p[level],
 416                                                 div_map[level],
 417                                                 index[level][k[level]], 1) < 0)
 418                                 goto error;
 419                         level++;
 420                         init = 1;
 421                         continue;
 422                 }
 423         }
 424
 425         isl_tab_free(tab);
 426         free(snap);
 427         free(n);
 428         free(k);
 429         for (i = 0; index && i < map->n; ++i)
 430                 free(index[i]);
 431         free(index);
 432         for (i = 0; div_map && i < map->n; ++i)
 433                 free(div_map[i]);
 434         free(div_map);
 435
 436         isl_basic_map_free(bmap);
 437         isl_map_free(map);
 438
 439         return 0;
 440 error:
 441         isl_tab_free(tab);
 442         free(snap);
 443         free(n);
 444         free(k);
 445         for (i = 0; index && i < map->n; ++i)
 446                 free(index[i]);
 447         free(index);
 448         for (i = 0; div_map && i < map->n; ++i)
 449                 free(div_map[i]);
 450         free(div_map);
 451         isl_basic_map_free(bmap);
 452         isl_map_free(map);
 453         return -1;
 454 }
 455
 456 /* A diff collector that actually collects all parts of the
 457  * set difference in the field diff.
 458  */
 459 struct isl_subtract_diff_collector {
 460         struct isl_diff_collector dc;
 461         struct isl_map *diff;
 462 };
 463
 464 /* isl_subtract_diff_collector callback.
 465  */
 466 static int basic_map_subtract_add(struct isl_diff_collector *dc,
 467                             __isl_take isl_basic_map *bmap)
 468 {
 469         struct isl_subtract_diff_collector *sdc;
 470         sdc = (struct isl_subtract_diff_collector *)dc;
 471
 472         sdc->diff = isl_map_union_disjoint(sdc->diff,
 473                         isl_map_from_basic_map(bmap));
 474
 475         return sdc->diff ? 0 : -1;
 476 }
 477
 478 /* Return the set difference between bmap and map.
 479  */
 480 static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
 481         __isl_take isl_map *map)
 482 {
 483         struct isl_subtract_diff_collector sdc;
 484         sdc.dc.add = &basic_map_subtract_add;
 485         sdc.diff = isl_map_empty_like_basic_map(bmap);
 486         if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
 487                 isl_map_free(sdc.diff);
 488                 sdc.diff = NULL;
 489         }
 490         return sdc.diff;
 491 }
 492
 493 /* Return the set difference between map1 and map2.
 494  * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
 495  */
 496 static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,
 497         __isl_take isl_map *map2)
 498 {
 499         int i;
 500         struct isl_map *diff;
 501
 502         if (!map1 || !map2)
 503                 goto error;
 504
 505         isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
 506
 507         if (isl_map_is_empty(map2)) {
 508                 isl_map_free(map2);
 509                 return map1;
 510         }
 511
 512         map1 = isl_map_compute_divs(map1);
 513         map2 = isl_map_compute_divs(map2);
 514         if (!map1 || !map2)
 515                 goto error;
 516
 517         map1 = isl_map_remove_empty_parts(map1);
 518         map2 = isl_map_remove_empty_parts(map2);
 519
 520         diff = isl_map_empty_like(map1);
 521         for (i = 0; i < map1->n; ++i) {
 522                 struct isl_map *d;
 523                 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
 524                                        isl_map_copy(map2));
 525                 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
 526                         diff = isl_map_union_disjoint(diff, d);
 527                 else
 528                         diff = isl_map_union(diff, d);
 529         }
 530
 531         isl_map_free(map1);
 532         isl_map_free(map2);
 533
 534         return diff;
 535 error:
 536         isl_map_free(map1);
 537         isl_map_free(map2);
 538         return NULL;
 539 }
 540
 541 __isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
 542         __isl_take isl_map *map2)
 543 {
 544         return isl_map_align_params_map_map_and(map1, map2, &map_subtract);
 545 }
 546
 547 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 548 {
 549         return (struct isl_set *)
 550                 isl_map_subtract(
 551                         (struct isl_map *)set1, (struct isl_map *)set2);
 552 }
 553
 554 /* Remove the elements of "dom" from the domain of "map".
 555  */
 556 static __isl_give isl_map *map_subtract_domain(__isl_take isl_map *map,
 557         __isl_take isl_set *dom)
 558 {
 559         isl_map *ext_dom;
 560
 561         if (!isl_map_compatible_domain(map, dom))
 562                 isl_die(isl_set_get_ctx(dom), isl_error_invalid,
 563                         "incompatible spaces", goto error);
 564
 565         ext_dom = isl_map_universe(isl_map_get_space(map));
 566         ext_dom = isl_map_intersect_domain(ext_dom, dom);
 567         return isl_map_subtract(map, ext_dom);
 568 error:
 569         isl_map_free(map);
 570         isl_set_free(dom);
 571         return NULL;
 572 }
 573
 574 __isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,
 575         __isl_take isl_set *dom)
 576 {
 577         return isl_map_align_params_map_map_and(map, dom, &map_subtract_domain);
 578 }
 579
 580 /* Remove the elements of "dom" from the range of "map".
 581  */
 582 static __isl_give isl_map *map_subtract_range(__isl_take isl_map *map,
 583         __isl_take isl_set *dom)
 584 {
 585         isl_map *ext_dom;
 586
 587         if (!isl_map_compatible_range(map, dom))
 588                 isl_die(isl_set_get_ctx(dom), isl_error_invalid,
 589                         "incompatible spaces", goto error);
 590
 591         ext_dom = isl_map_universe(isl_map_get_space(map));
 592         ext_dom = isl_map_intersect_range(ext_dom, dom);
 593         return isl_map_subtract(map, ext_dom);
 594 error:
 595         isl_map_free(map);
 596         isl_set_free(dom);
 597         return NULL;
 598 }
 599
 600 __isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,
 601         __isl_take isl_set *dom)
 602 {
 603         return isl_map_align_params_map_map_and(map, dom, &map_subtract_range);
 604 }
 605
 606 /* A diff collector that aborts as soon as its add function is called,
 607  * setting empty to 0.
 608  */
 609 struct isl_is_empty_diff_collector {
 610         struct isl_diff_collector dc;
 611         int empty;
 612 };
 613
 614 /* isl_is_empty_diff_collector callback.
 615  */
 616 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
 617                             __isl_take isl_basic_map *bmap)
 618 {
 619         struct isl_is_empty_diff_collector *edc;
 620         edc = (struct isl_is_empty_diff_collector *)dc;
 621
 622         edc->empty = 0;
 623
 624         isl_basic_map_free(bmap);
 625         return -1;
 626 }
 627
 628 /* Check if bmap \ map is empty by computing this set difference
 629  * and breaking off as soon as the difference is known to be non-empty.
 630  */
 631 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
 632         __isl_keep isl_map *map)
 633 {
 634         int r;
 635         struct isl_is_empty_diff_collector edc;
 636
 637         r = isl_basic_map_plain_is_empty(bmap);
 638         if (r)
 639                 return r;
 640
 641         edc.dc.add = &basic_map_is_empty_add;
 642         edc.empty = 1;
 643         r = basic_map_collect_diff(isl_basic_map_copy(bmap),
 644                                    isl_map_copy(map), &edc.dc);
 645         if (!edc.empty)
 646                 return 0;
 647
 648         return r < 0 ? -1 : 1;
 649 }
 650
 651 /* Check if map1 \ map2 is empty by checking if the set difference is empty
 652  * for each of the basic maps in map1.
 653  */
 654 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 655 {
 656         int i;
 657         int is_empty = 1;
 658
 659         if (!map1 || !map2)
 660                 return -1;
 661
 662         for (i = 0; i < map1->n; ++i) {
 663                 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
 664                 if (is_empty < 0 || !is_empty)
 665                          break;
 666         }
 667
 668         return is_empty;
 669 }
 670
 671 /* Return 1 if "bmap" contains a single element.
 672  */
 673 int isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
 674 {
 675         if (!bmap)
 676                 return -1;
 677         if (bmap->n_div)
 678                 return 0;
 679         if (bmap->n_ineq)
 680                 return 0;
 681         return bmap->n_eq == isl_basic_map_total_dim(bmap);
 682 }
 683
 684 /* Return 1 if "map" contains a single element.
 685  */
 686 int isl_map_plain_is_singleton(__isl_keep isl_map *map)
 687 {
 688         if (!map)
 689                 return -1;
 690         if (map->n != 1)
 691                 return 0;
 692
 693         return isl_basic_map_plain_is_singleton(map->p[0]);
 694 }
 695
 696 /* Given a singleton basic map, extract the single element
 697  * as an isl_point.
 698  */
 699 static __isl_give isl_point *singleton_extract_point(
 700         __isl_keep isl_basic_map *bmap)
 701 {
 702         int j;
 703         unsigned dim;
 704         struct isl_vec *point;
 705         isl_int m;
 706
 707         if (!bmap)
 708                 return NULL;
 709
 710         dim = isl_basic_map_total_dim(bmap);
 711         isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
 712         point = isl_vec_alloc(bmap->ctx, 1 + dim);
 713         if (!point)
 714                 return NULL;
 715
 716         isl_int_init(m);
 717
 718         isl_int_set_si(point->el[0], 1);
 719         for (j = 0; j < bmap->n_eq; ++j) {
 720                 int i = dim - 1 - j;
 721                 isl_assert(bmap->ctx,
 722                     isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
 723                     goto error);
 724                 isl_assert(bmap->ctx,
 725                     isl_int_is_one(bmap->eq[j][1 + i]) ||
 726                     isl_int_is_negone(bmap->eq[j][1 + i]),
 727                     goto error);
 728                 isl_assert(bmap->ctx,
 729                     isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
 730                     goto error);
 731
 732                 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
 733                 isl_int_divexact(m, bmap->eq[j][1 + i], m);
 734                 isl_int_abs(m, m);
 735                 isl_seq_scale(point->el, point->el, m, 1 + i);
 736                 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
 737                 isl_int_neg(m, m);
 738                 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
 739         }
 740
 741         isl_int_clear(m);
 742         return isl_point_alloc(isl_basic_map_get_space(bmap), point);
 743 error:
 744         isl_int_clear(m);
 745         isl_vec_free(point);
 746         return NULL;
 747 }
 748
 749 /* Return 1 is the singleton map "map1" is a subset of "map2",
 750  * i.e., if the single element of "map1" is also an element of "map2".
 751  * Assumes "map2" has known divs.
 752  */
 753 static int map_is_singleton_subset(__isl_keep isl_map *map1,
 754         __isl_keep isl_map *map2)
 755 {
 756         int i;
 757         int is_subset = 0;
 758         struct isl_point *point;
 759
 760         if (!map1 || !map2)
 761                 return -1;
 762         if (map1->n != 1)
 763                 return -1;
 764
 765         point = singleton_extract_point(map1->p[0]);
 766         if (!point)
 767                 return -1;
 768
 769         for (i = 0; i < map2->n; ++i) {
 770                 is_subset = isl_basic_map_contains_point(map2->p[i], point);
 771                 if (is_subset)
 772                         break;
 773         }
 774
 775         isl_point_free(point);
 776         return is_subset;
 777 }
 778
 779 static int map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 780 {
 781         int is_subset = 0;
 782         int empty;
 783         int rat1, rat2;
 784
 785         if (!map1 || !map2)
 786                 return -1;
 787
 788         if (!isl_map_has_equal_space(map1, map2))
 789                 return 0;
 790
 791         empty = isl_map_is_empty(map1);
 792         if (empty < 0)
 793                 return -1;
 794         if (empty)
 795                 return 1;
 796
 797         empty = isl_map_is_empty(map2);
 798         if (empty < 0)
 799                 return -1;
 800         if (empty)
 801                 return 0;
 802
 803         rat1 = isl_map_has_rational(map1);
 804         rat2 = isl_map_has_rational(map2);
 805         if (rat1 < 0 || rat2 < 0)
 806                 return -1;
 807         if (rat1 && !rat2)
 808                 return 0;
 809
 810         if (isl_map_plain_is_universe(map2))
 811                 return 1;
 812
 813         map2 = isl_map_compute_divs(isl_map_copy(map2));
 814         if (isl_map_plain_is_singleton(map1)) {
 815                 is_subset = map_is_singleton_subset(map1, map2);
 816                 isl_map_free(map2);
 817                 return is_subset;
 818         }
 819         is_subset = map_diff_is_empty(map1, map2);
 820         isl_map_free(map2);
 821
 822         return is_subset;
 823 }
 824
 825 int isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
 826 {
 827         return isl_map_align_params_map_map_and_test(map1, map2,
 828                                                         &map_is_subset);
 829 }
 830
 831 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 832 {
 833         return isl_map_is_subset(
 834                         (struct isl_map *)set1, (struct isl_map *)set2);
 835 }
 836
 837 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
 838 {
 839         int i;
 840         struct isl_subtract_diff_collector sdc;
 841         sdc.dc.add = &basic_map_subtract_add;
 842
 843         if (!map)
 844                 return NULL;
 845         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 846                 return map;
 847         if (map->n <= 1)
 848                 return map;
 849
 850         map = isl_map_compute_divs(map);
 851         map = isl_map_remove_empty_parts(map);
 852
 853         if (!map || map->n <= 1)
 854                 return map;
 855
 856         sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 857
 858         for (i = 1; i < map->n; ++i) {
 859                 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
 860                 struct isl_map *copy = isl_map_copy(sdc.diff);
 861                 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
 862                         isl_map_free(sdc.diff);
 863                         sdc.diff = NULL;
 864                         break;
 865                 }
 866         }
 867
 868         isl_map_free(map);
 869
 870         return sdc.diff;
 871 }
 872
 873 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
 874 {
 875         return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
 876 }
 877
 878 __isl_give isl_map *isl_map_complement(__isl_take isl_map *map)
 879 {
 880         isl_map *universe;
 881
 882         if (!map)
 883                 return NULL;
 884
 885         universe = isl_map_universe(isl_map_get_space(map));
 886
 887         return isl_map_subtract(universe, map);
 888 }
 889
 890 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
 891 {
 892         return isl_map_complement(set);
 893 }