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generalize isl_basic_set_list to generic lists
[isl.git] / isl_map_simplify.c
blob0e5a2f00fc1a7b1a7b2e856e33a84488d186fcb9
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 /* Remove all information from bset that is redundant in the context
1499 * of context. Both bset and context are assumed to be full-dimensional.
1500 *
1501 * We first * remove the inequalities from "bset"
1502 * that are obviously redundant with respect to some inequality in "context".
1503 *
1504 * If there are any inequalities left, we construct a tableau for
1505 * the context and then add the inequalities of "bset".
1506 * Before adding these inequalities, we freeze all constraints such that
1507 * they won't be considered redundant in terms of the constraints of "bset".
1508 * Then we detect all redundant constraints (among the
1509 * constraints that weren't frozen), first by checking for redundancy in the
1510 * the tableau and then by checking if replacing a constraint by its negation
1511 * would lead to an empty set. This last step is fairly expensive
1512 * and could be optimized by more reuse of the tableau.
1513 * Finally, we update bset according to the results.
1514 */
1515 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1516 __isl_take isl_basic_set *context)
1517 {
1518 int i, k;
1519 isl_basic_set *combined = NULL;
1520 struct isl_tab *tab = NULL;
1521 unsigned context_ineq;
1522 unsigned total;
1523
1524 if (!bset || !context)
1525 goto error;
1526
1527 if (isl_basic_set_is_universe(bset)) {
1528 isl_basic_set_free(context);
1529 return bset;
1530 }
1531
1532 if (isl_basic_set_is_universe(context)) {
1533 isl_basic_set_free(context);
1534 return bset;
1535 }
1536
1537 bset = remove_shifted_constraints(bset, context);
1538 if (!bset)
1539 goto error;
1540 if (bset->n_ineq == 0)
1541 goto done;
1542
1543 context_ineq = context->n_ineq;
1544 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1545 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1546 tab = isl_tab_from_basic_set(combined);
1547 for (i = 0; i < context_ineq; ++i)
1548 if (isl_tab_freeze_constraint(tab, i) < 0)
1549 goto error;
1550 tab = isl_tab_extend(tab, bset->n_ineq);
1551 for (i = 0; i < bset->n_ineq; ++i)
1552 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1553 goto error;
1554 bset = isl_basic_set_add_constraints(combined, bset, 0);
1555 combined = NULL;
1556 if (!bset)
1557 goto error;
1558 if (isl_tab_detect_redundant(tab) < 0)
1559 goto error;
1560 total = isl_basic_set_total_dim(bset);
1561 for (i = context_ineq; i < bset->n_ineq; ++i) {
1562 int is_empty;
1563 if (tab->con[i].is_redundant)
1564 continue;
1565 tab->con[i].is_redundant = 1;
1566 combined = isl_basic_set_dup(bset);
1567 combined = isl_basic_set_update_from_tab(combined, tab);
1568 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1569 k = isl_basic_set_alloc_inequality(combined);
1570 if (k < 0)
1571 goto error;
1572 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1573 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1574 is_empty = isl_basic_set_is_empty(combined);
1575 if (is_empty < 0)
1576 goto error;
1577 isl_basic_set_free(combined);
1578 combined = NULL;
1579 if (!is_empty)
1580 tab->con[i].is_redundant = 0;
1581 }
1582 for (i = 0; i < context_ineq; ++i)
1583 tab->con[i].is_redundant = 1;
1584 bset = isl_basic_set_update_from_tab(bset, tab);
1585 if (bset) {
1586 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1587 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1588 }
1589
1590 isl_tab_free(tab);
1591 done:
1592 bset = isl_basic_set_simplify(bset);
1593 bset = isl_basic_set_finalize(bset);
1594 isl_basic_set_free(context);
1595 return bset;
1596 error:
1597 isl_tab_free(tab);
1598 isl_basic_set_free(combined);
1599 isl_basic_set_free(context);
1600 isl_basic_set_free(bset);
1601 return NULL;
1602 }
1603
1604 /* Remove all information from bset that is redundant in the context
1605 * of context. In particular, equalities that are linear combinations
1606 * of those in context are removed. Then the inequalities that are
1607 * redundant in the context of the equalities and inequalities of
1608 * context are removed.
1609 *
1610 * We first compute the integer affine hull of the intersection,
1611 * compute the gist inside this affine hull and then add back
1612 * those equalities that are not implied by the context.
1613 *
1614 * If two constraints are mutually redundant, then uset_gist_full
1615 * will remove the second of those constraints. We therefore first
1616 * sort the constraints so that constraints not involving existentially
1617 * quantified variables are given precedence over those that do.
1618 * We have to perform this sorting before the variable compression,
1619 * because that may effect the order of the variables.
1620 */
1621 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1622 __isl_take isl_basic_set *context)
1623 {
1624 isl_mat *eq;
1625 isl_mat *T, *T2;
1626 isl_basic_set *aff;
1627 isl_basic_set *aff_context;
1628 unsigned total;
1629
1630 if (!bset || !context)
1631 goto error;
1632
1633 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1634 if (isl_basic_set_plain_is_empty(bset)) {
1635 isl_basic_set_free(context);
1636 return bset;
1637 }
1638 bset = isl_basic_set_sort_constraints(bset);
1639 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1640 if (!aff)
1641 goto error;
1642 if (isl_basic_set_plain_is_empty(aff)) {
1643 isl_basic_set_free(aff);
1644 isl_basic_set_free(context);
1645 return bset;
1646 }
1647 if (aff->n_eq == 0) {
1648 isl_basic_set_free(aff);
1649 return uset_gist_full(bset, context);
1650 }
1651 total = isl_basic_set_total_dim(bset);
1652 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1653 eq = isl_mat_cow(eq);
1654 T = isl_mat_variable_compression(eq, &T2);
1655 if (T && T->n_col == 0) {
1656 isl_mat_free(T);
1657 isl_mat_free(T2);
1658 isl_basic_set_free(context);
1659 isl_basic_set_free(aff);
1660 return isl_basic_set_set_to_empty(bset);
1661 }
1662
1663 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1664
1665 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1666 context = isl_basic_set_preimage(context, T);
1667
1668 bset = uset_gist_full(bset, context);
1669 bset = isl_basic_set_preimage(bset, T2);
1670 bset = isl_basic_set_intersect(bset, aff);
1671 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1672
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 return bset;
1679 error:
1680 isl_basic_set_free(bset);
1681 isl_basic_set_free(context);
1682 return NULL;
1683 }
1684
1685 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1686 * We simply add the equalities in context to bmap and then do a regular
1687 * div normalizations. Better results can be obtained by normalizing
1688 * only the divs in bmap than do not also appear in context.
1689 * We need to be careful to reduce the divs using the equalities
1690 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1691 * spurious constraints.
1692 */
1693 static struct isl_basic_map *normalize_divs_in_context(
1694 struct isl_basic_map *bmap, struct isl_basic_map *context)
1695 {
1696 int i;
1697 unsigned total_context;
1698 int div_eq;
1699
1700 div_eq = n_pure_div_eq(bmap);
1701 if (div_eq == 0)
1702 return bmap;
1703
1704 if (context->n_div > 0)
1705 bmap = isl_basic_map_align_divs(bmap, context);
1706
1707 total_context = isl_basic_map_total_dim(context);
1708 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1709 for (i = 0; i < context->n_eq; ++i) {
1710 int k;
1711 k = isl_basic_map_alloc_equality(bmap);
1712 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1713 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1714 isl_basic_map_total_dim(bmap) - total_context);
1715 }
1716 bmap = isl_basic_map_gauss(bmap, NULL);
1717 bmap = normalize_divs(bmap, NULL);
1718 bmap = isl_basic_map_gauss(bmap, NULL);
1719 return bmap;
1720 }
1721
1722 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1723 struct isl_basic_map *context)
1724 {
1725 struct isl_basic_set *bset;
1726
1727 if (!bmap || !context)
1728 goto error;
1729
1730 if (isl_basic_map_is_universe(bmap)) {
1731 isl_basic_map_free(context);
1732 return bmap;
1733 }
1734 if (isl_basic_map_plain_is_empty(context)) {
1735 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1736 isl_basic_map_free(context);
1737 isl_basic_map_free(bmap);
1738 return isl_basic_map_universe(dim);
1739 }
1740 if (isl_basic_map_plain_is_empty(bmap)) {
1741 isl_basic_map_free(context);
1742 return bmap;
1743 }
1744
1745 bmap = isl_basic_map_remove_redundancies(bmap);
1746 context = isl_basic_map_remove_redundancies(context);
1747
1748 if (context->n_eq)
1749 bmap = normalize_divs_in_context(bmap, context);
1750
1751 context = isl_basic_map_align_divs(context, bmap);
1752 bmap = isl_basic_map_align_divs(bmap, context);
1753
1754 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1755 isl_basic_map_underlying_set(context));
1756
1757 return isl_basic_map_overlying_set(bset, bmap);
1758 error:
1759 isl_basic_map_free(bmap);
1760 isl_basic_map_free(context);
1761 return NULL;
1762 }
1763
1764 /*
1765 * Assumes context has no implicit divs.
1766 */
1767 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1768 __isl_take isl_basic_map *context)
1769 {
1770 int i;
1771
1772 if (!map || !context)
1773 goto error;;
1774
1775 if (isl_basic_map_plain_is_empty(context)) {
1776 struct isl_dim *dim = isl_dim_copy(map->dim);
1777 isl_basic_map_free(context);
1778 isl_map_free(map);
1779 return isl_map_universe(dim);
1780 }
1781
1782 context = isl_basic_map_remove_redundancies(context);
1783 map = isl_map_cow(map);
1784 if (!map || !context)
1785 goto error;;
1786 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1787 map = isl_map_compute_divs(map);
1788 for (i = 0; i < map->n; ++i)
1789 context = isl_basic_map_align_divs(context, map->p[i]);
1790 for (i = map->n - 1; i >= 0; --i) {
1791 map->p[i] = isl_basic_map_gist(map->p[i],
1792 isl_basic_map_copy(context));
1793 if (!map->p[i])
1794 goto error;
1795 if (isl_basic_map_plain_is_empty(map->p[i])) {
1796 isl_basic_map_free(map->p[i]);
1797 if (i != map->n - 1)
1798 map->p[i] = map->p[map->n - 1];
1799 map->n--;
1800 }
1801 }
1802 isl_basic_map_free(context);
1803 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1804 return map;
1805 error:
1806 isl_map_free(map);
1807 isl_basic_map_free(context);
1808 return NULL;
1809 }
1810
1811 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1812 __isl_take isl_map *context)
1813 {
1814 context = isl_map_compute_divs(context);
1815 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1816 }
1817
1818 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1819 struct isl_basic_set *context)
1820 {
1821 return (struct isl_basic_set *)isl_basic_map_gist(
1822 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1823 }
1824
1825 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1826 __isl_take isl_basic_set *context)
1827 {
1828 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1829 (struct isl_basic_map *)context);
1830 }
1831
1832 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1833 __isl_take isl_set *context)
1834 {
1835 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1836 (struct isl_map *)context);
1837 }
1838
1839 /* Quick check to see if two basic maps are disjoint.
1840 * In particular, we reduce the equalities and inequalities of
1841 * one basic map in the context of the equalities of the other
1842 * basic map and check if we get a contradiction.
1843 */
1844 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1845 __isl_keep isl_basic_map *bmap2)
1846 {
1847 struct isl_vec *v = NULL;
1848 int *elim = NULL;
1849 unsigned total;
1850 int i;
1851
1852 if (!bmap1 || !bmap2)
1853 return -1;
1854 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1855 return -1);
1856 if (bmap1->n_div || bmap2->n_div)
1857 return 0;
1858 if (!bmap1->n_eq && !bmap2->n_eq)
1859 return 0;
1860
1861 total = isl_dim_total(bmap1->dim);
1862 if (total == 0)
1863 return 0;
1864 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1865 if (!v)
1866 goto error;
1867 elim = isl_alloc_array(bmap1->ctx, int, total);
1868 if (!elim)
1869 goto error;
1870 compute_elimination_index(bmap1, elim);
1871 for (i = 0; i < bmap2->n_eq; ++i) {
1872 int reduced;
1873 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1874 bmap1, elim);
1875 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1876 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1877 goto disjoint;
1878 }
1879 for (i = 0; i < bmap2->n_ineq; ++i) {
1880 int reduced;
1881 reduced = reduced_using_equalities(v->block.data,
1882 bmap2->ineq[i], bmap1, elim);
1883 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1884 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1885 goto disjoint;
1886 }
1887 compute_elimination_index(bmap2, elim);
1888 for (i = 0; i < bmap1->n_ineq; ++i) {
1889 int reduced;
1890 reduced = reduced_using_equalities(v->block.data,
1891 bmap1->ineq[i], bmap2, elim);
1892 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1893 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1894 goto disjoint;
1895 }
1896 isl_vec_free(v);
1897 free(elim);
1898 return 0;
1899 disjoint:
1900 isl_vec_free(v);
1901 free(elim);
1902 return 1;
1903 error:
1904 isl_vec_free(v);
1905 free(elim);
1906 return -1;
1907 }
1908
1909 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1910 __isl_keep isl_basic_set *bset2)
1911 {
1912 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1913 (struct isl_basic_map *)bset2);
1914 }
1915
1916 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1917 __isl_keep isl_map *map2)
1918 {
1919 int i, j;
1920
1921 if (!map1 || !map2)
1922 return -1;
1923
1924 if (isl_map_plain_is_equal(map1, map2))
1925 return 0;
1926
1927 for (i = 0; i < map1->n; ++i) {
1928 for (j = 0; j < map2->n; ++j) {
1929 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1930 map2->p[j]);
1931 if (d != 1)
1932 return d;
1933 }
1934 }
1935 return 1;
1936 }
1937
1938 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1939 __isl_keep isl_set *set2)
1940 {
1941 return isl_map_plain_is_disjoint((struct isl_map *)set1,
1942 (struct isl_map *)set2);
1943 }
1944
1945 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
1946 {
1947 return isl_set_plain_is_disjoint(set1, set2);
1948 }
1949
1950 /* Check if we can combine a given div with lower bound l and upper
1951 * bound u with some other div and if so return that other div.
1952 * Otherwise return -1.
1953 *
1954 * We first check that
1955 * - the bounds are opposites of each other (except for the constant
1956 * term)
1957 * - the bounds do not reference any other div
1958 * - no div is defined in terms of this div
1959 *
1960 * Let m be the size of the range allowed on the div by the bounds.
1961 * That is, the bounds are of the form
1962 *
1963 * e <= a <= e + m - 1
1964 *
1965 * with e some expression in the other variables.
1966 * We look for another div b such that no third div is defined in terms
1967 * of this second div b and such that in any constraint that contains
1968 * a (except for the given lower and upper bound), also contains b
1969 * with a coefficient that is m times that of b.
1970 * That is, all constraints (execpt for the lower and upper bound)
1971 * are of the form
1972 *
1973 * e + f (a + m b) >= 0
1974 *
1975 * If so, we return b so that "a + m b" can be replaced by
1976 * a single div "c = a + m b".
1977 */
1978 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1979 unsigned div, unsigned l, unsigned u)
1980 {
1981 int i, j;
1982 unsigned dim;
1983 int coalesce = -1;
1984
1985 if (bmap->n_div <= 1)
1986 return -1;
1987 dim = isl_dim_total(bmap->dim);
1988 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1989 return -1;
1990 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1991 bmap->n_div - div - 1) != -1)
1992 return -1;
1993 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1994 dim + bmap->n_div))
1995 return -1;
1996
1997 for (i = 0; i < bmap->n_div; ++i) {
1998 if (isl_int_is_zero(bmap->div[i][0]))
1999 continue;
2000 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2001 return -1;
2002 }
2003
2004 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2005 if (isl_int_is_neg(bmap->ineq[l][0])) {
2006 isl_int_sub(bmap->ineq[l][0],
2007 bmap->ineq[l][0], bmap->ineq[u][0]);
2008 bmap = isl_basic_map_copy(bmap);
2009 bmap = isl_basic_map_set_to_empty(bmap);
2010 isl_basic_map_free(bmap);
2011 return -1;
2012 }
2013 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2014 for (i = 0; i < bmap->n_div; ++i) {
2015 if (i == div)
2016 continue;
2017 if (!pairs[i])
2018 continue;
2019 for (j = 0; j < bmap->n_div; ++j) {
2020 if (isl_int_is_zero(bmap->div[j][0]))
2021 continue;
2022 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2023 break;
2024 }
2025 if (j < bmap->n_div)
2026 continue;
2027 for (j = 0; j < bmap->n_ineq; ++j) {
2028 int valid;
2029 if (j == l || j == u)
2030 continue;
2031 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2032 continue;
2033 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2034 break;
2035 isl_int_mul(bmap->ineq[j][1 + dim + div],
2036 bmap->ineq[j][1 + dim + div],
2037 bmap->ineq[l][0]);
2038 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2039 bmap->ineq[j][1 + dim + i]);
2040 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2041 bmap->ineq[j][1 + dim + div],
2042 bmap->ineq[l][0]);
2043 if (!valid)
2044 break;
2045 }
2046 if (j < bmap->n_ineq)
2047 continue;
2048 coalesce = i;
2049 break;
2050 }
2051 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2052 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2053 return coalesce;
2054 }
2055
2056 /* Given a lower and an upper bound on div i, construct an inequality
2057 * that when nonnegative ensures that this pair of bounds always allows
2058 * for an integer value of the given div.
2059 * The lower bound is inequality l, while the upper bound is inequality u.
2060 * The constructed inequality is stored in ineq.
2061 * g, fl, fu are temporary scalars.
2062 *
2063 * Let the upper bound be
2064 *
2065 * -n_u a + e_u >= 0
2066 *
2067 * and the lower bound
2068 *
2069 * n_l a + e_l >= 0
2070 *
2071 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2072 * We have
2073 *
2074 * - f_u e_l <= f_u f_l g a <= f_l e_u
2075 *
2076 * Since all variables are integer valued, this is equivalent to
2077 *
2078 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2079 *
2080 * If this interval is at least f_u f_l g, then it contains at least
2081 * one integer value for a.
2082 * That is, the test constraint is
2083 *
2084 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2085 */
2086 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2087 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2088 {
2089 unsigned dim;
2090 dim = isl_dim_total(bmap->dim);
2091
2092 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2093 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2094 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2095 isl_int_neg(fu, fu);
2096 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2097 1 + dim + bmap->n_div);
2098 isl_int_add(ineq[0], ineq[0], fl);
2099 isl_int_add(ineq[0], ineq[0], fu);
2100 isl_int_sub_ui(ineq[0], ineq[0], 1);
2101 isl_int_mul(g, g, fl);
2102 isl_int_mul(g, g, fu);
2103 isl_int_sub(ineq[0], ineq[0], g);
2104 }
2105
2106 /* Remove more kinds of divs that are not strictly needed.
2107 * In particular, if all pairs of lower and upper bounds on a div
2108 * are such that they allow at least one integer value of the div,
2109 * the we can eliminate the div using Fourier-Motzkin without
2110 * introducing any spurious solutions.
2111 */
2112 static struct isl_basic_map *drop_more_redundant_divs(
2113 struct isl_basic_map *bmap, int *pairs, int n)
2114 {
2115 struct isl_tab *tab = NULL;
2116 struct isl_vec *vec = NULL;
2117 unsigned dim;
2118 int remove = -1;
2119 isl_int g, fl, fu;
2120
2121 isl_int_init(g);
2122 isl_int_init(fl);
2123 isl_int_init(fu);
2124
2125 if (!bmap)
2126 goto error;
2127
2128 dim = isl_dim_total(bmap->dim);
2129 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2130 if (!vec)
2131 goto error;
2132
2133 tab = isl_tab_from_basic_map(bmap);
2134
2135 while (n > 0) {
2136 int i, l, u;
2137 int best = -1;
2138 enum isl_lp_result res;
2139
2140 for (i = 0; i < bmap->n_div; ++i) {
2141 if (!pairs[i])
2142 continue;
2143 if (best >= 0 && pairs[best] <= pairs[i])
2144 continue;
2145 best = i;
2146 }
2147
2148 i = best;
2149 for (l = 0; l < bmap->n_ineq; ++l) {
2150 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2151 continue;
2152 for (u = 0; u < bmap->n_ineq; ++u) {
2153 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2154 continue;
2155 construct_test_ineq(bmap, i, l, u,
2156 vec->el, g, fl, fu);
2157 res = isl_tab_min(tab, vec->el,
2158 bmap->ctx->one, &g, NULL, 0);
2159 if (res == isl_lp_error)
2160 goto error;
2161 if (res == isl_lp_empty) {
2162 bmap = isl_basic_map_set_to_empty(bmap);
2163 break;
2164 }
2165 if (res != isl_lp_ok || isl_int_is_neg(g))
2166 break;
2167 }
2168 if (u < bmap->n_ineq)
2169 break;
2170 }
2171 if (l == bmap->n_ineq) {
2172 remove = i;
2173 break;
2174 }
2175 pairs[i] = 0;
2176 --n;
2177 }
2178
2179 isl_tab_free(tab);
2180 isl_vec_free(vec);
2181
2182 isl_int_clear(g);
2183 isl_int_clear(fl);
2184 isl_int_clear(fu);
2185
2186 free(pairs);
2187
2188 if (remove < 0)
2189 return bmap;
2190
2191 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2192 return isl_basic_map_drop_redundant_divs(bmap);
2193 error:
2194 free(pairs);
2195 isl_basic_map_free(bmap);
2196 isl_tab_free(tab);
2197 isl_vec_free(vec);
2198 isl_int_clear(g);
2199 isl_int_clear(fl);
2200 isl_int_clear(fu);
2201 return NULL;
2202 }
2203
2204 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2205 * and the upper bound u, div1 always occurs together with div2 in the form
2206 * (div1 + m div2), where m is the constant range on the variable div1
2207 * allowed by l and u, replace the pair div1 and div2 by a single
2208 * div that is equal to div1 + m div2.
2209 *
2210 * The new div will appear in the location that contains div2.
2211 * We need to modify all constraints that contain
2212 * div2 = (div - div1) / m
2213 * (If a constraint does not contain div2, it will also not contain div1.)
2214 * If the constraint also contains div1, then we know they appear
2215 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2216 * i.e., the coefficient of div is f.
2217 *
2218 * Otherwise, we first need to introduce div1 into the constraint.
2219 * Let the l be
2220 *
2221 * div1 + f >=0
2222 *
2223 * and u
2224 *
2225 * -div1 + f' >= 0
2226 *
2227 * A lower bound on div2
2228 *
2229 * n div2 + t >= 0
2230 *
2231 * can be replaced by
2232 *
2233 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2234 *
2235 * with g = gcd(m,n).
2236 * An upper bound
2237 *
2238 * -n div2 + t >= 0
2239 *
2240 * can be replaced by
2241 *
2242 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2243 *
2244 * These constraint are those that we would obtain from eliminating
2245 * div1 using Fourier-Motzkin.
2246 *
2247 * After all constraints have been modified, we drop the lower and upper
2248 * bound and then drop div1.
2249 */
2250 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2251 unsigned div1, unsigned div2, unsigned l, unsigned u)
2252 {
2253 isl_int a;
2254 isl_int b;
2255 isl_int m;
2256 unsigned dim, total;
2257 int i;
2258
2259 dim = isl_dim_total(bmap->dim);
2260 total = 1 + dim + bmap->n_div;
2261
2262 isl_int_init(a);
2263 isl_int_init(b);
2264 isl_int_init(m);
2265 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2266 isl_int_add_ui(m, m, 1);
2267
2268 for (i = 0; i < bmap->n_ineq; ++i) {
2269 if (i == l || i == u)
2270 continue;
2271 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2272 continue;
2273 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2274 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2275 isl_int_divexact(a, m, b);
2276 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2277 if (isl_int_is_pos(b)) {
2278 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2279 b, bmap->ineq[l], total);
2280 } else {
2281 isl_int_neg(b, b);
2282 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2283 b, bmap->ineq[u], total);
2284 }
2285 }
2286 isl_int_set(bmap->ineq[i][1 + dim + div2],
2287 bmap->ineq[i][1 + dim + div1]);
2288 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2289 }
2290
2291 isl_int_clear(a);
2292 isl_int_clear(b);
2293 isl_int_clear(m);
2294 if (l > u) {
2295 isl_basic_map_drop_inequality(bmap, l);
2296 isl_basic_map_drop_inequality(bmap, u);
2297 } else {
2298 isl_basic_map_drop_inequality(bmap, u);
2299 isl_basic_map_drop_inequality(bmap, l);
2300 }
2301 bmap = isl_basic_map_drop_div(bmap, div1);
2302 return bmap;
2303 }
2304
2305 /* First check if we can coalesce any pair of divs and
2306 * then continue with dropping more redundant divs.
2307 *
2308 * We loop over all pairs of lower and upper bounds on a div
2309 * with coefficient 1 and -1, respectively, check if there
2310 * is any other div "c" with which we can coalesce the div
2311 * and if so, perform the coalescing.
2312 */
2313 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2314 struct isl_basic_map *bmap, int *pairs, int n)
2315 {
2316 int i, l, u;
2317 unsigned dim;
2318
2319 dim = isl_dim_total(bmap->dim);
2320
2321 for (i = 0; i < bmap->n_div; ++i) {
2322 if (!pairs[i])
2323 continue;
2324 for (l = 0; l < bmap->n_ineq; ++l) {
2325 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2326 continue;
2327 for (u = 0; u < bmap->n_ineq; ++u) {
2328 int c;
2329
2330 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2331 continue;
2332 c = div_find_coalesce(bmap, pairs, i, l, u);
2333 if (c < 0)
2334 continue;
2335 free(pairs);
2336 bmap = coalesce_divs(bmap, i, c, l, u);
2337 return isl_basic_map_drop_redundant_divs(bmap);
2338 }
2339 }
2340 }
2341
2342 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2343 return bmap;
2344
2345 return drop_more_redundant_divs(bmap, pairs, n);
2346 }
2347
2348 /* Remove divs that are not strictly needed.
2349 * In particular, if a div only occurs positively (or negatively)
2350 * in constraints, then it can simply be dropped.
2351 * Also, if a div occurs only occurs in two constraints and if moreover
2352 * those two constraints are opposite to each other, except for the constant
2353 * term and if the sum of the constant terms is such that for any value
2354 * of the other values, there is always at least one integer value of the
2355 * div, i.e., if one plus this sum is greater than or equal to
2356 * the (absolute value) of the coefficent of the div in the constraints,
2357 * then we can also simply drop the div.
2358 *
2359 * If any divs are left after these simple checks then we move on
2360 * to more complicated cases in drop_more_redundant_divs.
2361 */
2362 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2363 struct isl_basic_map *bmap)
2364 {
2365 int i, j;
2366 unsigned off;
2367 int *pairs = NULL;
2368 int n = 0;
2369
2370 if (!bmap)
2371 goto error;
2372
2373 off = isl_dim_total(bmap->dim);
2374 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2375 if (!pairs)
2376 goto error;
2377
2378 for (i = 0; i < bmap->n_div; ++i) {
2379 int pos, neg;
2380 int last_pos, last_neg;
2381 int redundant;
2382 int defined;
2383
2384 defined = !isl_int_is_zero(bmap->div[i][0]);
2385 for (j = 0; j < bmap->n_eq; ++j)
2386 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2387 break;
2388 if (j < bmap->n_eq)
2389 continue;
2390 ++n;
2391 pos = neg = 0;
2392 for (j = 0; j < bmap->n_ineq; ++j) {
2393 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2394 last_pos = j;
2395 ++pos;
2396 }
2397 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2398 last_neg = j;
2399 ++neg;
2400 }
2401 }
2402 pairs[i] = pos * neg;
2403 if (pairs[i] == 0) {
2404 for (j = bmap->n_ineq - 1; j >= 0; --j)
2405 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2406 isl_basic_map_drop_inequality(bmap, j);
2407 bmap = isl_basic_map_drop_div(bmap, i);
2408 free(pairs);
2409 return isl_basic_map_drop_redundant_divs(bmap);
2410 }
2411 if (pairs[i] != 1)
2412 continue;
2413 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2414 bmap->ineq[last_neg] + 1,
2415 off + bmap->n_div))
2416 continue;
2417
2418 isl_int_add(bmap->ineq[last_pos][0],
2419 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2420 isl_int_add_ui(bmap->ineq[last_pos][0],
2421 bmap->ineq[last_pos][0], 1);
2422 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2423 bmap->ineq[last_pos][1+off+i]);
2424 isl_int_sub_ui(bmap->ineq[last_pos][0],
2425 bmap->ineq[last_pos][0], 1);
2426 isl_int_sub(bmap->ineq[last_pos][0],
2427 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2428 if (!redundant) {
2429 if (defined ||
2430 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2431 pairs[i] = 0;
2432 --n;
2433 continue;
2434 }
2435 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2436 bmap = isl_basic_map_simplify(bmap);
2437 free(pairs);
2438 return isl_basic_map_drop_redundant_divs(bmap);
2439 }
2440 if (last_pos > last_neg) {
2441 isl_basic_map_drop_inequality(bmap, last_pos);
2442 isl_basic_map_drop_inequality(bmap, last_neg);
2443 } else {
2444 isl_basic_map_drop_inequality(bmap, last_neg);
2445 isl_basic_map_drop_inequality(bmap, last_pos);
2446 }
2447 bmap = isl_basic_map_drop_div(bmap, i);
2448 free(pairs);
2449 return isl_basic_map_drop_redundant_divs(bmap);
2450 }
2451
2452 if (n > 0)
2453 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2454
2455 free(pairs);
2456 return bmap;
2457 error:
2458 free(pairs);
2459 isl_basic_map_free(bmap);
2460 return NULL;
2461 }
2462
2463 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2464 struct isl_basic_set *bset)
2465 {
2466 return (struct isl_basic_set *)
2467 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2468 }
2469
2470 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2471 {
2472 int i;
2473
2474 if (!map)
2475 return NULL;
2476 for (i = 0; i < map->n; ++i) {
2477 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2478 if (!map->p[i])
2479 goto error;
2480 }
2481 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2482 return map;
2483 error:
2484 isl_map_free(map);
2485 return NULL;
2486 }
2487
2488 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2489 {
2490 return (struct isl_set *)
2491 isl_map_drop_redundant_divs((struct isl_map *)set);
2492 }
Integer set library