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add isl_pw_*_plain_is_equal
[isl.git] / isl_map_simplify.c
blobdb025ebd3f03aded4e0eaa6b0d659930850daaa5
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 <strings.h>
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include "isl_equalities.h"
14 #include <isl/map.h>
15 #include <isl/seq.h>
16 #include "isl_tab.h"
17 #include <isl_space_private.h>
18 #include <isl_mat_private.h>
19
20 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
21 {
22 isl_int *t = bmap->eq[a];
23 bmap->eq[a] = bmap->eq[b];
24 bmap->eq[b] = t;
25 }
26
27 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
28 {
29 if (a != b) {
30 isl_int *t = bmap->ineq[a];
31 bmap->ineq[a] = bmap->ineq[b];
32 bmap->ineq[b] = t;
33 }
34 }
35
36 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
37 {
38 isl_seq_cpy(c, c + n, rem);
39 isl_seq_clr(c + rem, n);
40 }
41
42 /* Drop n dimensions starting at first.
43 *
44 * In principle, this frees up some extra variables as the number
45 * of columns remains constant, but we would have to extend
46 * the div array too as the number of rows in this array is assumed
47 * to be equal to extra.
48 */
49 struct isl_basic_set *isl_basic_set_drop_dims(
50 struct isl_basic_set *bset, unsigned first, unsigned n)
51 {
52 int i;
53
54 if (!bset)
55 goto error;
56
57 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
58
59 if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
60 return bset;
61
62 bset = isl_basic_set_cow(bset);
63 if (!bset)
64 return NULL;
65
66 for (i = 0; i < bset->n_eq; ++i)
67 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
68 (bset->dim->n_out-first-n)+bset->extra);
69
70 for (i = 0; i < bset->n_ineq; ++i)
71 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
72 (bset->dim->n_out-first-n)+bset->extra);
73
74 for (i = 0; i < bset->n_div; ++i)
75 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
76 (bset->dim->n_out-first-n)+bset->extra);
77
78 bset->dim = isl_space_drop_outputs(bset->dim, first, n);
79 if (!bset->dim)
80 goto error;
81
82 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
83 bset = isl_basic_set_simplify(bset);
84 return isl_basic_set_finalize(bset);
85 error:
86 isl_basic_set_free(bset);
87 return NULL;
88 }
89
90 struct isl_set *isl_set_drop_dims(
91 struct isl_set *set, unsigned first, unsigned n)
92 {
93 int i;
94
95 if (!set)
96 goto error;
97
98 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
99
100 if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
101 return set;
102 set = isl_set_cow(set);
103 if (!set)
104 goto error;
105 set->dim = isl_space_drop_outputs(set->dim, first, n);
106 if (!set->dim)
107 goto error;
108
109 for (i = 0; i < set->n; ++i) {
110 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
111 if (!set->p[i])
112 goto error;
113 }
114
115 ISL_F_CLR(set, ISL_SET_NORMALIZED);
116 return set;
117 error:
118 isl_set_free(set);
119 return NULL;
120 }
121
122 /* Move "n" divs starting at "first" to the end of the list of divs.
123 */
124 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
125 unsigned first, unsigned n)
126 {
127 isl_int **div;
128 int i;
129
130 if (first + n == bmap->n_div)
131 return bmap;
132
133 div = isl_alloc_array(bmap->ctx, isl_int *, n);
134 if (!div)
135 goto error;
136 for (i = 0; i < n; ++i)
137 div[i] = bmap->div[first + i];
138 for (i = 0; i < bmap->n_div - first - n; ++i)
139 bmap->div[first + i] = bmap->div[first + n + i];
140 for (i = 0; i < n; ++i)
141 bmap->div[bmap->n_div - n + i] = div[i];
142 free(div);
143 return bmap;
144 error:
145 isl_basic_map_free(bmap);
146 return NULL;
147 }
148
149 /* Drop "n" dimensions of type "type" starting at "first".
150 *
151 * In principle, this frees up some extra variables as the number
152 * of columns remains constant, but we would have to extend
153 * the div array too as the number of rows in this array is assumed
154 * to be equal to extra.
155 */
156 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
157 enum isl_dim_type type, unsigned first, unsigned n)
158 {
159 int i;
160 unsigned dim;
161 unsigned offset;
162 unsigned left;
163
164 if (!bmap)
165 goto error;
166
167 dim = isl_basic_map_dim(bmap, type);
168 isl_assert(bmap->ctx, first + n <= dim, goto error);
169
170 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
171 return bmap;
172
173 bmap = isl_basic_map_cow(bmap);
174 if (!bmap)
175 return NULL;
176
177 offset = isl_basic_map_offset(bmap, type) + first;
178 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
179 for (i = 0; i < bmap->n_eq; ++i)
180 constraint_drop_vars(bmap->eq[i]+offset, n, left);
181
182 for (i = 0; i < bmap->n_ineq; ++i)
183 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
184
185 for (i = 0; i < bmap->n_div; ++i)
186 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
187
188 if (type == isl_dim_div) {
189 bmap = move_divs_last(bmap, first, n);
190 if (!bmap)
191 goto error;
192 isl_basic_map_free_div(bmap, n);
193 } else
194 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
195 if (!bmap->dim)
196 goto error;
197
198 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
199 bmap = isl_basic_map_simplify(bmap);
200 return isl_basic_map_finalize(bmap);
201 error:
202 isl_basic_map_free(bmap);
203 return NULL;
204 }
205
206 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
207 enum isl_dim_type type, unsigned first, unsigned n)
208 {
209 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
210 type, first, n);
211 }
212
213 struct isl_basic_map *isl_basic_map_drop_inputs(
214 struct isl_basic_map *bmap, unsigned first, unsigned n)
215 {
216 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
217 }
218
219 struct isl_map *isl_map_drop(struct isl_map *map,
220 enum isl_dim_type type, unsigned first, unsigned n)
221 {
222 int i;
223
224 if (!map)
225 goto error;
226
227 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
228
229 if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
230 return map;
231 map = isl_map_cow(map);
232 if (!map)
233 goto error;
234 map->dim = isl_space_drop_dims(map->dim, type, first, n);
235 if (!map->dim)
236 goto error;
237
238 for (i = 0; i < map->n; ++i) {
239 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
240 if (!map->p[i])
241 goto error;
242 }
243 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
244
245 return map;
246 error:
247 isl_map_free(map);
248 return NULL;
249 }
250
251 struct isl_set *isl_set_drop(struct isl_set *set,
252 enum isl_dim_type type, unsigned first, unsigned n)
253 {
254 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
255 }
256
257 struct isl_map *isl_map_drop_inputs(
258 struct isl_map *map, unsigned first, unsigned n)
259 {
260 return isl_map_drop(map, isl_dim_in, first, n);
261 }
262
263 /*
264 * We don't cow, as the div is assumed to be redundant.
265 */
266 static struct isl_basic_map *isl_basic_map_drop_div(
267 struct isl_basic_map *bmap, unsigned div)
268 {
269 int i;
270 unsigned pos;
271
272 if (!bmap)
273 goto error;
274
275 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
276
277 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
278
279 for (i = 0; i < bmap->n_eq; ++i)
280 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
281
282 for (i = 0; i < bmap->n_ineq; ++i) {
283 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
284 isl_basic_map_drop_inequality(bmap, i);
285 --i;
286 continue;
287 }
288 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
289 }
290
291 for (i = 0; i < bmap->n_div; ++i)
292 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
293
294 if (div != bmap->n_div - 1) {
295 int j;
296 isl_int *t = bmap->div[div];
297
298 for (j = div; j < bmap->n_div - 1; ++j)
299 bmap->div[j] = bmap->div[j+1];
300
301 bmap->div[bmap->n_div - 1] = t;
302 }
303 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
304 isl_basic_map_free_div(bmap, 1);
305
306 return bmap;
307 error:
308 isl_basic_map_free(bmap);
309 return NULL;
310 }
311
312 struct isl_basic_map *isl_basic_map_normalize_constraints(
313 struct isl_basic_map *bmap)
314 {
315 int i;
316 isl_int gcd;
317 unsigned total = isl_basic_map_total_dim(bmap);
318
319 if (!bmap)
320 return NULL;
321
322 isl_int_init(gcd);
323 for (i = bmap->n_eq - 1; i >= 0; --i) {
324 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
325 if (isl_int_is_zero(gcd)) {
326 if (!isl_int_is_zero(bmap->eq[i][0])) {
327 bmap = isl_basic_map_set_to_empty(bmap);
328 break;
329 }
330 isl_basic_map_drop_equality(bmap, i);
331 continue;
332 }
333 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
334 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
335 if (isl_int_is_one(gcd))
336 continue;
337 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
338 bmap = isl_basic_map_set_to_empty(bmap);
339 break;
340 }
341 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
342 }
343
344 for (i = bmap->n_ineq - 1; i >= 0; --i) {
345 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
346 if (isl_int_is_zero(gcd)) {
347 if (isl_int_is_neg(bmap->ineq[i][0])) {
348 bmap = isl_basic_map_set_to_empty(bmap);
349 break;
350 }
351 isl_basic_map_drop_inequality(bmap, i);
352 continue;
353 }
354 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
355 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
356 if (isl_int_is_one(gcd))
357 continue;
358 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
359 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
360 }
361 isl_int_clear(gcd);
362
363 return bmap;
364 }
365
366 struct isl_basic_set *isl_basic_set_normalize_constraints(
367 struct isl_basic_set *bset)
368 {
369 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
370 (struct isl_basic_map *)bset);
371 }
372
373 /* Assumes divs have been ordered if keep_divs is set.
374 */
375 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
376 unsigned pos, isl_int *eq, int keep_divs, int *progress)
377 {
378 unsigned total;
379 unsigned space_total;
380 int k;
381 int last_div;
382
383 total = isl_basic_map_total_dim(bmap);
384 space_total = isl_space_dim(bmap->dim, isl_dim_all);
385 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
386 for (k = 0; k < bmap->n_eq; ++k) {
387 if (bmap->eq[k] == eq)
388 continue;
389 if (isl_int_is_zero(bmap->eq[k][1+pos]))
390 continue;
391 if (progress)
392 *progress = 1;
393 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
394 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
395 }
396
397 for (k = 0; k < bmap->n_ineq; ++k) {
398 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
399 continue;
400 if (progress)
401 *progress = 1;
402 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
403 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
404 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
405 }
406
407 for (k = 0; k < bmap->n_div; ++k) {
408 if (isl_int_is_zero(bmap->div[k][0]))
409 continue;
410 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
411 continue;
412 if (progress)
413 *progress = 1;
414 /* We need to be careful about circular definitions,
415 * so for now we just remove the definition of div k
416 * if the equality contains any divs.
417 * If keep_divs is set, then the divs have been ordered
418 * and we can keep the definition as long as the result
419 * is still ordered.
420 */
421 if (last_div == -1 || (keep_divs && last_div < k))
422 isl_seq_elim(bmap->div[k]+1, eq,
423 1+pos, 1+total, &bmap->div[k][0]);
424 else
425 isl_seq_clr(bmap->div[k], 1 + total);
426 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
427 }
428 }
429
430 /* Assumes divs have been ordered if keep_divs is set.
431 */
432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
433 unsigned div, int keep_divs)
434 {
435 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
436
437 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
438
439 isl_basic_map_drop_div(bmap, div);
440 }
441
442 /* Check if elimination of div "div" using equality "eq" would not
443 * result in a div depending on a later div.
444 */
445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
446 unsigned div)
447 {
448 int k;
449 int last_div;
450 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
451 unsigned pos = space_total + div;
452
453 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
454 if (last_div < 0 || last_div <= div)
455 return 1;
456
457 for (k = 0; k <= last_div; ++k) {
458 if (isl_int_is_zero(bmap->div[k][0]))
459 return 1;
460 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
461 return 0;
462 }
463
464 return 1;
465 }
466
467 /* Elimininate divs based on equalities
468 */
469 static struct isl_basic_map *eliminate_divs_eq(
470 struct isl_basic_map *bmap, int *progress)
471 {
472 int d;
473 int i;
474 int modified = 0;
475 unsigned off;
476
477 bmap = isl_basic_map_order_divs(bmap);
478
479 if (!bmap)
480 return NULL;
481
482 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
483
484 for (d = bmap->n_div - 1; d >= 0 ; --d) {
485 for (i = 0; i < bmap->n_eq; ++i) {
486 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
487 !isl_int_is_negone(bmap->eq[i][off + d]))
488 continue;
489 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
490 continue;
491 modified = 1;
492 *progress = 1;
493 eliminate_div(bmap, bmap->eq[i], d, 1);
494 isl_basic_map_drop_equality(bmap, i);
495 break;
496 }
497 }
498 if (modified)
499 return eliminate_divs_eq(bmap, progress);
500 return bmap;
501 }
502
503 /* Elimininate divs based on inequalities
504 */
505 static struct isl_basic_map *eliminate_divs_ineq(
506 struct isl_basic_map *bmap, int *progress)
507 {
508 int d;
509 int i;
510 unsigned off;
511 struct isl_ctx *ctx;
512
513 if (!bmap)
514 return NULL;
515
516 ctx = bmap->ctx;
517 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
518
519 for (d = bmap->n_div - 1; d >= 0 ; --d) {
520 for (i = 0; i < bmap->n_eq; ++i)
521 if (!isl_int_is_zero(bmap->eq[i][off + d]))
522 break;
523 if (i < bmap->n_eq)
524 continue;
525 for (i = 0; i < bmap->n_ineq; ++i)
526 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
527 break;
528 if (i < bmap->n_ineq)
529 continue;
530 *progress = 1;
531 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
532 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
533 break;
534 bmap = isl_basic_map_drop_div(bmap, d);
535 if (!bmap)
536 break;
537 }
538 return bmap;
539 }
540
541 struct isl_basic_map *isl_basic_map_gauss(
542 struct isl_basic_map *bmap, int *progress)
543 {
544 int k;
545 int done;
546 int last_var;
547 unsigned total_var;
548 unsigned total;
549
550 bmap = isl_basic_map_order_divs(bmap);
551
552 if (!bmap)
553 return NULL;
554
555 total = isl_basic_map_total_dim(bmap);
556 total_var = total - bmap->n_div;
557
558 last_var = total - 1;
559 for (done = 0; done < bmap->n_eq; ++done) {
560 for (; last_var >= 0; --last_var) {
561 for (k = done; k < bmap->n_eq; ++k)
562 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
563 break;
564 if (k < bmap->n_eq)
565 break;
566 }
567 if (last_var < 0)
568 break;
569 if (k != done)
570 swap_equality(bmap, k, done);
571 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
572 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
573
574 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
575 progress);
576
577 if (last_var >= total_var &&
578 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
579 unsigned div = last_var - total_var;
580 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
581 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
582 isl_int_set(bmap->div[div][0],
583 bmap->eq[done][1+last_var]);
584 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
585 }
586 }
587 if (done == bmap->n_eq)
588 return bmap;
589 for (k = done; k < bmap->n_eq; ++k) {
590 if (isl_int_is_zero(bmap->eq[k][0]))
591 continue;
592 return isl_basic_map_set_to_empty(bmap);
593 }
594 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
595 return bmap;
596 }
597
598 struct isl_basic_set *isl_basic_set_gauss(
599 struct isl_basic_set *bset, int *progress)
600 {
601 return (struct isl_basic_set*)isl_basic_map_gauss(
602 (struct isl_basic_map *)bset, progress);
603 }
604
605
606 static unsigned int round_up(unsigned int v)
607 {
608 int old_v = v;
609
610 while (v) {
611 old_v = v;
612 v ^= v & -v;
613 }
614 return old_v << 1;
615 }
616
617 static int hash_index(isl_int ***index, unsigned int size, int bits,
618 struct isl_basic_map *bmap, int k)
619 {
620 int h;
621 unsigned total = isl_basic_map_total_dim(bmap);
622 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
623 for (h = hash; index[h]; h = (h+1) % size)
624 if (&bmap->ineq[k] != index[h] &&
625 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
626 break;
627 return h;
628 }
629
630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
631 struct isl_basic_set *bset, int k)
632 {
633 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
634 }
635
636 /* If we can eliminate more than one div, then we need to make
637 * sure we do it from last div to first div, in order not to
638 * change the position of the other divs that still need to
639 * be removed.
640 */
641 static struct isl_basic_map *remove_duplicate_divs(
642 struct isl_basic_map *bmap, int *progress)
643 {
644 unsigned int size;
645 int *index;
646 int *elim_for;
647 int k, l, h;
648 int bits;
649 struct isl_blk eq;
650 unsigned total_var;
651 unsigned total;
652 struct isl_ctx *ctx;
653
654 if (!bmap || bmap->n_div <= 1)
655 return bmap;
656
657 total_var = isl_space_dim(bmap->dim, isl_dim_all);
658 total = total_var + bmap->n_div;
659
660 ctx = bmap->ctx;
661 for (k = bmap->n_div - 1; k >= 0; --k)
662 if (!isl_int_is_zero(bmap->div[k][0]))
663 break;
664 if (k <= 0)
665 return bmap;
666
667 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
668 size = round_up(4 * bmap->n_div / 3 - 1);
669 bits = ffs(size) - 1;
670 index = isl_calloc_array(ctx, int, size);
671 if (!index)
672 return bmap;
673 eq = isl_blk_alloc(ctx, 1+total);
674 if (isl_blk_is_error(eq))
675 goto out;
676
677 isl_seq_clr(eq.data, 1+total);
678 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
679 for (--k; k >= 0; --k) {
680 uint32_t hash;
681
682 if (isl_int_is_zero(bmap->div[k][0]))
683 continue;
684
685 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
686 for (h = hash; index[h]; h = (h+1) % size)
687 if (isl_seq_eq(bmap->div[k],
688 bmap->div[index[h]-1], 2+total))
689 break;
690 if (index[h]) {
691 *progress = 1;
692 l = index[h] - 1;
693 elim_for[l] = k + 1;
694 }
695 index[h] = k+1;
696 }
697 for (l = bmap->n_div - 1; l >= 0; --l) {
698 if (!elim_for[l])
699 continue;
700 k = elim_for[l] - 1;
701 isl_int_set_si(eq.data[1+total_var+k], -1);
702 isl_int_set_si(eq.data[1+total_var+l], 1);
703 eliminate_div(bmap, eq.data, l, 0);
704 isl_int_set_si(eq.data[1+total_var+k], 0);
705 isl_int_set_si(eq.data[1+total_var+l], 0);
706 }
707
708 isl_blk_free(ctx, eq);
709 out:
710 free(index);
711 free(elim_for);
712 return bmap;
713 }
714
715 static int n_pure_div_eq(struct isl_basic_map *bmap)
716 {
717 int i, j;
718 unsigned total;
719
720 total = isl_space_dim(bmap->dim, isl_dim_all);
721 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
722 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
723 --j;
724 if (j < 0)
725 break;
726 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
727 return 0;
728 }
729 return i;
730 }
731
732 /* Normalize divs that appear in equalities.
733 *
734 * In particular, we assume that bmap contains some equalities
735 * of the form
736 *
737 * a x = m * e_i
738 *
739 * and we want to replace the set of e_i by a minimal set and
740 * such that the new e_i have a canonical representation in terms
741 * of the vector x.
742 * If any of the equalities involves more than one divs, then
743 * we currently simply bail out.
744 *
745 * Let us first additionally assume that all equalities involve
746 * a div. The equalities then express modulo constraints on the
747 * remaining variables and we can use "parameter compression"
748 * to find a minimal set of constraints. The result is a transformation
749 *
750 * x = T(x') = x_0 + G x'
751 *
752 * with G a lower-triangular matrix with all elements below the diagonal
753 * non-negative and smaller than the diagonal element on the same row.
754 * We first normalize x_0 by making the same property hold in the affine
755 * T matrix.
756 * The rows i of G with a 1 on the diagonal do not impose any modulo
757 * constraint and simply express x_i = x'_i.
758 * For each of the remaining rows i, we introduce a div and a corresponding
759 * equality. In particular
760 *
761 * g_ii e_j = x_i - g_i(x')
762 *
763 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
764 * corresponding div (if g_kk != 1).
765 *
766 * If there are any equalities not involving any div, then we
767 * first apply a variable compression on the variables x:
768 *
769 * x = C x'' x'' = C_2 x
770 *
771 * and perform the above parameter compression on A C instead of on A.
772 * The resulting compression is then of the form
773 *
774 * x'' = T(x') = x_0 + G x'
775 *
776 * and in constructing the new divs and the corresponding equalities,
777 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
778 * by the corresponding row from C_2.
779 */
780 static struct isl_basic_map *normalize_divs(
781 struct isl_basic_map *bmap, int *progress)
782 {
783 int i, j, k;
784 int total;
785 int div_eq;
786 struct isl_mat *B;
787 struct isl_vec *d;
788 struct isl_mat *T = NULL;
789 struct isl_mat *C = NULL;
790 struct isl_mat *C2 = NULL;
791 isl_int v;
792 int *pos;
793 int dropped, needed;
794
795 if (!bmap)
796 return NULL;
797
798 if (bmap->n_div == 0)
799 return bmap;
800
801 if (bmap->n_eq == 0)
802 return bmap;
803
804 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
805 return bmap;
806
807 total = isl_space_dim(bmap->dim, isl_dim_all);
808 div_eq = n_pure_div_eq(bmap);
809 if (div_eq == 0)
810 return bmap;
811
812 if (div_eq < bmap->n_eq) {
813 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
814 bmap->n_eq - div_eq, 0, 1 + total);
815 C = isl_mat_variable_compression(B, &C2);
816 if (!C || !C2)
817 goto error;
818 if (C->n_col == 0) {
819 bmap = isl_basic_map_set_to_empty(bmap);
820 isl_mat_free(C);
821 isl_mat_free(C2);
822 goto done;
823 }
824 }
825
826 d = isl_vec_alloc(bmap->ctx, div_eq);
827 if (!d)
828 goto error;
829 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
831 --j;
832 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
833 }
834 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
835
836 if (C) {
837 B = isl_mat_product(B, C);
838 C = NULL;
839 }
840
841 T = isl_mat_parameter_compression(B, d);
842 if (!T)
843 goto error;
844 if (T->n_col == 0) {
845 bmap = isl_basic_map_set_to_empty(bmap);
846 isl_mat_free(C2);
847 isl_mat_free(T);
848 goto done;
849 }
850 isl_int_init(v);
851 for (i = 0; i < T->n_row - 1; ++i) {
852 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
853 if (isl_int_is_zero(v))
854 continue;
855 isl_mat_col_submul(T, 0, v, 1 + i);
856 }
857 isl_int_clear(v);
858 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
859 if (!pos)
860 goto error;
861 /* We have to be careful because dropping equalities may reorder them */
862 dropped = 0;
863 for (j = bmap->n_div - 1; j >= 0; --j) {
864 for (i = 0; i < bmap->n_eq; ++i)
865 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
866 break;
867 if (i < bmap->n_eq) {
868 bmap = isl_basic_map_drop_div(bmap, j);
869 isl_basic_map_drop_equality(bmap, i);
870 ++dropped;
871 }
872 }
873 pos[0] = 0;
874 needed = 0;
875 for (i = 1; i < T->n_row; ++i) {
876 if (isl_int_is_one(T->row[i][i]))
877 pos[i] = i;
878 else
879 needed++;
880 }
881 if (needed > dropped) {
882 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
883 needed, needed, 0);
884 if (!bmap)
885 goto error;
886 }
887 for (i = 1; i < T->n_row; ++i) {
888 if (isl_int_is_one(T->row[i][i]))
889 continue;
890 k = isl_basic_map_alloc_div(bmap);
891 pos[i] = 1 + total + k;
892 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
893 isl_int_set(bmap->div[k][0], T->row[i][i]);
894 if (C2)
895 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
896 else
897 isl_int_set_si(bmap->div[k][1 + i], 1);
898 for (j = 0; j < i; ++j) {
899 if (isl_int_is_zero(T->row[i][j]))
900 continue;
901 if (pos[j] < T->n_row && C2)
902 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
903 C2->row[pos[j]], 1 + total);
904 else
905 isl_int_neg(bmap->div[k][1 + pos[j]],
906 T->row[i][j]);
907 }
908 j = isl_basic_map_alloc_equality(bmap);
909 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
910 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
911 }
912 free(pos);
913 isl_mat_free(C2);
914 isl_mat_free(T);
915
916 if (progress)
917 *progress = 1;
918 done:
919 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
920
921 return bmap;
922 error:
923 isl_mat_free(C);
924 isl_mat_free(C2);
925 isl_mat_free(T);
926 return bmap;
927 }
928
929 static struct isl_basic_map *set_div_from_lower_bound(
930 struct isl_basic_map *bmap, int div, int ineq)
931 {
932 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
933
934 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
935 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
936 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
937 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
938 isl_int_set_si(bmap->div[div][1 + total + div], 0);
939
940 return bmap;
941 }
942
943 /* Check whether it is ok to define a div based on an inequality.
944 * To avoid the introduction of circular definitions of divs, we
945 * do not allow such a definition if the resulting expression would refer to
946 * any other undefined divs or if any known div is defined in
947 * terms of the unknown div.
948 */
949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
950 int div, int ineq)
951 {
952 int j;
953 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
954
955 /* Not defined in terms of unknown divs */
956 for (j = 0; j < bmap->n_div; ++j) {
957 if (div == j)
958 continue;
959 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
960 continue;
961 if (isl_int_is_zero(bmap->div[j][0]))
962 return 0;
963 }
964
965 /* No other div defined in terms of this one => avoid loops */
966 for (j = 0; j < bmap->n_div; ++j) {
967 if (div == j)
968 continue;
969 if (isl_int_is_zero(bmap->div[j][0]))
970 continue;
971 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
972 return 0;
973 }
974
975 return 1;
976 }
977
978 /* Given two constraints "k" and "l" that are opposite to each other,
979 * except for the constant term, check if we can use them
980 * to obtain an expression for one of the hitherto unknown divs.
981 * "sum" is the sum of the constant terms of the constraints.
982 * If this sum is strictly smaller than the coefficient of one
983 * of the divs, then this pair can be used define the div.
984 * To avoid the introduction of circular definitions of divs, we
985 * do not use the pair if the resulting expression would refer to
986 * any other undefined divs or if any known div is defined in
987 * terms of the unknown div.
988 */
989 static struct isl_basic_map *check_for_div_constraints(
990 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
991 {
992 int i;
993 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
994
995 for (i = 0; i < bmap->n_div; ++i) {
996 if (!isl_int_is_zero(bmap->div[i][0]))
997 continue;
998 if (isl_int_is_zero(bmap->ineq[k][total + i]))
999 continue;
1000 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1001 continue;
1002 if (!ok_to_set_div_from_bound(bmap, i, k))
1003 break;
1004 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005 bmap = set_div_from_lower_bound(bmap, i, k);
1006 else
1007 bmap = set_div_from_lower_bound(bmap, i, l);
1008 if (progress)
1009 *progress = 1;
1010 break;
1011 }
1012 return bmap;
1013 }
1014
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016 struct isl_basic_map *bmap, int *progress, int detect_divs)
1017 {
1018 unsigned int size;
1019 isl_int ***index;
1020 int k, l, h;
1021 int bits;
1022 unsigned total = isl_basic_map_total_dim(bmap);
1023 isl_int sum;
1024 isl_ctx *ctx;
1025
1026 if (!bmap || bmap->n_ineq <= 1)
1027 return bmap;
1028
1029 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1030 bits = ffs(size) - 1;
1031 ctx = isl_basic_map_get_ctx(bmap);
1032 index = isl_calloc_array(ctx, isl_int **, size);
1033 if (!index)
1034 return bmap;
1035
1036 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1037 for (k = 1; k < bmap->n_ineq; ++k) {
1038 h = hash_index(index, size, bits, bmap, k);
1039 if (!index[h]) {
1040 index[h] = &bmap->ineq[k];
1041 continue;
1042 }
1043 if (progress)
1044 *progress = 1;
1045 l = index[h] - &bmap->ineq[0];
1046 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1047 swap_inequality(bmap, k, l);
1048 isl_basic_map_drop_inequality(bmap, k);
1049 --k;
1050 }
1051 isl_int_init(sum);
1052 for (k = 0; k < bmap->n_ineq-1; ++k) {
1053 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054 h = hash_index(index, size, bits, bmap, k);
1055 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1056 if (!index[h])
1057 continue;
1058 l = index[h] - &bmap->ineq[0];
1059 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1060 if (isl_int_is_pos(sum)) {
1061 if (detect_divs)
1062 bmap = check_for_div_constraints(bmap, k, l,
1063 sum, progress);
1064 continue;
1065 }
1066 if (isl_int_is_zero(sum)) {
1067 /* We need to break out of the loop after these
1068 * changes since the contents of the hash
1069 * will no longer be valid.
1070 * Plus, we probably we want to regauss first.
1071 */
1072 if (progress)
1073 *progress = 1;
1074 isl_basic_map_drop_inequality(bmap, l);
1075 isl_basic_map_inequality_to_equality(bmap, k);
1076 } else
1077 bmap = isl_basic_map_set_to_empty(bmap);
1078 break;
1079 }
1080 isl_int_clear(sum);
1081
1082 free(index);
1083 return bmap;
1084 }
1085
1086
1087 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1088 {
1089 int progress = 1;
1090 if (!bmap)
1091 return NULL;
1092 while (progress) {
1093 progress = 0;
1094 bmap = isl_basic_map_normalize_constraints(bmap);
1095 bmap = remove_duplicate_divs(bmap, &progress);
1096 bmap = eliminate_divs_eq(bmap, &progress);
1097 bmap = eliminate_divs_ineq(bmap, &progress);
1098 bmap = isl_basic_map_gauss(bmap, &progress);
1099 /* requires equalities in normal form */
1100 bmap = normalize_divs(bmap, &progress);
1101 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1102 }
1103 return bmap;
1104 }
1105
1106 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1107 {
1108 return (struct isl_basic_set *)
1109 isl_basic_map_simplify((struct isl_basic_map *)bset);
1110 }
1111
1112
1113 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1114 isl_int *constraint, unsigned div)
1115 {
1116 unsigned pos;
1117
1118 if (!bmap)
1119 return -1;
1120
1121 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1122
1123 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1124 int neg;
1125 isl_int_sub(bmap->div[div][1],
1126 bmap->div[div][1], bmap->div[div][0]);
1127 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1128 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1129 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1130 isl_int_add(bmap->div[div][1],
1131 bmap->div[div][1], bmap->div[div][0]);
1132 if (!neg)
1133 return 0;
1134 if (isl_seq_first_non_zero(constraint+pos+1,
1135 bmap->n_div-div-1) != -1)
1136 return 0;
1137 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1138 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1139 return 0;
1140 if (isl_seq_first_non_zero(constraint+pos+1,
1141 bmap->n_div-div-1) != -1)
1142 return 0;
1143 } else
1144 return 0;
1145
1146 return 1;
1147 }
1148
1149
1150 /* If the only constraints a div d=floor(f/m)
1151 * appears in are its two defining constraints
1152 *
1153 * f - m d >=0
1154 * -(f - (m - 1)) + m d >= 0
1155 *
1156 * then it can safely be removed.
1157 */
1158 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1159 {
1160 int i;
1161 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1162
1163 for (i = 0; i < bmap->n_eq; ++i)
1164 if (!isl_int_is_zero(bmap->eq[i][pos]))
1165 return 0;
1166
1167 for (i = 0; i < bmap->n_ineq; ++i) {
1168 if (isl_int_is_zero(bmap->ineq[i][pos]))
1169 continue;
1170 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1171 return 0;
1172 }
1173
1174 for (i = 0; i < bmap->n_div; ++i)
1175 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1176 return 0;
1177
1178 return 1;
1179 }
1180
1181 /*
1182 * Remove divs that don't occur in any of the constraints or other divs.
1183 * These can arise when dropping some of the variables in a quast
1184 * returned by piplib.
1185 */
1186 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1187 {
1188 int i;
1189
1190 if (!bmap)
1191 return NULL;
1192
1193 for (i = bmap->n_div-1; i >= 0; --i) {
1194 if (!div_is_redundant(bmap, i))
1195 continue;
1196 bmap = isl_basic_map_drop_div(bmap, i);
1197 }
1198 return bmap;
1199 }
1200
1201 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1202 {
1203 bmap = remove_redundant_divs(bmap);
1204 if (!bmap)
1205 return NULL;
1206 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1207 return bmap;
1208 }
1209
1210 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1211 {
1212 return (struct isl_basic_set *)
1213 isl_basic_map_finalize((struct isl_basic_map *)bset);
1214 }
1215
1216 struct isl_set *isl_set_finalize(struct isl_set *set)
1217 {
1218 int i;
1219
1220 if (!set)
1221 return NULL;
1222 for (i = 0; i < set->n; ++i) {
1223 set->p[i] = isl_basic_set_finalize(set->p[i]);
1224 if (!set->p[i])
1225 goto error;
1226 }
1227 return set;
1228 error:
1229 isl_set_free(set);
1230 return NULL;
1231 }
1232
1233 struct isl_map *isl_map_finalize(struct isl_map *map)
1234 {
1235 int i;
1236
1237 if (!map)
1238 return NULL;
1239 for (i = 0; i < map->n; ++i) {
1240 map->p[i] = isl_basic_map_finalize(map->p[i]);
1241 if (!map->p[i])
1242 goto error;
1243 }
1244 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1245 return map;
1246 error:
1247 isl_map_free(map);
1248 return NULL;
1249 }
1250
1251
1252 /* Remove definition of any div that is defined in terms of the given variable.
1253 * The div itself is not removed. Functions such as
1254 * eliminate_divs_ineq depend on the other divs remaining in place.
1255 */
1256 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1257 int pos)
1258 {
1259 int i;
1260
1261 for (i = 0; i < bmap->n_div; ++i) {
1262 if (isl_int_is_zero(bmap->div[i][0]))
1263 continue;
1264 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1265 continue;
1266 isl_int_set_si(bmap->div[i][0], 0);
1267 }
1268 return bmap;
1269 }
1270
1271 /* Eliminate the specified variables from the constraints using
1272 * Fourier-Motzkin. The variables themselves are not removed.
1273 */
1274 struct isl_basic_map *isl_basic_map_eliminate_vars(
1275 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1276 {
1277 int d;
1278 int i, j, k;
1279 unsigned total;
1280
1281 if (n == 0)
1282 return bmap;
1283 if (!bmap)
1284 return NULL;
1285 total = isl_basic_map_total_dim(bmap);
1286
1287 bmap = isl_basic_map_cow(bmap);
1288 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1289 bmap = remove_dependent_vars(bmap, d);
1290
1291 for (d = pos + n - 1;
1292 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1293 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1294 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1295 int n_lower, n_upper;
1296 if (!bmap)
1297 return NULL;
1298 for (i = 0; i < bmap->n_eq; ++i) {
1299 if (isl_int_is_zero(bmap->eq[i][1+d]))
1300 continue;
1301 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1302 isl_basic_map_drop_equality(bmap, i);
1303 break;
1304 }
1305 if (i < bmap->n_eq)
1306 continue;
1307 n_lower = 0;
1308 n_upper = 0;
1309 for (i = 0; i < bmap->n_ineq; ++i) {
1310 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1311 n_lower++;
1312 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1313 n_upper++;
1314 }
1315 bmap = isl_basic_map_extend_constraints(bmap,
1316 0, n_lower * n_upper);
1317 if (!bmap)
1318 goto error;
1319 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1320 int last;
1321 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1322 continue;
1323 last = -1;
1324 for (j = 0; j < i; ++j) {
1325 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1326 continue;
1327 last = j;
1328 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1329 isl_int_sgn(bmap->ineq[j][1+d]))
1330 continue;
1331 k = isl_basic_map_alloc_inequality(bmap);
1332 if (k < 0)
1333 goto error;
1334 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1335 1+total);
1336 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1337 1+d, 1+total, NULL);
1338 }
1339 isl_basic_map_drop_inequality(bmap, i);
1340 i = last + 1;
1341 }
1342 if (n_lower > 0 && n_upper > 0) {
1343 bmap = isl_basic_map_normalize_constraints(bmap);
1344 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1345 bmap = isl_basic_map_gauss(bmap, NULL);
1346 bmap = isl_basic_map_remove_redundancies(bmap);
1347 if (!bmap)
1348 goto error;
1349 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1350 break;
1351 }
1352 }
1353 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1354 return bmap;
1355 error:
1356 isl_basic_map_free(bmap);
1357 return NULL;
1358 }
1359
1360 struct isl_basic_set *isl_basic_set_eliminate_vars(
1361 struct isl_basic_set *bset, unsigned pos, unsigned n)
1362 {
1363 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1364 (struct isl_basic_map *)bset, pos, n);
1365 }
1366
1367 /* Don't assume equalities are in order, because align_divs
1368 * may have changed the order of the divs.
1369 */
1370 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1371 {
1372 int d, i;
1373 unsigned total;
1374
1375 total = isl_space_dim(bmap->dim, isl_dim_all);
1376 for (d = 0; d < total; ++d)
1377 elim[d] = -1;
1378 for (i = 0; i < bmap->n_eq; ++i) {
1379 for (d = total - 1; d >= 0; --d) {
1380 if (isl_int_is_zero(bmap->eq[i][1+d]))
1381 continue;
1382 elim[d] = i;
1383 break;
1384 }
1385 }
1386 }
1387
1388 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1389 {
1390 compute_elimination_index((struct isl_basic_map *)bset, elim);
1391 }
1392
1393 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1394 struct isl_basic_map *bmap, int *elim)
1395 {
1396 int d;
1397 int copied = 0;
1398 unsigned total;
1399
1400 total = isl_space_dim(bmap->dim, isl_dim_all);
1401 for (d = total - 1; d >= 0; --d) {
1402 if (isl_int_is_zero(src[1+d]))
1403 continue;
1404 if (elim[d] == -1)
1405 continue;
1406 if (!copied) {
1407 isl_seq_cpy(dst, src, 1 + total);
1408 copied = 1;
1409 }
1410 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1411 }
1412 return copied;
1413 }
1414
1415 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1416 struct isl_basic_set *bset, int *elim)
1417 {
1418 return reduced_using_equalities(dst, src,
1419 (struct isl_basic_map *)bset, elim);
1420 }
1421
1422 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1423 struct isl_basic_set *bset, struct isl_basic_set *context)
1424 {
1425 int i;
1426 int *elim;
1427
1428 if (!bset || !context)
1429 goto error;
1430
1431 if (context->n_eq == 0) {
1432 isl_basic_set_free(context);
1433 return bset;
1434 }
1435
1436 bset = isl_basic_set_cow(bset);
1437 if (!bset)
1438 goto error;
1439
1440 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1441 if (!elim)
1442 goto error;
1443 set_compute_elimination_index(context, elim);
1444 for (i = 0; i < bset->n_eq; ++i)
1445 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1446 context, elim);
1447 for (i = 0; i < bset->n_ineq; ++i)
1448 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1449 context, elim);
1450 isl_basic_set_free(context);
1451 free(elim);
1452 bset = isl_basic_set_simplify(bset);
1453 bset = isl_basic_set_finalize(bset);
1454 return bset;
1455 error:
1456 isl_basic_set_free(bset);
1457 isl_basic_set_free(context);
1458 return NULL;
1459 }
1460
1461 static struct isl_basic_set *remove_shifted_constraints(
1462 struct isl_basic_set *bset, struct isl_basic_set *context)
1463 {
1464 unsigned int size;
1465 isl_int ***index;
1466 int bits;
1467 int k, h, l;
1468 isl_ctx *ctx;
1469
1470 if (!bset)
1471 return NULL;
1472
1473 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1474 bits = ffs(size) - 1;
1475 ctx = isl_basic_set_get_ctx(bset);
1476 index = isl_calloc_array(ctx, isl_int **, size);
1477 if (!index)
1478 return bset;
1479
1480 for (k = 0; k < context->n_ineq; ++k) {
1481 h = set_hash_index(index, size, bits, context, k);
1482 index[h] = &context->ineq[k];
1483 }
1484 for (k = 0; k < bset->n_ineq; ++k) {
1485 h = set_hash_index(index, size, bits, bset, k);
1486 if (!index[h])
1487 continue;
1488 l = index[h] - &context->ineq[0];
1489 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1490 continue;
1491 bset = isl_basic_set_cow(bset);
1492 if (!bset)
1493 goto error;
1494 isl_basic_set_drop_inequality(bset, k);
1495 --k;
1496 }
1497 free(index);
1498 return bset;
1499 error:
1500 free(index);
1501 return bset;
1502 }
1503
1504 /* Remove all information from bset that is redundant in the context
1505 * of context. Both bset and context are assumed to be full-dimensional.
1506 *
1507 * We first * remove the inequalities from "bset"
1508 * that are obviously redundant with respect to some inequality in "context".
1509 *
1510 * If there are any inequalities left, we construct a tableau for
1511 * the context and then add the inequalities of "bset".
1512 * Before adding these inequalities, we freeze all constraints such that
1513 * they won't be considered redundant in terms of the constraints of "bset".
1514 * Then we detect all redundant constraints (among the
1515 * constraints that weren't frozen), first by checking for redundancy in the
1516 * the tableau and then by checking if replacing a constraint by its negation
1517 * would lead to an empty set. This last step is fairly expensive
1518 * and could be optimized by more reuse of the tableau.
1519 * Finally, we update bset according to the results.
1520 */
1521 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1522 __isl_take isl_basic_set *context)
1523 {
1524 int i, k;
1525 isl_basic_set *combined = NULL;
1526 struct isl_tab *tab = NULL;
1527 unsigned context_ineq;
1528 unsigned total;
1529
1530 if (!bset || !context)
1531 goto error;
1532
1533 if (isl_basic_set_is_universe(bset)) {
1534 isl_basic_set_free(context);
1535 return bset;
1536 }
1537
1538 if (isl_basic_set_is_universe(context)) {
1539 isl_basic_set_free(context);
1540 return bset;
1541 }
1542
1543 bset = remove_shifted_constraints(bset, context);
1544 if (!bset)
1545 goto error;
1546 if (bset->n_ineq == 0)
1547 goto done;
1548
1549 context_ineq = context->n_ineq;
1550 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1551 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1552 tab = isl_tab_from_basic_set(combined);
1553 for (i = 0; i < context_ineq; ++i)
1554 if (isl_tab_freeze_constraint(tab, i) < 0)
1555 goto error;
1556 tab = isl_tab_extend(tab, bset->n_ineq);
1557 for (i = 0; i < bset->n_ineq; ++i)
1558 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1559 goto error;
1560 bset = isl_basic_set_add_constraints(combined, bset, 0);
1561 combined = NULL;
1562 if (!bset)
1563 goto error;
1564 if (isl_tab_detect_redundant(tab) < 0)
1565 goto error;
1566 total = isl_basic_set_total_dim(bset);
1567 for (i = context_ineq; i < bset->n_ineq; ++i) {
1568 int is_empty;
1569 if (tab->con[i].is_redundant)
1570 continue;
1571 tab->con[i].is_redundant = 1;
1572 combined = isl_basic_set_dup(bset);
1573 combined = isl_basic_set_update_from_tab(combined, tab);
1574 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1575 k = isl_basic_set_alloc_inequality(combined);
1576 if (k < 0)
1577 goto error;
1578 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1579 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1580 is_empty = isl_basic_set_is_empty(combined);
1581 if (is_empty < 0)
1582 goto error;
1583 isl_basic_set_free(combined);
1584 combined = NULL;
1585 if (!is_empty)
1586 tab->con[i].is_redundant = 0;
1587 }
1588 for (i = 0; i < context_ineq; ++i)
1589 tab->con[i].is_redundant = 1;
1590 bset = isl_basic_set_update_from_tab(bset, tab);
1591 if (bset) {
1592 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1593 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1594 }
1595
1596 isl_tab_free(tab);
1597 done:
1598 bset = isl_basic_set_simplify(bset);
1599 bset = isl_basic_set_finalize(bset);
1600 isl_basic_set_free(context);
1601 return bset;
1602 error:
1603 isl_tab_free(tab);
1604 isl_basic_set_free(combined);
1605 isl_basic_set_free(context);
1606 isl_basic_set_free(bset);
1607 return NULL;
1608 }
1609
1610 /* Remove all information from bset that is redundant in the context
1611 * of context. In particular, equalities that are linear combinations
1612 * of those in context are removed. Then the inequalities that are
1613 * redundant in the context of the equalities and inequalities of
1614 * context are removed.
1615 *
1616 * We first compute the integer affine hull of the intersection,
1617 * compute the gist inside this affine hull and then add back
1618 * those equalities that are not implied by the context.
1619 *
1620 * If two constraints are mutually redundant, then uset_gist_full
1621 * will remove the second of those constraints. We therefore first
1622 * sort the constraints so that constraints not involving existentially
1623 * quantified variables are given precedence over those that do.
1624 * We have to perform this sorting before the variable compression,
1625 * because that may effect the order of the variables.
1626 */
1627 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1628 __isl_take isl_basic_set *context)
1629 {
1630 isl_mat *eq;
1631 isl_mat *T, *T2;
1632 isl_basic_set *aff;
1633 isl_basic_set *aff_context;
1634 unsigned total;
1635
1636 if (!bset || !context)
1637 goto error;
1638
1639 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1640 if (isl_basic_set_plain_is_empty(bset)) {
1641 isl_basic_set_free(context);
1642 return bset;
1643 }
1644 bset = isl_basic_set_sort_constraints(bset);
1645 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1646 if (!aff)
1647 goto error;
1648 if (isl_basic_set_plain_is_empty(aff)) {
1649 isl_basic_set_free(aff);
1650 isl_basic_set_free(context);
1651 return bset;
1652 }
1653 if (aff->n_eq == 0) {
1654 isl_basic_set_free(aff);
1655 return uset_gist_full(bset, context);
1656 }
1657 total = isl_basic_set_total_dim(bset);
1658 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1659 eq = isl_mat_cow(eq);
1660 T = isl_mat_variable_compression(eq, &T2);
1661 if (T && T->n_col == 0) {
1662 isl_mat_free(T);
1663 isl_mat_free(T2);
1664 isl_basic_set_free(context);
1665 isl_basic_set_free(aff);
1666 return isl_basic_set_set_to_empty(bset);
1667 }
1668
1669 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1670
1671 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1672 context = isl_basic_set_preimage(context, T);
1673
1674 bset = uset_gist_full(bset, context);
1675 bset = isl_basic_set_preimage(bset, T2);
1676 bset = isl_basic_set_intersect(bset, aff);
1677 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1678
1679 if (bset) {
1680 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1681 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1682 }
1683
1684 return bset;
1685 error:
1686 isl_basic_set_free(bset);
1687 isl_basic_set_free(context);
1688 return NULL;
1689 }
1690
1691 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1692 * We simply add the equalities in context to bmap and then do a regular
1693 * div normalizations. Better results can be obtained by normalizing
1694 * only the divs in bmap than do not also appear in context.
1695 * We need to be careful to reduce the divs using the equalities
1696 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1697 * spurious constraints.
1698 */
1699 static struct isl_basic_map *normalize_divs_in_context(
1700 struct isl_basic_map *bmap, struct isl_basic_map *context)
1701 {
1702 int i;
1703 unsigned total_context;
1704 int div_eq;
1705
1706 div_eq = n_pure_div_eq(bmap);
1707 if (div_eq == 0)
1708 return bmap;
1709
1710 if (context->n_div > 0)
1711 bmap = isl_basic_map_align_divs(bmap, context);
1712
1713 total_context = isl_basic_map_total_dim(context);
1714 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1715 for (i = 0; i < context->n_eq; ++i) {
1716 int k;
1717 k = isl_basic_map_alloc_equality(bmap);
1718 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1719 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1720 isl_basic_map_total_dim(bmap) - total_context);
1721 }
1722 bmap = isl_basic_map_gauss(bmap, NULL);
1723 bmap = normalize_divs(bmap, NULL);
1724 bmap = isl_basic_map_gauss(bmap, NULL);
1725 return bmap;
1726 }
1727
1728 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1729 struct isl_basic_map *context)
1730 {
1731 struct isl_basic_set *bset;
1732
1733 if (!bmap || !context)
1734 goto error;
1735
1736 if (isl_basic_map_is_universe(bmap)) {
1737 isl_basic_map_free(context);
1738 return bmap;
1739 }
1740 if (isl_basic_map_plain_is_empty(context)) {
1741 isl_space *dim = isl_space_copy(bmap->dim);
1742 isl_basic_map_free(context);
1743 isl_basic_map_free(bmap);
1744 return isl_basic_map_universe(dim);
1745 }
1746 if (isl_basic_map_plain_is_empty(bmap)) {
1747 isl_basic_map_free(context);
1748 return bmap;
1749 }
1750
1751 bmap = isl_basic_map_remove_redundancies(bmap);
1752 context = isl_basic_map_remove_redundancies(context);
1753
1754 if (context->n_eq)
1755 bmap = normalize_divs_in_context(bmap, context);
1756
1757 context = isl_basic_map_align_divs(context, bmap);
1758 bmap = isl_basic_map_align_divs(bmap, context);
1759
1760 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1761 isl_basic_map_underlying_set(context));
1762
1763 return isl_basic_map_overlying_set(bset, bmap);
1764 error:
1765 isl_basic_map_free(bmap);
1766 isl_basic_map_free(context);
1767 return NULL;
1768 }
1769
1770 /*
1771 * Assumes context has no implicit divs.
1772 */
1773 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1774 __isl_take isl_basic_map *context)
1775 {
1776 int i;
1777
1778 if (!map || !context)
1779 goto error;;
1780
1781 if (isl_basic_map_plain_is_empty(context)) {
1782 isl_space *dim = isl_space_copy(map->dim);
1783 isl_basic_map_free(context);
1784 isl_map_free(map);
1785 return isl_map_universe(dim);
1786 }
1787
1788 context = isl_basic_map_remove_redundancies(context);
1789 map = isl_map_cow(map);
1790 if (!map || !context)
1791 goto error;;
1792 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1793 map = isl_map_compute_divs(map);
1794 for (i = 0; i < map->n; ++i)
1795 context = isl_basic_map_align_divs(context, map->p[i]);
1796 for (i = map->n - 1; i >= 0; --i) {
1797 map->p[i] = isl_basic_map_gist(map->p[i],
1798 isl_basic_map_copy(context));
1799 if (!map->p[i])
1800 goto error;
1801 if (isl_basic_map_plain_is_empty(map->p[i])) {
1802 isl_basic_map_free(map->p[i]);
1803 if (i != map->n - 1)
1804 map->p[i] = map->p[map->n - 1];
1805 map->n--;
1806 }
1807 }
1808 isl_basic_map_free(context);
1809 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1810 return map;
1811 error:
1812 isl_map_free(map);
1813 isl_basic_map_free(context);
1814 return NULL;
1815 }
1816
1817 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1818 __isl_take isl_map *context)
1819 {
1820 context = isl_map_compute_divs(context);
1821 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1822 }
1823
1824 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1825 __isl_take isl_map *context)
1826 {
1827 return isl_map_align_params_map_map_and(map, context, &map_gist);
1828 }
1829
1830 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1831 struct isl_basic_set *context)
1832 {
1833 return (struct isl_basic_set *)isl_basic_map_gist(
1834 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1835 }
1836
1837 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1838 __isl_take isl_basic_set *context)
1839 {
1840 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1841 (struct isl_basic_map *)context);
1842 }
1843
1844 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1845 __isl_take isl_set *context)
1846 {
1847 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1848 (struct isl_map *)context);
1849 }
1850
1851 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1852 __isl_take isl_set *context)
1853 {
1854 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1855 map_context = isl_map_intersect_params(map_context, context);
1856 return isl_map_gist(map, map_context);
1857 }
1858
1859 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1860 __isl_take isl_set *context)
1861 {
1862 return isl_map_gist_params(set, context);
1863 }
1864
1865 /* Quick check to see if two basic maps are disjoint.
1866 * In particular, we reduce the equalities and inequalities of
1867 * one basic map in the context of the equalities of the other
1868 * basic map and check if we get a contradiction.
1869 */
1870 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1871 __isl_keep isl_basic_map *bmap2)
1872 {
1873 struct isl_vec *v = NULL;
1874 int *elim = NULL;
1875 unsigned total;
1876 int i;
1877
1878 if (!bmap1 || !bmap2)
1879 return -1;
1880 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1881 return -1);
1882 if (bmap1->n_div || bmap2->n_div)
1883 return 0;
1884 if (!bmap1->n_eq && !bmap2->n_eq)
1885 return 0;
1886
1887 total = isl_space_dim(bmap1->dim, isl_dim_all);
1888 if (total == 0)
1889 return 0;
1890 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1891 if (!v)
1892 goto error;
1893 elim = isl_alloc_array(bmap1->ctx, int, total);
1894 if (!elim)
1895 goto error;
1896 compute_elimination_index(bmap1, elim);
1897 for (i = 0; i < bmap2->n_eq; ++i) {
1898 int reduced;
1899 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1900 bmap1, elim);
1901 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1902 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1903 goto disjoint;
1904 }
1905 for (i = 0; i < bmap2->n_ineq; ++i) {
1906 int reduced;
1907 reduced = reduced_using_equalities(v->block.data,
1908 bmap2->ineq[i], bmap1, elim);
1909 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1910 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1911 goto disjoint;
1912 }
1913 compute_elimination_index(bmap2, elim);
1914 for (i = 0; i < bmap1->n_ineq; ++i) {
1915 int reduced;
1916 reduced = reduced_using_equalities(v->block.data,
1917 bmap1->ineq[i], bmap2, elim);
1918 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1919 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1920 goto disjoint;
1921 }
1922 isl_vec_free(v);
1923 free(elim);
1924 return 0;
1925 disjoint:
1926 isl_vec_free(v);
1927 free(elim);
1928 return 1;
1929 error:
1930 isl_vec_free(v);
1931 free(elim);
1932 return -1;
1933 }
1934
1935 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1936 __isl_keep isl_basic_set *bset2)
1937 {
1938 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1939 (struct isl_basic_map *)bset2);
1940 }
1941
1942 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1943 __isl_keep isl_map *map2)
1944 {
1945 int i, j;
1946
1947 if (!map1 || !map2)
1948 return -1;
1949
1950 if (isl_map_plain_is_equal(map1, map2))
1951 return 0;
1952
1953 for (i = 0; i < map1->n; ++i) {
1954 for (j = 0; j < map2->n; ++j) {
1955 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1956 map2->p[j]);
1957 if (d != 1)
1958 return d;
1959 }
1960 }
1961 return 1;
1962 }
1963
1964 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1965 __isl_keep isl_set *set2)
1966 {
1967 return isl_map_plain_is_disjoint((struct isl_map *)set1,
1968 (struct isl_map *)set2);
1969 }
1970
1971 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
1972 {
1973 return isl_set_plain_is_disjoint(set1, set2);
1974 }
1975
1976 /* Check if we can combine a given div with lower bound l and upper
1977 * bound u with some other div and if so return that other div.
1978 * Otherwise return -1.
1979 *
1980 * We first check that
1981 * - the bounds are opposites of each other (except for the constant
1982 * term)
1983 * - the bounds do not reference any other div
1984 * - no div is defined in terms of this div
1985 *
1986 * Let m be the size of the range allowed on the div by the bounds.
1987 * That is, the bounds are of the form
1988 *
1989 * e <= a <= e + m - 1
1990 *
1991 * with e some expression in the other variables.
1992 * We look for another div b such that no third div is defined in terms
1993 * of this second div b and such that in any constraint that contains
1994 * a (except for the given lower and upper bound), also contains b
1995 * with a coefficient that is m times that of b.
1996 * That is, all constraints (execpt for the lower and upper bound)
1997 * are of the form
1998 *
1999 * e + f (a + m b) >= 0
2000 *
2001 * If so, we return b so that "a + m b" can be replaced by
2002 * a single div "c = a + m b".
2003 */
2004 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2005 unsigned div, unsigned l, unsigned u)
2006 {
2007 int i, j;
2008 unsigned dim;
2009 int coalesce = -1;
2010
2011 if (bmap->n_div <= 1)
2012 return -1;
2013 dim = isl_space_dim(bmap->dim, isl_dim_all);
2014 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2015 return -1;
2016 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2017 bmap->n_div - div - 1) != -1)
2018 return -1;
2019 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2020 dim + bmap->n_div))
2021 return -1;
2022
2023 for (i = 0; i < bmap->n_div; ++i) {
2024 if (isl_int_is_zero(bmap->div[i][0]))
2025 continue;
2026 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2027 return -1;
2028 }
2029
2030 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2031 if (isl_int_is_neg(bmap->ineq[l][0])) {
2032 isl_int_sub(bmap->ineq[l][0],
2033 bmap->ineq[l][0], bmap->ineq[u][0]);
2034 bmap = isl_basic_map_copy(bmap);
2035 bmap = isl_basic_map_set_to_empty(bmap);
2036 isl_basic_map_free(bmap);
2037 return -1;
2038 }
2039 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2040 for (i = 0; i < bmap->n_div; ++i) {
2041 if (i == div)
2042 continue;
2043 if (!pairs[i])
2044 continue;
2045 for (j = 0; j < bmap->n_div; ++j) {
2046 if (isl_int_is_zero(bmap->div[j][0]))
2047 continue;
2048 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2049 break;
2050 }
2051 if (j < bmap->n_div)
2052 continue;
2053 for (j = 0; j < bmap->n_ineq; ++j) {
2054 int valid;
2055 if (j == l || j == u)
2056 continue;
2057 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2058 continue;
2059 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2060 break;
2061 isl_int_mul(bmap->ineq[j][1 + dim + div],
2062 bmap->ineq[j][1 + dim + div],
2063 bmap->ineq[l][0]);
2064 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2065 bmap->ineq[j][1 + dim + i]);
2066 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2067 bmap->ineq[j][1 + dim + div],
2068 bmap->ineq[l][0]);
2069 if (!valid)
2070 break;
2071 }
2072 if (j < bmap->n_ineq)
2073 continue;
2074 coalesce = i;
2075 break;
2076 }
2077 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2078 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2079 return coalesce;
2080 }
2081
2082 /* Given a lower and an upper bound on div i, construct an inequality
2083 * that when nonnegative ensures that this pair of bounds always allows
2084 * for an integer value of the given div.
2085 * The lower bound is inequality l, while the upper bound is inequality u.
2086 * The constructed inequality is stored in ineq.
2087 * g, fl, fu are temporary scalars.
2088 *
2089 * Let the upper bound be
2090 *
2091 * -n_u a + e_u >= 0
2092 *
2093 * and the lower bound
2094 *
2095 * n_l a + e_l >= 0
2096 *
2097 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2098 * We have
2099 *
2100 * - f_u e_l <= f_u f_l g a <= f_l e_u
2101 *
2102 * Since all variables are integer valued, this is equivalent to
2103 *
2104 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2105 *
2106 * If this interval is at least f_u f_l g, then it contains at least
2107 * one integer value for a.
2108 * That is, the test constraint is
2109 *
2110 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2111 */
2112 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2113 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2114 {
2115 unsigned dim;
2116 dim = isl_space_dim(bmap->dim, isl_dim_all);
2117
2118 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2119 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2120 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2121 isl_int_neg(fu, fu);
2122 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2123 1 + dim + bmap->n_div);
2124 isl_int_add(ineq[0], ineq[0], fl);
2125 isl_int_add(ineq[0], ineq[0], fu);
2126 isl_int_sub_ui(ineq[0], ineq[0], 1);
2127 isl_int_mul(g, g, fl);
2128 isl_int_mul(g, g, fu);
2129 isl_int_sub(ineq[0], ineq[0], g);
2130 }
2131
2132 /* Remove more kinds of divs that are not strictly needed.
2133 * In particular, if all pairs of lower and upper bounds on a div
2134 * are such that they allow at least one integer value of the div,
2135 * the we can eliminate the div using Fourier-Motzkin without
2136 * introducing any spurious solutions.
2137 */
2138 static struct isl_basic_map *drop_more_redundant_divs(
2139 struct isl_basic_map *bmap, int *pairs, int n)
2140 {
2141 struct isl_tab *tab = NULL;
2142 struct isl_vec *vec = NULL;
2143 unsigned dim;
2144 int remove = -1;
2145 isl_int g, fl, fu;
2146
2147 isl_int_init(g);
2148 isl_int_init(fl);
2149 isl_int_init(fu);
2150
2151 if (!bmap)
2152 goto error;
2153
2154 dim = isl_space_dim(bmap->dim, isl_dim_all);
2155 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2156 if (!vec)
2157 goto error;
2158
2159 tab = isl_tab_from_basic_map(bmap);
2160
2161 while (n > 0) {
2162 int i, l, u;
2163 int best = -1;
2164 enum isl_lp_result res;
2165
2166 for (i = 0; i < bmap->n_div; ++i) {
2167 if (!pairs[i])
2168 continue;
2169 if (best >= 0 && pairs[best] <= pairs[i])
2170 continue;
2171 best = i;
2172 }
2173
2174 i = best;
2175 for (l = 0; l < bmap->n_ineq; ++l) {
2176 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2177 continue;
2178 for (u = 0; u < bmap->n_ineq; ++u) {
2179 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2180 continue;
2181 construct_test_ineq(bmap, i, l, u,
2182 vec->el, g, fl, fu);
2183 res = isl_tab_min(tab, vec->el,
2184 bmap->ctx->one, &g, NULL, 0);
2185 if (res == isl_lp_error)
2186 goto error;
2187 if (res == isl_lp_empty) {
2188 bmap = isl_basic_map_set_to_empty(bmap);
2189 break;
2190 }
2191 if (res != isl_lp_ok || isl_int_is_neg(g))
2192 break;
2193 }
2194 if (u < bmap->n_ineq)
2195 break;
2196 }
2197 if (l == bmap->n_ineq) {
2198 remove = i;
2199 break;
2200 }
2201 pairs[i] = 0;
2202 --n;
2203 }
2204
2205 isl_tab_free(tab);
2206 isl_vec_free(vec);
2207
2208 isl_int_clear(g);
2209 isl_int_clear(fl);
2210 isl_int_clear(fu);
2211
2212 free(pairs);
2213
2214 if (remove < 0)
2215 return bmap;
2216
2217 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2218 return isl_basic_map_drop_redundant_divs(bmap);
2219 error:
2220 free(pairs);
2221 isl_basic_map_free(bmap);
2222 isl_tab_free(tab);
2223 isl_vec_free(vec);
2224 isl_int_clear(g);
2225 isl_int_clear(fl);
2226 isl_int_clear(fu);
2227 return NULL;
2228 }
2229
2230 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2231 * and the upper bound u, div1 always occurs together with div2 in the form
2232 * (div1 + m div2), where m is the constant range on the variable div1
2233 * allowed by l and u, replace the pair div1 and div2 by a single
2234 * div that is equal to div1 + m div2.
2235 *
2236 * The new div will appear in the location that contains div2.
2237 * We need to modify all constraints that contain
2238 * div2 = (div - div1) / m
2239 * (If a constraint does not contain div2, it will also not contain div1.)
2240 * If the constraint also contains div1, then we know they appear
2241 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2242 * i.e., the coefficient of div is f.
2243 *
2244 * Otherwise, we first need to introduce div1 into the constraint.
2245 * Let the l be
2246 *
2247 * div1 + f >=0
2248 *
2249 * and u
2250 *
2251 * -div1 + f' >= 0
2252 *
2253 * A lower bound on div2
2254 *
2255 * n div2 + t >= 0
2256 *
2257 * can be replaced by
2258 *
2259 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2260 *
2261 * with g = gcd(m,n).
2262 * An upper bound
2263 *
2264 * -n div2 + t >= 0
2265 *
2266 * can be replaced by
2267 *
2268 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2269 *
2270 * These constraint are those that we would obtain from eliminating
2271 * div1 using Fourier-Motzkin.
2272 *
2273 * After all constraints have been modified, we drop the lower and upper
2274 * bound and then drop div1.
2275 */
2276 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2277 unsigned div1, unsigned div2, unsigned l, unsigned u)
2278 {
2279 isl_int a;
2280 isl_int b;
2281 isl_int m;
2282 unsigned dim, total;
2283 int i;
2284
2285 dim = isl_space_dim(bmap->dim, isl_dim_all);
2286 total = 1 + dim + bmap->n_div;
2287
2288 isl_int_init(a);
2289 isl_int_init(b);
2290 isl_int_init(m);
2291 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2292 isl_int_add_ui(m, m, 1);
2293
2294 for (i = 0; i < bmap->n_ineq; ++i) {
2295 if (i == l || i == u)
2296 continue;
2297 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2298 continue;
2299 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2300 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2301 isl_int_divexact(a, m, b);
2302 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2303 if (isl_int_is_pos(b)) {
2304 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2305 b, bmap->ineq[l], total);
2306 } else {
2307 isl_int_neg(b, b);
2308 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2309 b, bmap->ineq[u], total);
2310 }
2311 }
2312 isl_int_set(bmap->ineq[i][1 + dim + div2],
2313 bmap->ineq[i][1 + dim + div1]);
2314 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2315 }
2316
2317 isl_int_clear(a);
2318 isl_int_clear(b);
2319 isl_int_clear(m);
2320 if (l > u) {
2321 isl_basic_map_drop_inequality(bmap, l);
2322 isl_basic_map_drop_inequality(bmap, u);
2323 } else {
2324 isl_basic_map_drop_inequality(bmap, u);
2325 isl_basic_map_drop_inequality(bmap, l);
2326 }
2327 bmap = isl_basic_map_drop_div(bmap, div1);
2328 return bmap;
2329 }
2330
2331 /* First check if we can coalesce any pair of divs and
2332 * then continue with dropping more redundant divs.
2333 *
2334 * We loop over all pairs of lower and upper bounds on a div
2335 * with coefficient 1 and -1, respectively, check if there
2336 * is any other div "c" with which we can coalesce the div
2337 * and if so, perform the coalescing.
2338 */
2339 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2340 struct isl_basic_map *bmap, int *pairs, int n)
2341 {
2342 int i, l, u;
2343 unsigned dim;
2344
2345 dim = isl_space_dim(bmap->dim, isl_dim_all);
2346
2347 for (i = 0; i < bmap->n_div; ++i) {
2348 if (!pairs[i])
2349 continue;
2350 for (l = 0; l < bmap->n_ineq; ++l) {
2351 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2352 continue;
2353 for (u = 0; u < bmap->n_ineq; ++u) {
2354 int c;
2355
2356 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2357 continue;
2358 c = div_find_coalesce(bmap, pairs, i, l, u);
2359 if (c < 0)
2360 continue;
2361 free(pairs);
2362 bmap = coalesce_divs(bmap, i, c, l, u);
2363 return isl_basic_map_drop_redundant_divs(bmap);
2364 }
2365 }
2366 }
2367
2368 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2369 return bmap;
2370
2371 return drop_more_redundant_divs(bmap, pairs, n);
2372 }
2373
2374 /* Remove divs that are not strictly needed.
2375 * In particular, if a div only occurs positively (or negatively)
2376 * in constraints, then it can simply be dropped.
2377 * Also, if a div occurs only occurs in two constraints and if moreover
2378 * those two constraints are opposite to each other, except for the constant
2379 * term and if the sum of the constant terms is such that for any value
2380 * of the other values, there is always at least one integer value of the
2381 * div, i.e., if one plus this sum is greater than or equal to
2382 * the (absolute value) of the coefficent of the div in the constraints,
2383 * then we can also simply drop the div.
2384 *
2385 * If any divs are left after these simple checks then we move on
2386 * to more complicated cases in drop_more_redundant_divs.
2387 */
2388 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2389 struct isl_basic_map *bmap)
2390 {
2391 int i, j;
2392 unsigned off;
2393 int *pairs = NULL;
2394 int n = 0;
2395
2396 if (!bmap)
2397 goto error;
2398
2399 off = isl_space_dim(bmap->dim, isl_dim_all);
2400 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2401 if (!pairs)
2402 goto error;
2403
2404 for (i = 0; i < bmap->n_div; ++i) {
2405 int pos, neg;
2406 int last_pos, last_neg;
2407 int redundant;
2408 int defined;
2409
2410 defined = !isl_int_is_zero(bmap->div[i][0]);
2411 for (j = 0; j < bmap->n_eq; ++j)
2412 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2413 break;
2414 if (j < bmap->n_eq)
2415 continue;
2416 ++n;
2417 pos = neg = 0;
2418 for (j = 0; j < bmap->n_ineq; ++j) {
2419 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2420 last_pos = j;
2421 ++pos;
2422 }
2423 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2424 last_neg = j;
2425 ++neg;
2426 }
2427 }
2428 pairs[i] = pos * neg;
2429 if (pairs[i] == 0) {
2430 for (j = bmap->n_ineq - 1; j >= 0; --j)
2431 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2432 isl_basic_map_drop_inequality(bmap, j);
2433 bmap = isl_basic_map_drop_div(bmap, i);
2434 free(pairs);
2435 return isl_basic_map_drop_redundant_divs(bmap);
2436 }
2437 if (pairs[i] != 1)
2438 continue;
2439 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2440 bmap->ineq[last_neg] + 1,
2441 off + bmap->n_div))
2442 continue;
2443
2444 isl_int_add(bmap->ineq[last_pos][0],
2445 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2446 isl_int_add_ui(bmap->ineq[last_pos][0],
2447 bmap->ineq[last_pos][0], 1);
2448 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2449 bmap->ineq[last_pos][1+off+i]);
2450 isl_int_sub_ui(bmap->ineq[last_pos][0],
2451 bmap->ineq[last_pos][0], 1);
2452 isl_int_sub(bmap->ineq[last_pos][0],
2453 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2454 if (!redundant) {
2455 if (defined ||
2456 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2457 pairs[i] = 0;
2458 --n;
2459 continue;
2460 }
2461 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2462 bmap = isl_basic_map_simplify(bmap);
2463 free(pairs);
2464 return isl_basic_map_drop_redundant_divs(bmap);
2465 }
2466 if (last_pos > last_neg) {
2467 isl_basic_map_drop_inequality(bmap, last_pos);
2468 isl_basic_map_drop_inequality(bmap, last_neg);
2469 } else {
2470 isl_basic_map_drop_inequality(bmap, last_neg);
2471 isl_basic_map_drop_inequality(bmap, last_pos);
2472 }
2473 bmap = isl_basic_map_drop_div(bmap, i);
2474 free(pairs);
2475 return isl_basic_map_drop_redundant_divs(bmap);
2476 }
2477
2478 if (n > 0)
2479 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2480
2481 free(pairs);
2482 return bmap;
2483 error:
2484 free(pairs);
2485 isl_basic_map_free(bmap);
2486 return NULL;
2487 }
2488
2489 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2490 struct isl_basic_set *bset)
2491 {
2492 return (struct isl_basic_set *)
2493 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2494 }
2495
2496 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2497 {
2498 int i;
2499
2500 if (!map)
2501 return NULL;
2502 for (i = 0; i < map->n; ++i) {
2503 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2504 if (!map->p[i])
2505 goto error;
2506 }
2507 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2508 return map;
2509 error:
2510 isl_map_free(map);
2511 return NULL;
2512 }
2513
2514 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2515 {
2516 return (struct isl_set *)
2517 isl_map_drop_redundant_divs((struct isl_map *)set);
2518 }
Integer set library