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isl_map_simplify.c: remove unused set_swap_inequality
[isl.git] / isl_map_simplify.c
blob984d6efc6e27154b22ac2e5c4d8f6962b8112ba4
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include <isl_ctx_private.h>
11 #include <isl_map_private.h>
12 #include "isl_equalities.h"
13 #include <isl/map.h>
14 #include <isl/seq.h>
15 #include "isl_tab.h"
16 #include <isl_dim_private.h>
17 #include <isl_mat_private.h>
18
19 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
20 {
21 isl_int *t = bmap->eq[a];
22 bmap->eq[a] = bmap->eq[b];
23 bmap->eq[b] = t;
24 }
25
26 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
27 {
28 if (a != b) {
29 isl_int *t = bmap->ineq[a];
30 bmap->ineq[a] = bmap->ineq[b];
31 bmap->ineq[b] = t;
32 }
33 }
34
35 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
36 {
37 isl_seq_cpy(c, c + n, rem);
38 isl_seq_clr(c + rem, n);
39 }
40
41 /* Drop n dimensions starting at first.
42 *
43 * In principle, this frees up some extra variables as the number
44 * of columns remains constant, but we would have to extend
45 * the div array too as the number of rows in this array is assumed
46 * to be equal to extra.
47 */
48 struct isl_basic_set *isl_basic_set_drop_dims(
49 struct isl_basic_set *bset, unsigned first, unsigned n)
50 {
51 int i;
52
53 if (!bset)
54 goto error;
55
56 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
57
58 if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
59 return bset;
60
61 bset = isl_basic_set_cow(bset);
62 if (!bset)
63 return NULL;
64
65 for (i = 0; i < bset->n_eq; ++i)
66 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
67 (bset->dim->n_out-first-n)+bset->extra);
68
69 for (i = 0; i < bset->n_ineq; ++i)
70 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
71 (bset->dim->n_out-first-n)+bset->extra);
72
73 for (i = 0; i < bset->n_div; ++i)
74 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
75 (bset->dim->n_out-first-n)+bset->extra);
76
77 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
78 if (!bset->dim)
79 goto error;
80
81 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
82 bset = isl_basic_set_simplify(bset);
83 return isl_basic_set_finalize(bset);
84 error:
85 isl_basic_set_free(bset);
86 return NULL;
87 }
88
89 struct isl_set *isl_set_drop_dims(
90 struct isl_set *set, unsigned first, unsigned n)
91 {
92 int i;
93
94 if (!set)
95 goto error;
96
97 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
98
99 if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
100 return set;
101 set = isl_set_cow(set);
102 if (!set)
103 goto error;
104 set->dim = isl_dim_drop_outputs(set->dim, first, n);
105 if (!set->dim)
106 goto error;
107
108 for (i = 0; i < set->n; ++i) {
109 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
110 if (!set->p[i])
111 goto error;
112 }
113
114 ISL_F_CLR(set, ISL_SET_NORMALIZED);
115 return set;
116 error:
117 isl_set_free(set);
118 return NULL;
119 }
120
121 /* Move "n" divs starting at "first" to the end of the list of divs.
122 */
123 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
124 unsigned first, unsigned n)
125 {
126 isl_int **div;
127 int i;
128
129 if (first + n == bmap->n_div)
130 return bmap;
131
132 div = isl_alloc_array(bmap->ctx, isl_int *, n);
133 if (!div)
134 goto error;
135 for (i = 0; i < n; ++i)
136 div[i] = bmap->div[first + i];
137 for (i = 0; i < bmap->n_div - first - n; ++i)
138 bmap->div[first + i] = bmap->div[first + n + i];
139 for (i = 0; i < n; ++i)
140 bmap->div[bmap->n_div - n + i] = div[i];
141 free(div);
142 return bmap;
143 error:
144 isl_basic_map_free(bmap);
145 return NULL;
146 }
147
148 /* Drop "n" dimensions of type "type" starting at "first".
149 *
150 * In principle, this frees up some extra variables as the number
151 * of columns remains constant, but we would have to extend
152 * the div array too as the number of rows in this array is assumed
153 * to be equal to extra.
154 */
155 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
156 enum isl_dim_type type, unsigned first, unsigned n)
157 {
158 int i;
159 unsigned dim;
160 unsigned offset;
161 unsigned left;
162
163 if (!bmap)
164 goto error;
165
166 dim = isl_basic_map_dim(bmap, type);
167 isl_assert(bmap->ctx, first + n <= dim, goto error);
168
169 if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
170 return bmap;
171
172 bmap = isl_basic_map_cow(bmap);
173 if (!bmap)
174 return NULL;
175
176 offset = isl_basic_map_offset(bmap, type) + first;
177 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
178 for (i = 0; i < bmap->n_eq; ++i)
179 constraint_drop_vars(bmap->eq[i]+offset, n, left);
180
181 for (i = 0; i < bmap->n_ineq; ++i)
182 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
183
184 for (i = 0; i < bmap->n_div; ++i)
185 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
186
187 if (type == isl_dim_div) {
188 bmap = move_divs_last(bmap, first, n);
189 if (!bmap)
190 goto error;
191 isl_basic_map_free_div(bmap, n);
192 } else
193 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
194 if (!bmap->dim)
195 goto error;
196
197 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
198 bmap = isl_basic_map_simplify(bmap);
199 return isl_basic_map_finalize(bmap);
200 error:
201 isl_basic_map_free(bmap);
202 return NULL;
203 }
204
205 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
206 enum isl_dim_type type, unsigned first, unsigned n)
207 {
208 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
209 type, first, n);
210 }
211
212 struct isl_basic_map *isl_basic_map_drop_inputs(
213 struct isl_basic_map *bmap, unsigned first, unsigned n)
214 {
215 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
216 }
217
218 struct isl_map *isl_map_drop(struct isl_map *map,
219 enum isl_dim_type type, unsigned first, unsigned n)
220 {
221 int i;
222
223 if (!map)
224 goto error;
225
226 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
227
228 if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
229 return map;
230 map = isl_map_cow(map);
231 if (!map)
232 goto error;
233 map->dim = isl_dim_drop(map->dim, type, first, n);
234 if (!map->dim)
235 goto error;
236
237 for (i = 0; i < map->n; ++i) {
238 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
239 if (!map->p[i])
240 goto error;
241 }
242 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
243
244 return map;
245 error:
246 isl_map_free(map);
247 return NULL;
248 }
249
250 struct isl_set *isl_set_drop(struct isl_set *set,
251 enum isl_dim_type type, unsigned first, unsigned n)
252 {
253 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
254 }
255
256 struct isl_map *isl_map_drop_inputs(
257 struct isl_map *map, unsigned first, unsigned n)
258 {
259 return isl_map_drop(map, isl_dim_in, first, n);
260 }
261
262 /*
263 * We don't cow, as the div is assumed to be redundant.
264 */
265 static struct isl_basic_map *isl_basic_map_drop_div(
266 struct isl_basic_map *bmap, unsigned div)
267 {
268 int i;
269 unsigned pos;
270
271 if (!bmap)
272 goto error;
273
274 pos = 1 + isl_dim_total(bmap->dim) + div;
275
276 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
277
278 for (i = 0; i < bmap->n_eq; ++i)
279 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
280
281 for (i = 0; i < bmap->n_ineq; ++i) {
282 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
283 isl_basic_map_drop_inequality(bmap, i);
284 --i;
285 continue;
286 }
287 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
288 }
289
290 for (i = 0; i < bmap->n_div; ++i)
291 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
292
293 if (div != bmap->n_div - 1) {
294 int j;
295 isl_int *t = bmap->div[div];
296
297 for (j = div; j < bmap->n_div - 1; ++j)
298 bmap->div[j] = bmap->div[j+1];
299
300 bmap->div[bmap->n_div - 1] = t;
301 }
302 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
303 isl_basic_map_free_div(bmap, 1);
304
305 return bmap;
306 error:
307 isl_basic_map_free(bmap);
308 return NULL;
309 }
310
311 struct isl_basic_map *isl_basic_map_normalize_constraints(
312 struct isl_basic_map *bmap)
313 {
314 int i;
315 isl_int gcd;
316 unsigned total = isl_basic_map_total_dim(bmap);
317
318 if (!bmap)
319 return NULL;
320
321 isl_int_init(gcd);
322 for (i = bmap->n_eq - 1; i >= 0; --i) {
323 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
324 if (isl_int_is_zero(gcd)) {
325 if (!isl_int_is_zero(bmap->eq[i][0])) {
326 bmap = isl_basic_map_set_to_empty(bmap);
327 break;
328 }
329 isl_basic_map_drop_equality(bmap, i);
330 continue;
331 }
332 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
333 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
334 if (isl_int_is_one(gcd))
335 continue;
336 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
337 bmap = isl_basic_map_set_to_empty(bmap);
338 break;
339 }
340 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
341 }
342
343 for (i = bmap->n_ineq - 1; i >= 0; --i) {
344 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
345 if (isl_int_is_zero(gcd)) {
346 if (isl_int_is_neg(bmap->ineq[i][0])) {
347 bmap = isl_basic_map_set_to_empty(bmap);
348 break;
349 }
350 isl_basic_map_drop_inequality(bmap, i);
351 continue;
352 }
353 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
354 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
355 if (isl_int_is_one(gcd))
356 continue;
357 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
358 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
359 }
360 isl_int_clear(gcd);
361
362 return bmap;
363 }
364
365 struct isl_basic_set *isl_basic_set_normalize_constraints(
366 struct isl_basic_set *bset)
367 {
368 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
369 (struct isl_basic_map *)bset);
370 }
371
372 /* Assumes divs have been ordered if keep_divs is set.
373 */
374 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
375 unsigned pos, isl_int *eq, int keep_divs, int *progress)
376 {
377 unsigned total;
378 int k;
379 int last_div;
380
381 total = isl_basic_map_total_dim(bmap);
382 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
383 bmap->n_div);
384 for (k = 0; k < bmap->n_eq; ++k) {
385 if (bmap->eq[k] == eq)
386 continue;
387 if (isl_int_is_zero(bmap->eq[k][1+pos]))
388 continue;
389 if (progress)
390 *progress = 1;
391 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
392 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
393 }
394
395 for (k = 0; k < bmap->n_ineq; ++k) {
396 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
397 continue;
398 if (progress)
399 *progress = 1;
400 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
401 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
402 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
403 }
404
405 for (k = 0; k < bmap->n_div; ++k) {
406 if (isl_int_is_zero(bmap->div[k][0]))
407 continue;
408 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
409 continue;
410 if (progress)
411 *progress = 1;
412 /* We need to be careful about circular definitions,
413 * so for now we just remove the definition of div k
414 * if the equality contains any divs.
415 * If keep_divs is set, then the divs have been ordered
416 * and we can keep the definition as long as the result
417 * is still ordered.
418 */
419 if (last_div == -1 || (keep_divs && last_div < k))
420 isl_seq_elim(bmap->div[k]+1, eq,
421 1+pos, 1+total, &bmap->div[k][0]);
422 else
423 isl_seq_clr(bmap->div[k], 1 + total);
424 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
425 }
426 }
427
428 /* Assumes divs have been ordered if keep_divs is set.
429 */
430 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
431 unsigned div, int keep_divs)
432 {
433 unsigned pos = isl_dim_total(bmap->dim) + div;
434
435 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
436
437 isl_basic_map_drop_div(bmap, div);
438 }
439
440 /* Check if elimination of div "div" using equality "eq" would not
441 * result in a div depending on a later div.
442 */
443 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
444 unsigned div)
445 {
446 int k;
447 int last_div;
448 unsigned pos = isl_dim_total(bmap->dim) + div;
449
450 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
451 bmap->n_div);
452 if (last_div < 0 || last_div <= div)
453 return 1;
454
455 for (k = 0; k <= last_div; ++k) {
456 if (isl_int_is_zero(bmap->div[k][0]))
457 return 1;
458 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
459 return 0;
460 }
461
462 return 1;
463 }
464
465 /* Elimininate divs based on equalities
466 */
467 static struct isl_basic_map *eliminate_divs_eq(
468 struct isl_basic_map *bmap, int *progress)
469 {
470 int d;
471 int i;
472 int modified = 0;
473 unsigned off;
474
475 bmap = isl_basic_map_order_divs(bmap);
476
477 if (!bmap)
478 return NULL;
479
480 off = 1 + isl_dim_total(bmap->dim);
481
482 for (d = bmap->n_div - 1; d >= 0 ; --d) {
483 for (i = 0; i < bmap->n_eq; ++i) {
484 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
485 !isl_int_is_negone(bmap->eq[i][off + d]))
486 continue;
487 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
488 continue;
489 modified = 1;
490 *progress = 1;
491 eliminate_div(bmap, bmap->eq[i], d, 1);
492 isl_basic_map_drop_equality(bmap, i);
493 break;
494 }
495 }
496 if (modified)
497 return eliminate_divs_eq(bmap, progress);
498 return bmap;
499 }
500
501 /* Elimininate divs based on inequalities
502 */
503 static struct isl_basic_map *eliminate_divs_ineq(
504 struct isl_basic_map *bmap, int *progress)
505 {
506 int d;
507 int i;
508 unsigned off;
509 struct isl_ctx *ctx;
510
511 if (!bmap)
512 return NULL;
513
514 ctx = bmap->ctx;
515 off = 1 + isl_dim_total(bmap->dim);
516
517 for (d = bmap->n_div - 1; d >= 0 ; --d) {
518 for (i = 0; i < bmap->n_eq; ++i)
519 if (!isl_int_is_zero(bmap->eq[i][off + d]))
520 break;
521 if (i < bmap->n_eq)
522 continue;
523 for (i = 0; i < bmap->n_ineq; ++i)
524 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
525 break;
526 if (i < bmap->n_ineq)
527 continue;
528 *progress = 1;
529 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
530 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
531 break;
532 bmap = isl_basic_map_drop_div(bmap, d);
533 if (!bmap)
534 break;
535 }
536 return bmap;
537 }
538
539 struct isl_basic_map *isl_basic_map_gauss(
540 struct isl_basic_map *bmap, int *progress)
541 {
542 int k;
543 int done;
544 int last_var;
545 unsigned total_var;
546 unsigned total;
547
548 bmap = isl_basic_map_order_divs(bmap);
549
550 if (!bmap)
551 return NULL;
552
553 total = isl_basic_map_total_dim(bmap);
554 total_var = total - bmap->n_div;
555
556 last_var = total - 1;
557 for (done = 0; done < bmap->n_eq; ++done) {
558 for (; last_var >= 0; --last_var) {
559 for (k = done; k < bmap->n_eq; ++k)
560 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
561 break;
562 if (k < bmap->n_eq)
563 break;
564 }
565 if (last_var < 0)
566 break;
567 if (k != done)
568 swap_equality(bmap, k, done);
569 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
570 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
571
572 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
573 progress);
574
575 if (last_var >= total_var &&
576 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
577 unsigned div = last_var - total_var;
578 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
579 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
580 isl_int_set(bmap->div[div][0],
581 bmap->eq[done][1+last_var]);
582 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
583 }
584 }
585 if (done == bmap->n_eq)
586 return bmap;
587 for (k = done; k < bmap->n_eq; ++k) {
588 if (isl_int_is_zero(bmap->eq[k][0]))
589 continue;
590 return isl_basic_map_set_to_empty(bmap);
591 }
592 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
593 return bmap;
594 }
595
596 struct isl_basic_set *isl_basic_set_gauss(
597 struct isl_basic_set *bset, int *progress)
598 {
599 return (struct isl_basic_set*)isl_basic_map_gauss(
600 (struct isl_basic_map *)bset, progress);
601 }
602
603
604 static unsigned int round_up(unsigned int v)
605 {
606 int old_v = v;
607
608 while (v) {
609 old_v = v;
610 v ^= v & -v;
611 }
612 return old_v << 1;
613 }
614
615 static int hash_index(isl_int ***index, unsigned int size, int bits,
616 struct isl_basic_map *bmap, int k)
617 {
618 int h;
619 unsigned total = isl_basic_map_total_dim(bmap);
620 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
621 for (h = hash; index[h]; h = (h+1) % size)
622 if (&bmap->ineq[k] != index[h] &&
623 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
624 break;
625 return h;
626 }
627
628 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
629 struct isl_basic_set *bset, int k)
630 {
631 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
632 }
633
634 /* If we can eliminate more than one div, then we need to make
635 * sure we do it from last div to first div, in order not to
636 * change the position of the other divs that still need to
637 * be removed.
638 */
639 static struct isl_basic_map *remove_duplicate_divs(
640 struct isl_basic_map *bmap, int *progress)
641 {
642 unsigned int size;
643 int *index;
644 int *elim_for;
645 int k, l, h;
646 int bits;
647 struct isl_blk eq;
648 unsigned total_var;
649 unsigned total;
650 struct isl_ctx *ctx;
651
652 if (!bmap || bmap->n_div <= 1)
653 return bmap;
654
655 total_var = isl_dim_total(bmap->dim);
656 total = total_var + bmap->n_div;
657
658 ctx = bmap->ctx;
659 for (k = bmap->n_div - 1; k >= 0; --k)
660 if (!isl_int_is_zero(bmap->div[k][0]))
661 break;
662 if (k <= 0)
663 return bmap;
664
665 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
666 size = round_up(4 * bmap->n_div / 3 - 1);
667 bits = ffs(size) - 1;
668 index = isl_calloc_array(ctx, int, size);
669 if (!index)
670 return bmap;
671 eq = isl_blk_alloc(ctx, 1+total);
672 if (isl_blk_is_error(eq))
673 goto out;
674
675 isl_seq_clr(eq.data, 1+total);
676 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
677 for (--k; k >= 0; --k) {
678 uint32_t hash;
679
680 if (isl_int_is_zero(bmap->div[k][0]))
681 continue;
682
683 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
684 for (h = hash; index[h]; h = (h+1) % size)
685 if (isl_seq_eq(bmap->div[k],
686 bmap->div[index[h]-1], 2+total))
687 break;
688 if (index[h]) {
689 *progress = 1;
690 l = index[h] - 1;
691 elim_for[l] = k + 1;
692 }
693 index[h] = k+1;
694 }
695 for (l = bmap->n_div - 1; l >= 0; --l) {
696 if (!elim_for[l])
697 continue;
698 k = elim_for[l] - 1;
699 isl_int_set_si(eq.data[1+total_var+k], -1);
700 isl_int_set_si(eq.data[1+total_var+l], 1);
701 eliminate_div(bmap, eq.data, l, 0);
702 isl_int_set_si(eq.data[1+total_var+k], 0);
703 isl_int_set_si(eq.data[1+total_var+l], 0);
704 }
705
706 isl_blk_free(ctx, eq);
707 out:
708 free(index);
709 free(elim_for);
710 return bmap;
711 }
712
713 static int n_pure_div_eq(struct isl_basic_map *bmap)
714 {
715 int i, j;
716 unsigned total;
717
718 total = isl_dim_total(bmap->dim);
719 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
720 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
721 --j;
722 if (j < 0)
723 break;
724 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
725 return 0;
726 }
727 return i;
728 }
729
730 /* Normalize divs that appear in equalities.
731 *
732 * In particular, we assume that bmap contains some equalities
733 * of the form
734 *
735 * a x = m * e_i
736 *
737 * and we want to replace the set of e_i by a minimal set and
738 * such that the new e_i have a canonical representation in terms
739 * of the vector x.
740 * If any of the equalities involves more than one divs, then
741 * we currently simply bail out.
742 *
743 * Let us first additionally assume that all equalities involve
744 * a div. The equalities then express modulo constraints on the
745 * remaining variables and we can use "parameter compression"
746 * to find a minimal set of constraints. The result is a transformation
747 *
748 * x = T(x') = x_0 + G x'
749 *
750 * with G a lower-triangular matrix with all elements below the diagonal
751 * non-negative and smaller than the diagonal element on the same row.
752 * We first normalize x_0 by making the same property hold in the affine
753 * T matrix.
754 * The rows i of G with a 1 on the diagonal do not impose any modulo
755 * constraint and simply express x_i = x'_i.
756 * For each of the remaining rows i, we introduce a div and a corresponding
757 * equality. In particular
758 *
759 * g_ii e_j = x_i - g_i(x')
760 *
761 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
762 * corresponding div (if g_kk != 1).
763 *
764 * If there are any equalities not involving any div, then we
765 * first apply a variable compression on the variables x:
766 *
767 * x = C x'' x'' = C_2 x
768 *
769 * and perform the above parameter compression on A C instead of on A.
770 * The resulting compression is then of the form
771 *
772 * x'' = T(x') = x_0 + G x'
773 *
774 * and in constructing the new divs and the corresponding equalities,
775 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
776 * by the corresponding row from C_2.
777 */
778 static struct isl_basic_map *normalize_divs(
779 struct isl_basic_map *bmap, int *progress)
780 {
781 int i, j, k;
782 int total;
783 int div_eq;
784 struct isl_mat *B;
785 struct isl_vec *d;
786 struct isl_mat *T = NULL;
787 struct isl_mat *C = NULL;
788 struct isl_mat *C2 = NULL;
789 isl_int v;
790 int *pos;
791 int dropped, needed;
792
793 if (!bmap)
794 return NULL;
795
796 if (bmap->n_div == 0)
797 return bmap;
798
799 if (bmap->n_eq == 0)
800 return bmap;
801
802 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
803 return bmap;
804
805 total = isl_dim_total(bmap->dim);
806 div_eq = n_pure_div_eq(bmap);
807 if (div_eq == 0)
808 return bmap;
809
810 if (div_eq < bmap->n_eq) {
811 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
812 bmap->n_eq - div_eq, 0, 1 + total);
813 C = isl_mat_variable_compression(B, &C2);
814 if (!C || !C2)
815 goto error;
816 if (C->n_col == 0) {
817 bmap = isl_basic_map_set_to_empty(bmap);
818 isl_mat_free(C);
819 isl_mat_free(C2);
820 goto done;
821 }
822 }
823
824 d = isl_vec_alloc(bmap->ctx, div_eq);
825 if (!d)
826 goto error;
827 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
828 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
829 --j;
830 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
831 }
832 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
833
834 if (C) {
835 B = isl_mat_product(B, C);
836 C = NULL;
837 }
838
839 T = isl_mat_parameter_compression(B, d);
840 if (!T)
841 goto error;
842 if (T->n_col == 0) {
843 bmap = isl_basic_map_set_to_empty(bmap);
844 isl_mat_free(C2);
845 isl_mat_free(T);
846 goto done;
847 }
848 isl_int_init(v);
849 for (i = 0; i < T->n_row - 1; ++i) {
850 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
851 if (isl_int_is_zero(v))
852 continue;
853 isl_mat_col_submul(T, 0, v, 1 + i);
854 }
855 isl_int_clear(v);
856 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
857 if (!pos)
858 goto error;
859 /* We have to be careful because dropping equalities may reorder them */
860 dropped = 0;
861 for (j = bmap->n_div - 1; j >= 0; --j) {
862 for (i = 0; i < bmap->n_eq; ++i)
863 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
864 break;
865 if (i < bmap->n_eq) {
866 bmap = isl_basic_map_drop_div(bmap, j);
867 isl_basic_map_drop_equality(bmap, i);
868 ++dropped;
869 }
870 }
871 pos[0] = 0;
872 needed = 0;
873 for (i = 1; i < T->n_row; ++i) {
874 if (isl_int_is_one(T->row[i][i]))
875 pos[i] = i;
876 else
877 needed++;
878 }
879 if (needed > dropped) {
880 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
881 needed, needed, 0);
882 if (!bmap)
883 goto error;
884 }
885 for (i = 1; i < T->n_row; ++i) {
886 if (isl_int_is_one(T->row[i][i]))
887 continue;
888 k = isl_basic_map_alloc_div(bmap);
889 pos[i] = 1 + total + k;
890 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
891 isl_int_set(bmap->div[k][0], T->row[i][i]);
892 if (C2)
893 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
894 else
895 isl_int_set_si(bmap->div[k][1 + i], 1);
896 for (j = 0; j < i; ++j) {
897 if (isl_int_is_zero(T->row[i][j]))
898 continue;
899 if (pos[j] < T->n_row && C2)
900 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
901 C2->row[pos[j]], 1 + total);
902 else
903 isl_int_neg(bmap->div[k][1 + pos[j]],
904 T->row[i][j]);
905 }
906 j = isl_basic_map_alloc_equality(bmap);
907 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
908 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
909 }
910 free(pos);
911 isl_mat_free(C2);
912 isl_mat_free(T);
913
914 if (progress)
915 *progress = 1;
916 done:
917 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
918
919 return bmap;
920 error:
921 isl_mat_free(C);
922 isl_mat_free(C2);
923 isl_mat_free(T);
924 return bmap;
925 }
926
927 static struct isl_basic_map *set_div_from_lower_bound(
928 struct isl_basic_map *bmap, int div, int ineq)
929 {
930 unsigned total = 1 + isl_dim_total(bmap->dim);
931
932 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
933 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
934 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
935 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
936 isl_int_set_si(bmap->div[div][1 + total + div], 0);
937
938 return bmap;
939 }
940
941 /* Check whether it is ok to define a div based on an inequality.
942 * To avoid the introduction of circular definitions of divs, we
943 * do not allow such a definition if the resulting expression would refer to
944 * any other undefined divs or if any known div is defined in
945 * terms of the unknown div.
946 */
947 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
948 int div, int ineq)
949 {
950 int j;
951 unsigned total = 1 + isl_dim_total(bmap->dim);
952
953 /* Not defined in terms of unknown divs */
954 for (j = 0; j < bmap->n_div; ++j) {
955 if (div == j)
956 continue;
957 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
958 continue;
959 if (isl_int_is_zero(bmap->div[j][0]))
960 return 0;
961 }
962
963 /* No other div defined in terms of this one => avoid loops */
964 for (j = 0; j < bmap->n_div; ++j) {
965 if (div == j)
966 continue;
967 if (isl_int_is_zero(bmap->div[j][0]))
968 continue;
969 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
970 return 0;
971 }
972
973 return 1;
974 }
975
976 /* Given two constraints "k" and "l" that are opposite to each other,
977 * except for the constant term, check if we can use them
978 * to obtain an expression for one of the hitherto unknown divs.
979 * "sum" is the sum of the constant terms of the constraints.
980 * If this sum is strictly smaller than the coefficient of one
981 * of the divs, then this pair can be used define the div.
982 * To avoid the introduction of circular definitions of divs, we
983 * do not use the pair if the resulting expression would refer to
984 * any other undefined divs or if any known div is defined in
985 * terms of the unknown div.
986 */
987 static struct isl_basic_map *check_for_div_constraints(
988 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
989 {
990 int i;
991 unsigned total = 1 + isl_dim_total(bmap->dim);
992
993 for (i = 0; i < bmap->n_div; ++i) {
994 if (!isl_int_is_zero(bmap->div[i][0]))
995 continue;
996 if (isl_int_is_zero(bmap->ineq[k][total + i]))
997 continue;
998 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
999 continue;
1000 if (!ok_to_set_div_from_bound(bmap, i, k))
1001 break;
1002 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1003 bmap = set_div_from_lower_bound(bmap, i, k);
1004 else
1005 bmap = set_div_from_lower_bound(bmap, i, l);
1006 if (progress)
1007 *progress = 1;
1008 break;
1009 }
1010 return bmap;
1011 }
1012
1013 static struct isl_basic_map *remove_duplicate_constraints(
1014 struct isl_basic_map *bmap, int *progress, int detect_divs)
1015 {
1016 unsigned int size;
1017 isl_int ***index;
1018 int k, l, h;
1019 int bits;
1020 unsigned total = isl_basic_map_total_dim(bmap);
1021 isl_int sum;
1022
1023 if (!bmap || bmap->n_ineq <= 1)
1024 return bmap;
1025
1026 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1027 bits = ffs(size) - 1;
1028 index = isl_calloc_array(ctx, isl_int **, size);
1029 if (!index)
1030 return bmap;
1031
1032 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1033 for (k = 1; k < bmap->n_ineq; ++k) {
1034 h = hash_index(index, size, bits, bmap, k);
1035 if (!index[h]) {
1036 index[h] = &bmap->ineq[k];
1037 continue;
1038 }
1039 if (progress)
1040 *progress = 1;
1041 l = index[h] - &bmap->ineq[0];
1042 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1043 swap_inequality(bmap, k, l);
1044 isl_basic_map_drop_inequality(bmap, k);
1045 --k;
1046 }
1047 isl_int_init(sum);
1048 for (k = 0; k < bmap->n_ineq-1; ++k) {
1049 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1050 h = hash_index(index, size, bits, bmap, k);
1051 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1052 if (!index[h])
1053 continue;
1054 l = index[h] - &bmap->ineq[0];
1055 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1056 if (isl_int_is_pos(sum)) {
1057 if (detect_divs)
1058 bmap = check_for_div_constraints(bmap, k, l,
1059 sum, progress);
1060 continue;
1061 }
1062 if (isl_int_is_zero(sum)) {
1063 /* We need to break out of the loop after these
1064 * changes since the contents of the hash
1065 * will no longer be valid.
1066 * Plus, we probably we want to regauss first.
1067 */
1068 if (progress)
1069 *progress = 1;
1070 isl_basic_map_drop_inequality(bmap, l);
1071 isl_basic_map_inequality_to_equality(bmap, k);
1072 } else
1073 bmap = isl_basic_map_set_to_empty(bmap);
1074 break;
1075 }
1076 isl_int_clear(sum);
1077
1078 free(index);
1079 return bmap;
1080 }
1081
1082
1083 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1084 {
1085 int progress = 1;
1086 if (!bmap)
1087 return NULL;
1088 while (progress) {
1089 progress = 0;
1090 bmap = isl_basic_map_normalize_constraints(bmap);
1091 bmap = remove_duplicate_divs(bmap, &progress);
1092 bmap = eliminate_divs_eq(bmap, &progress);
1093 bmap = eliminate_divs_ineq(bmap, &progress);
1094 bmap = isl_basic_map_gauss(bmap, &progress);
1095 /* requires equalities in normal form */
1096 bmap = normalize_divs(bmap, &progress);
1097 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1098 }
1099 return bmap;
1100 }
1101
1102 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1103 {
1104 return (struct isl_basic_set *)
1105 isl_basic_map_simplify((struct isl_basic_map *)bset);
1106 }
1107
1108
1109 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1110 isl_int *constraint, unsigned div)
1111 {
1112 unsigned pos;
1113
1114 if (!bmap)
1115 return -1;
1116
1117 pos = 1 + isl_dim_total(bmap->dim) + div;
1118
1119 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1120 int neg;
1121 isl_int_sub(bmap->div[div][1],
1122 bmap->div[div][1], bmap->div[div][0]);
1123 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1124 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1125 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1126 isl_int_add(bmap->div[div][1],
1127 bmap->div[div][1], bmap->div[div][0]);
1128 if (!neg)
1129 return 0;
1130 if (isl_seq_first_non_zero(constraint+pos+1,
1131 bmap->n_div-div-1) != -1)
1132 return 0;
1133 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1134 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1135 return 0;
1136 if (isl_seq_first_non_zero(constraint+pos+1,
1137 bmap->n_div-div-1) != -1)
1138 return 0;
1139 } else
1140 return 0;
1141
1142 return 1;
1143 }
1144
1145
1146 /* If the only constraints a div d=floor(f/m)
1147 * appears in are its two defining constraints
1148 *
1149 * f - m d >=0
1150 * -(f - (m - 1)) + m d >= 0
1151 *
1152 * then it can safely be removed.
1153 */
1154 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1155 {
1156 int i;
1157 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1158
1159 for (i = 0; i < bmap->n_eq; ++i)
1160 if (!isl_int_is_zero(bmap->eq[i][pos]))
1161 return 0;
1162
1163 for (i = 0; i < bmap->n_ineq; ++i) {
1164 if (isl_int_is_zero(bmap->ineq[i][pos]))
1165 continue;
1166 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1167 return 0;
1168 }
1169
1170 for (i = 0; i < bmap->n_div; ++i)
1171 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1172 return 0;
1173
1174 return 1;
1175 }
1176
1177 /*
1178 * Remove divs that don't occur in any of the constraints or other divs.
1179 * These can arise when dropping some of the variables in a quast
1180 * returned by piplib.
1181 */
1182 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1183 {
1184 int i;
1185
1186 if (!bmap)
1187 return NULL;
1188
1189 for (i = bmap->n_div-1; i >= 0; --i) {
1190 if (!div_is_redundant(bmap, i))
1191 continue;
1192 bmap = isl_basic_map_drop_div(bmap, i);
1193 }
1194 return bmap;
1195 }
1196
1197 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1198 {
1199 bmap = remove_redundant_divs(bmap);
1200 if (!bmap)
1201 return NULL;
1202 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1203 return bmap;
1204 }
1205
1206 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1207 {
1208 return (struct isl_basic_set *)
1209 isl_basic_map_finalize((struct isl_basic_map *)bset);
1210 }
1211
1212 struct isl_set *isl_set_finalize(struct isl_set *set)
1213 {
1214 int i;
1215
1216 if (!set)
1217 return NULL;
1218 for (i = 0; i < set->n; ++i) {
1219 set->p[i] = isl_basic_set_finalize(set->p[i]);
1220 if (!set->p[i])
1221 goto error;
1222 }
1223 return set;
1224 error:
1225 isl_set_free(set);
1226 return NULL;
1227 }
1228
1229 struct isl_map *isl_map_finalize(struct isl_map *map)
1230 {
1231 int i;
1232
1233 if (!map)
1234 return NULL;
1235 for (i = 0; i < map->n; ++i) {
1236 map->p[i] = isl_basic_map_finalize(map->p[i]);
1237 if (!map->p[i])
1238 goto error;
1239 }
1240 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1241 return map;
1242 error:
1243 isl_map_free(map);
1244 return NULL;
1245 }
1246
1247
1248 /* Remove definition of any div that is defined in terms of the given variable.
1249 * The div itself is not removed. Functions such as
1250 * eliminate_divs_ineq depend on the other divs remaining in place.
1251 */
1252 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1253 int pos)
1254 {
1255 int i;
1256
1257 for (i = 0; i < bmap->n_div; ++i) {
1258 if (isl_int_is_zero(bmap->div[i][0]))
1259 continue;
1260 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1261 continue;
1262 isl_int_set_si(bmap->div[i][0], 0);
1263 }
1264 return bmap;
1265 }
1266
1267 /* Eliminate the specified variables from the constraints using
1268 * Fourier-Motzkin. The variables themselves are not removed.
1269 */
1270 struct isl_basic_map *isl_basic_map_eliminate_vars(
1271 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1272 {
1273 int d;
1274 int i, j, k;
1275 unsigned total;
1276
1277 if (n == 0)
1278 return bmap;
1279 if (!bmap)
1280 return NULL;
1281 total = isl_basic_map_total_dim(bmap);
1282
1283 bmap = isl_basic_map_cow(bmap);
1284 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1285 bmap = remove_dependent_vars(bmap, d);
1286
1287 for (d = pos + n - 1;
1288 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1289 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1290 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1291 int n_lower, n_upper;
1292 if (!bmap)
1293 return NULL;
1294 for (i = 0; i < bmap->n_eq; ++i) {
1295 if (isl_int_is_zero(bmap->eq[i][1+d]))
1296 continue;
1297 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1298 isl_basic_map_drop_equality(bmap, i);
1299 break;
1300 }
1301 if (i < bmap->n_eq)
1302 continue;
1303 n_lower = 0;
1304 n_upper = 0;
1305 for (i = 0; i < bmap->n_ineq; ++i) {
1306 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1307 n_lower++;
1308 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1309 n_upper++;
1310 }
1311 bmap = isl_basic_map_extend_constraints(bmap,
1312 0, n_lower * n_upper);
1313 if (!bmap)
1314 goto error;
1315 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1316 int last;
1317 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1318 continue;
1319 last = -1;
1320 for (j = 0; j < i; ++j) {
1321 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1322 continue;
1323 last = j;
1324 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1325 isl_int_sgn(bmap->ineq[j][1+d]))
1326 continue;
1327 k = isl_basic_map_alloc_inequality(bmap);
1328 if (k < 0)
1329 goto error;
1330 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1331 1+total);
1332 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1333 1+d, 1+total, NULL);
1334 }
1335 isl_basic_map_drop_inequality(bmap, i);
1336 i = last + 1;
1337 }
1338 if (n_lower > 0 && n_upper > 0) {
1339 bmap = isl_basic_map_normalize_constraints(bmap);
1340 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1341 bmap = isl_basic_map_gauss(bmap, NULL);
1342 bmap = isl_basic_map_remove_redundancies(bmap);
1343 if (!bmap)
1344 goto error;
1345 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1346 break;
1347 }
1348 }
1349 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1350 return bmap;
1351 error:
1352 isl_basic_map_free(bmap);
1353 return NULL;
1354 }
1355
1356 struct isl_basic_set *isl_basic_set_eliminate_vars(
1357 struct isl_basic_set *bset, unsigned pos, unsigned n)
1358 {
1359 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1360 (struct isl_basic_map *)bset, pos, n);
1361 }
1362
1363 /* Don't assume equalities are in order, because align_divs
1364 * may have changed the order of the divs.
1365 */
1366 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1367 {
1368 int d, i;
1369 unsigned total;
1370
1371 total = isl_dim_total(bmap->dim);
1372 for (d = 0; d < total; ++d)
1373 elim[d] = -1;
1374 for (i = 0; i < bmap->n_eq; ++i) {
1375 for (d = total - 1; d >= 0; --d) {
1376 if (isl_int_is_zero(bmap->eq[i][1+d]))
1377 continue;
1378 elim[d] = i;
1379 break;
1380 }
1381 }
1382 }
1383
1384 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1385 {
1386 compute_elimination_index((struct isl_basic_map *)bset, elim);
1387 }
1388
1389 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1390 struct isl_basic_map *bmap, int *elim)
1391 {
1392 int d;
1393 int copied = 0;
1394 unsigned total;
1395
1396 total = isl_dim_total(bmap->dim);
1397 for (d = total - 1; d >= 0; --d) {
1398 if (isl_int_is_zero(src[1+d]))
1399 continue;
1400 if (elim[d] == -1)
1401 continue;
1402 if (!copied) {
1403 isl_seq_cpy(dst, src, 1 + total);
1404 copied = 1;
1405 }
1406 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1407 }
1408 return copied;
1409 }
1410
1411 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1412 struct isl_basic_set *bset, int *elim)
1413 {
1414 return reduced_using_equalities(dst, src,
1415 (struct isl_basic_map *)bset, elim);
1416 }
1417
1418 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1419 struct isl_basic_set *bset, struct isl_basic_set *context)
1420 {
1421 int i;
1422 int *elim;
1423
1424 if (!bset || !context)
1425 goto error;
1426
1427 if (context->n_eq == 0) {
1428 isl_basic_set_free(context);
1429 return bset;
1430 }
1431
1432 bset = isl_basic_set_cow(bset);
1433 if (!bset)
1434 goto error;
1435
1436 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1437 if (!elim)
1438 goto error;
1439 set_compute_elimination_index(context, elim);
1440 for (i = 0; i < bset->n_eq; ++i)
1441 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1442 context, elim);
1443 for (i = 0; i < bset->n_ineq; ++i)
1444 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1445 context, elim);
1446 isl_basic_set_free(context);
1447 free(elim);
1448 bset = isl_basic_set_simplify(bset);
1449 bset = isl_basic_set_finalize(bset);
1450 return bset;
1451 error:
1452 isl_basic_set_free(bset);
1453 isl_basic_set_free(context);
1454 return NULL;
1455 }
1456
1457 static struct isl_basic_set *remove_shifted_constraints(
1458 struct isl_basic_set *bset, struct isl_basic_set *context)
1459 {
1460 unsigned int size;
1461 isl_int ***index;
1462 int bits;
1463 int k, h, l;
1464
1465 if (!bset)
1466 return NULL;
1467
1468 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1469 bits = ffs(size) - 1;
1470 index = isl_calloc_array(ctx, isl_int **, size);
1471 if (!index)
1472 return bset;
1473
1474 for (k = 0; k < context->n_ineq; ++k) {
1475 h = set_hash_index(index, size, bits, context, k);
1476 index[h] = &context->ineq[k];
1477 }
1478 for (k = 0; k < bset->n_ineq; ++k) {
1479 h = set_hash_index(index, size, bits, bset, k);
1480 if (!index[h])
1481 continue;
1482 l = index[h] - &context->ineq[0];
1483 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1484 continue;
1485 bset = isl_basic_set_cow(bset);
1486 if (!bset)
1487 goto error;
1488 isl_basic_set_drop_inequality(bset, k);
1489 --k;
1490 }
1491 free(index);
1492 return bset;
1493 error:
1494 free(index);
1495 return bset;
1496 }
1497
1498 /* Tighten (decrease) the constant terms of the inequalities based
1499 * on the equalities, without removing any integer points.
1500 * For example, if there is an equality
1501 *
1502 * i = 3 * j
1503 *
1504 * and an inequality
1505 *
1506 * i >= 1
1507 *
1508 * then we want to replace the inequality by
1509 *
1510 * i >= 3
1511 *
1512 * We do this by computing a variable compression and translating
1513 * the constraints to the compressed space.
1514 * If any constraint has coefficients (except the contant term)
1515 * with a common factor "f", then we can replace the constant term "c"
1516 * by
1517 *
1518 * f * floor(c/f)
1519 *
1520 * That is, we add
1521 *
1522 * f * floor(c/f) - c = -fract(c/f)
1523 *
1524 * and we can add the same value to the original constraint.
1525 *
1526 * In the example, the compressed space only contains "j",
1527 * and the inequality translates to
1528 *
1529 * 3 * j - 1 >= 0
1530 *
1531 * We add -fract(-1/3) = -2 to the original constraint to obtain
1532 *
1533 * i - 3 >= 0
1534 */
1535 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1536 struct isl_basic_set *bset)
1537 {
1538 int i;
1539 unsigned total;
1540 struct isl_mat *B, *C;
1541 isl_int gcd;
1542
1543 if (!bset)
1544 return NULL;
1545
1546 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1547 return bset;
1548
1549 if (!bset->n_ineq)
1550 return bset;
1551
1552 bset = isl_basic_set_cow(bset);
1553 if (!bset)
1554 return NULL;
1555
1556 total = isl_basic_set_total_dim(bset);
1557 B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1558 C = isl_mat_variable_compression(B, NULL);
1559 if (!C)
1560 return bset;
1561 if (C->n_col == 0) {
1562 isl_mat_free(C);
1563 return isl_basic_set_set_to_empty(bset);
1564 }
1565 B = isl_mat_sub_alloc6(bset->ctx, bset->ineq,
1566 0, bset->n_ineq, 0, 1 + total);
1567 C = isl_mat_product(B, C);
1568 if (!C)
1569 return bset;
1570
1571 isl_int_init(gcd);
1572 for (i = 0; i < bset->n_ineq; ++i) {
1573 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1574 if (isl_int_is_one(gcd))
1575 continue;
1576 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1577 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1578 }
1579 isl_int_clear(gcd);
1580
1581 isl_mat_free(C);
1582
1583 return bset;
1584 }
1585
1586 /* Remove all information from bset that is redundant in the context
1587 * of context. Both bset and context are assumed to be full-dimensional.
1588 *
1589 * We first * remove the inequalities from "bset"
1590 * that are obviously redundant with respect to some inequality in "context".
1591 *
1592 * If there are any inequalities left, we construct a tableau for
1593 * the context and then add the inequalities of "bset".
1594 * Before adding these inequalities, we freeze all constraints such that
1595 * they won't be considered redundant in terms of the constraints of "bset".
1596 * Then we detect all redundant constraints (among the
1597 * constraints that weren't frozen), first by checking for redundancy in the
1598 * the tableau and then by checking if replacing a constraint by its negation
1599 * would lead to an empty set. This last step is fairly expensive
1600 * and could be optimized by more reuse of the tableau.
1601 * Finally, we update bset according to the results.
1602 */
1603 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1604 __isl_take isl_basic_set *context)
1605 {
1606 int i, k;
1607 isl_basic_set *combined = NULL;
1608 struct isl_tab *tab = NULL;
1609 unsigned context_ineq;
1610 unsigned total;
1611
1612 if (!bset || !context)
1613 goto error;
1614
1615 if (isl_basic_set_is_universe(bset)) {
1616 isl_basic_set_free(context);
1617 return bset;
1618 }
1619
1620 if (isl_basic_set_is_universe(context)) {
1621 isl_basic_set_free(context);
1622 return bset;
1623 }
1624
1625 bset = remove_shifted_constraints(bset, context);
1626 if (!bset)
1627 goto error;
1628 if (bset->n_ineq == 0)
1629 goto done;
1630
1631 context_ineq = context->n_ineq;
1632 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1633 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1634 tab = isl_tab_from_basic_set(combined);
1635 for (i = 0; i < context_ineq; ++i)
1636 if (isl_tab_freeze_constraint(tab, i) < 0)
1637 goto error;
1638 tab = isl_tab_extend(tab, bset->n_ineq);
1639 for (i = 0; i < bset->n_ineq; ++i)
1640 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1641 goto error;
1642 bset = isl_basic_set_add_constraints(combined, bset, 0);
1643 combined = NULL;
1644 if (!bset)
1645 goto error;
1646 if (isl_tab_detect_redundant(tab) < 0)
1647 goto error;
1648 total = isl_basic_set_total_dim(bset);
1649 for (i = context_ineq; i < bset->n_ineq; ++i) {
1650 int is_empty;
1651 if (tab->con[i].is_redundant)
1652 continue;
1653 tab->con[i].is_redundant = 1;
1654 combined = isl_basic_set_dup(bset);
1655 combined = isl_basic_set_update_from_tab(combined, tab);
1656 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1657 k = isl_basic_set_alloc_inequality(combined);
1658 if (k < 0)
1659 goto error;
1660 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1661 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1662 is_empty = isl_basic_set_is_empty(combined);
1663 if (is_empty < 0)
1664 goto error;
1665 isl_basic_set_free(combined);
1666 combined = NULL;
1667 if (!is_empty)
1668 tab->con[i].is_redundant = 0;
1669 }
1670 for (i = 0; i < context_ineq; ++i)
1671 tab->con[i].is_redundant = 1;
1672 bset = isl_basic_set_update_from_tab(bset, tab);
1673 if (bset) {
1674 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1675 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1676 }
1677
1678 isl_tab_free(tab);
1679 done:
1680 bset = isl_basic_set_simplify(bset);
1681 bset = isl_basic_set_finalize(bset);
1682 isl_basic_set_free(context);
1683 return bset;
1684 error:
1685 isl_tab_free(tab);
1686 isl_basic_set_free(combined);
1687 isl_basic_set_free(context);
1688 isl_basic_set_free(bset);
1689 return NULL;
1690 }
1691
1692 /* Remove all information from bset that is redundant in the context
1693 * of context. In particular, equalities that are linear combinations
1694 * of those in context are removed. Then the inequalities that are
1695 * redundant in the context of the equalities and inequalities of
1696 * context are removed.
1697 *
1698 * We first compute the integer affine hull of the intersection,
1699 * compute the gist inside this affine hull and then add back
1700 * those equalities that are not implied by the context.
1701 *
1702 * If two constraints are mutually redundant, then uset_gist_full
1703 * will remove the second of those constraints. We therefore first
1704 * sort the constraints so that constraints not involving existentially
1705 * quantified variables are given precedence over those that do.
1706 * We have to perform this sorting before the variable compression,
1707 * because that may effect the order of the variables.
1708 */
1709 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1710 __isl_take isl_basic_set *context)
1711 {
1712 isl_mat *eq;
1713 isl_mat *T, *T2;
1714 isl_basic_set *aff;
1715 isl_basic_set *aff_context;
1716 unsigned total;
1717
1718 if (!bset || !context)
1719 goto error;
1720
1721 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1722 if (isl_basic_set_plain_is_empty(bset)) {
1723 isl_basic_set_free(context);
1724 return bset;
1725 }
1726 bset = isl_basic_set_sort_constraints(bset);
1727 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1728 if (!aff)
1729 goto error;
1730 if (isl_basic_set_plain_is_empty(aff)) {
1731 isl_basic_set_free(aff);
1732 isl_basic_set_free(context);
1733 return bset;
1734 }
1735 if (aff->n_eq == 0) {
1736 isl_basic_set_free(aff);
1737 return uset_gist_full(bset, context);
1738 }
1739 total = isl_basic_set_total_dim(bset);
1740 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1741 eq = isl_mat_cow(eq);
1742 T = isl_mat_variable_compression(eq, &T2);
1743 if (T && T->n_col == 0) {
1744 isl_mat_free(T);
1745 isl_mat_free(T2);
1746 isl_basic_set_free(context);
1747 isl_basic_set_free(aff);
1748 return isl_basic_set_set_to_empty(bset);
1749 }
1750
1751 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1752
1753 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1754 context = isl_basic_set_preimage(context, T);
1755
1756 bset = uset_gist_full(bset, context);
1757 bset = isl_basic_set_preimage(bset, T2);
1758 bset = isl_basic_set_intersect(bset, aff);
1759 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1760
1761 if (bset) {
1762 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1763 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1764 }
1765
1766 return bset;
1767 error:
1768 isl_basic_set_free(bset);
1769 isl_basic_set_free(context);
1770 return NULL;
1771 }
1772
1773 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1774 * We simply add the equalities in context to bmap and then do a regular
1775 * div normalizations. Better results can be obtained by normalizing
1776 * only the divs in bmap than do not also appear in context.
1777 * We need to be careful to reduce the divs using the equalities
1778 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1779 * spurious constraints.
1780 */
1781 static struct isl_basic_map *normalize_divs_in_context(
1782 struct isl_basic_map *bmap, struct isl_basic_map *context)
1783 {
1784 int i;
1785 unsigned total_context;
1786 int div_eq;
1787
1788 div_eq = n_pure_div_eq(bmap);
1789 if (div_eq == 0)
1790 return bmap;
1791
1792 if (context->n_div > 0)
1793 bmap = isl_basic_map_align_divs(bmap, context);
1794
1795 total_context = isl_basic_map_total_dim(context);
1796 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1797 for (i = 0; i < context->n_eq; ++i) {
1798 int k;
1799 k = isl_basic_map_alloc_equality(bmap);
1800 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1801 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1802 isl_basic_map_total_dim(bmap) - total_context);
1803 }
1804 bmap = isl_basic_map_gauss(bmap, NULL);
1805 bmap = normalize_divs(bmap, NULL);
1806 bmap = isl_basic_map_gauss(bmap, NULL);
1807 return bmap;
1808 }
1809
1810 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1811 struct isl_basic_map *context)
1812 {
1813 struct isl_basic_set *bset;
1814
1815 if (!bmap || !context)
1816 goto error;
1817
1818 if (isl_basic_map_is_universe(bmap)) {
1819 isl_basic_map_free(context);
1820 return bmap;
1821 }
1822 if (isl_basic_map_plain_is_empty(context)) {
1823 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1824 isl_basic_map_free(context);
1825 isl_basic_map_free(bmap);
1826 return isl_basic_map_universe(dim);
1827 }
1828 if (isl_basic_map_plain_is_empty(bmap)) {
1829 isl_basic_map_free(context);
1830 return bmap;
1831 }
1832
1833 bmap = isl_basic_map_remove_redundancies(bmap);
1834 context = isl_basic_map_remove_redundancies(context);
1835
1836 if (context->n_eq)
1837 bmap = normalize_divs_in_context(bmap, context);
1838
1839 context = isl_basic_map_align_divs(context, bmap);
1840 bmap = isl_basic_map_align_divs(bmap, context);
1841
1842 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1843 isl_basic_map_underlying_set(context));
1844
1845 return isl_basic_map_overlying_set(bset, bmap);
1846 error:
1847 isl_basic_map_free(bmap);
1848 isl_basic_map_free(context);
1849 return NULL;
1850 }
1851
1852 /*
1853 * Assumes context has no implicit divs.
1854 */
1855 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1856 __isl_take isl_basic_map *context)
1857 {
1858 int i;
1859
1860 if (!map || !context)
1861 goto error;;
1862
1863 if (isl_basic_map_plain_is_empty(context)) {
1864 struct isl_dim *dim = isl_dim_copy(map->dim);
1865 isl_basic_map_free(context);
1866 isl_map_free(map);
1867 return isl_map_universe(dim);
1868 }
1869
1870 context = isl_basic_map_remove_redundancies(context);
1871 map = isl_map_cow(map);
1872 if (!map || !context)
1873 goto error;;
1874 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1875 map = isl_map_compute_divs(map);
1876 for (i = 0; i < map->n; ++i)
1877 context = isl_basic_map_align_divs(context, map->p[i]);
1878 for (i = map->n - 1; i >= 0; --i) {
1879 map->p[i] = isl_basic_map_gist(map->p[i],
1880 isl_basic_map_copy(context));
1881 if (!map->p[i])
1882 goto error;
1883 if (isl_basic_map_plain_is_empty(map->p[i])) {
1884 isl_basic_map_free(map->p[i]);
1885 if (i != map->n - 1)
1886 map->p[i] = map->p[map->n - 1];
1887 map->n--;
1888 }
1889 }
1890 isl_basic_map_free(context);
1891 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1892 return map;
1893 error:
1894 isl_map_free(map);
1895 isl_basic_map_free(context);
1896 return NULL;
1897 }
1898
1899 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1900 __isl_take isl_map *context)
1901 {
1902 context = isl_map_compute_divs(context);
1903 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1904 }
1905
1906 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1907 struct isl_basic_set *context)
1908 {
1909 return (struct isl_basic_set *)isl_basic_map_gist(
1910 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1911 }
1912
1913 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1914 __isl_take isl_basic_set *context)
1915 {
1916 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1917 (struct isl_basic_map *)context);
1918 }
1919
1920 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1921 __isl_take isl_set *context)
1922 {
1923 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1924 (struct isl_map *)context);
1925 }
1926
1927 /* Quick check to see if two basic maps are disjoint.
1928 * In particular, we reduce the equalities and inequalities of
1929 * one basic map in the context of the equalities of the other
1930 * basic map and check if we get a contradiction.
1931 */
1932 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1933 __isl_keep isl_basic_map *bmap2)
1934 {
1935 struct isl_vec *v = NULL;
1936 int *elim = NULL;
1937 unsigned total;
1938 int i;
1939
1940 if (!bmap1 || !bmap2)
1941 return -1;
1942 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1943 return -1);
1944 if (bmap1->n_div || bmap2->n_div)
1945 return 0;
1946 if (!bmap1->n_eq && !bmap2->n_eq)
1947 return 0;
1948
1949 total = isl_dim_total(bmap1->dim);
1950 if (total == 0)
1951 return 0;
1952 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1953 if (!v)
1954 goto error;
1955 elim = isl_alloc_array(bmap1->ctx, int, total);
1956 if (!elim)
1957 goto error;
1958 compute_elimination_index(bmap1, elim);
1959 for (i = 0; i < bmap2->n_eq; ++i) {
1960 int reduced;
1961 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1962 bmap1, elim);
1963 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1964 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1965 goto disjoint;
1966 }
1967 for (i = 0; i < bmap2->n_ineq; ++i) {
1968 int reduced;
1969 reduced = reduced_using_equalities(v->block.data,
1970 bmap2->ineq[i], bmap1, elim);
1971 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1972 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1973 goto disjoint;
1974 }
1975 compute_elimination_index(bmap2, elim);
1976 for (i = 0; i < bmap1->n_ineq; ++i) {
1977 int reduced;
1978 reduced = reduced_using_equalities(v->block.data,
1979 bmap1->ineq[i], bmap2, elim);
1980 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1981 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1982 goto disjoint;
1983 }
1984 isl_vec_free(v);
1985 free(elim);
1986 return 0;
1987 disjoint:
1988 isl_vec_free(v);
1989 free(elim);
1990 return 1;
1991 error:
1992 isl_vec_free(v);
1993 free(elim);
1994 return -1;
1995 }
1996
1997 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1998 __isl_keep isl_basic_set *bset2)
1999 {
2000 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2001 (struct isl_basic_map *)bset2);
2002 }
2003
2004 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2005 __isl_keep isl_map *map2)
2006 {
2007 int i, j;
2008
2009 if (!map1 || !map2)
2010 return -1;
2011
2012 if (isl_map_plain_is_equal(map1, map2))
2013 return 0;
2014
2015 for (i = 0; i < map1->n; ++i) {
2016 for (j = 0; j < map2->n; ++j) {
2017 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2018 map2->p[j]);
2019 if (d != 1)
2020 return d;
2021 }
2022 }
2023 return 1;
2024 }
2025
2026 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2027 __isl_keep isl_set *set2)
2028 {
2029 return isl_map_plain_is_disjoint((struct isl_map *)set1,
2030 (struct isl_map *)set2);
2031 }
2032
2033 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2034 {
2035 return isl_set_plain_is_disjoint(set1, set2);
2036 }
2037
2038 /* Check if we can combine a given div with lower bound l and upper
2039 * bound u with some other div and if so return that other div.
2040 * Otherwise return -1.
2041 *
2042 * We first check that
2043 * - the bounds are opposites of each other (except for the constant
2044 * term)
2045 * - the bounds do not reference any other div
2046 * - no div is defined in terms of this div
2047 *
2048 * Let m be the size of the range allowed on the div by the bounds.
2049 * That is, the bounds are of the form
2050 *
2051 * e <= a <= e + m - 1
2052 *
2053 * with e some expression in the other variables.
2054 * We look for another div b such that no third div is defined in terms
2055 * of this second div b and such that in any constraint that contains
2056 * a (except for the given lower and upper bound), also contains b
2057 * with a coefficient that is m times that of b.
2058 * That is, all constraints (execpt for the lower and upper bound)
2059 * are of the form
2060 *
2061 * e + f (a + m b) >= 0
2062 *
2063 * If so, we return b so that "a + m b" can be replaced by
2064 * a single div "c = a + m b".
2065 */
2066 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2067 unsigned div, unsigned l, unsigned u)
2068 {
2069 int i, j;
2070 unsigned dim;
2071 int coalesce = -1;
2072
2073 if (bmap->n_div <= 1)
2074 return -1;
2075 dim = isl_dim_total(bmap->dim);
2076 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2077 return -1;
2078 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2079 bmap->n_div - div - 1) != -1)
2080 return -1;
2081 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2082 dim + bmap->n_div))
2083 return -1;
2084
2085 for (i = 0; i < bmap->n_div; ++i) {
2086 if (isl_int_is_zero(bmap->div[i][0]))
2087 continue;
2088 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2089 return -1;
2090 }
2091
2092 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2093 if (isl_int_is_neg(bmap->ineq[l][0])) {
2094 isl_int_sub(bmap->ineq[l][0],
2095 bmap->ineq[l][0], bmap->ineq[u][0]);
2096 bmap = isl_basic_map_copy(bmap);
2097 bmap = isl_basic_map_set_to_empty(bmap);
2098 isl_basic_map_free(bmap);
2099 return -1;
2100 }
2101 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2102 for (i = 0; i < bmap->n_div; ++i) {
2103 if (i == div)
2104 continue;
2105 if (!pairs[i])
2106 continue;
2107 for (j = 0; j < bmap->n_div; ++j) {
2108 if (isl_int_is_zero(bmap->div[j][0]))
2109 continue;
2110 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2111 break;
2112 }
2113 if (j < bmap->n_div)
2114 continue;
2115 for (j = 0; j < bmap->n_ineq; ++j) {
2116 int valid;
2117 if (j == l || j == u)
2118 continue;
2119 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2120 continue;
2121 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2122 break;
2123 isl_int_mul(bmap->ineq[j][1 + dim + div],
2124 bmap->ineq[j][1 + dim + div],
2125 bmap->ineq[l][0]);
2126 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2127 bmap->ineq[j][1 + dim + i]);
2128 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2129 bmap->ineq[j][1 + dim + div],
2130 bmap->ineq[l][0]);
2131 if (!valid)
2132 break;
2133 }
2134 if (j < bmap->n_ineq)
2135 continue;
2136 coalesce = i;
2137 break;
2138 }
2139 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2140 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2141 return coalesce;
2142 }
2143
2144 /* Given a lower and an upper bound on div i, construct an inequality
2145 * that when nonnegative ensures that this pair of bounds always allows
2146 * for an integer value of the given div.
2147 * The lower bound is inequality l, while the upper bound is inequality u.
2148 * The constructed inequality is stored in ineq.
2149 * g, fl, fu are temporary scalars.
2150 *
2151 * Let the upper bound be
2152 *
2153 * -n_u a + e_u >= 0
2154 *
2155 * and the lower bound
2156 *
2157 * n_l a + e_l >= 0
2158 *
2159 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2160 * We have
2161 *
2162 * - f_u e_l <= f_u f_l g a <= f_l e_u
2163 *
2164 * Since all variables are integer valued, this is equivalent to
2165 *
2166 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2167 *
2168 * If this interval is at least f_u f_l g, then it contains at least
2169 * one integer value for a.
2170 * That is, the test constraint is
2171 *
2172 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2173 */
2174 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2175 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2176 {
2177 unsigned dim;
2178 dim = isl_dim_total(bmap->dim);
2179
2180 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2181 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2182 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2183 isl_int_neg(fu, fu);
2184 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2185 1 + dim + bmap->n_div);
2186 isl_int_add(ineq[0], ineq[0], fl);
2187 isl_int_add(ineq[0], ineq[0], fu);
2188 isl_int_sub_ui(ineq[0], ineq[0], 1);
2189 isl_int_mul(g, g, fl);
2190 isl_int_mul(g, g, fu);
2191 isl_int_sub(ineq[0], ineq[0], g);
2192 }
2193
2194 /* Remove more kinds of divs that are not strictly needed.
2195 * In particular, if all pairs of lower and upper bounds on a div
2196 * are such that they allow at least one integer value of the div,
2197 * the we can eliminate the div using Fourier-Motzkin without
2198 * introducing any spurious solutions.
2199 */
2200 static struct isl_basic_map *drop_more_redundant_divs(
2201 struct isl_basic_map *bmap, int *pairs, int n)
2202 {
2203 struct isl_tab *tab = NULL;
2204 struct isl_vec *vec = NULL;
2205 unsigned dim;
2206 int remove = -1;
2207 isl_int g, fl, fu;
2208
2209 isl_int_init(g);
2210 isl_int_init(fl);
2211 isl_int_init(fu);
2212
2213 if (!bmap)
2214 goto error;
2215
2216 dim = isl_dim_total(bmap->dim);
2217 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2218 if (!vec)
2219 goto error;
2220
2221 tab = isl_tab_from_basic_map(bmap);
2222
2223 while (n > 0) {
2224 int i, l, u;
2225 int best = -1;
2226 enum isl_lp_result res;
2227
2228 for (i = 0; i < bmap->n_div; ++i) {
2229 if (!pairs[i])
2230 continue;
2231 if (best >= 0 && pairs[best] <= pairs[i])
2232 continue;
2233 best = i;
2234 }
2235
2236 i = best;
2237 for (l = 0; l < bmap->n_ineq; ++l) {
2238 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2239 continue;
2240 for (u = 0; u < bmap->n_ineq; ++u) {
2241 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2242 continue;
2243 construct_test_ineq(bmap, i, l, u,
2244 vec->el, g, fl, fu);
2245 res = isl_tab_min(tab, vec->el,
2246 bmap->ctx->one, &g, NULL, 0);
2247 if (res == isl_lp_error)
2248 goto error;
2249 if (res == isl_lp_empty) {
2250 bmap = isl_basic_map_set_to_empty(bmap);
2251 break;
2252 }
2253 if (res != isl_lp_ok || isl_int_is_neg(g))
2254 break;
2255 }
2256 if (u < bmap->n_ineq)
2257 break;
2258 }
2259 if (l == bmap->n_ineq) {
2260 remove = i;
2261 break;
2262 }
2263 pairs[i] = 0;
2264 --n;
2265 }
2266
2267 isl_tab_free(tab);
2268 isl_vec_free(vec);
2269
2270 isl_int_clear(g);
2271 isl_int_clear(fl);
2272 isl_int_clear(fu);
2273
2274 free(pairs);
2275
2276 if (remove < 0)
2277 return bmap;
2278
2279 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2280 return isl_basic_map_drop_redundant_divs(bmap);
2281 error:
2282 free(pairs);
2283 isl_basic_map_free(bmap);
2284 isl_tab_free(tab);
2285 isl_vec_free(vec);
2286 isl_int_clear(g);
2287 isl_int_clear(fl);
2288 isl_int_clear(fu);
2289 return NULL;
2290 }
2291
2292 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2293 * and the upper bound u, div1 always occurs together with div2 in the form
2294 * (div1 + m div2), where m is the constant range on the variable div1
2295 * allowed by l and u, replace the pair div1 and div2 by a single
2296 * div that is equal to div1 + m div2.
2297 *
2298 * The new div will appear in the location that contains div2.
2299 * We need to modify all constraints that contain
2300 * div2 = (div - div1) / m
2301 * (If a constraint does not contain div2, it will also not contain div1.)
2302 * If the constraint also contains div1, then we know they appear
2303 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2304 * i.e., the coefficient of div is f.
2305 *
2306 * Otherwise, we first need to introduce div1 into the constraint.
2307 * Let the l be
2308 *
2309 * div1 + f >=0
2310 *
2311 * and u
2312 *
2313 * -div1 + f' >= 0
2314 *
2315 * A lower bound on div2
2316 *
2317 * n div2 + t >= 0
2318 *
2319 * can be replaced by
2320 *
2321 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2322 *
2323 * with g = gcd(m,n).
2324 * An upper bound
2325 *
2326 * -n div2 + t >= 0
2327 *
2328 * can be replaced by
2329 *
2330 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2331 *
2332 * These constraint are those that we would obtain from eliminating
2333 * div1 using Fourier-Motzkin.
2334 *
2335 * After all constraints have been modified, we drop the lower and upper
2336 * bound and then drop div1.
2337 */
2338 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2339 unsigned div1, unsigned div2, unsigned l, unsigned u)
2340 {
2341 isl_int a;
2342 isl_int b;
2343 isl_int m;
2344 unsigned dim, total;
2345 int i;
2346
2347 dim = isl_dim_total(bmap->dim);
2348 total = 1 + dim + bmap->n_div;
2349
2350 isl_int_init(a);
2351 isl_int_init(b);
2352 isl_int_init(m);
2353 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2354 isl_int_add_ui(m, m, 1);
2355
2356 for (i = 0; i < bmap->n_ineq; ++i) {
2357 if (i == l || i == u)
2358 continue;
2359 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2360 continue;
2361 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2362 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2363 isl_int_divexact(a, m, b);
2364 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2365 if (isl_int_is_pos(b)) {
2366 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2367 b, bmap->ineq[l], total);
2368 } else {
2369 isl_int_neg(b, b);
2370 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2371 b, bmap->ineq[u], total);
2372 }
2373 }
2374 isl_int_set(bmap->ineq[i][1 + dim + div2],
2375 bmap->ineq[i][1 + dim + div1]);
2376 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2377 }
2378
2379 isl_int_clear(a);
2380 isl_int_clear(b);
2381 isl_int_clear(m);
2382 if (l > u) {
2383 isl_basic_map_drop_inequality(bmap, l);
2384 isl_basic_map_drop_inequality(bmap, u);
2385 } else {
2386 isl_basic_map_drop_inequality(bmap, u);
2387 isl_basic_map_drop_inequality(bmap, l);
2388 }
2389 bmap = isl_basic_map_drop_div(bmap, div1);
2390 return bmap;
2391 }
2392
2393 /* First check if we can coalesce any pair of divs and
2394 * then continue with dropping more redundant divs.
2395 *
2396 * We loop over all pairs of lower and upper bounds on a div
2397 * with coefficient 1 and -1, respectively, check if there
2398 * is any other div "c" with which we can coalesce the div
2399 * and if so, perform the coalescing.
2400 */
2401 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2402 struct isl_basic_map *bmap, int *pairs, int n)
2403 {
2404 int i, l, u;
2405 unsigned dim;
2406
2407 dim = isl_dim_total(bmap->dim);
2408
2409 for (i = 0; i < bmap->n_div; ++i) {
2410 if (!pairs[i])
2411 continue;
2412 for (l = 0; l < bmap->n_ineq; ++l) {
2413 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2414 continue;
2415 for (u = 0; u < bmap->n_ineq; ++u) {
2416 int c;
2417
2418 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2419 continue;
2420 c = div_find_coalesce(bmap, pairs, i, l, u);
2421 if (c < 0)
2422 continue;
2423 free(pairs);
2424 bmap = coalesce_divs(bmap, i, c, l, u);
2425 return isl_basic_map_drop_redundant_divs(bmap);
2426 }
2427 }
2428 }
2429
2430 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2431 return bmap;
2432
2433 return drop_more_redundant_divs(bmap, pairs, n);
2434 }
2435
2436 /* Remove divs that are not strictly needed.
2437 * In particular, if a div only occurs positively (or negatively)
2438 * in constraints, then it can simply be dropped.
2439 * Also, if a div occurs only occurs in two constraints and if moreover
2440 * those two constraints are opposite to each other, except for the constant
2441 * term and if the sum of the constant terms is such that for any value
2442 * of the other values, there is always at least one integer value of the
2443 * div, i.e., if one plus this sum is greater than or equal to
2444 * the (absolute value) of the coefficent of the div in the constraints,
2445 * then we can also simply drop the div.
2446 *
2447 * If any divs are left after these simple checks then we move on
2448 * to more complicated cases in drop_more_redundant_divs.
2449 */
2450 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2451 struct isl_basic_map *bmap)
2452 {
2453 int i, j;
2454 unsigned off;
2455 int *pairs = NULL;
2456 int n = 0;
2457
2458 if (!bmap)
2459 goto error;
2460
2461 off = isl_dim_total(bmap->dim);
2462 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2463 if (!pairs)
2464 goto error;
2465
2466 for (i = 0; i < bmap->n_div; ++i) {
2467 int pos, neg;
2468 int last_pos, last_neg;
2469 int redundant;
2470 int defined;
2471
2472 defined = !isl_int_is_zero(bmap->div[i][0]);
2473 for (j = 0; j < bmap->n_eq; ++j)
2474 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2475 break;
2476 if (j < bmap->n_eq)
2477 continue;
2478 ++n;
2479 pos = neg = 0;
2480 for (j = 0; j < bmap->n_ineq; ++j) {
2481 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2482 last_pos = j;
2483 ++pos;
2484 }
2485 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2486 last_neg = j;
2487 ++neg;
2488 }
2489 }
2490 pairs[i] = pos * neg;
2491 if (pairs[i] == 0) {
2492 for (j = bmap->n_ineq - 1; j >= 0; --j)
2493 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2494 isl_basic_map_drop_inequality(bmap, j);
2495 bmap = isl_basic_map_drop_div(bmap, i);
2496 free(pairs);
2497 return isl_basic_map_drop_redundant_divs(bmap);
2498 }
2499 if (pairs[i] != 1)
2500 continue;
2501 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2502 bmap->ineq[last_neg] + 1,
2503 off + bmap->n_div))
2504 continue;
2505
2506 isl_int_add(bmap->ineq[last_pos][0],
2507 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2508 isl_int_add_ui(bmap->ineq[last_pos][0],
2509 bmap->ineq[last_pos][0], 1);
2510 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2511 bmap->ineq[last_pos][1+off+i]);
2512 isl_int_sub_ui(bmap->ineq[last_pos][0],
2513 bmap->ineq[last_pos][0], 1);
2514 isl_int_sub(bmap->ineq[last_pos][0],
2515 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2516 if (!redundant) {
2517 if (defined ||
2518 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2519 pairs[i] = 0;
2520 --n;
2521 continue;
2522 }
2523 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2524 bmap = isl_basic_map_simplify(bmap);
2525 free(pairs);
2526 return isl_basic_map_drop_redundant_divs(bmap);
2527 }
2528 if (last_pos > last_neg) {
2529 isl_basic_map_drop_inequality(bmap, last_pos);
2530 isl_basic_map_drop_inequality(bmap, last_neg);
2531 } else {
2532 isl_basic_map_drop_inequality(bmap, last_neg);
2533 isl_basic_map_drop_inequality(bmap, last_pos);
2534 }
2535 bmap = isl_basic_map_drop_div(bmap, i);
2536 free(pairs);
2537 return isl_basic_map_drop_redundant_divs(bmap);
2538 }
2539
2540 if (n > 0)
2541 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2542
2543 free(pairs);
2544 return bmap;
2545 error:
2546 free(pairs);
2547 isl_basic_map_free(bmap);
2548 return NULL;
2549 }
2550
2551 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2552 struct isl_basic_set *bset)
2553 {
2554 return (struct isl_basic_set *)
2555 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2556 }
2557
2558 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2559 {
2560 int i;
2561
2562 if (!map)
2563 return NULL;
2564 for (i = 0; i < map->n; ++i) {
2565 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2566 if (!map->p[i])
2567 goto error;
2568 }
2569 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2570 return map;
2571 error:
2572 isl_map_free(map);
2573 return NULL;
2574 }
2575
2576 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2577 {
2578 return (struct isl_set *)
2579 isl_map_drop_redundant_divs((struct isl_map *)set);
2580 }
Integer set library