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add isl_seq_fdiv_q
[isl.git] / isl_map_simplify.c
blob273523bc7bc84b7ad669c9f77ba096c942301f33
1 #include "isl_equalities.h"
2 #include "isl_map.h"
3 #include "isl_map_private.h"
4 #include "isl_tab.h"
5
6 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
7 {
8 isl_int *t = bmap->eq[a];
9 bmap->eq[a] = bmap->eq[b];
10 bmap->eq[b] = t;
11 }
12
13 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
14 {
15 if (a != b) {
16 isl_int *t = bmap->ineq[a];
17 bmap->ineq[a] = bmap->ineq[b];
18 bmap->ineq[b] = t;
19 }
20 }
21
22 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
23 {
24 swap_inequality((struct isl_basic_map *)bset, a, b);
25 }
26
27 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
28 {
29 isl_seq_cpy(c, c + n, rem);
30 isl_seq_clr(c + rem, n);
31 }
32
33 /* Drop n dimensions starting at first.
34 *
35 * In principle, this frees up some extra variables as the number
36 * of columns remains constant, but we would have to extend
37 * the div array too as the number of rows in this array is assumed
38 * to be equal to extra.
39 */
40 struct isl_basic_set *isl_basic_set_drop_dims(
41 struct isl_basic_set *bset, unsigned first, unsigned n)
42 {
43 int i;
44
45 if (!bset)
46 goto error;
47
48 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
49
50 if (n == 0)
51 return bset;
52
53 bset = isl_basic_set_cow(bset);
54 if (!bset)
55 return NULL;
56
57 for (i = 0; i < bset->n_eq; ++i)
58 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
59 (bset->dim->n_out-first-n)+bset->extra);
60
61 for (i = 0; i < bset->n_ineq; ++i)
62 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
63 (bset->dim->n_out-first-n)+bset->extra);
64
65 for (i = 0; i < bset->n_div; ++i)
66 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
67 (bset->dim->n_out-first-n)+bset->extra);
68
69 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
70 if (!bset->dim)
71 goto error;
72
73 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
74 bset = isl_basic_set_simplify(bset);
75 return isl_basic_set_finalize(bset);
76 error:
77 isl_basic_set_free(bset);
78 return NULL;
79 }
80
81 struct isl_set *isl_set_drop_dims(
82 struct isl_set *set, unsigned first, unsigned n)
83 {
84 int i;
85
86 if (!set)
87 goto error;
88
89 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
90
91 if (n == 0)
92 return set;
93 set = isl_set_cow(set);
94 if (!set)
95 goto error;
96 set->dim = isl_dim_drop_outputs(set->dim, first, n);
97 if (!set->dim)
98 goto error;
99
100 for (i = 0; i < set->n; ++i) {
101 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
102 if (!set->p[i])
103 goto error;
104 }
105
106 ISL_F_CLR(set, ISL_SET_NORMALIZED);
107 return set;
108 error:
109 isl_set_free(set);
110 return NULL;
111 }
112
113 /* Drop n input dimensions starting at first.
114 *
115 * In principle, this frees up some extra variables as the number
116 * of columns remains constant, but we would have to extend
117 * the div array too as the number of rows in this array is assumed
118 * to be equal to extra.
119 */
120 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
121 enum isl_dim_type type, unsigned first, unsigned n)
122 {
123 int i;
124 unsigned dim;
125 unsigned offset;
126 unsigned left;
127
128 if (!bmap)
129 goto error;
130
131 dim = isl_basic_map_dim(bmap, type);
132 isl_assert(bmap->ctx, first + n <= dim, goto error);
133
134 if (n == 0)
135 return bmap;
136
137 bmap = isl_basic_map_cow(bmap);
138 if (!bmap)
139 return NULL;
140
141 offset = isl_basic_map_offset(bmap, type) + first;
142 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
143 for (i = 0; i < bmap->n_eq; ++i)
144 constraint_drop_vars(bmap->eq[i]+offset, n, left);
145
146 for (i = 0; i < bmap->n_ineq; ++i)
147 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
148
149 for (i = 0; i < bmap->n_div; ++i)
150 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
151
152 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
153 if (!bmap->dim)
154 goto error;
155
156 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
157 bmap = isl_basic_map_simplify(bmap);
158 return isl_basic_map_finalize(bmap);
159 error:
160 isl_basic_map_free(bmap);
161 return NULL;
162 }
163
164 struct isl_basic_map *isl_basic_map_drop_inputs(
165 struct isl_basic_map *bmap, unsigned first, unsigned n)
166 {
167 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
168 }
169
170 struct isl_map *isl_map_drop(struct isl_map *map,
171 enum isl_dim_type type, unsigned first, unsigned n)
172 {
173 int i;
174
175 if (!map)
176 goto error;
177
178 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
179
180 if (n == 0)
181 return map;
182 map = isl_map_cow(map);
183 if (!map)
184 goto error;
185 map->dim = isl_dim_drop(map->dim, type, first, n);
186 if (!map->dim)
187 goto error;
188
189 for (i = 0; i < map->n; ++i) {
190 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
191 if (!map->p[i])
192 goto error;
193 }
194 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
195
196 return map;
197 error:
198 isl_map_free(map);
199 return NULL;
200 }
201
202 struct isl_map *isl_map_drop_inputs(
203 struct isl_map *map, unsigned first, unsigned n)
204 {
205 return isl_map_drop(map, isl_dim_in, first, n);
206 }
207
208 /*
209 * We don't cow, as the div is assumed to be redundant.
210 */
211 static struct isl_basic_map *isl_basic_map_drop_div(
212 struct isl_basic_map *bmap, unsigned div)
213 {
214 int i;
215 unsigned pos;
216
217 if (!bmap)
218 goto error;
219
220 pos = 1 + isl_dim_total(bmap->dim) + div;
221
222 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
223
224 for (i = 0; i < bmap->n_eq; ++i)
225 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
226
227 for (i = 0; i < bmap->n_ineq; ++i) {
228 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
229 isl_basic_map_drop_inequality(bmap, i);
230 --i;
231 continue;
232 }
233 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
234 }
235
236 for (i = 0; i < bmap->n_div; ++i)
237 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
238
239 if (div != bmap->n_div - 1) {
240 int j;
241 isl_int *t = bmap->div[div];
242
243 for (j = div; j < bmap->n_div - 1; ++j)
244 bmap->div[j] = bmap->div[j+1];
245
246 bmap->div[bmap->n_div - 1] = t;
247 }
248 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
249 isl_basic_map_free_div(bmap, 1);
250
251 return bmap;
252 error:
253 isl_basic_map_free(bmap);
254 return NULL;
255 }
256
257 struct isl_basic_map *isl_basic_map_normalize_constraints(
258 struct isl_basic_map *bmap)
259 {
260 int i;
261 isl_int gcd;
262 unsigned total = isl_basic_map_total_dim(bmap);
263
264 isl_int_init(gcd);
265 for (i = bmap->n_eq - 1; i >= 0; --i) {
266 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
267 if (isl_int_is_zero(gcd)) {
268 if (!isl_int_is_zero(bmap->eq[i][0])) {
269 bmap = isl_basic_map_set_to_empty(bmap);
270 break;
271 }
272 isl_basic_map_drop_equality(bmap, i);
273 continue;
274 }
275 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
276 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
277 if (isl_int_is_one(gcd))
278 continue;
279 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
280 bmap = isl_basic_map_set_to_empty(bmap);
281 break;
282 }
283 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
284 }
285
286 for (i = bmap->n_ineq - 1; i >= 0; --i) {
287 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
288 if (isl_int_is_zero(gcd)) {
289 if (isl_int_is_neg(bmap->ineq[i][0])) {
290 bmap = isl_basic_map_set_to_empty(bmap);
291 break;
292 }
293 isl_basic_map_drop_inequality(bmap, i);
294 continue;
295 }
296 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
297 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
298 if (isl_int_is_one(gcd))
299 continue;
300 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
301 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
302 }
303 isl_int_clear(gcd);
304
305 return bmap;
306 }
307
308 struct isl_basic_set *isl_basic_set_normalize_constraints(
309 struct isl_basic_set *bset)
310 {
311 (struct isl_basic_set *)isl_basic_map_normalize_constraints(
312 (struct isl_basic_map *)bset);
313 }
314
315 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
316 {
317 int i;
318 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
319 unsigned len;
320 len = 1 + isl_basic_map_total_dim(bmap);
321
322 for (i = 0; i < bmap->n_eq; ++i)
323 if (bmap->eq[i] != eq)
324 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
325
326 for (i = 0; i < bmap->n_ineq; ++i)
327 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
328
329 /* We need to be careful about circular definitions,
330 * so for now we just remove the definitions of other divs that
331 * depend on this div and (possibly) recompute them later.
332 */
333 for (i = 0; i < bmap->n_div; ++i)
334 if (!isl_int_is_zero(bmap->div[i][0]) &&
335 !isl_int_is_zero(bmap->div[i][1 + pos]))
336 isl_seq_clr(bmap->div[i], 1 + len);
337
338 isl_basic_map_drop_div(bmap, div);
339 }
340
341 /* Elimininate divs based on equalities
342 */
343 static struct isl_basic_map *eliminate_divs_eq(
344 struct isl_basic_map *bmap, int *progress)
345 {
346 int d;
347 int i;
348 int modified = 0;
349 unsigned off;
350
351 if (!bmap)
352 return NULL;
353
354 off = 1 + isl_dim_total(bmap->dim);
355
356 for (d = bmap->n_div - 1; d >= 0 ; --d) {
357 for (i = 0; i < bmap->n_eq; ++i) {
358 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
359 !isl_int_is_negone(bmap->eq[i][off + d]))
360 continue;
361 modified = 1;
362 *progress = 1;
363 eliminate_div(bmap, bmap->eq[i], d);
364 isl_basic_map_drop_equality(bmap, i);
365 break;
366 }
367 }
368 if (modified)
369 return eliminate_divs_eq(bmap, progress);
370 return bmap;
371 }
372
373 /* Elimininate divs based on inequalities
374 */
375 static struct isl_basic_map *eliminate_divs_ineq(
376 struct isl_basic_map *bmap, int *progress)
377 {
378 int d;
379 int i;
380 unsigned off;
381 struct isl_ctx *ctx;
382
383 if (!bmap)
384 return NULL;
385
386 ctx = bmap->ctx;
387 off = 1 + isl_dim_total(bmap->dim);
388
389 for (d = bmap->n_div - 1; d >= 0 ; --d) {
390 for (i = 0; i < bmap->n_eq; ++i)
391 if (!isl_int_is_zero(bmap->eq[i][off + d]))
392 break;
393 if (i < bmap->n_eq)
394 continue;
395 for (i = 0; i < bmap->n_ineq; ++i)
396 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
397 break;
398 if (i < bmap->n_ineq)
399 continue;
400 *progress = 1;
401 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
402 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
403 break;
404 bmap = isl_basic_map_drop_div(bmap, d);
405 if (!bmap)
406 break;
407 }
408 return bmap;
409 }
410
411 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
412 unsigned pos, isl_int *eq, int *progress)
413 {
414 unsigned total;
415 int k;
416 int contains_divs;
417
418 total = isl_basic_map_total_dim(bmap);
419 contains_divs =
420 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
421 bmap->n_div) != -1;
422 for (k = 0; k < bmap->n_eq; ++k) {
423 if (bmap->eq[k] == eq)
424 continue;
425 if (isl_int_is_zero(bmap->eq[k][1+pos]))
426 continue;
427 if (progress)
428 *progress = 1;
429 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
430 }
431
432 for (k = 0; k < bmap->n_ineq; ++k) {
433 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
434 continue;
435 if (progress)
436 *progress = 1;
437 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
438 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
439 }
440
441 for (k = 0; k < bmap->n_div; ++k) {
442 if (isl_int_is_zero(bmap->div[k][0]))
443 continue;
444 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
445 continue;
446 if (progress)
447 *progress = 1;
448 /* We need to be careful about circular definitions,
449 * so for now we just remove the definition of div k
450 * if the equality contains any divs.
451 */
452 if (contains_divs)
453 isl_seq_clr(bmap->div[k], 1 + total);
454 else
455 isl_seq_elim(bmap->div[k]+1, eq,
456 1+pos, 1+total, &bmap->div[k][0]);
457 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
458 }
459 }
460
461 struct isl_basic_map *isl_basic_map_gauss(
462 struct isl_basic_map *bmap, int *progress)
463 {
464 int k;
465 int done;
466 int last_var;
467 unsigned total_var;
468 unsigned total;
469
470 if (!bmap)
471 return NULL;
472
473 total = isl_basic_map_total_dim(bmap);
474 total_var = total - bmap->n_div;
475
476 last_var = total - 1;
477 for (done = 0; done < bmap->n_eq; ++done) {
478 for (; last_var >= 0; --last_var) {
479 for (k = done; k < bmap->n_eq; ++k)
480 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
481 break;
482 if (k < bmap->n_eq)
483 break;
484 }
485 if (last_var < 0)
486 break;
487 if (k != done)
488 swap_equality(bmap, k, done);
489 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
490 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
491
492 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
493 progress);
494
495 if (last_var >= total_var &&
496 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
497 unsigned div = last_var - total_var;
498 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
499 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
500 isl_int_set(bmap->div[div][0],
501 bmap->eq[done][1+last_var]);
502 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
503 }
504 }
505 if (done == bmap->n_eq)
506 return bmap;
507 for (k = done; k < bmap->n_eq; ++k) {
508 if (isl_int_is_zero(bmap->eq[k][0]))
509 continue;
510 return isl_basic_map_set_to_empty(bmap);
511 }
512 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
513 return bmap;
514 }
515
516 struct isl_basic_set *isl_basic_set_gauss(
517 struct isl_basic_set *bset, int *progress)
518 {
519 return (struct isl_basic_set*)isl_basic_map_gauss(
520 (struct isl_basic_map *)bset, progress);
521 }
522
523
524 static unsigned int round_up(unsigned int v)
525 {
526 int old_v = v;
527
528 while (v) {
529 old_v = v;
530 v ^= v & -v;
531 }
532 return old_v << 1;
533 }
534
535 static int hash_index(isl_int ***index, unsigned int size, int bits,
536 struct isl_basic_map *bmap, int k)
537 {
538 int h;
539 unsigned total = isl_basic_map_total_dim(bmap);
540 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
541 for (h = hash; index[h]; h = (h+1) % size)
542 if (&bmap->ineq[k] != index[h] &&
543 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
544 break;
545 return h;
546 }
547
548 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
549 struct isl_basic_set *bset, int k)
550 {
551 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
552 }
553
554 /* If we can eliminate more than one div, then we need to make
555 * sure we do it from last div to first div, in order not to
556 * change the position of the other divs that still need to
557 * be removed.
558 */
559 static struct isl_basic_map *remove_duplicate_divs(
560 struct isl_basic_map *bmap, int *progress)
561 {
562 unsigned int size;
563 int *index;
564 int *elim_for;
565 int k, l, h;
566 int bits;
567 struct isl_blk eq;
568 unsigned total_var = isl_dim_total(bmap->dim);
569 unsigned total = total_var + bmap->n_div;
570 struct isl_ctx *ctx;
571
572 if (bmap->n_div <= 1)
573 return bmap;
574
575 ctx = bmap->ctx;
576 for (k = bmap->n_div - 1; k >= 0; --k)
577 if (!isl_int_is_zero(bmap->div[k][0]))
578 break;
579 if (k <= 0)
580 return bmap;
581
582 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
583 size = round_up(4 * bmap->n_div / 3 - 1);
584 bits = ffs(size) - 1;
585 index = isl_calloc_array(ctx, int, size);
586 if (!index)
587 return bmap;
588 eq = isl_blk_alloc(ctx, 1+total);
589 if (isl_blk_is_error(eq))
590 goto out;
591
592 isl_seq_clr(eq.data, 1+total);
593 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
594 for (--k; k >= 0; --k) {
595 uint32_t hash;
596
597 if (isl_int_is_zero(bmap->div[k][0]))
598 continue;
599
600 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
601 for (h = hash; index[h]; h = (h+1) % size)
602 if (isl_seq_eq(bmap->div[k],
603 bmap->div[index[h]-1], 2+total))
604 break;
605 if (index[h]) {
606 *progress = 1;
607 l = index[h] - 1;
608 elim_for[l] = k + 1;
609 }
610 index[h] = k+1;
611 }
612 for (l = bmap->n_div - 1; l >= 0; --l) {
613 if (!elim_for[l])
614 continue;
615 k = elim_for[l] - 1;
616 isl_int_set_si(eq.data[1+total_var+k], -1);
617 isl_int_set_si(eq.data[1+total_var+l], 1);
618 eliminate_div(bmap, eq.data, l);
619 isl_int_set_si(eq.data[1+total_var+k], 0);
620 isl_int_set_si(eq.data[1+total_var+l], 0);
621 }
622
623 isl_blk_free(ctx, eq);
624 out:
625 free(index);
626 free(elim_for);
627 return bmap;
628 }
629
630 static int n_pure_div_eq(struct isl_basic_map *bmap)
631 {
632 int i, j;
633 unsigned total;
634
635 total = isl_dim_total(bmap->dim);
636 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
637 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
638 --j;
639 if (j < 0)
640 break;
641 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
642 return 0;
643 }
644 return i;
645 }
646
647 /* Normalize divs that appear in equalities.
648 *
649 * In particular, we assume that bmap contains some equalities
650 * of the form
651 *
652 * a x = m * e_i
653 *
654 * and we want to replace the set of e_i by a minimal set and
655 * such that the new e_i have a canonical representation in terms
656 * of the vector x.
657 * If any of the equalities involves more than one divs, then
658 * we currently simply bail out.
659 *
660 * Let us first additionally assume that all equalities involve
661 * a div. The equalities then express modulo constraints on the
662 * remaining variables and we can use "parameter compression"
663 * to find a minimal set of constraints. The result is a transformation
664 *
665 * x = T(x') = x_0 + G x'
666 *
667 * with G a lower-triangular matrix with all elements below the diagonal
668 * non-negative and smaller than the diagonal element on the same row.
669 * We first normalize x_0 by making the same property hold in the affine
670 * T matrix.
671 * The rows i of G with a 1 on the diagonal do not impose any modulo
672 * constraint and simply express x_i = x'_i.
673 * For each of the remaining rows i, we introduce a div and a corresponding
674 * equality. In particular
675 *
676 * g_ii e_j = x_i - g_i(x')
677 *
678 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
679 * corresponding div (if g_kk != 1).
680 *
681 * If there are any equalities not involving any div, then we
682 * first apply a variable compression on the variables x:
683 *
684 * x = C x'' x'' = C_2 x
685 *
686 * and perform the above parameter compression on A C instead of on A.
687 * The resulting compression is then of the form
688 *
689 * x'' = T(x') = x_0 + G x'
690 *
691 * and in constructing the new divs and the corresponding equalities,
692 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
693 * by the corresponding row from C_2.
694 */
695 static struct isl_basic_map *normalize_divs(
696 struct isl_basic_map *bmap, int *progress)
697 {
698 int i, j, k;
699 int total;
700 int div_eq;
701 struct isl_mat *B;
702 struct isl_vec *d;
703 struct isl_mat *T = NULL;
704 struct isl_mat *C = NULL;
705 struct isl_mat *C2 = NULL;
706 isl_int v;
707 int *pos;
708 int dropped, needed;
709
710 if (!bmap)
711 return NULL;
712
713 if (bmap->n_div == 0)
714 return bmap;
715
716 if (bmap->n_eq == 0)
717 return bmap;
718
719 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
720 return bmap;
721
722 total = isl_dim_total(bmap->dim);
723 div_eq = n_pure_div_eq(bmap);
724 if (div_eq == 0)
725 return bmap;
726
727 if (div_eq < bmap->n_eq) {
728 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
729 bmap->n_eq - div_eq, 0, 1 + total);
730 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
731 if (!C || !C2)
732 goto error;
733 if (C->n_col == 0) {
734 bmap = isl_basic_map_set_to_empty(bmap);
735 isl_mat_free(bmap->ctx, C);
736 isl_mat_free(bmap->ctx, C2);
737 goto done;
738 }
739 }
740
741 d = isl_vec_alloc(bmap->ctx, div_eq);
742 if (!d)
743 goto error;
744 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
745 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
746 --j;
747 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
748 }
749 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
750
751 if (C) {
752 B = isl_mat_product(bmap->ctx, B, C);
753 C = NULL;
754 }
755
756 T = isl_mat_parameter_compression(bmap->ctx, B, d);
757 if (!T)
758 goto error;
759 if (T->n_col == 0) {
760 bmap = isl_basic_map_set_to_empty(bmap);
761 isl_mat_free(bmap->ctx, C2);
762 isl_mat_free(bmap->ctx, T);
763 goto done;
764 }
765 isl_int_init(v);
766 for (i = 0; i < T->n_row - 1; ++i) {
767 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
768 if (isl_int_is_zero(v))
769 continue;
770 isl_mat_col_submul(T, 0, v, 1 + i);
771 }
772 isl_int_clear(v);
773 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
774 /* We have to be careful because dropping equalities may reorder them */
775 dropped = 0;
776 for (j = bmap->n_div - 1; j >= 0; --j) {
777 for (i = 0; i < bmap->n_eq; ++i)
778 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
779 break;
780 if (i < bmap->n_eq) {
781 bmap = isl_basic_map_drop_div(bmap, j);
782 isl_basic_map_drop_equality(bmap, i);
783 ++dropped;
784 }
785 }
786 pos[0] = 0;
787 needed = 0;
788 for (i = 1; i < T->n_row; ++i) {
789 if (isl_int_is_one(T->row[i][i]))
790 pos[i] = i;
791 else
792 needed++;
793 }
794 if (needed > dropped) {
795 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
796 needed, needed, 0);
797 if (!bmap)
798 goto error;
799 }
800 for (i = 1; i < T->n_row; ++i) {
801 if (isl_int_is_one(T->row[i][i]))
802 continue;
803 k = isl_basic_map_alloc_div(bmap);
804 pos[i] = 1 + total + k;
805 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
806 isl_int_set(bmap->div[k][0], T->row[i][i]);
807 if (C2)
808 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
809 else
810 isl_int_set_si(bmap->div[k][1 + i], 1);
811 for (j = 0; j < i; ++j) {
812 if (isl_int_is_zero(T->row[i][j]))
813 continue;
814 if (pos[j] < T->n_row && C2)
815 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
816 C2->row[pos[j]], 1 + total);
817 else
818 isl_int_neg(bmap->div[k][1 + pos[j]],
819 T->row[i][j]);
820 }
821 j = isl_basic_map_alloc_equality(bmap);
822 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
823 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
824 }
825 free(pos);
826 isl_mat_free(bmap->ctx, C2);
827 isl_mat_free(bmap->ctx, T);
828
829 if (progress)
830 *progress = 1;
831 done:
832 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
833
834 return bmap;
835 error:
836 isl_mat_free(bmap->ctx, C);
837 isl_mat_free(bmap->ctx, C2);
838 isl_mat_free(bmap->ctx, T);
839 return bmap;
840 }
841
842 static struct isl_basic_map *remove_duplicate_constraints(
843 struct isl_basic_map *bmap, int *progress)
844 {
845 unsigned int size;
846 isl_int ***index;
847 int k, l, h;
848 int bits;
849 unsigned total = isl_basic_map_total_dim(bmap);
850 isl_int sum;
851
852 if (bmap->n_ineq <= 1)
853 return bmap;
854
855 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
856 bits = ffs(size) - 1;
857 index = isl_calloc_array(ctx, isl_int **, size);
858 if (!index)
859 return bmap;
860
861 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
862 for (k = 1; k < bmap->n_ineq; ++k) {
863 h = hash_index(index, size, bits, bmap, k);
864 if (!index[h]) {
865 index[h] = &bmap->ineq[k];
866 continue;
867 }
868 if (progress)
869 *progress = 1;
870 l = index[h] - &bmap->ineq[0];
871 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
872 swap_inequality(bmap, k, l);
873 isl_basic_map_drop_inequality(bmap, k);
874 --k;
875 }
876 isl_int_init(sum);
877 for (k = 0; k < bmap->n_ineq-1; ++k) {
878 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
879 h = hash_index(index, size, bits, bmap, k);
880 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
881 if (!index[h])
882 continue;
883 l = index[h] - &bmap->ineq[0];
884 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
885 if (isl_int_is_pos(sum))
886 continue;
887 if (isl_int_is_zero(sum)) {
888 /* We need to break out of the loop after these
889 * changes since the contents of the hash
890 * will no longer be valid.
891 * Plus, we probably we want to regauss first.
892 */
893 isl_basic_map_drop_inequality(bmap, l);
894 isl_basic_map_inequality_to_equality(bmap, k);
895 } else
896 bmap = isl_basic_map_set_to_empty(bmap);
897 break;
898 }
899 isl_int_clear(sum);
900
901 free(index);
902 return bmap;
903 }
904
905
906 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
907 {
908 int progress = 1;
909 if (!bmap)
910 return NULL;
911 while (progress) {
912 progress = 0;
913 bmap = isl_basic_map_normalize_constraints(bmap);
914 bmap = remove_duplicate_divs(bmap, &progress);
915 bmap = eliminate_divs_eq(bmap, &progress);
916 bmap = eliminate_divs_ineq(bmap, &progress);
917 bmap = isl_basic_map_gauss(bmap, &progress);
918 /* requires equalities in normal form */
919 bmap = normalize_divs(bmap, &progress);
920 bmap = remove_duplicate_constraints(bmap, &progress);
921 }
922 return bmap;
923 }
924
925 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
926 {
927 return (struct isl_basic_set *)
928 isl_basic_map_simplify((struct isl_basic_map *)bset);
929 }
930
931
932 /* If the only constraints a div d=floor(f/m)
933 * appears in are its two defining constraints
934 *
935 * f - m d >=0
936 * -(f - (m - 1)) + m d >= 0
937 *
938 * then it can safely be removed.
939 */
940 static int div_is_redundant(struct isl_basic_map *bmap, int div)
941 {
942 int i;
943 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
944
945 for (i = 0; i < bmap->n_eq; ++i)
946 if (!isl_int_is_zero(bmap->eq[i][pos]))
947 return 0;
948
949 for (i = 0; i < bmap->n_ineq; ++i) {
950 if (isl_int_is_zero(bmap->ineq[i][pos]))
951 continue;
952 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
953 int neg;
954 isl_int_sub(bmap->div[div][1],
955 bmap->div[div][1], bmap->div[div][0]);
956 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
957 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
958 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
959 isl_int_add(bmap->div[div][1],
960 bmap->div[div][1], bmap->div[div][0]);
961 if (!neg)
962 return 0;
963 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
964 bmap->n_div-div-1) != -1)
965 return 0;
966 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
967 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
968 return 0;
969 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
970 bmap->n_div-div-1) != -1)
971 return 0;
972 } else
973 return 0;
974 }
975
976 for (i = 0; i < bmap->n_div; ++i)
977 if (!isl_int_is_zero(bmap->div[i][1+pos]))
978 return 0;
979
980 return 1;
981 }
982
983 /*
984 * Remove divs that don't occur in any of the constraints or other divs.
985 * These can arise when dropping some of the variables in a quast
986 * returned by piplib.
987 */
988 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
989 {
990 int i;
991
992 if (!bmap)
993 return NULL;
994
995 for (i = bmap->n_div-1; i >= 0; --i) {
996 if (!div_is_redundant(bmap, i))
997 continue;
998 bmap = isl_basic_map_drop_div(bmap, i);
999 }
1000 return bmap;
1001 }
1002
1003 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1004 {
1005 bmap = remove_redundant_divs(bmap);
1006 if (!bmap)
1007 return NULL;
1008 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1009 return bmap;
1010 }
1011
1012 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1013 {
1014 return (struct isl_basic_set *)
1015 isl_basic_map_finalize((struct isl_basic_map *)bset);
1016 }
1017
1018 struct isl_set *isl_set_finalize(struct isl_set *set)
1019 {
1020 int i;
1021
1022 if (!set)
1023 return NULL;
1024 for (i = 0; i < set->n; ++i) {
1025 set->p[i] = isl_basic_set_finalize(set->p[i]);
1026 if (!set->p[i])
1027 goto error;
1028 }
1029 return set;
1030 error:
1031 isl_set_free(set);
1032 return NULL;
1033 }
1034
1035 struct isl_map *isl_map_finalize(struct isl_map *map)
1036 {
1037 int i;
1038
1039 if (!map)
1040 return NULL;
1041 for (i = 0; i < map->n; ++i) {
1042 map->p[i] = isl_basic_map_finalize(map->p[i]);
1043 if (!map->p[i])
1044 goto error;
1045 }
1046 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1047 return map;
1048 error:
1049 isl_map_free(map);
1050 return NULL;
1051 }
1052
1053
1054 /* Remove any div that is defined in terms of the given variable.
1055 */
1056 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1057 int pos)
1058 {
1059 int i;
1060 unsigned dim = isl_dim_total(bmap->dim);
1061
1062 for (i = 0; i < bmap->n_div; ++i) {
1063 if (isl_int_is_zero(bmap->div[i][0]))
1064 continue;
1065 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1066 continue;
1067 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1068 if (!bmap)
1069 return NULL;
1070 }
1071 return bmap;
1072 }
1073
1074 /* Eliminate the specified variables from the constraints using
1075 * Fourier-Motzkin. The variables themselves are not removed.
1076 */
1077 struct isl_basic_map *isl_basic_map_eliminate_vars(
1078 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1079 {
1080 int d;
1081 int i, j, k;
1082 unsigned total;
1083
1084 if (n == 0)
1085 return bmap;
1086 if (!bmap)
1087 return NULL;
1088 total = isl_basic_map_total_dim(bmap);
1089
1090 bmap = isl_basic_map_cow(bmap);
1091 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1092 bmap = remove_dependent_vars(bmap, d);
1093
1094 for (d = pos + n - 1;
1095 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1096 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1097 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1098 int n_lower, n_upper;
1099 if (!bmap)
1100 return NULL;
1101 for (i = 0; i < bmap->n_eq; ++i) {
1102 if (isl_int_is_zero(bmap->eq[i][1+d]))
1103 continue;
1104 eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1105 isl_basic_map_drop_equality(bmap, i);
1106 break;
1107 }
1108 if (i < bmap->n_eq)
1109 continue;
1110 n_lower = 0;
1111 n_upper = 0;
1112 for (i = 0; i < bmap->n_ineq; ++i) {
1113 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1114 n_lower++;
1115 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1116 n_upper++;
1117 }
1118 bmap = isl_basic_map_extend_constraints(bmap,
1119 0, n_lower * n_upper);
1120 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1121 int last;
1122 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1123 continue;
1124 last = -1;
1125 for (j = 0; j < i; ++j) {
1126 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1127 continue;
1128 last = j;
1129 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1130 isl_int_sgn(bmap->ineq[j][1+d]))
1131 continue;
1132 k = isl_basic_map_alloc_inequality(bmap);
1133 if (k < 0)
1134 goto error;
1135 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1136 1+total);
1137 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1138 1+d, 1+total, NULL);
1139 }
1140 isl_basic_map_drop_inequality(bmap, i);
1141 i = last + 1;
1142 }
1143 if (n_lower > 0 && n_upper > 0) {
1144 bmap = isl_basic_map_normalize_constraints(bmap);
1145 bmap = remove_duplicate_constraints(bmap, NULL);
1146 bmap = isl_basic_map_gauss(bmap, NULL);
1147 bmap = isl_basic_map_convex_hull(bmap);
1148 if (!bmap)
1149 goto error;
1150 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1151 break;
1152 }
1153 }
1154 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1155 return bmap;
1156 error:
1157 isl_basic_map_free(bmap);
1158 return NULL;
1159 }
1160
1161 struct isl_basic_set *isl_basic_set_eliminate_vars(
1162 struct isl_basic_set *bset, unsigned pos, unsigned n)
1163 {
1164 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1165 (struct isl_basic_map *)bset, pos, n);
1166 }
1167
1168 /* Don't assume equalities are in order, because align_divs
1169 * may have changed the order of the divs.
1170 */
1171 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1172 {
1173 int d, i;
1174 unsigned total;
1175
1176 total = isl_dim_total(bmap->dim);
1177 for (d = 0; d < total; ++d)
1178 elim[d] = -1;
1179 for (i = 0; i < bmap->n_eq; ++i) {
1180 for (d = total - 1; d >= 0; --d) {
1181 if (isl_int_is_zero(bmap->eq[i][1+d]))
1182 continue;
1183 elim[d] = i;
1184 break;
1185 }
1186 }
1187 }
1188
1189 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1190 {
1191 return compute_elimination_index((struct isl_basic_map *)bset, elim);
1192 }
1193
1194 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1195 struct isl_basic_map *bmap, int *elim)
1196 {
1197 int d, i;
1198 int copied = 0;
1199 unsigned total;
1200
1201 total = isl_dim_total(bmap->dim);
1202 for (d = total - 1; d >= 0; --d) {
1203 if (isl_int_is_zero(src[1+d]))
1204 continue;
1205 if (elim[d] == -1)
1206 continue;
1207 if (!copied) {
1208 isl_seq_cpy(dst, src, 1 + total);
1209 copied = 1;
1210 }
1211 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1212 }
1213 return copied;
1214 }
1215
1216 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1217 struct isl_basic_set *bset, int *elim)
1218 {
1219 return reduced_using_equalities(dst, src,
1220 (struct isl_basic_map *)bset, elim);
1221 }
1222
1223 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1224 struct isl_basic_set *bset, struct isl_basic_set *context)
1225 {
1226 int i;
1227 int *elim;
1228
1229 if (!bset || !context)
1230 goto error;
1231
1232 bset = isl_basic_set_cow(bset);
1233 if (!bset)
1234 goto error;
1235
1236 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1237 if (!elim)
1238 goto error;
1239 set_compute_elimination_index(context, elim);
1240 for (i = 0; i < bset->n_eq; ++i)
1241 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1242 context, elim);
1243 for (i = 0; i < bset->n_ineq; ++i)
1244 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1245 context, elim);
1246 isl_basic_set_free(context);
1247 free(elim);
1248 bset = isl_basic_set_simplify(bset);
1249 bset = isl_basic_set_finalize(bset);
1250 return bset;
1251 error:
1252 isl_basic_set_free(bset);
1253 isl_basic_set_free(context);
1254 return NULL;
1255 }
1256
1257 static struct isl_basic_set *remove_shifted_constraints(
1258 struct isl_basic_set *bset, struct isl_basic_set *context)
1259 {
1260 unsigned int size;
1261 isl_int ***index;
1262 int bits;
1263 int k, h, l;
1264
1265 if (!bset)
1266 return NULL;
1267
1268 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1269 bits = ffs(size) - 1;
1270 index = isl_calloc_array(ctx, isl_int **, size);
1271 if (!index)
1272 return bset;
1273
1274 for (k = 0; k < context->n_ineq; ++k) {
1275 h = set_hash_index(index, size, bits, context, k);
1276 index[h] = &context->ineq[k];
1277 }
1278 for (k = 0; k < bset->n_ineq; ++k) {
1279 h = set_hash_index(index, size, bits, bset, k);
1280 if (!index[h])
1281 continue;
1282 l = index[h] - &context->ineq[0];
1283 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1284 continue;
1285 bset = isl_basic_set_cow(bset);
1286 if (!bset)
1287 goto error;
1288 isl_basic_set_drop_inequality(bset, k);
1289 --k;
1290 }
1291 free(index);
1292 return bset;
1293 error:
1294 free(index);
1295 return bset;
1296 }
1297
1298 /* Tighten (decrease) the constant terms of the inequalities based
1299 * on the equalities, without removing any integer points.
1300 * For example, if there is an equality
1301 *
1302 * i = 3 * j
1303 *
1304 * and an inequality
1305 *
1306 * i >= 1
1307 *
1308 * then we want to replace the inequality by
1309 *
1310 * i >= 3
1311 *
1312 * We do this by computing a variable compression and translating
1313 * the constraints to the compressed space.
1314 * If any constraint has coefficients (except the contant term)
1315 * with a common factor "f", then we can replace the constant term "c"
1316 * by
1317 *
1318 * f * floor(c/f)
1319 *
1320 * That is, we add
1321 *
1322 * f * floor(c/f) - c = -fract(c/f)
1323 *
1324 * and we can add the same value to the original constraint.
1325 *
1326 * In the example, the compressed space only contains "j",
1327 * and the inequality translates to
1328 *
1329 * 3 * j - 1 >= 0
1330 *
1331 * We add -fract(-1/3) = -2 to the original constraint to obtain
1332 *
1333 * i - 3 >= 0
1334 */
1335 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1336 struct isl_basic_set *bset)
1337 {
1338 int i;
1339 unsigned total;
1340 struct isl_mat *B, *C;
1341 isl_int gcd;
1342
1343 if (!bset)
1344 return NULL;
1345
1346 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1347 return bset;
1348
1349 if (!bset->n_ineq)
1350 return bset;
1351
1352 bset = isl_basic_set_cow(bset);
1353 if (!bset)
1354 return NULL;
1355
1356 total = isl_basic_set_total_dim(bset);
1357 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1358 C = isl_mat_variable_compression(bset->ctx, B, NULL);
1359 if (!C)
1360 return bset;
1361 if (C->n_col == 0) {
1362 isl_mat_free(bset->ctx, C);
1363 return isl_basic_set_set_to_empty(bset);
1364 }
1365 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1366 0, bset->n_ineq, 0, 1 + total);
1367 C = isl_mat_product(bset->ctx, B, C);
1368 if (!C)
1369 return bset;
1370
1371 isl_int_init(gcd);
1372 for (i = 0; i < bset->n_ineq; ++i) {
1373 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1374 if (isl_int_is_one(gcd))
1375 continue;
1376 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1377 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1378 }
1379 isl_int_clear(gcd);
1380
1381 isl_mat_free(bset->ctx, C);
1382
1383 return bset;
1384 }
1385
1386 /* Remove all information from bset that is redundant in the context
1387 * of context. In particular, equalities that are linear combinations
1388 * of those in context are removed. Then the inequalities that are
1389 * redundant in the context of the equalities and inequalities of
1390 * context are removed.
1391 *
1392 * We first simplify the constraints of "bset" in the context of the
1393 * equalities of "context".
1394 * Then we simplify the inequalities of the context in the context
1395 * of the equalities of bset and remove the inequalities from "bset"
1396 * that are obviously redundant with respect to some inequality in "context".
1397 *
1398 * If there are any inequalities left, we construct a tableau for
1399 * the context and then add the inequalities of "bset".
1400 * Before adding these equalities, we freeze all constraints such that
1401 * they won't be considered redundant in terms of the constraints of "bset".
1402 * Then we detect all equalities and redundant constraints (among the
1403 * constraints that weren't frozen) and update bset according to the results.
1404 * We have to be careful here because we don't want any of the context
1405 * constraints to remain and because we haven't added the equalities of "bset"
1406 * to the tableau so we temporarily have to pretend that there were no
1407 * equalities.
1408 */
1409 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1410 struct isl_basic_set *context)
1411 {
1412 int i;
1413 struct isl_tab *tab;
1414 unsigned context_ineq;
1415 struct isl_basic_set *combined = NULL;
1416
1417 if (!context || !bset)
1418 goto error;
1419
1420 if (context->n_eq > 0)
1421 bset = isl_basic_set_reduce_using_equalities(bset,
1422 isl_basic_set_copy(context));
1423 if (!bset)
1424 goto error;
1425 if (isl_basic_set_fast_is_empty(bset))
1426 goto done;
1427 if (!bset->n_ineq)
1428 goto done;
1429
1430 if (bset->n_eq > 0) {
1431 struct isl_basic_set *affine_hull;
1432 affine_hull = isl_basic_set_copy(bset);
1433 affine_hull = isl_basic_set_cow(affine_hull);
1434 if (!affine_hull)
1435 goto error;
1436 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1437 context = isl_basic_set_intersect(context, affine_hull);
1438 context = isl_basic_set_gauss(context, NULL);
1439 context = normalize_constraints_in_compressed_space(context);
1440 }
1441 if (!context)
1442 goto error;
1443 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1444 isl_basic_set_free(bset);
1445 return context;
1446 }
1447 if (!context->n_ineq)
1448 goto done;
1449 bset = remove_shifted_constraints(bset, context);
1450 if (!bset->n_ineq)
1451 goto done;
1452 isl_basic_set_free_equality(context, context->n_eq);
1453 context_ineq = context->n_ineq;
1454 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1455 combined = isl_basic_set_extend_constraints(combined,
1456 bset->n_eq, bset->n_ineq);
1457 tab = isl_tab_from_basic_set(combined);
1458 if (!tab)
1459 goto error;
1460 for (i = 0; i < context_ineq; ++i)
1461 tab->con[i].frozen = 1;
1462 tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
1463 if (!tab)
1464 goto error;
1465 for (i = 0; i < bset->n_ineq; ++i)
1466 tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
1467 bset = isl_basic_set_add_constraints(combined, bset, 0);
1468 tab = isl_tab_detect_equalities(bset->ctx, tab);
1469 tab = isl_tab_detect_redundant(bset->ctx, tab);
1470 if (!tab)
1471 goto error2;
1472 for (i = 0; i < context_ineq; ++i) {
1473 tab->con[i].is_zero = 0;
1474 tab->con[i].is_redundant = 1;
1475 }
1476 bset = isl_basic_set_update_from_tab(bset, tab);
1477 isl_tab_free(bset->ctx, tab);
1478 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1479 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1480 done:
1481 bset = isl_basic_set_simplify(bset);
1482 bset = isl_basic_set_finalize(bset);
1483 isl_basic_set_free(context);
1484 return bset;
1485 error:
1486 isl_basic_set_free(combined);
1487 error2:
1488 isl_basic_set_free(bset);
1489 isl_basic_set_free(context);
1490 return NULL;
1491 }
1492
1493 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1494 * We simply add the equalities in context to bmap and then do a regular
1495 * div normalizations. Better results can be obtained by normalizing
1496 * only the divs in bmap than do not also appear in context.
1497 * We need to be careful to reduce the divs using the equalities
1498 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1499 * spurious constraints.
1500 */
1501 static struct isl_basic_map *normalize_divs_in_context(
1502 struct isl_basic_map *bmap, struct isl_basic_map *context)
1503 {
1504 int i;
1505 unsigned total_context;
1506 int div_eq;
1507
1508 div_eq = n_pure_div_eq(bmap);
1509 if (div_eq == 0)
1510 return bmap;
1511
1512 if (context->n_div > 0)
1513 bmap = isl_basic_map_align_divs(bmap, context);
1514
1515 total_context = isl_basic_map_total_dim(context);
1516 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1517 for (i = 0; i < context->n_eq; ++i) {
1518 int k;
1519 k = isl_basic_map_alloc_equality(bmap);
1520 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1521 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1522 isl_basic_map_total_dim(bmap) - total_context);
1523 }
1524 bmap = isl_basic_map_gauss(bmap, NULL);
1525 bmap = normalize_divs(bmap, NULL);
1526 bmap = isl_basic_map_gauss(bmap, NULL);
1527 return bmap;
1528 }
1529
1530 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1531 struct isl_basic_map *context)
1532 {
1533 struct isl_basic_set *bset;
1534
1535 if (!bmap || !context)
1536 goto error;
1537
1538 if (isl_basic_map_is_universe(context)) {
1539 isl_basic_map_free(context);
1540 return bmap;
1541 }
1542 if (isl_basic_map_is_universe(bmap)) {
1543 isl_basic_map_free(context);
1544 return bmap;
1545 }
1546 if (isl_basic_map_fast_is_empty(context)) {
1547 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1548 isl_basic_map_free(context);
1549 isl_basic_map_free(bmap);
1550 return isl_basic_map_universe(dim);
1551 }
1552 if (isl_basic_map_fast_is_empty(bmap)) {
1553 isl_basic_map_free(context);
1554 return bmap;
1555 }
1556
1557 bmap = isl_basic_map_convex_hull(bmap);
1558 context = isl_basic_map_convex_hull(context);
1559
1560 if (context->n_eq)
1561 bmap = normalize_divs_in_context(bmap, context);
1562
1563 context = isl_basic_map_align_divs(context, bmap);
1564 bmap = isl_basic_map_align_divs(bmap, context);
1565
1566 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1567 isl_basic_map_underlying_set(context));
1568
1569 return isl_basic_map_overlying_set(bset, bmap);
1570 error:
1571 isl_basic_map_free(bmap);
1572 isl_basic_map_free(context);
1573 return NULL;
1574 }
1575
1576 /*
1577 * Assumes context has no implicit divs.
1578 */
1579 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1580 {
1581 int i;
1582
1583 if (!map || !context)
1584 goto error;;
1585
1586 if (isl_basic_map_is_universe(context)) {
1587 isl_basic_map_free(context);
1588 return map;
1589 }
1590 if (isl_basic_map_fast_is_empty(context)) {
1591 struct isl_dim *dim = isl_dim_copy(map->dim);
1592 isl_basic_map_free(context);
1593 isl_map_free(map);
1594 return isl_map_universe(dim);
1595 }
1596
1597 context = isl_basic_map_convex_hull(context);
1598 map = isl_map_cow(map);
1599 if (!map || !context)
1600 goto error;;
1601 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1602 map = isl_map_compute_divs(map);
1603 for (i = 0; i < map->n; ++i)
1604 context = isl_basic_map_align_divs(context, map->p[i]);
1605 for (i = 0; i < map->n; ++i) {
1606 map->p[i] = isl_basic_map_gist(map->p[i],
1607 isl_basic_map_copy(context));
1608 if (!map->p[i])
1609 goto error;
1610 }
1611 isl_basic_map_free(context);
1612 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1613 return map;
1614 error:
1615 isl_map_free(map);
1616 isl_basic_map_free(context);
1617 return NULL;
1618 }
1619
1620 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1621 struct isl_basic_set *context)
1622 {
1623 return (struct isl_basic_set *)isl_basic_map_gist(
1624 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1625 }
1626
1627 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1628 {
1629 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1630 (struct isl_basic_map *)context);
1631 }
1632
1633 /* Quick check to see if two basic maps are disjoint.
1634 * In particular, we reduce the equalities and inequalities of
1635 * one basic map in the context of the equalities of the other
1636 * basic map and check if we get a contradiction.
1637 */
1638 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1639 struct isl_basic_map *bmap2)
1640 {
1641 struct isl_vec *v = NULL;
1642 int *elim = NULL;
1643 unsigned total;
1644 int d, i;
1645
1646 if (!bmap1 || !bmap2)
1647 return -1;
1648 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1649 return -1);
1650 if (bmap1->n_div || bmap2->n_div)
1651 return 0;
1652 if (!bmap1->n_eq && !bmap2->n_eq)
1653 return 0;
1654
1655 total = isl_dim_total(bmap1->dim);
1656 if (total == 0)
1657 return 0;
1658 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1659 if (!v)
1660 goto error;
1661 elim = isl_alloc_array(bmap1->ctx, int, total);
1662 if (!elim)
1663 goto error;
1664 compute_elimination_index(bmap1, elim);
1665 for (i = 0; i < bmap2->n_eq; ++i) {
1666 int reduced;
1667 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1668 bmap1, elim);
1669 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1670 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1671 goto disjoint;
1672 }
1673 for (i = 0; i < bmap2->n_ineq; ++i) {
1674 int reduced;
1675 reduced = reduced_using_equalities(v->block.data,
1676 bmap2->ineq[i], bmap1, elim);
1677 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1678 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1679 goto disjoint;
1680 }
1681 compute_elimination_index(bmap2, elim);
1682 for (i = 0; i < bmap1->n_ineq; ++i) {
1683 int reduced;
1684 reduced = reduced_using_equalities(v->block.data,
1685 bmap1->ineq[i], bmap2, elim);
1686 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1687 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1688 goto disjoint;
1689 }
1690 isl_vec_free(bmap1->ctx, v);
1691 free(elim);
1692 return 0;
1693 disjoint:
1694 isl_vec_free(bmap1->ctx, v);
1695 free(elim);
1696 return 1;
1697 error:
1698 isl_vec_free(bmap1->ctx, v);
1699 free(elim);
1700 return -1;
1701 }
1702
1703 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1704 struct isl_basic_set *bset2)
1705 {
1706 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1707 (struct isl_basic_map *)bset2);
1708 }
1709
1710 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1711 {
1712 int i, j;
1713
1714 if (!map1 || !map2)
1715 return -1;
1716
1717 if (isl_map_fast_is_equal(map1, map2))
1718 return 0;
1719
1720 for (i = 0; i < map1->n; ++i) {
1721 for (j = 0; j < map2->n; ++j) {
1722 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1723 map2->p[j]);
1724 if (d != 1)
1725 return d;
1726 }
1727 }
1728 return 1;
1729 }
1730
1731 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1732 {
1733 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1734 (struct isl_map *)set2);
1735 }
Integer set library