Line data Source code
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 : #include <set_to_map.c>
19 : #include <set_from_map.c>
20 :
21 : /* Expand the constraint "c" into "v". The initial "dim" dimensions
22 : * 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 mapping
25 : * of divs in "c" to divs in "v" is given by "div_map".
26 : *
27 : * Although it shouldn't happen in practice, it is theoretically
28 : * 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 their
30 : * coefficients.
31 : */
32 15632195 : static void expand_constraint(isl_vec *v, unsigned dim,
33 : isl_int *c, int *div_map, unsigned n_div)
34 : {
35 : int i;
36 :
37 15632195 : isl_seq_cpy(v->el, c, 1 + dim);
38 15632195 : isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
39 :
40 16977565 : for (i = 0; i < n_div; ++i) {
41 1345370 : int pos = 1 + dim + div_map[i];
42 1345370 : isl_int_add(v->el[pos], v->el[pos], c[1 + dim + i]);
43 : }
44 15632195 : }
45 :
46 : /* Add all constraints of bmap to tab. The equalities of bmap
47 : * are added as a pair of inequalities.
48 : */
49 5558841 : static 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 : unsigned tab_total;
55 : unsigned bmap_total;
56 : isl_vec *v;
57 :
58 5558841 : if (!tab || !bmap)
59 0 : return isl_stat_error;
60 :
61 5558841 : tab_total = isl_basic_map_total_dim(tab->bmap);
62 5558841 : bmap_total = isl_basic_map_total_dim(bmap);
63 5558841 : dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
64 :
65 5558841 : if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
66 0 : return isl_stat_error;
67 :
68 5558841 : v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
69 5558841 : if (!v)
70 0 : return isl_stat_error;
71 :
72 6319997 : for (i = 0; i < bmap->n_eq; ++i) {
73 1422279 : expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
74 1422279 : if (isl_tab_add_ineq(tab, v->el) < 0)
75 0 : goto error;
76 1422279 : isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
77 1422279 : expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
78 1422279 : if (isl_tab_add_ineq(tab, v->el) < 0)
79 0 : goto error;
80 1422279 : isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
81 1422279 : if (tab->empty)
82 661123 : break;
83 : }
84 :
85 12711507 : for (i = 0; i < bmap->n_ineq; ++i) {
86 12526669 : expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
87 12526669 : if (isl_tab_add_ineq(tab, v->el) < 0)
88 0 : goto error;
89 12526669 : if (tab->empty)
90 5374003 : break;
91 : }
92 :
93 5558841 : isl_vec_free(v);
94 5558841 : return isl_stat_ok;
95 : error:
96 0 : isl_vec_free(v);
97 0 : return isl_stat_error;
98 : }
99 :
100 : /* Add a specific constraint of bmap (or its opposite) to tab.
101 : * The position of the constraint is specified by "c", where
102 : * the equalities of bmap are counted twice, once for the inequality
103 : * that is equal to the equality, and once for its negation.
104 : *
105 : * Each of these constraints has been added to "tab" before by
106 : * tab_add_constraints (and later removed again), so there should
107 : * already be a row available for the constraint.
108 : */
109 260968 : static isl_stat tab_add_constraint(struct isl_tab *tab,
110 : __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
111 : {
112 : unsigned dim;
113 : unsigned tab_total;
114 : unsigned bmap_total;
115 : isl_vec *v;
116 : isl_stat r;
117 :
118 260968 : if (!tab || !bmap)
119 0 : return isl_stat_error;
120 :
121 260968 : tab_total = isl_basic_map_total_dim(tab->bmap);
122 260968 : bmap_total = isl_basic_map_total_dim(bmap);
123 260968 : dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
124 :
125 260968 : v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
126 260968 : if (!v)
127 0 : return isl_stat_error;
128 :
129 260968 : if (c < 2 * bmap->n_eq) {
130 10118 : if ((c % 2) != oppose)
131 4841 : isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
132 : 1 + bmap_total);
133 10118 : if (oppose)
134 6057 : isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
135 10118 : expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
136 10118 : r = isl_tab_add_ineq(tab, v->el);
137 10118 : if (oppose)
138 6057 : isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
139 10118 : if ((c % 2) != oppose)
140 4841 : isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
141 : 1 + bmap_total);
142 : } else {
143 250850 : c -= 2 * bmap->n_eq;
144 250850 : if (oppose) {
145 178559 : isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
146 : 1 + bmap_total);
147 178559 : isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
148 : }
149 250850 : expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
150 250850 : r = isl_tab_add_ineq(tab, v->el);
151 250850 : if (oppose) {
152 178559 : isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
153 178559 : isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
154 : 1 + bmap_total);
155 : }
156 : }
157 :
158 260968 : isl_vec_free(v);
159 260968 : return r;
160 : }
161 :
162 5558841 : static isl_stat tab_add_divs(struct isl_tab *tab,
163 : __isl_keep isl_basic_map *bmap, int **div_map)
164 : {
165 : int i, j;
166 : struct isl_vec *vec;
167 : unsigned total;
168 : unsigned dim;
169 :
170 5558841 : if (!bmap)
171 0 : return isl_stat_error;
172 5558841 : if (!bmap->n_div)
173 5066566 : return isl_stat_ok;
174 :
175 492275 : if (!*div_map)
176 57419 : *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
177 492275 : if (!*div_map)
178 0 : return isl_stat_error;
179 :
180 492275 : total = isl_basic_map_total_dim(tab->bmap);
181 492275 : dim = total - tab->bmap->n_div;
182 492275 : vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
183 492275 : if (!vec)
184 0 : return isl_stat_error;
185 :
186 986404 : for (i = 0; i < bmap->n_div; ++i) {
187 494129 : isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
188 494129 : isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
189 495983 : for (j = 0; j < i; ++j)
190 1854 : isl_int_add(vec->el[2 + dim + (*div_map)[j]],
191 : vec->el[2 + dim + (*div_map)[j]],
192 : bmap->div[i][2 + dim + j]);
193 502780 : for (j = 0; j < tab->bmap->n_div; ++j)
194 70628 : if (isl_seq_eq(tab->bmap->div[j],
195 70628 : vec->el, 2 + dim + tab->bmap->n_div))
196 61977 : break;
197 494129 : (*div_map)[i] = j;
198 494129 : if (j == tab->bmap->n_div) {
199 432152 : vec->size = 2 + dim + tab->bmap->n_div;
200 432152 : if (isl_tab_add_div(tab, vec) < 0)
201 0 : goto error;
202 : }
203 : }
204 :
205 492275 : isl_vec_free(vec);
206 :
207 492275 : return isl_stat_ok;
208 : error:
209 0 : isl_vec_free(vec);
210 :
211 0 : return isl_stat_error;
212 : }
213 :
214 : /* Freeze all constraints of tableau tab.
215 : */
216 5558841 : static int tab_freeze_constraints(struct isl_tab *tab)
217 : {
218 : int i;
219 :
220 56054062 : for (i = 0; i < tab->n_con; ++i)
221 50495221 : if (isl_tab_freeze_constraint(tab, i) < 0)
222 0 : return -1;
223 :
224 5558841 : return 0;
225 : }
226 :
227 : /* Check for redundant constraints starting at offset.
228 : * Put the indices of the redundant constraints in index
229 : * and return the number of redundant constraints.
230 : */
231 177277 : static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,
232 : int offset, int **index)
233 : {
234 : int i, n;
235 177277 : int n_test = tab->n_con - offset;
236 :
237 177277 : if (isl_tab_detect_redundant(tab) < 0)
238 0 : return -1;
239 :
240 177277 : if (n_test == 0)
241 806 : return 0;
242 176471 : if (!*index)
243 115909 : *index = isl_alloc_array(ctx, int, n_test);
244 176471 : if (!*index)
245 0 : return -1;
246 :
247 1130130 : for (n = 0, i = 0; i < n_test; ++i) {
248 : int r;
249 953659 : r = isl_tab_is_redundant(tab, offset + i);
250 953659 : if (r < 0)
251 0 : return -1;
252 953659 : if (r)
253 769043 : continue;
254 184616 : (*index)[n++] = i;
255 : }
256 :
257 176471 : return n;
258 : }
259 :
260 : /* basic_map_collect_diff calls add on each of the pieces of
261 : * the set difference between bmap and map until the add method
262 : * return a negative value.
263 : */
264 : struct isl_diff_collector {
265 : isl_stat (*add)(struct isl_diff_collector *dc,
266 : __isl_take isl_basic_map *bmap);
267 : };
268 :
269 : /* Compute the set difference between bmap and map and call
270 : * dc->add on each of the piece until this function returns
271 : * a negative value.
272 : * Return 0 on success and -1 on error. dc->add returning
273 : * a negative value is treated as an error, but the calling
274 : * function can interpret the results based on the state of dc.
275 : *
276 : * Assumes that map has known divs.
277 : *
278 : * The difference is computed by a backtracking algorithm.
279 : * Each level corresponds to a basic map in "map".
280 : * When a node in entered for the first time, we check
281 : * if the corresonding basic map intersects the current piece
282 : * of "bmap". If not, we move to the next level.
283 : * Otherwise, we split the current piece into as many
284 : * pieces as there are non-redundant constraints of the current
285 : * basic map in the intersection. Each of these pieces is
286 : * handled by a child of the current node.
287 : * In particular, if there are n non-redundant constraints,
288 : * then for each 0 <= i < n, a piece is cut off by adding
289 : * constraints 0 <= j < i and adding the opposite of constraint i.
290 : * If there are no non-redundant constraints, meaning that the current
291 : * piece is a subset of the current basic map, then we simply backtrack.
292 : *
293 : * In the leaves, we check if the remaining piece has any integer points
294 : * and if so, pass it along to dc->add. As a special case, if nothing
295 : * has been removed when we end up in a leaf, we simply pass along
296 : * the original basic map.
297 : */
298 47235 : static isl_stat basic_map_collect_diff(__isl_take isl_basic_map *bmap,
299 : __isl_take isl_map *map, struct isl_diff_collector *dc)
300 : {
301 : int i;
302 : int modified;
303 : int level;
304 : int init;
305 : isl_bool empty;
306 : isl_ctx *ctx;
307 47235 : struct isl_tab *tab = NULL;
308 47235 : struct isl_tab_undo **snap = NULL;
309 47235 : int *k = NULL;
310 47235 : int *n = NULL;
311 47235 : int **index = NULL;
312 47235 : int **div_map = NULL;
313 :
314 47235 : empty = isl_basic_map_is_empty(bmap);
315 47235 : if (empty) {
316 0 : isl_basic_map_free(bmap);
317 0 : isl_map_free(map);
318 0 : return empty < 0 ? isl_stat_error : isl_stat_ok;
319 : }
320 :
321 47235 : bmap = isl_basic_map_cow(bmap);
322 47235 : map = isl_map_cow(map);
323 :
324 47235 : if (!bmap || !map)
325 : goto error;
326 :
327 47235 : ctx = map->ctx;
328 47235 : snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
329 47235 : k = isl_alloc_array(map->ctx, int, map->n);
330 47235 : n = isl_alloc_array(map->ctx, int, map->n);
331 47235 : index = isl_calloc_array(map->ctx, int *, map->n);
332 47235 : div_map = isl_calloc_array(map->ctx, int *, map->n);
333 47235 : if (!snap || !k || !n || !index || !div_map)
334 : goto error;
335 :
336 47235 : bmap = isl_basic_map_order_divs(bmap);
337 47235 : map = isl_map_order_divs(map);
338 :
339 47235 : tab = isl_tab_from_basic_map(bmap, 1);
340 47235 : if (!tab)
341 0 : goto error;
342 :
343 47235 : modified = 0;
344 47235 : level = 0;
345 47235 : init = 1;
346 :
347 10890627 : while (level >= 0) {
348 10800981 : if (level >= map->n) {
349 : int empty;
350 : struct isl_basic_map *bm;
351 54574 : if (!modified) {
352 4824 : if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
353 0 : goto error;
354 4824 : break;
355 : }
356 49750 : bm = isl_basic_map_copy(tab->bmap);
357 49750 : bm = isl_basic_map_cow(bm);
358 49750 : bm = isl_basic_map_update_from_tab(bm, tab);
359 49750 : bm = isl_basic_map_simplify(bm);
360 49750 : bm = isl_basic_map_finalize(bm);
361 49750 : empty = isl_basic_map_is_empty(bm);
362 49750 : if (empty)
363 1153 : isl_basic_map_free(bm);
364 48597 : else if (dc->add(dc, bm) < 0)
365 0 : goto error;
366 49750 : if (empty < 0)
367 0 : goto error;
368 49750 : level--;
369 49750 : init = 0;
370 49750 : continue;
371 : }
372 10746407 : if (init) {
373 : int offset;
374 : struct isl_tab_undo *snap2;
375 5558841 : snap2 = isl_tab_snap(tab);
376 11117682 : if (tab_add_divs(tab, map->p[level],
377 5558841 : &div_map[level]) < 0)
378 0 : goto error;
379 5558841 : offset = tab->n_con;
380 5558841 : snap[level] = isl_tab_snap(tab);
381 5558841 : if (tab_freeze_constraints(tab) < 0)
382 0 : goto error;
383 5558841 : if (tab_add_constraints(tab, map->p[level],
384 5558841 : div_map[level]) < 0)
385 0 : goto error;
386 5558841 : k[level] = 0;
387 5558841 : n[level] = 0;
388 5558841 : if (tab->empty) {
389 5381564 : if (isl_tab_rollback(tab, snap2) < 0)
390 0 : goto error;
391 5381564 : level++;
392 5381564 : continue;
393 : }
394 177277 : modified = 1;
395 354554 : n[level] = n_non_redundant(ctx, tab, offset,
396 177277 : &index[level]);
397 177277 : if (n[level] < 0)
398 0 : goto error;
399 177277 : if (n[level] == 0) {
400 69013 : level--;
401 69013 : init = 0;
402 69013 : continue;
403 : }
404 108264 : if (isl_tab_rollback(tab, snap[level]) < 0)
405 0 : goto error;
406 216528 : if (tab_add_constraint(tab, map->p[level],
407 216528 : div_map[level], index[level][0], 1) < 0)
408 0 : goto error;
409 108264 : level++;
410 108264 : continue;
411 : } else {
412 5187566 : if (k[level] + 1 >= n[level]) {
413 5111214 : level--;
414 5111214 : continue;
415 : }
416 76352 : if (isl_tab_rollback(tab, snap[level]) < 0)
417 0 : goto error;
418 152704 : if (tab_add_constraint(tab, map->p[level],
419 76352 : div_map[level],
420 76352 : index[level][k[level]], 0) < 0)
421 0 : goto error;
422 76352 : snap[level] = isl_tab_snap(tab);
423 76352 : k[level]++;
424 152704 : if (tab_add_constraint(tab, map->p[level],
425 76352 : div_map[level],
426 76352 : index[level][k[level]], 1) < 0)
427 0 : goto error;
428 76352 : level++;
429 76352 : init = 1;
430 76352 : continue;
431 : }
432 : }
433 :
434 47235 : isl_tab_free(tab);
435 47235 : free(snap);
436 47235 : free(n);
437 47235 : free(k);
438 9465365 : for (i = 0; index && i < map->n; ++i)
439 9418130 : free(index[i]);
440 47235 : free(index);
441 9465365 : for (i = 0; div_map && i < map->n; ++i)
442 9418130 : free(div_map[i]);
443 47235 : free(div_map);
444 :
445 47235 : isl_basic_map_free(bmap);
446 47235 : isl_map_free(map);
447 :
448 47235 : return isl_stat_ok;
449 : error:
450 0 : isl_tab_free(tab);
451 0 : free(snap);
452 0 : free(n);
453 0 : free(k);
454 0 : for (i = 0; index && i < map->n; ++i)
455 0 : free(index[i]);
456 0 : free(index);
457 0 : for (i = 0; div_map && i < map->n; ++i)
458 0 : free(div_map[i]);
459 0 : free(div_map);
460 0 : isl_basic_map_free(bmap);
461 0 : isl_map_free(map);
462 0 : return isl_stat_error;
463 : }
464 :
465 : /* A diff collector that actually collects all parts of the
466 : * set difference in the field diff.
467 : */
468 : struct isl_subtract_diff_collector {
469 : struct isl_diff_collector dc;
470 : struct isl_map *diff;
471 : };
472 :
473 : /* isl_subtract_diff_collector callback.
474 : */
475 53421 : static isl_stat basic_map_subtract_add(struct isl_diff_collector *dc,
476 : __isl_take isl_basic_map *bmap)
477 : {
478 : struct isl_subtract_diff_collector *sdc;
479 53421 : sdc = (struct isl_subtract_diff_collector *)dc;
480 :
481 53421 : sdc->diff = isl_map_union_disjoint(sdc->diff,
482 : isl_map_from_basic_map(bmap));
483 :
484 53421 : return sdc->diff ? isl_stat_ok : isl_stat_error;
485 : }
486 :
487 : /* Return the set difference between bmap and map.
488 : */
489 28252 : static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
490 : __isl_take isl_map *map)
491 : {
492 : struct isl_subtract_diff_collector sdc;
493 28252 : sdc.dc.add = &basic_map_subtract_add;
494 28252 : sdc.diff = isl_map_empty(isl_basic_map_get_space(bmap));
495 28252 : if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
496 0 : isl_map_free(sdc.diff);
497 0 : sdc.diff = NULL;
498 : }
499 28252 : return sdc.diff;
500 : }
501 :
502 : /* Return an empty map living in the same space as "map1" and "map2".
503 : */
504 1017 : static __isl_give isl_map *replace_pair_by_empty( __isl_take isl_map *map1,
505 : __isl_take isl_map *map2)
506 : {
507 : isl_space *space;
508 :
509 1017 : space = isl_map_get_space(map1);
510 1017 : isl_map_free(map1);
511 1017 : isl_map_free(map2);
512 1017 : return isl_map_empty(space);
513 : }
514 :
515 : /* Return the set difference between map1 and map2.
516 : * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
517 : *
518 : * If "map1" and "map2" are obviously equal to each other,
519 : * then return an empty map in the same space.
520 : *
521 : * If "map1" and "map2" are disjoint, then simply return "map1".
522 : */
523 5702 : static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,
524 : __isl_take isl_map *map2)
525 : {
526 : int i;
527 : int equal, disjoint;
528 : struct isl_map *diff;
529 :
530 5702 : if (!map1 || !map2)
531 : goto error;
532 :
533 5702 : isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
534 :
535 5702 : equal = isl_map_plain_is_equal(map1, map2);
536 5702 : if (equal < 0)
537 0 : goto error;
538 5702 : if (equal)
539 1017 : return replace_pair_by_empty(map1, map2);
540 :
541 4685 : disjoint = isl_map_is_disjoint(map1, map2);
542 4685 : if (disjoint < 0)
543 0 : goto error;
544 4685 : if (disjoint) {
545 1550 : isl_map_free(map2);
546 1550 : return map1;
547 : }
548 :
549 3135 : map1 = isl_map_compute_divs(map1);
550 3135 : map2 = isl_map_compute_divs(map2);
551 3135 : if (!map1 || !map2)
552 : goto error;
553 :
554 3135 : map1 = isl_map_remove_empty_parts(map1);
555 3135 : map2 = isl_map_remove_empty_parts(map2);
556 :
557 3135 : diff = isl_map_empty(isl_map_get_space(map1));
558 31387 : for (i = 0; i < map1->n; ++i) {
559 : struct isl_map *d;
560 28252 : d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
561 : isl_map_copy(map2));
562 28252 : if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
563 15178 : diff = isl_map_union_disjoint(diff, d);
564 : else
565 13074 : diff = isl_map_union(diff, d);
566 : }
567 :
568 3135 : isl_map_free(map1);
569 3135 : isl_map_free(map2);
570 :
571 3135 : return diff;
572 : error:
573 0 : isl_map_free(map1);
574 0 : isl_map_free(map2);
575 0 : return NULL;
576 : }
577 :
578 5702 : __isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
579 : __isl_take isl_map *map2)
580 : {
581 5702 : return isl_map_align_params_map_map_and(map1, map2, &map_subtract);
582 : }
583 :
584 2223 : struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
585 : {
586 2223 : return set_from_map(isl_map_subtract(set_to_map(set1),
587 : set_to_map(set2)));
588 : }
589 :
590 : /* Remove the elements of "dom" from the domain of "map".
591 : */
592 0 : static __isl_give isl_map *map_subtract_domain(__isl_take isl_map *map,
593 : __isl_take isl_set *dom)
594 : {
595 : isl_bool ok;
596 : isl_map *ext_dom;
597 :
598 0 : ok = isl_map_compatible_domain(map, dom);
599 0 : if (ok < 0)
600 0 : goto error;
601 0 : if (!ok)
602 0 : isl_die(isl_set_get_ctx(dom), isl_error_invalid,
603 : "incompatible spaces", goto error);
604 :
605 0 : ext_dom = isl_map_universe(isl_map_get_space(map));
606 0 : ext_dom = isl_map_intersect_domain(ext_dom, dom);
607 0 : return isl_map_subtract(map, ext_dom);
608 : error:
609 0 : isl_map_free(map);
610 0 : isl_set_free(dom);
611 0 : return NULL;
612 : }
613 :
614 0 : __isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,
615 : __isl_take isl_set *dom)
616 : {
617 0 : return isl_map_align_params_map_map_and(map, dom, &map_subtract_domain);
618 : }
619 :
620 : /* Remove the elements of "dom" from the range of "map".
621 : */
622 0 : static __isl_give isl_map *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 0 : ok = isl_map_compatible_range(map, dom);
629 0 : if (ok < 0)
630 0 : goto error;
631 0 : if (!ok)
632 0 : isl_die(isl_set_get_ctx(dom), isl_error_invalid,
633 : "incompatible spaces", goto error);
634 :
635 0 : ext_dom = isl_map_universe(isl_map_get_space(map));
636 0 : ext_dom = isl_map_intersect_range(ext_dom, dom);
637 0 : return isl_map_subtract(map, ext_dom);
638 : error:
639 0 : isl_map_free(map);
640 0 : isl_set_free(dom);
641 0 : return NULL;
642 : }
643 :
644 0 : __isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,
645 : __isl_take isl_set *dom)
646 : {
647 0 : return isl_map_align_params_map_map_and(map, dom, &map_subtract_range);
648 : }
649 :
650 : /* A diff collector that aborts as soon as its add function is called,
651 : * setting empty to 0.
652 : */
653 : struct isl_is_empty_diff_collector {
654 : struct isl_diff_collector dc;
655 : isl_bool empty;
656 : };
657 :
658 : /* isl_is_empty_diff_collector callback.
659 : */
660 0 : static isl_stat basic_map_is_empty_add(struct isl_diff_collector *dc,
661 : __isl_take isl_basic_map *bmap)
662 : {
663 : struct isl_is_empty_diff_collector *edc;
664 0 : edc = (struct isl_is_empty_diff_collector *)dc;
665 :
666 0 : edc->empty = 0;
667 :
668 0 : isl_basic_map_free(bmap);
669 0 : return isl_stat_error;
670 : }
671 :
672 : /* Check if bmap \ map is empty by computing this set difference
673 : * and breaking off as soon as the difference is known to be non-empty.
674 : */
675 18983 : static isl_bool basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
676 : __isl_keep isl_map *map)
677 : {
678 : isl_bool empty;
679 : isl_stat r;
680 : struct isl_is_empty_diff_collector edc;
681 :
682 18983 : empty = isl_basic_map_plain_is_empty(bmap);
683 18983 : if (empty)
684 0 : return empty;
685 :
686 18983 : edc.dc.add = &basic_map_is_empty_add;
687 18983 : edc.empty = isl_bool_true;
688 18983 : r = basic_map_collect_diff(isl_basic_map_copy(bmap),
689 : isl_map_copy(map), &edc.dc);
690 18983 : if (!edc.empty)
691 0 : return isl_bool_false;
692 :
693 18983 : return r < 0 ? isl_bool_error : isl_bool_true;
694 : }
695 :
696 : /* Check if map1 \ map2 is empty by checking if the set difference is empty
697 : * for each of the basic maps in map1.
698 : */
699 292 : static isl_bool map_diff_is_empty(__isl_keep isl_map *map1,
700 : __isl_keep isl_map *map2)
701 : {
702 : int i;
703 292 : isl_bool is_empty = isl_bool_true;
704 :
705 292 : if (!map1 || !map2)
706 0 : return isl_bool_error;
707 :
708 19275 : for (i = 0; i < map1->n; ++i) {
709 18983 : is_empty = basic_map_diff_is_empty(map1->p[i], map2);
710 18983 : if (is_empty < 0 || !is_empty)
711 : break;
712 : }
713 :
714 292 : return is_empty;
715 : }
716 :
717 : /* Return true if "bmap" contains a single element.
718 : */
719 33 : isl_bool isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
720 : {
721 33 : if (!bmap)
722 0 : return isl_bool_error;
723 33 : if (bmap->n_div)
724 0 : return isl_bool_false;
725 33 : if (bmap->n_ineq)
726 22 : return isl_bool_false;
727 11 : return bmap->n_eq == isl_basic_map_total_dim(bmap);
728 : }
729 :
730 : /* Return true if "map" contains a single element.
731 : */
732 292 : isl_bool isl_map_plain_is_singleton(__isl_keep isl_map *map)
733 : {
734 292 : if (!map)
735 0 : return isl_bool_error;
736 292 : if (map->n != 1)
737 259 : return isl_bool_false;
738 :
739 33 : return isl_basic_map_plain_is_singleton(map->p[0]);
740 : }
741 :
742 : /* Given a singleton basic map, extract the single element
743 : * as an isl_point.
744 : */
745 0 : static __isl_give isl_point *singleton_extract_point(
746 : __isl_keep isl_basic_map *bmap)
747 : {
748 : int j;
749 : unsigned dim;
750 : struct isl_vec *point;
751 : isl_int m;
752 :
753 0 : if (!bmap)
754 0 : return NULL;
755 :
756 0 : dim = isl_basic_map_total_dim(bmap);
757 0 : isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
758 0 : point = isl_vec_alloc(bmap->ctx, 1 + dim);
759 0 : if (!point)
760 0 : return NULL;
761 :
762 0 : isl_int_init(m);
763 :
764 0 : isl_int_set_si(point->el[0], 1);
765 0 : for (j = 0; j < bmap->n_eq; ++j) {
766 0 : int i = dim - 1 - j;
767 0 : isl_assert(bmap->ctx,
768 : isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
769 : goto error);
770 0 : 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 0 : 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 0 : isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
779 0 : isl_int_divexact(m, bmap->eq[j][1 + i], m);
780 0 : isl_int_abs(m, m);
781 0 : isl_seq_scale(point->el, point->el, m, 1 + i);
782 0 : isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
783 0 : isl_int_neg(m, m);
784 0 : isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
785 : }
786 :
787 0 : isl_int_clear(m);
788 0 : return isl_point_alloc(isl_basic_map_get_space(bmap), point);
789 : error:
790 0 : isl_int_clear(m);
791 0 : isl_vec_free(point);
792 0 : 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 : */
799 0 : static isl_bool map_is_singleton_subset(__isl_keep isl_map *map1,
800 : __isl_keep isl_map *map2)
801 : {
802 : int i;
803 0 : isl_bool is_subset = isl_bool_false;
804 : struct isl_point *point;
805 :
806 0 : if (!map1 || !map2)
807 0 : return isl_bool_error;
808 0 : if (map1->n != 1)
809 0 : isl_die(isl_map_get_ctx(map1), isl_error_invalid,
810 : "expecting single-disjunct input",
811 : return isl_bool_error);
812 :
813 0 : point = singleton_extract_point(map1->p[0]);
814 0 : if (!point)
815 0 : return isl_bool_error;
816 :
817 0 : for (i = 0; i < map2->n; ++i) {
818 0 : is_subset = isl_basic_map_contains_point(map2->p[i], point);
819 0 : if (is_subset)
820 0 : break;
821 : }
822 :
823 0 : isl_point_free(point);
824 0 : return is_subset;
825 : }
826 :
827 396 : static isl_bool map_is_subset(__isl_keep isl_map *map1,
828 : __isl_keep isl_map *map2)
829 : {
830 396 : isl_bool is_subset = isl_bool_false;
831 : isl_bool empty, single;
832 : isl_bool rat1, rat2;
833 :
834 396 : if (!map1 || !map2)
835 0 : return isl_bool_error;
836 :
837 396 : if (!isl_map_has_equal_space(map1, map2))
838 0 : return isl_bool_false;
839 :
840 396 : empty = isl_map_is_empty(map1);
841 396 : if (empty < 0)
842 0 : return isl_bool_error;
843 396 : if (empty)
844 0 : return isl_bool_true;
845 :
846 396 : empty = isl_map_is_empty(map2);
847 396 : if (empty < 0)
848 0 : return isl_bool_error;
849 396 : if (empty)
850 0 : return isl_bool_false;
851 :
852 396 : rat1 = isl_map_has_rational(map1);
853 396 : rat2 = isl_map_has_rational(map2);
854 396 : if (rat1 < 0 || rat2 < 0)
855 0 : return isl_bool_error;
856 396 : if (rat1 && !rat2)
857 0 : return isl_bool_false;
858 :
859 396 : if (isl_map_plain_is_universe(map2))
860 104 : return isl_bool_true;
861 :
862 292 : single = isl_map_plain_is_singleton(map1);
863 292 : if (single < 0)
864 0 : return isl_bool_error;
865 292 : map2 = isl_map_compute_divs(isl_map_copy(map2));
866 292 : if (single) {
867 0 : is_subset = map_is_singleton_subset(map1, map2);
868 0 : isl_map_free(map2);
869 0 : return is_subset;
870 : }
871 292 : is_subset = map_diff_is_empty(map1, map2);
872 292 : isl_map_free(map2);
873 :
874 292 : return is_subset;
875 : }
876 :
877 396 : isl_bool isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
878 : {
879 396 : return isl_map_align_params_map_map_and_test(map1, map2,
880 : &map_is_subset);
881 : }
882 :
883 0 : isl_bool isl_set_is_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
884 : {
885 0 : return isl_map_is_subset(set_to_map(set1), set_to_map(set2));
886 : }
887 :
888 0 : __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 0 : sdc.dc.add = &basic_map_subtract_add;
893 :
894 0 : if (!map)
895 0 : return NULL;
896 0 : if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
897 0 : return map;
898 0 : if (map->n <= 1)
899 0 : return map;
900 :
901 0 : map = isl_map_compute_divs(map);
902 0 : map = isl_map_remove_empty_parts(map);
903 :
904 0 : if (!map || map->n <= 1)
905 0 : return map;
906 :
907 0 : sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
908 :
909 0 : for (i = 1; i < map->n; ++i) {
910 0 : struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
911 0 : struct isl_map *copy = isl_map_copy(sdc.diff);
912 0 : if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
913 0 : isl_map_free(sdc.diff);
914 0 : sdc.diff = NULL;
915 0 : break;
916 : }
917 : }
918 :
919 0 : isl_map_free(map);
920 :
921 0 : return sdc.diff;
922 : }
923 :
924 0 : __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
925 : {
926 0 : return set_from_map(isl_map_make_disjoint(set_to_map(set)));
927 : }
928 :
929 3479 : __isl_give isl_map *isl_map_complement(__isl_take isl_map *map)
930 : {
931 : isl_map *universe;
932 :
933 3479 : if (!map)
934 0 : return NULL;
935 :
936 3479 : universe = isl_map_universe(isl_map_get_space(map));
937 :
938 3479 : return isl_map_subtract(universe, map);
939 : }
940 :
941 3479 : __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
942 : {
943 3479 : return isl_map_complement(set);
944 : }
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