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1/*2 * Copyright 2008-2009 Katholieke Universiteit Leuven3 *4 * Use of this software is governed by the MIT license5 *6 * Written by Sven Verdoolaege, K.U.Leuven, Departement7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium8 */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#include <set_to_map.c>19#include <set_from_map.c>20 21/* Expand the constraint "c" into "v". The initial "dim" dimensions22 * are the same, but "v" may have more divs than "c" and the divs of "c"23 * may appear in different positions in "v".24 * The number of divs in "c" is given by "n_div" and the mapping25 * of divs in "c" to divs in "v" is given by "div_map".26 *27 * Although it shouldn't happen in practice, it is theoretically28 * possible that two or more divs in "c" are mapped to the same div in "v".29 * These divs are then necessarily the same, so we simply add their30 * coefficients.31 */32static void expand_constraint(isl_vec *v, unsigned dim,33 isl_int *c, int *div_map, unsigned n_div)34{35 int i;36 37 isl_seq_cpy(v->el, c, 1 + dim);38 isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));39 40 for (i = 0; i < n_div; ++i) {41 int pos = 1 + dim + div_map[i];42 isl_int_add(v->el[pos], v->el[pos], c[1 + dim + i]);43 }44}45 46/* Add all constraints of bmap to tab. The equalities of bmap47 * are added as a pair of inequalities.48 */49static isl_stat tab_add_constraints(struct isl_tab *tab,50 __isl_keep isl_basic_map *bmap, int *div_map)51{52 int i;53 unsigned dim;54 isl_size tab_total;55 isl_size bmap_n_div;56 isl_size bmap_total;57 isl_vec *v;58 59 if (!tab || !bmap)60 return isl_stat_error;61 62 tab_total = isl_basic_map_dim(tab->bmap, isl_dim_all);63 bmap_total = isl_basic_map_dim(bmap, isl_dim_all);64 bmap_n_div = isl_basic_map_dim(bmap, isl_dim_div);65 dim = bmap_total - bmap_n_div;66 if (tab_total < 0 || bmap_total < 0 || bmap_n_div < 0)67 return isl_stat_error;68 69 if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)70 return isl_stat_error;71 72 v = isl_vec_alloc(bmap->ctx, 1 + tab_total);73 if (!v)74 return isl_stat_error;75 76 for (i = 0; i < bmap->n_eq; ++i) {77 expand_constraint(v, dim, bmap->eq[i], div_map, bmap_n_div);78 if (isl_tab_add_ineq(tab, v->el) < 0)79 goto error;80 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);81 expand_constraint(v, dim, bmap->eq[i], div_map, bmap_n_div);82 if (isl_tab_add_ineq(tab, v->el) < 0)83 goto error;84 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);85 if (tab->empty)86 break;87 }88 89 for (i = 0; i < bmap->n_ineq; ++i) {90 expand_constraint(v, dim, bmap->ineq[i], div_map, bmap_n_div);91 if (isl_tab_add_ineq(tab, v->el) < 0)92 goto error;93 if (tab->empty)94 break;95 }96 97 isl_vec_free(v);98 return isl_stat_ok;99error:100 isl_vec_free(v);101 return isl_stat_error;102}103 104/* Add a specific constraint of bmap (or its opposite) to tab.105 * The position of the constraint is specified by "c", where106 * the equalities of bmap are counted twice, once for the inequality107 * that is equal to the equality, and once for its negation.108 *109 * Each of these constraints has been added to "tab" before by110 * tab_add_constraints (and later removed again), so there should111 * already be a row available for the constraint.112 */113static isl_stat tab_add_constraint(struct isl_tab *tab,114 __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)115{116 unsigned dim;117 isl_size tab_total;118 isl_size bmap_n_div;119 isl_size bmap_total;120 isl_vec *v;121 isl_stat r;122 123 if (!tab || !bmap)124 return isl_stat_error;125 126 tab_total = isl_basic_map_dim(tab->bmap, isl_dim_all);127 bmap_total = isl_basic_map_dim(bmap, isl_dim_all);128 bmap_n_div = isl_basic_map_dim(bmap, isl_dim_div);129 dim = bmap_total - bmap_n_div;130 if (tab_total < 0 || bmap_total < 0 || bmap_n_div < 0)131 return isl_stat_error;132 133 v = isl_vec_alloc(bmap->ctx, 1 + tab_total);134 if (!v)135 return isl_stat_error;136 137 if (c < 2 * bmap->n_eq) {138 if ((c % 2) != oppose)139 isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],140 1 + bmap_total);141 if (oppose)142 isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);143 expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap_n_div);144 r = isl_tab_add_ineq(tab, v->el);145 if (oppose)146 isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);147 if ((c % 2) != oppose)148 isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],149 1 + bmap_total);150 } else {151 c -= 2 * bmap->n_eq;152 if (oppose) {153 isl_seq_neg(bmap->ineq[c], bmap->ineq[c],154 1 + bmap_total);155 isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);156 }157 expand_constraint(v, dim, bmap->ineq[c], div_map, bmap_n_div);158 r = isl_tab_add_ineq(tab, v->el);159 if (oppose) {160 isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);161 isl_seq_neg(bmap->ineq[c], bmap->ineq[c],162 1 + bmap_total);163 }164 }165 166 isl_vec_free(v);167 return r;168}169 170static isl_stat tab_add_divs(struct isl_tab *tab,171 __isl_keep isl_basic_map *bmap, int **div_map)172{173 int i, j;174 struct isl_vec *vec;175 isl_size total;176 unsigned dim;177 178 if (!bmap)179 return isl_stat_error;180 if (!bmap->n_div)181 return isl_stat_ok;182 183 if (!*div_map)184 *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);185 if (!*div_map)186 return isl_stat_error;187 188 total = isl_basic_map_dim(tab->bmap, isl_dim_all);189 if (total < 0)190 return isl_stat_error;191 dim = total - tab->bmap->n_div;192 vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);193 if (!vec)194 return isl_stat_error;195 196 for (i = 0; i < bmap->n_div; ++i) {197 isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);198 isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);199 for (j = 0; j < i; ++j)200 isl_int_add(vec->el[2 + dim + (*div_map)[j]],201 vec->el[2 + dim + (*div_map)[j]],202 bmap->div[i][2 + dim + j]);203 for (j = 0; j < tab->bmap->n_div; ++j)204 if (isl_seq_eq(tab->bmap->div[j],205 vec->el, 2 + dim + tab->bmap->n_div))206 break;207 (*div_map)[i] = j;208 if (j == tab->bmap->n_div) {209 vec->size = 2 + dim + tab->bmap->n_div;210 if (isl_tab_add_div(tab, vec) < 0)211 goto error;212 }213 }214 215 isl_vec_free(vec);216 217 return isl_stat_ok;218error:219 isl_vec_free(vec);220 221 return isl_stat_error;222}223 224/* Freeze all constraints of tableau tab.225 */226static int tab_freeze_constraints(struct isl_tab *tab)227{228 int i;229 230 for (i = 0; i < tab->n_con; ++i)231 if (isl_tab_freeze_constraint(tab, i) < 0)232 return -1;233 234 return 0;235}236 237/* Check for redundant constraints starting at offset.238 * Put the indices of the non-redundant constraints in index239 * and return the number of non-redundant constraints.240 */241static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,242 int offset, int **index)243{244 int i, n;245 int n_test = tab->n_con - offset;246 247 if (isl_tab_detect_redundant(tab) < 0)248 return -1;249 250 if (n_test == 0)251 return 0;252 if (!*index)253 *index = isl_alloc_array(ctx, int, n_test);254 if (!*index)255 return -1;256 257 for (n = 0, i = 0; i < n_test; ++i) {258 int r;259 r = isl_tab_is_redundant(tab, offset + i);260 if (r < 0)261 return -1;262 if (r)263 continue;264 (*index)[n++] = i;265 }266 267 return n;268}269 270/* basic_map_collect_diff calls add on each of the pieces of271 * the set difference between bmap and map until the add method272 * return a negative value.273 */274struct isl_diff_collector {275 isl_stat (*add)(struct isl_diff_collector *dc,276 __isl_take isl_basic_map *bmap);277};278 279/* Compute the set difference between bmap and map and call280 * dc->add on each of the piece until this function returns281 * a negative value.282 * Return 0 on success and -1 on error. dc->add returning283 * a negative value is treated as an error, but the calling284 * function can interpret the results based on the state of dc.285 *286 * Assumes that map has known divs.287 *288 * The difference is computed by a backtracking algorithm.289 * Each level corresponds to a basic map in "map".290 * When a node in entered for the first time, we check291 * if the corresonding basic map intersects the current piece292 * of "bmap". If not, we move to the next level.293 * Otherwise, we split the current piece into as many294 * pieces as there are non-redundant constraints of the current295 * basic map in the intersection. Each of these pieces is296 * handled by a child of the current node.297 * In particular, if there are n non-redundant constraints,298 * then for each 0 <= i < n, a piece is cut off by adding299 * constraints 0 <= j < i and adding the opposite of constraint i.300 * If there are no non-redundant constraints, meaning that the current301 * piece is a subset of the current basic map, then we simply backtrack.302 *303 * In the leaves, we check if the remaining piece has any integer points304 * and if so, pass it along to dc->add. As a special case, if nothing305 * has been removed when we end up in a leaf, we simply pass along306 * the original basic map.307 */308static isl_stat basic_map_collect_diff(__isl_take isl_basic_map *bmap,309 __isl_take isl_map *map, struct isl_diff_collector *dc)310{311 int i;312 int modified;313 int level;314 int init;315 isl_bool empty;316 isl_ctx *ctx;317 struct isl_tab *tab = NULL;318 struct isl_tab_undo **snap = NULL;319 int *k = NULL;320 int *n = NULL;321 int **index = NULL;322 int **div_map = NULL;323 324 empty = isl_basic_map_is_empty(bmap);325 if (empty) {326 isl_basic_map_free(bmap);327 isl_map_free(map);328 return empty < 0 ? isl_stat_error : isl_stat_ok;329 }330 331 bmap = isl_basic_map_cow(bmap);332 map = isl_map_cow(map);333 334 if (!bmap || !map)335 goto error;336 337 ctx = map->ctx;338 snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);339 k = isl_alloc_array(map->ctx, int, map->n);340 n = isl_alloc_array(map->ctx, int, map->n);341 index = isl_calloc_array(map->ctx, int *, map->n);342 div_map = isl_calloc_array(map->ctx, int *, map->n);343 if (!snap || !k || !n || !index || !div_map)344 goto error;345 346 bmap = isl_basic_map_order_divs(bmap);347 map = isl_map_order_divs(map);348 349 tab = isl_tab_from_basic_map(bmap, 1);350 if (!tab)351 goto error;352 353 modified = 0;354 level = 0;355 init = 1;356 357 while (level >= 0) {358 if (level >= map->n) {359 int empty;360 struct isl_basic_map *bm;361 if (!modified) {362 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)363 goto error;364 break;365 }366 bm = isl_basic_map_copy(tab->bmap);367 bm = isl_basic_map_cow(bm);368 bm = isl_basic_map_update_from_tab(bm, tab);369 bm = isl_basic_map_simplify(bm);370 bm = isl_basic_map_finalize(bm);371 empty = isl_basic_map_is_empty(bm);372 if (empty)373 isl_basic_map_free(bm);374 else if (dc->add(dc, bm) < 0)375 goto error;376 if (empty < 0)377 goto error;378 level--;379 init = 0;380 continue;381 }382 if (init) {383 int offset;384 struct isl_tab_undo *snap2;385 snap2 = isl_tab_snap(tab);386 if (tab_add_divs(tab, map->p[level],387 &div_map[level]) < 0)388 goto error;389 offset = tab->n_con;390 snap[level] = isl_tab_snap(tab);391 if (tab_freeze_constraints(tab) < 0)392 goto error;393 if (tab_add_constraints(tab, map->p[level],394 div_map[level]) < 0)395 goto error;396 k[level] = 0;397 n[level] = 0;398 if (tab->empty) {399 if (isl_tab_rollback(tab, snap2) < 0)400 goto error;401 level++;402 continue;403 }404 modified = 1;405 n[level] = n_non_redundant(ctx, tab, offset,406 &index[level]);407 if (n[level] < 0)408 goto error;409 if (n[level] == 0) {410 level--;411 init = 0;412 continue;413 }414 if (isl_tab_rollback(tab, snap[level]) < 0)415 goto error;416 if (tab_add_constraint(tab, map->p[level],417 div_map[level], index[level][0], 1) < 0)418 goto error;419 level++;420 continue;421 } else {422 if (k[level] + 1 >= n[level]) {423 level--;424 continue;425 }426 if (isl_tab_rollback(tab, snap[level]) < 0)427 goto error;428 if (tab_add_constraint(tab, map->p[level],429 div_map[level],430 index[level][k[level]], 0) < 0)431 goto error;432 snap[level] = isl_tab_snap(tab);433 k[level]++;434 if (tab_add_constraint(tab, map->p[level],435 div_map[level],436 index[level][k[level]], 1) < 0)437 goto error;438 level++;439 init = 1;440 continue;441 }442 }443 444 isl_tab_free(tab);445 free(snap);446 free(n);447 free(k);448 for (i = 0; index && i < map->n; ++i)449 free(index[i]);450 free(index);451 for (i = 0; div_map && i < map->n; ++i)452 free(div_map[i]);453 free(div_map);454 455 isl_basic_map_free(bmap);456 isl_map_free(map);457 458 return isl_stat_ok;459error:460 isl_tab_free(tab);461 free(snap);462 free(n);463 free(k);464 for (i = 0; index && i < map->n; ++i)465 free(index[i]);466 free(index);467 for (i = 0; div_map && i < map->n; ++i)468 free(div_map[i]);469 free(div_map);470 isl_basic_map_free(bmap);471 isl_map_free(map);472 return isl_stat_error;473}474 475/* A diff collector that actually collects all parts of the476 * set difference in the field diff.477 */478struct isl_subtract_diff_collector {479 struct isl_diff_collector dc;480 struct isl_map *diff;481};482 483/* isl_subtract_diff_collector callback.484 */485static isl_stat basic_map_subtract_add(struct isl_diff_collector *dc,486 __isl_take isl_basic_map *bmap)487{488 struct isl_subtract_diff_collector *sdc;489 sdc = (struct isl_subtract_diff_collector *)dc;490 491 sdc->diff = isl_map_union_disjoint(sdc->diff,492 isl_map_from_basic_map(bmap));493 494 return sdc->diff ? isl_stat_ok : isl_stat_error;495}496 497/* Return the set difference between bmap and map.498 */499static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,500 __isl_take isl_map *map)501{502 struct isl_subtract_diff_collector sdc;503 sdc.dc.add = &basic_map_subtract_add;504 sdc.diff = isl_map_empty(isl_basic_map_get_space(bmap));505 if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {506 isl_map_free(sdc.diff);507 sdc.diff = NULL;508 }509 return sdc.diff;510}511 512/* Return an empty map living in the same space as "map1" and "map2".513 */514static __isl_give isl_map *replace_pair_by_empty( __isl_take isl_map *map1,515 __isl_take isl_map *map2)516{517 isl_space *space;518 519 space = isl_map_get_space(map1);520 isl_map_free(map1);521 isl_map_free(map2);522 return isl_map_empty(space);523}524 525/* Return the set difference between map1 and map2.526 * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))527 *528 * If "map1" and "map2" are obviously equal to each other,529 * then return an empty map in the same space.530 *531 * If "map1" and "map2" are disjoint, then simply return "map1".532 */533__isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,534 __isl_take isl_map *map2)535{536 int i;537 int equal, disjoint;538 struct isl_map *diff;539 540 if (isl_map_align_params_bin(&map1, &map2) < 0)541 goto error;542 if (isl_map_check_equal_space(map1, map2) < 0)543 goto error;544 545 equal = isl_map_plain_is_equal(map1, map2);546 if (equal < 0)547 goto error;548 if (equal)549 return replace_pair_by_empty(map1, map2);550 551 disjoint = isl_map_is_disjoint(map1, map2);552 if (disjoint < 0)553 goto error;554 if (disjoint) {555 isl_map_free(map2);556 return map1;557 }558 559 map1 = isl_map_compute_divs(map1);560 map2 = isl_map_compute_divs(map2);561 if (!map1 || !map2)562 goto error;563 564 map1 = isl_map_remove_empty_parts(map1);565 map2 = isl_map_remove_empty_parts(map2);566 567 diff = isl_map_empty(isl_map_get_space(map1));568 for (i = 0; i < map1->n; ++i) {569 struct isl_map *d;570 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),571 isl_map_copy(map2));572 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))573 diff = isl_map_union_disjoint(diff, d);574 else575 diff = isl_map_union(diff, d);576 }577 578 isl_map_free(map1);579 isl_map_free(map2);580 581 return diff;582error:583 isl_map_free(map1);584 isl_map_free(map2);585 return NULL;586}587 588__isl_give isl_set *isl_set_subtract(__isl_take isl_set *set1,589 __isl_take isl_set *set2)590{591 return set_from_map(isl_map_subtract(set_to_map(set1),592 set_to_map(set2)));593}594 595/* Remove the elements of "dom" from the domain of "map".596 */597__isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,598 __isl_take isl_set *dom)599{600 isl_bool ok;601 isl_map *ext_dom;602 603 isl_map_align_params_set(&map, &dom);604 ok = isl_map_compatible_domain(map, dom);605 if (ok < 0)606 goto error;607 if (!ok)608 isl_die(isl_set_get_ctx(dom), isl_error_invalid,609 "incompatible spaces", goto error);610 611 ext_dom = isl_map_universe(isl_map_get_space(map));612 ext_dom = isl_map_intersect_domain(ext_dom, dom);613 return isl_map_subtract(map, ext_dom);614error:615 isl_map_free(map);616 isl_set_free(dom);617 return NULL;618}619 620/* Remove the elements of "dom" from the range of "map".621 */622__isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,623 __isl_take isl_set *dom)624{625 isl_bool ok;626 isl_map *ext_dom;627 628 isl_map_align_params_set(&map, &dom);629 ok = isl_map_compatible_range(map, dom);630 if (ok < 0)631 goto error;632 if (!ok)633 isl_die(isl_set_get_ctx(dom), isl_error_invalid,634 "incompatible spaces", goto error);635 636 ext_dom = isl_map_universe(isl_map_get_space(map));637 ext_dom = isl_map_intersect_range(ext_dom, dom);638 return isl_map_subtract(map, ext_dom);639error:640 isl_map_free(map);641 isl_set_free(dom);642 return NULL;643}644 645/* A diff collector that aborts as soon as its add function is called,646 * setting empty to isl_false.647 */648struct isl_is_empty_diff_collector {649 struct isl_diff_collector dc;650 isl_bool empty;651};652 653/* isl_is_empty_diff_collector callback.654 */655static isl_stat basic_map_is_empty_add(struct isl_diff_collector *dc,656 __isl_take isl_basic_map *bmap)657{658 struct isl_is_empty_diff_collector *edc;659 edc = (struct isl_is_empty_diff_collector *)dc;660 661 edc->empty = isl_bool_false;662 663 isl_basic_map_free(bmap);664 return isl_stat_error;665}666 667/* Check if bmap \ map is empty by computing this set difference668 * and breaking off as soon as the difference is known to be non-empty.669 */670static isl_bool basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,671 __isl_keep isl_map *map)672{673 isl_bool empty;674 isl_stat r;675 struct isl_is_empty_diff_collector edc;676 677 empty = isl_basic_map_plain_is_empty(bmap);678 if (empty)679 return empty;680 681 edc.dc.add = &basic_map_is_empty_add;682 edc.empty = isl_bool_true;683 r = basic_map_collect_diff(isl_basic_map_copy(bmap),684 isl_map_copy(map), &edc.dc);685 if (!edc.empty)686 return isl_bool_false;687 688 return r < 0 ? isl_bool_error : isl_bool_true;689}690 691/* Check if map1 \ map2 is empty by checking if the set difference is empty692 * for each of the basic maps in map1.693 */694static isl_bool map_diff_is_empty(__isl_keep isl_map *map1,695 __isl_keep isl_map *map2)696{697 int i;698 isl_bool is_empty = isl_bool_true;699 700 if (!map1 || !map2)701 return isl_bool_error;702 703 for (i = 0; i < map1->n; ++i) {704 is_empty = basic_map_diff_is_empty(map1->p[i], map2);705 if (is_empty < 0 || !is_empty)706 break;707 }708 709 return is_empty;710}711 712/* Return true if "bmap" contains a single element.713 */714isl_bool isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)715{716 isl_size total;717 718 if (!bmap)719 return isl_bool_error;720 if (bmap->n_div)721 return isl_bool_false;722 if (bmap->n_ineq)723 return isl_bool_false;724 total = isl_basic_map_dim(bmap, isl_dim_all);725 if (total < 0)726 return isl_bool_error;727 return bmap->n_eq == total;728}729 730/* Return true if "map" contains a single element.731 */732isl_bool isl_map_plain_is_singleton(__isl_keep isl_map *map)733{734 if (!map)735 return isl_bool_error;736 if (map->n != 1)737 return isl_bool_false;738 739 return isl_basic_map_plain_is_singleton(map->p[0]);740}741 742/* Given a singleton basic map, extract the single element743 * as an isl_point.744 */745static __isl_give isl_point *singleton_extract_point(746 __isl_keep isl_basic_map *bmap)747{748 int j;749 isl_size dim;750 struct isl_vec *point;751 isl_int m;752 753 dim = isl_basic_map_dim(bmap, isl_dim_all);754 if (dim < 0)755 return NULL;756 757 isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);758 point = isl_vec_alloc(bmap->ctx, 1 + dim);759 if (!point)760 return NULL;761 762 isl_int_init(m);763 764 isl_int_set_si(point->el[0], 1);765 for (j = 0; j < bmap->n_eq; ++j) {766 int i = dim - 1 - j;767 isl_assert(bmap->ctx,768 isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,769 goto error);770 isl_assert(bmap->ctx,771 isl_int_is_one(bmap->eq[j][1 + i]) ||772 isl_int_is_negone(bmap->eq[j][1 + i]),773 goto error);774 isl_assert(bmap->ctx,775 isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,776 goto error);777 778 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);779 isl_int_divexact(m, bmap->eq[j][1 + i], m);780 isl_int_abs(m, m);781 isl_seq_scale(point->el, point->el, m, 1 + i);782 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);783 isl_int_neg(m, m);784 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);785 }786 787 isl_int_clear(m);788 return isl_point_alloc(isl_basic_map_get_space(bmap), point);789error:790 isl_int_clear(m);791 isl_vec_free(point);792 return NULL;793}794 795/* Return isl_bool_true if the singleton map "map1" is a subset of "map2",796 * i.e., if the single element of "map1" is also an element of "map2".797 * Assumes "map2" has known divs.798 */799static isl_bool map_is_singleton_subset(__isl_keep isl_map *map1,800 __isl_keep isl_map *map2)801{802 int i;803 isl_bool is_subset = isl_bool_false;804 struct isl_point *point;805 806 if (!map1 || !map2)807 return isl_bool_error;808 if (map1->n != 1)809 isl_die(isl_map_get_ctx(map1), isl_error_invalid,810 "expecting single-disjunct input",811 return isl_bool_error);812 813 point = singleton_extract_point(map1->p[0]);814 if (!point)815 return isl_bool_error;816 817 for (i = 0; i < map2->n; ++i) {818 is_subset = isl_basic_map_contains_point(map2->p[i], point);819 if (is_subset)820 break;821 }822 823 isl_point_free(point);824 return is_subset;825}826 827static isl_bool map_is_subset(__isl_keep isl_map *map1,828 __isl_keep isl_map *map2)829{830 isl_bool is_subset = isl_bool_false;831 isl_bool empty, single;832 isl_bool rat1, rat2;833 834 if (!map1 || !map2)835 return isl_bool_error;836 837 if (!isl_map_has_equal_space(map1, map2))838 return isl_bool_false;839 840 empty = isl_map_is_empty(map1);841 if (empty < 0)842 return isl_bool_error;843 if (empty)844 return isl_bool_true;845 846 empty = isl_map_is_empty(map2);847 if (empty < 0)848 return isl_bool_error;849 if (empty)850 return isl_bool_false;851 852 rat1 = isl_map_has_rational(map1);853 rat2 = isl_map_has_rational(map2);854 if (rat1 < 0 || rat2 < 0)855 return isl_bool_error;856 if (rat1 && !rat2)857 return isl_bool_false;858 859 if (isl_map_plain_is_universe(map2))860 return isl_bool_true;861 862 single = isl_map_plain_is_singleton(map1);863 if (single < 0)864 return isl_bool_error;865 map2 = isl_map_compute_divs(isl_map_copy(map2));866 if (single) {867 is_subset = map_is_singleton_subset(map1, map2);868 isl_map_free(map2);869 return is_subset;870 }871 is_subset = map_diff_is_empty(map1, map2);872 isl_map_free(map2);873 874 return is_subset;875}876 877isl_bool isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)878{879 return isl_map_align_params_map_map_and_test(map1, map2,880 &map_is_subset);881}882 883isl_bool isl_set_is_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)884{885 return isl_map_is_subset(set_to_map(set1), set_to_map(set2));886}887 888__isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)889{890 int i;891 struct isl_subtract_diff_collector sdc;892 sdc.dc.add = &basic_map_subtract_add;893 894 if (!map)895 return NULL;896 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))897 return map;898 if (map->n <= 1)899 return map;900 901 map = isl_map_compute_divs(map);902 map = isl_map_remove_empty_parts(map);903 904 if (!map || map->n <= 1)905 return map;906 907 sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));908 909 for (i = 1; i < map->n; ++i) {910 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);911 struct isl_map *copy = isl_map_copy(sdc.diff);912 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {913 isl_map_free(sdc.diff);914 sdc.diff = NULL;915 break;916 }917 }918 919 isl_map_free(map);920 921 return sdc.diff;922}923 924__isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)925{926 return set_from_map(isl_map_make_disjoint(set_to_map(set)));927}928 929__isl_give isl_map *isl_map_complement(__isl_take isl_map *map)930{931 isl_map *universe;932 933 if (!map)934 return NULL;935 936 universe = isl_map_universe(isl_map_get_space(map));937 938 return isl_map_subtract(universe, map);939}940 941__isl_give isl_set *isl_set_complement(__isl_take isl_set *set)942{943 return isl_map_complement(set);944}945