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isl_map_subtract.c: tab_add_constraints: avoid NULL pointer dereference
[isl.git] / isl_map_simplify.c
blob18daf9429690fcdd9bb302a9b6a1df7d74b8533e
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_equalities.h"
11 #include "isl_map.h"
12 #include "isl_map_private.h"
13 #include "isl_seq.h"
14 #include "isl_tab.h"
15
16 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
17 {
18 isl_int *t = bmap->eq[a];
19 bmap->eq[a] = bmap->eq[b];
20 bmap->eq[b] = t;
21 }
22
23 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
24 {
25 if (a != b) {
26 isl_int *t = bmap->ineq[a];
27 bmap->ineq[a] = bmap->ineq[b];
28 bmap->ineq[b] = t;
29 }
30 }
31
32 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
33 {
34 swap_inequality((struct isl_basic_map *)bset, a, b);
35 }
36
37 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
38 {
39 isl_seq_cpy(c, c + n, rem);
40 isl_seq_clr(c + rem, n);
41 }
42
43 /* Drop n dimensions starting at first.
44 *
45 * In principle, this frees up some extra variables as the number
46 * of columns remains constant, but we would have to extend
47 * the div array too as the number of rows in this array is assumed
48 * to be equal to extra.
49 */
50 struct isl_basic_set *isl_basic_set_drop_dims(
51 struct isl_basic_set *bset, unsigned first, unsigned n)
52 {
53 int i;
54
55 if (!bset)
56 goto error;
57
58 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
59
60 if (n == 0)
61 return bset;
62
63 bset = isl_basic_set_cow(bset);
64 if (!bset)
65 return NULL;
66
67 for (i = 0; i < bset->n_eq; ++i)
68 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
69 (bset->dim->n_out-first-n)+bset->extra);
70
71 for (i = 0; i < bset->n_ineq; ++i)
72 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
73 (bset->dim->n_out-first-n)+bset->extra);
74
75 for (i = 0; i < bset->n_div; ++i)
76 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
77 (bset->dim->n_out-first-n)+bset->extra);
78
79 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
80 if (!bset->dim)
81 goto error;
82
83 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
84 bset = isl_basic_set_simplify(bset);
85 return isl_basic_set_finalize(bset);
86 error:
87 isl_basic_set_free(bset);
88 return NULL;
89 }
90
91 struct isl_set *isl_set_drop_dims(
92 struct isl_set *set, unsigned first, unsigned n)
93 {
94 int i;
95
96 if (!set)
97 goto error;
98
99 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
100
101 if (n == 0)
102 return set;
103 set = isl_set_cow(set);
104 if (!set)
105 goto error;
106 set->dim = isl_dim_drop_outputs(set->dim, first, n);
107 if (!set->dim)
108 goto error;
109
110 for (i = 0; i < set->n; ++i) {
111 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
112 if (!set->p[i])
113 goto error;
114 }
115
116 ISL_F_CLR(set, ISL_SET_NORMALIZED);
117 return set;
118 error:
119 isl_set_free(set);
120 return NULL;
121 }
122
123 /* Move "n" divs starting at "first" to the end of the list of divs.
124 */
125 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
126 unsigned first, unsigned n)
127 {
128 isl_int **div;
129 int i;
130
131 if (first + n == bmap->n_div)
132 return bmap;
133
134 div = isl_alloc_array(bmap->ctx, isl_int *, n);
135 if (!div)
136 goto error;
137 for (i = 0; i < n; ++i)
138 div[i] = bmap->div[first + i];
139 for (i = 0; i < bmap->n_div - first - n; ++i)
140 bmap->div[first + i] = bmap->div[first + n + i];
141 for (i = 0; i < n; ++i)
142 bmap->div[bmap->n_div - n + i] = div[i];
143 free(div);
144 return bmap;
145 error:
146 isl_basic_map_free(bmap);
147 return NULL;
148 }
149
150 /* Drop "n" dimensions of type "type" starting at "first".
151 *
152 * In principle, this frees up some extra variables as the number
153 * of columns remains constant, but we would have to extend
154 * the div array too as the number of rows in this array is assumed
155 * to be equal to extra.
156 */
157 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
158 enum isl_dim_type type, unsigned first, unsigned n)
159 {
160 int i;
161 unsigned dim;
162 unsigned offset;
163 unsigned left;
164
165 if (!bmap)
166 goto error;
167
168 dim = isl_basic_map_dim(bmap, type);
169 isl_assert(bmap->ctx, first + n <= dim, goto error);
170
171 if (n == 0)
172 return bmap;
173
174 bmap = isl_basic_map_cow(bmap);
175 if (!bmap)
176 return NULL;
177
178 offset = isl_basic_map_offset(bmap, type) + first;
179 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
180 for (i = 0; i < bmap->n_eq; ++i)
181 constraint_drop_vars(bmap->eq[i]+offset, n, left);
182
183 for (i = 0; i < bmap->n_ineq; ++i)
184 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
185
186 for (i = 0; i < bmap->n_div; ++i)
187 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
188
189 if (type == isl_dim_div) {
190 bmap = move_divs_last(bmap, first, n);
191 if (!bmap)
192 goto error;
193 isl_basic_map_free_div(bmap, n);
194 } else
195 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
196 if (!bmap->dim)
197 goto error;
198
199 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
200 bmap = isl_basic_map_simplify(bmap);
201 return isl_basic_map_finalize(bmap);
202 error:
203 isl_basic_map_free(bmap);
204 return NULL;
205 }
206
207 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
208 enum isl_dim_type type, unsigned first, unsigned n)
209 {
210 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
211 type, first, n);
212 }
213
214 struct isl_basic_map *isl_basic_map_drop_inputs(
215 struct isl_basic_map *bmap, unsigned first, unsigned n)
216 {
217 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
218 }
219
220 struct isl_map *isl_map_drop(struct isl_map *map,
221 enum isl_dim_type type, unsigned first, unsigned n)
222 {
223 int i;
224
225 if (!map)
226 goto error;
227
228 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
229
230 if (n == 0)
231 return map;
232 map = isl_map_cow(map);
233 if (!map)
234 goto error;
235 map->dim = isl_dim_drop(map->dim, type, first, n);
236 if (!map->dim)
237 goto error;
238
239 for (i = 0; i < map->n; ++i) {
240 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
241 if (!map->p[i])
242 goto error;
243 }
244 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
245
246 return map;
247 error:
248 isl_map_free(map);
249 return NULL;
250 }
251
252 struct isl_set *isl_set_drop(struct isl_set *set,
253 enum isl_dim_type type, unsigned first, unsigned n)
254 {
255 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
256 }
257
258 struct isl_map *isl_map_drop_inputs(
259 struct isl_map *map, unsigned first, unsigned n)
260 {
261 return isl_map_drop(map, isl_dim_in, first, n);
262 }
263
264 /*
265 * We don't cow, as the div is assumed to be redundant.
266 */
267 static struct isl_basic_map *isl_basic_map_drop_div(
268 struct isl_basic_map *bmap, unsigned div)
269 {
270 int i;
271 unsigned pos;
272
273 if (!bmap)
274 goto error;
275
276 pos = 1 + isl_dim_total(bmap->dim) + div;
277
278 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
279
280 for (i = 0; i < bmap->n_eq; ++i)
281 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
282
283 for (i = 0; i < bmap->n_ineq; ++i) {
284 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
285 isl_basic_map_drop_inequality(bmap, i);
286 --i;
287 continue;
288 }
289 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
290 }
291
292 for (i = 0; i < bmap->n_div; ++i)
293 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
294
295 if (div != bmap->n_div - 1) {
296 int j;
297 isl_int *t = bmap->div[div];
298
299 for (j = div; j < bmap->n_div - 1; ++j)
300 bmap->div[j] = bmap->div[j+1];
301
302 bmap->div[bmap->n_div - 1] = t;
303 }
304 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
305 isl_basic_map_free_div(bmap, 1);
306
307 return bmap;
308 error:
309 isl_basic_map_free(bmap);
310 return NULL;
311 }
312
313 struct isl_basic_map *isl_basic_map_normalize_constraints(
314 struct isl_basic_map *bmap)
315 {
316 int i;
317 isl_int gcd;
318 unsigned total = isl_basic_map_total_dim(bmap);
319
320 if (!bmap)
321 return NULL;
322
323 isl_int_init(gcd);
324 for (i = bmap->n_eq - 1; i >= 0; --i) {
325 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
326 if (isl_int_is_zero(gcd)) {
327 if (!isl_int_is_zero(bmap->eq[i][0])) {
328 bmap = isl_basic_map_set_to_empty(bmap);
329 break;
330 }
331 isl_basic_map_drop_equality(bmap, i);
332 continue;
333 }
334 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
335 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
336 if (isl_int_is_one(gcd))
337 continue;
338 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
339 bmap = isl_basic_map_set_to_empty(bmap);
340 break;
341 }
342 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
343 }
344
345 for (i = bmap->n_ineq - 1; i >= 0; --i) {
346 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
347 if (isl_int_is_zero(gcd)) {
348 if (isl_int_is_neg(bmap->ineq[i][0])) {
349 bmap = isl_basic_map_set_to_empty(bmap);
350 break;
351 }
352 isl_basic_map_drop_inequality(bmap, i);
353 continue;
354 }
355 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
356 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
357 if (isl_int_is_one(gcd))
358 continue;
359 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
360 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
361 }
362 isl_int_clear(gcd);
363
364 return bmap;
365 }
366
367 struct isl_basic_set *isl_basic_set_normalize_constraints(
368 struct isl_basic_set *bset)
369 {
370 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
371 (struct isl_basic_map *)bset);
372 }
373
374 /* Assumes divs have been ordered if keep_divs is set.
375 */
376 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
377 unsigned pos, isl_int *eq, int keep_divs, int *progress)
378 {
379 unsigned total;
380 int k;
381 int last_div;
382
383 total = isl_basic_map_total_dim(bmap);
384 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
385 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 }
395
396 for (k = 0; k < bmap->n_ineq; ++k) {
397 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
398 continue;
399 if (progress)
400 *progress = 1;
401 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
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_alloc(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_alloc(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 /* We have to be careful because dropping equalities may reorder them */
858 dropped = 0;
859 for (j = bmap->n_div - 1; j >= 0; --j) {
860 for (i = 0; i < bmap->n_eq; ++i)
861 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
862 break;
863 if (i < bmap->n_eq) {
864 bmap = isl_basic_map_drop_div(bmap, j);
865 isl_basic_map_drop_equality(bmap, i);
866 ++dropped;
867 }
868 }
869 pos[0] = 0;
870 needed = 0;
871 for (i = 1; i < T->n_row; ++i) {
872 if (isl_int_is_one(T->row[i][i]))
873 pos[i] = i;
874 else
875 needed++;
876 }
877 if (needed > dropped) {
878 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
879 needed, needed, 0);
880 if (!bmap)
881 goto error;
882 }
883 for (i = 1; i < T->n_row; ++i) {
884 if (isl_int_is_one(T->row[i][i]))
885 continue;
886 k = isl_basic_map_alloc_div(bmap);
887 pos[i] = 1 + total + k;
888 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
889 isl_int_set(bmap->div[k][0], T->row[i][i]);
890 if (C2)
891 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
892 else
893 isl_int_set_si(bmap->div[k][1 + i], 1);
894 for (j = 0; j < i; ++j) {
895 if (isl_int_is_zero(T->row[i][j]))
896 continue;
897 if (pos[j] < T->n_row && C2)
898 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
899 C2->row[pos[j]], 1 + total);
900 else
901 isl_int_neg(bmap->div[k][1 + pos[j]],
902 T->row[i][j]);
903 }
904 j = isl_basic_map_alloc_equality(bmap);
905 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
906 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
907 }
908 free(pos);
909 isl_mat_free(C2);
910 isl_mat_free(T);
911
912 if (progress)
913 *progress = 1;
914 done:
915 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
916
917 return bmap;
918 error:
919 isl_mat_free(C);
920 isl_mat_free(C2);
921 isl_mat_free(T);
922 return bmap;
923 }
924
925 static struct isl_basic_map *set_div_from_lower_bound(
926 struct isl_basic_map *bmap, int div, int ineq)
927 {
928 unsigned total = 1 + isl_dim_total(bmap->dim);
929
930 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
931 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
932 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
933 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
934 isl_int_set_si(bmap->div[div][1 + total + div], 0);
935
936 return bmap;
937 }
938
939 /* Check whether it is ok to define a div based on an inequality.
940 * To avoid the introduction of circular definitions of divs, we
941 * do not allow such a definition if the resulting expression would refer to
942 * any other undefined divs or if any known div is defined in
943 * terms of the unknown div.
944 */
945 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
946 int div, int ineq)
947 {
948 int j;
949 unsigned total = 1 + isl_dim_total(bmap->dim);
950
951 /* Not defined in terms of unknown divs */
952 for (j = 0; j < bmap->n_div; ++j) {
953 if (div == j)
954 continue;
955 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
956 continue;
957 if (isl_int_is_zero(bmap->div[j][0]))
958 return 0;
959 }
960
961 /* No other div defined in terms of this one => avoid loops */
962 for (j = 0; j < bmap->n_div; ++j) {
963 if (div == j)
964 continue;
965 if (isl_int_is_zero(bmap->div[j][0]))
966 continue;
967 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
968 return 0;
969 }
970
971 return 1;
972 }
973
974 /* Given two constraints "k" and "l" that are opposite to each other,
975 * except for the constant term, check if we can use them
976 * to obtain an expression for one of the hitherto unknown divs.
977 * "sum" is the sum of the constant terms of the constraints.
978 * If this sum is strictly smaller than the coefficient of one
979 * of the divs, then this pair can be used define the div.
980 * To avoid the introduction of circular definitions of divs, we
981 * do not use the pair if the resulting expression would refer to
982 * any other undefined divs or if any known div is defined in
983 * terms of the unknown div.
984 */
985 static struct isl_basic_map *check_for_div_constraints(
986 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
987 {
988 int i;
989 unsigned total = 1 + isl_dim_total(bmap->dim);
990
991 for (i = 0; i < bmap->n_div; ++i) {
992 if (!isl_int_is_zero(bmap->div[i][0]))
993 continue;
994 if (isl_int_is_zero(bmap->ineq[k][total + i]))
995 continue;
996 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
997 continue;
998 if (!ok_to_set_div_from_bound(bmap, i, k))
999 break;
1000 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1001 bmap = set_div_from_lower_bound(bmap, i, k);
1002 else
1003 bmap = set_div_from_lower_bound(bmap, i, l);
1004 if (progress)
1005 *progress = 1;
1006 break;
1007 }
1008 return bmap;
1009 }
1010
1011 static struct isl_basic_map *remove_duplicate_constraints(
1012 struct isl_basic_map *bmap, int *progress)
1013 {
1014 unsigned int size;
1015 isl_int ***index;
1016 int k, l, h;
1017 int bits;
1018 unsigned total = isl_basic_map_total_dim(bmap);
1019 isl_int sum;
1020
1021 if (!bmap || bmap->n_ineq <= 1)
1022 return bmap;
1023
1024 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1025 bits = ffs(size) - 1;
1026 index = isl_calloc_array(ctx, isl_int **, size);
1027 if (!index)
1028 return bmap;
1029
1030 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1031 for (k = 1; k < bmap->n_ineq; ++k) {
1032 h = hash_index(index, size, bits, bmap, k);
1033 if (!index[h]) {
1034 index[h] = &bmap->ineq[k];
1035 continue;
1036 }
1037 if (progress)
1038 *progress = 1;
1039 l = index[h] - &bmap->ineq[0];
1040 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1041 swap_inequality(bmap, k, l);
1042 isl_basic_map_drop_inequality(bmap, k);
1043 --k;
1044 }
1045 isl_int_init(sum);
1046 for (k = 0; k < bmap->n_ineq-1; ++k) {
1047 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1048 h = hash_index(index, size, bits, bmap, k);
1049 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1050 if (!index[h])
1051 continue;
1052 l = index[h] - &bmap->ineq[0];
1053 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1054 if (isl_int_is_pos(sum)) {
1055 bmap = check_for_div_constraints(bmap, k, l, sum,
1056 progress);
1057 continue;
1058 }
1059 if (isl_int_is_zero(sum)) {
1060 /* We need to break out of the loop after these
1061 * changes since the contents of the hash
1062 * will no longer be valid.
1063 * Plus, we probably we want to regauss first.
1064 */
1065 if (progress)
1066 *progress = 1;
1067 isl_basic_map_drop_inequality(bmap, l);
1068 isl_basic_map_inequality_to_equality(bmap, k);
1069 } else
1070 bmap = isl_basic_map_set_to_empty(bmap);
1071 break;
1072 }
1073 isl_int_clear(sum);
1074
1075 free(index);
1076 return bmap;
1077 }
1078
1079
1080 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1081 {
1082 int progress = 1;
1083 if (!bmap)
1084 return NULL;
1085 while (progress) {
1086 progress = 0;
1087 bmap = isl_basic_map_normalize_constraints(bmap);
1088 bmap = remove_duplicate_divs(bmap, &progress);
1089 bmap = eliminate_divs_eq(bmap, &progress);
1090 bmap = eliminate_divs_ineq(bmap, &progress);
1091 bmap = isl_basic_map_gauss(bmap, &progress);
1092 /* requires equalities in normal form */
1093 bmap = normalize_divs(bmap, &progress);
1094 bmap = remove_duplicate_constraints(bmap, &progress);
1095 }
1096 return bmap;
1097 }
1098
1099 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1100 {
1101 return (struct isl_basic_set *)
1102 isl_basic_map_simplify((struct isl_basic_map *)bset);
1103 }
1104
1105
1106 /* If the only constraints a div d=floor(f/m)
1107 * appears in are its two defining constraints
1108 *
1109 * f - m d >=0
1110 * -(f - (m - 1)) + m d >= 0
1111 *
1112 * then it can safely be removed.
1113 */
1114 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1115 {
1116 int i;
1117 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1118
1119 for (i = 0; i < bmap->n_eq; ++i)
1120 if (!isl_int_is_zero(bmap->eq[i][pos]))
1121 return 0;
1122
1123 for (i = 0; i < bmap->n_ineq; ++i) {
1124 if (isl_int_is_zero(bmap->ineq[i][pos]))
1125 continue;
1126 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1127 int neg;
1128 isl_int_sub(bmap->div[div][1],
1129 bmap->div[div][1], bmap->div[div][0]);
1130 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1131 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1132 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1133 isl_int_add(bmap->div[div][1],
1134 bmap->div[div][1], bmap->div[div][0]);
1135 if (!neg)
1136 return 0;
1137 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1138 bmap->n_div-div-1) != -1)
1139 return 0;
1140 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1141 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1142 return 0;
1143 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1144 bmap->n_div-div-1) != -1)
1145 return 0;
1146 } else
1147 return 0;
1148 }
1149
1150 for (i = 0; i < bmap->n_div; ++i)
1151 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1152 return 0;
1153
1154 return 1;
1155 }
1156
1157 /*
1158 * Remove divs that don't occur in any of the constraints or other divs.
1159 * These can arise when dropping some of the variables in a quast
1160 * returned by piplib.
1161 */
1162 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1163 {
1164 int i;
1165
1166 if (!bmap)
1167 return NULL;
1168
1169 for (i = bmap->n_div-1; i >= 0; --i) {
1170 if (!div_is_redundant(bmap, i))
1171 continue;
1172 bmap = isl_basic_map_drop_div(bmap, i);
1173 }
1174 return bmap;
1175 }
1176
1177 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1178 {
1179 bmap = remove_redundant_divs(bmap);
1180 if (!bmap)
1181 return NULL;
1182 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1183 return bmap;
1184 }
1185
1186 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1187 {
1188 return (struct isl_basic_set *)
1189 isl_basic_map_finalize((struct isl_basic_map *)bset);
1190 }
1191
1192 struct isl_set *isl_set_finalize(struct isl_set *set)
1193 {
1194 int i;
1195
1196 if (!set)
1197 return NULL;
1198 for (i = 0; i < set->n; ++i) {
1199 set->p[i] = isl_basic_set_finalize(set->p[i]);
1200 if (!set->p[i])
1201 goto error;
1202 }
1203 return set;
1204 error:
1205 isl_set_free(set);
1206 return NULL;
1207 }
1208
1209 struct isl_map *isl_map_finalize(struct isl_map *map)
1210 {
1211 int i;
1212
1213 if (!map)
1214 return NULL;
1215 for (i = 0; i < map->n; ++i) {
1216 map->p[i] = isl_basic_map_finalize(map->p[i]);
1217 if (!map->p[i])
1218 goto error;
1219 }
1220 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1221 return map;
1222 error:
1223 isl_map_free(map);
1224 return NULL;
1225 }
1226
1227
1228 /* Remove definition of any div that is defined in terms of the given variable.
1229 * The div itself is not removed. Functions such as
1230 * eliminate_divs_ineq depend on the other divs remaining in place.
1231 */
1232 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1233 int pos)
1234 {
1235 int i;
1236
1237 for (i = 0; i < bmap->n_div; ++i) {
1238 if (isl_int_is_zero(bmap->div[i][0]))
1239 continue;
1240 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1241 continue;
1242 isl_int_set_si(bmap->div[i][0], 0);
1243 }
1244 return bmap;
1245 }
1246
1247 /* Eliminate the specified variables from the constraints using
1248 * Fourier-Motzkin. The variables themselves are not removed.
1249 */
1250 struct isl_basic_map *isl_basic_map_eliminate_vars(
1251 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1252 {
1253 int d;
1254 int i, j, k;
1255 unsigned total;
1256
1257 if (n == 0)
1258 return bmap;
1259 if (!bmap)
1260 return NULL;
1261 total = isl_basic_map_total_dim(bmap);
1262
1263 bmap = isl_basic_map_cow(bmap);
1264 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1265 bmap = remove_dependent_vars(bmap, d);
1266
1267 for (d = pos + n - 1;
1268 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1269 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1270 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1271 int n_lower, n_upper;
1272 if (!bmap)
1273 return NULL;
1274 for (i = 0; i < bmap->n_eq; ++i) {
1275 if (isl_int_is_zero(bmap->eq[i][1+d]))
1276 continue;
1277 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1278 isl_basic_map_drop_equality(bmap, i);
1279 break;
1280 }
1281 if (i < bmap->n_eq)
1282 continue;
1283 n_lower = 0;
1284 n_upper = 0;
1285 for (i = 0; i < bmap->n_ineq; ++i) {
1286 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1287 n_lower++;
1288 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1289 n_upper++;
1290 }
1291 bmap = isl_basic_map_extend_constraints(bmap,
1292 0, n_lower * n_upper);
1293 if (!bmap)
1294 goto error;
1295 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1296 int last;
1297 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1298 continue;
1299 last = -1;
1300 for (j = 0; j < i; ++j) {
1301 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1302 continue;
1303 last = j;
1304 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1305 isl_int_sgn(bmap->ineq[j][1+d]))
1306 continue;
1307 k = isl_basic_map_alloc_inequality(bmap);
1308 if (k < 0)
1309 goto error;
1310 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1311 1+total);
1312 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1313 1+d, 1+total, NULL);
1314 }
1315 isl_basic_map_drop_inequality(bmap, i);
1316 i = last + 1;
1317 }
1318 if (n_lower > 0 && n_upper > 0) {
1319 bmap = isl_basic_map_normalize_constraints(bmap);
1320 bmap = remove_duplicate_constraints(bmap, NULL);
1321 bmap = isl_basic_map_gauss(bmap, NULL);
1322 bmap = isl_basic_map_convex_hull(bmap);
1323 if (!bmap)
1324 goto error;
1325 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1326 break;
1327 }
1328 }
1329 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1330 return bmap;
1331 error:
1332 isl_basic_map_free(bmap);
1333 return NULL;
1334 }
1335
1336 struct isl_basic_set *isl_basic_set_eliminate_vars(
1337 struct isl_basic_set *bset, unsigned pos, unsigned n)
1338 {
1339 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1340 (struct isl_basic_map *)bset, pos, n);
1341 }
1342
1343 /* Don't assume equalities are in order, because align_divs
1344 * may have changed the order of the divs.
1345 */
1346 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1347 {
1348 int d, i;
1349 unsigned total;
1350
1351 total = isl_dim_total(bmap->dim);
1352 for (d = 0; d < total; ++d)
1353 elim[d] = -1;
1354 for (i = 0; i < bmap->n_eq; ++i) {
1355 for (d = total - 1; d >= 0; --d) {
1356 if (isl_int_is_zero(bmap->eq[i][1+d]))
1357 continue;
1358 elim[d] = i;
1359 break;
1360 }
1361 }
1362 }
1363
1364 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1365 {
1366 compute_elimination_index((struct isl_basic_map *)bset, elim);
1367 }
1368
1369 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1370 struct isl_basic_map *bmap, int *elim)
1371 {
1372 int d;
1373 int copied = 0;
1374 unsigned total;
1375
1376 total = isl_dim_total(bmap->dim);
1377 for (d = total - 1; d >= 0; --d) {
1378 if (isl_int_is_zero(src[1+d]))
1379 continue;
1380 if (elim[d] == -1)
1381 continue;
1382 if (!copied) {
1383 isl_seq_cpy(dst, src, 1 + total);
1384 copied = 1;
1385 }
1386 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1387 }
1388 return copied;
1389 }
1390
1391 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1392 struct isl_basic_set *bset, int *elim)
1393 {
1394 return reduced_using_equalities(dst, src,
1395 (struct isl_basic_map *)bset, elim);
1396 }
1397
1398 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1399 struct isl_basic_set *bset, struct isl_basic_set *context)
1400 {
1401 int i;
1402 int *elim;
1403
1404 if (!bset || !context)
1405 goto error;
1406
1407 if (context->n_eq == 0) {
1408 isl_basic_set_free(context);
1409 return bset;
1410 }
1411
1412 bset = isl_basic_set_cow(bset);
1413 if (!bset)
1414 goto error;
1415
1416 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1417 if (!elim)
1418 goto error;
1419 set_compute_elimination_index(context, elim);
1420 for (i = 0; i < bset->n_eq; ++i)
1421 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1422 context, elim);
1423 for (i = 0; i < bset->n_ineq; ++i)
1424 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1425 context, elim);
1426 isl_basic_set_free(context);
1427 free(elim);
1428 bset = isl_basic_set_simplify(bset);
1429 bset = isl_basic_set_finalize(bset);
1430 return bset;
1431 error:
1432 isl_basic_set_free(bset);
1433 isl_basic_set_free(context);
1434 return NULL;
1435 }
1436
1437 static struct isl_basic_set *remove_shifted_constraints(
1438 struct isl_basic_set *bset, struct isl_basic_set *context)
1439 {
1440 unsigned int size;
1441 isl_int ***index;
1442 int bits;
1443 int k, h, l;
1444
1445 if (!bset)
1446 return NULL;
1447
1448 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1449 bits = ffs(size) - 1;
1450 index = isl_calloc_array(ctx, isl_int **, size);
1451 if (!index)
1452 return bset;
1453
1454 for (k = 0; k < context->n_ineq; ++k) {
1455 h = set_hash_index(index, size, bits, context, k);
1456 index[h] = &context->ineq[k];
1457 }
1458 for (k = 0; k < bset->n_ineq; ++k) {
1459 h = set_hash_index(index, size, bits, bset, k);
1460 if (!index[h])
1461 continue;
1462 l = index[h] - &context->ineq[0];
1463 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1464 continue;
1465 bset = isl_basic_set_cow(bset);
1466 if (!bset)
1467 goto error;
1468 isl_basic_set_drop_inequality(bset, k);
1469 --k;
1470 }
1471 free(index);
1472 return bset;
1473 error:
1474 free(index);
1475 return bset;
1476 }
1477
1478 /* Tighten (decrease) the constant terms of the inequalities based
1479 * on the equalities, without removing any integer points.
1480 * For example, if there is an equality
1481 *
1482 * i = 3 * j
1483 *
1484 * and an inequality
1485 *
1486 * i >= 1
1487 *
1488 * then we want to replace the inequality by
1489 *
1490 * i >= 3
1491 *
1492 * We do this by computing a variable compression and translating
1493 * the constraints to the compressed space.
1494 * If any constraint has coefficients (except the contant term)
1495 * with a common factor "f", then we can replace the constant term "c"
1496 * by
1497 *
1498 * f * floor(c/f)
1499 *
1500 * That is, we add
1501 *
1502 * f * floor(c/f) - c = -fract(c/f)
1503 *
1504 * and we can add the same value to the original constraint.
1505 *
1506 * In the example, the compressed space only contains "j",
1507 * and the inequality translates to
1508 *
1509 * 3 * j - 1 >= 0
1510 *
1511 * We add -fract(-1/3) = -2 to the original constraint to obtain
1512 *
1513 * i - 3 >= 0
1514 */
1515 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1516 struct isl_basic_set *bset)
1517 {
1518 int i;
1519 unsigned total;
1520 struct isl_mat *B, *C;
1521 isl_int gcd;
1522
1523 if (!bset)
1524 return NULL;
1525
1526 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1527 return bset;
1528
1529 if (!bset->n_ineq)
1530 return bset;
1531
1532 bset = isl_basic_set_cow(bset);
1533 if (!bset)
1534 return NULL;
1535
1536 total = isl_basic_set_total_dim(bset);
1537 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1538 C = isl_mat_variable_compression(B, NULL);
1539 if (!C)
1540 return bset;
1541 if (C->n_col == 0) {
1542 isl_mat_free(C);
1543 return isl_basic_set_set_to_empty(bset);
1544 }
1545 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1546 0, bset->n_ineq, 0, 1 + total);
1547 C = isl_mat_product(B, C);
1548 if (!C)
1549 return bset;
1550
1551 isl_int_init(gcd);
1552 for (i = 0; i < bset->n_ineq; ++i) {
1553 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1554 if (isl_int_is_one(gcd))
1555 continue;
1556 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1557 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1558 }
1559 isl_int_clear(gcd);
1560
1561 isl_mat_free(C);
1562
1563 return bset;
1564 }
1565
1566 /* Remove all information from bset that is redundant in the context
1567 * of context. Both bset and context are assumed to be full-dimensional.
1568 *
1569 * We first * remove the inequalities from "bset"
1570 * that are obviously redundant with respect to some inequality in "context".
1571 *
1572 * If there are any inequalities left, we construct a tableau for
1573 * the context and then add the inequalities of "bset".
1574 * Before adding these inequalities, we freeze all constraints such that
1575 * they won't be considered redundant in terms of the constraints of "bset".
1576 * Then we detect all redundant constraints (among the
1577 * constraints that weren't frozen), first by checking for redundancy in the
1578 * the tableau and then by checking if replacing a constraint by its negation
1579 * would lead to an empty set. This last step is fairly expensive
1580 * and could be optimized by more reuse of the tableau.
1581 * Finally, we update bset according to the results.
1582 */
1583 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1584 __isl_take isl_basic_set *context)
1585 {
1586 int i, k;
1587 isl_basic_set *combined = NULL;
1588 struct isl_tab *tab = NULL;
1589 unsigned context_ineq;
1590 unsigned total;
1591
1592 if (!bset || !context)
1593 goto error;
1594
1595 if (isl_basic_set_is_universe(bset)) {
1596 isl_basic_set_free(context);
1597 return bset;
1598 }
1599
1600 if (isl_basic_set_is_universe(context)) {
1601 isl_basic_set_free(context);
1602 return bset;
1603 }
1604
1605 bset = remove_shifted_constraints(bset, context);
1606 if (!bset)
1607 goto error;
1608 if (bset->n_ineq == 0)
1609 goto done;
1610
1611 context_ineq = context->n_ineq;
1612 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1613 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1614 tab = isl_tab_from_basic_set(combined);
1615 for (i = 0; i < context_ineq; ++i)
1616 if (isl_tab_freeze_constraint(tab, i) < 0)
1617 goto error;
1618 tab = isl_tab_extend(tab, bset->n_ineq);
1619 for (i = 0; i < bset->n_ineq; ++i)
1620 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1621 goto error;
1622 bset = isl_basic_set_add_constraints(combined, bset, 0);
1623 combined = NULL;
1624 if (!bset)
1625 goto error;
1626 if (isl_tab_detect_redundant(tab) < 0)
1627 goto error;
1628 total = isl_basic_set_total_dim(bset);
1629 for (i = context_ineq; i < bset->n_ineq; ++i) {
1630 int is_empty;
1631 if (tab->con[i].is_redundant)
1632 continue;
1633 tab->con[i].is_redundant = 1;
1634 combined = isl_basic_set_dup(bset);
1635 combined = isl_basic_set_update_from_tab(combined, tab);
1636 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1637 k = isl_basic_set_alloc_inequality(combined);
1638 if (k < 0)
1639 goto error;
1640 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1641 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1642 is_empty = isl_basic_set_is_empty(combined);
1643 if (is_empty < 0)
1644 goto error;
1645 isl_basic_set_free(combined);
1646 combined = NULL;
1647 if (!is_empty)
1648 tab->con[i].is_redundant = 0;
1649 }
1650 for (i = 0; i < context_ineq; ++i)
1651 tab->con[i].is_redundant = 1;
1652 bset = isl_basic_set_update_from_tab(bset, tab);
1653 if (bset) {
1654 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1655 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1656 }
1657
1658 isl_tab_free(tab);
1659 done:
1660 bset = isl_basic_set_simplify(bset);
1661 bset = isl_basic_set_finalize(bset);
1662 isl_basic_set_free(context);
1663 return bset;
1664 error:
1665 isl_tab_free(tab);
1666 isl_basic_set_free(combined);
1667 isl_basic_set_free(context);
1668 isl_basic_set_free(bset);
1669 return NULL;
1670 }
1671
1672 /* Remove all information from bset that is redundant in the context
1673 * of context. In particular, equalities that are linear combinations
1674 * of those in context are removed. Then the inequalities that are
1675 * redundant in the context of the equalities and inequalities of
1676 * context are removed.
1677 *
1678 * We first compute the integer affine hull of the intersection,
1679 * compute the gist inside this affine hull and then add back
1680 * those equalities that are not implied by the context.
1681 */
1682 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1683 __isl_take isl_basic_set *context)
1684 {
1685 isl_mat *eq;
1686 isl_mat *T, *T2;
1687 isl_basic_set *aff;
1688 isl_basic_set *aff_context;
1689 unsigned total;
1690
1691 if (!bset || !context)
1692 goto error;
1693
1694 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1695 if (isl_basic_set_fast_is_empty(bset)) {
1696 isl_basic_set_free(context);
1697 return bset;
1698 }
1699 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1700 if (!aff)
1701 goto error;
1702 if (isl_basic_set_fast_is_empty(aff)) {
1703 isl_basic_set_free(aff);
1704 isl_basic_set_free(context);
1705 return bset;
1706 }
1707 if (aff->n_eq == 0) {
1708 isl_basic_set_free(aff);
1709 return uset_gist_full(bset, context);
1710 }
1711 total = isl_basic_set_total_dim(bset);
1712 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1713 eq = isl_mat_cow(eq);
1714 T = isl_mat_variable_compression(eq, &T2);
1715 if (T && T->n_col == 0) {
1716 isl_mat_free(T);
1717 isl_mat_free(T2);
1718 isl_basic_set_free(context);
1719 isl_basic_set_free(aff);
1720 return isl_basic_set_set_to_empty(bset);
1721 }
1722
1723 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1724
1725 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1726 context = isl_basic_set_preimage(context, T);
1727
1728 bset = uset_gist_full(bset, context);
1729 bset = isl_basic_set_preimage(bset, T2);
1730 bset = isl_basic_set_intersect(bset, aff);
1731 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1732
1733 if (bset) {
1734 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1735 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1736 }
1737
1738 return bset;
1739 error:
1740 isl_basic_set_free(bset);
1741 isl_basic_set_free(context);
1742 return NULL;
1743 }
1744
1745 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1746 * We simply add the equalities in context to bmap and then do a regular
1747 * div normalizations. Better results can be obtained by normalizing
1748 * only the divs in bmap than do not also appear in context.
1749 * We need to be careful to reduce the divs using the equalities
1750 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1751 * spurious constraints.
1752 */
1753 static struct isl_basic_map *normalize_divs_in_context(
1754 struct isl_basic_map *bmap, struct isl_basic_map *context)
1755 {
1756 int i;
1757 unsigned total_context;
1758 int div_eq;
1759
1760 div_eq = n_pure_div_eq(bmap);
1761 if (div_eq == 0)
1762 return bmap;
1763
1764 if (context->n_div > 0)
1765 bmap = isl_basic_map_align_divs(bmap, context);
1766
1767 total_context = isl_basic_map_total_dim(context);
1768 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1769 for (i = 0; i < context->n_eq; ++i) {
1770 int k;
1771 k = isl_basic_map_alloc_equality(bmap);
1772 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1773 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1774 isl_basic_map_total_dim(bmap) - total_context);
1775 }
1776 bmap = isl_basic_map_gauss(bmap, NULL);
1777 bmap = normalize_divs(bmap, NULL);
1778 bmap = isl_basic_map_gauss(bmap, NULL);
1779 return bmap;
1780 }
1781
1782 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1783 struct isl_basic_map *context)
1784 {
1785 struct isl_basic_set *bset;
1786
1787 if (!bmap || !context)
1788 goto error;
1789
1790 if (isl_basic_map_is_universe(context)) {
1791 isl_basic_map_free(context);
1792 return bmap;
1793 }
1794 if (isl_basic_map_is_universe(bmap)) {
1795 isl_basic_map_free(context);
1796 return bmap;
1797 }
1798 if (isl_basic_map_fast_is_empty(context)) {
1799 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1800 isl_basic_map_free(context);
1801 isl_basic_map_free(bmap);
1802 return isl_basic_map_universe(dim);
1803 }
1804 if (isl_basic_map_fast_is_empty(bmap)) {
1805 isl_basic_map_free(context);
1806 return bmap;
1807 }
1808
1809 bmap = isl_basic_map_convex_hull(bmap);
1810 context = isl_basic_map_convex_hull(context);
1811
1812 if (context->n_eq)
1813 bmap = normalize_divs_in_context(bmap, context);
1814
1815 context = isl_basic_map_align_divs(context, bmap);
1816 bmap = isl_basic_map_align_divs(bmap, context);
1817
1818 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1819 isl_basic_map_underlying_set(context));
1820
1821 return isl_basic_map_overlying_set(bset, bmap);
1822 error:
1823 isl_basic_map_free(bmap);
1824 isl_basic_map_free(context);
1825 return NULL;
1826 }
1827
1828 /*
1829 * Assumes context has no implicit divs.
1830 */
1831 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1832 __isl_take isl_basic_map *context)
1833 {
1834 int i;
1835
1836 if (!map || !context)
1837 goto error;;
1838
1839 if (isl_basic_map_is_universe(context)) {
1840 isl_basic_map_free(context);
1841 return map;
1842 }
1843 if (isl_basic_map_fast_is_empty(context)) {
1844 struct isl_dim *dim = isl_dim_copy(map->dim);
1845 isl_basic_map_free(context);
1846 isl_map_free(map);
1847 return isl_map_universe(dim);
1848 }
1849
1850 context = isl_basic_map_convex_hull(context);
1851 map = isl_map_cow(map);
1852 if (!map || !context)
1853 goto error;;
1854 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1855 map = isl_map_compute_divs(map);
1856 for (i = 0; i < map->n; ++i)
1857 context = isl_basic_map_align_divs(context, map->p[i]);
1858 for (i = 0; i < map->n; ++i) {
1859 map->p[i] = isl_basic_map_gist(map->p[i],
1860 isl_basic_map_copy(context));
1861 if (!map->p[i])
1862 goto error;
1863 }
1864 isl_basic_map_free(context);
1865 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1866 return map;
1867 error:
1868 isl_map_free(map);
1869 isl_basic_map_free(context);
1870 return NULL;
1871 }
1872
1873 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1874 __isl_take isl_map *context)
1875 {
1876 return isl_map_gist_basic_map(map, isl_map_convex_hull(context));
1877 }
1878
1879 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1880 struct isl_basic_set *context)
1881 {
1882 return (struct isl_basic_set *)isl_basic_map_gist(
1883 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1884 }
1885
1886 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1887 __isl_take isl_basic_set *context)
1888 {
1889 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1890 (struct isl_basic_map *)context);
1891 }
1892
1893 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1894 __isl_take isl_set *context)
1895 {
1896 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1897 (struct isl_map *)context);
1898 }
1899
1900 /* Quick check to see if two basic maps are disjoint.
1901 * In particular, we reduce the equalities and inequalities of
1902 * one basic map in the context of the equalities of the other
1903 * basic map and check if we get a contradiction.
1904 */
1905 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1906 struct isl_basic_map *bmap2)
1907 {
1908 struct isl_vec *v = NULL;
1909 int *elim = NULL;
1910 unsigned total;
1911 int i;
1912
1913 if (!bmap1 || !bmap2)
1914 return -1;
1915 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1916 return -1);
1917 if (bmap1->n_div || bmap2->n_div)
1918 return 0;
1919 if (!bmap1->n_eq && !bmap2->n_eq)
1920 return 0;
1921
1922 total = isl_dim_total(bmap1->dim);
1923 if (total == 0)
1924 return 0;
1925 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1926 if (!v)
1927 goto error;
1928 elim = isl_alloc_array(bmap1->ctx, int, total);
1929 if (!elim)
1930 goto error;
1931 compute_elimination_index(bmap1, elim);
1932 for (i = 0; i < bmap2->n_eq; ++i) {
1933 int reduced;
1934 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1935 bmap1, elim);
1936 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1937 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1938 goto disjoint;
1939 }
1940 for (i = 0; i < bmap2->n_ineq; ++i) {
1941 int reduced;
1942 reduced = reduced_using_equalities(v->block.data,
1943 bmap2->ineq[i], bmap1, elim);
1944 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1945 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1946 goto disjoint;
1947 }
1948 compute_elimination_index(bmap2, elim);
1949 for (i = 0; i < bmap1->n_ineq; ++i) {
1950 int reduced;
1951 reduced = reduced_using_equalities(v->block.data,
1952 bmap1->ineq[i], bmap2, elim);
1953 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1954 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1955 goto disjoint;
1956 }
1957 isl_vec_free(v);
1958 free(elim);
1959 return 0;
1960 disjoint:
1961 isl_vec_free(v);
1962 free(elim);
1963 return 1;
1964 error:
1965 isl_vec_free(v);
1966 free(elim);
1967 return -1;
1968 }
1969
1970 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1971 struct isl_basic_set *bset2)
1972 {
1973 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1974 (struct isl_basic_map *)bset2);
1975 }
1976
1977 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1978 {
1979 int i, j;
1980
1981 if (!map1 || !map2)
1982 return -1;
1983
1984 if (isl_map_fast_is_equal(map1, map2))
1985 return 0;
1986
1987 for (i = 0; i < map1->n; ++i) {
1988 for (j = 0; j < map2->n; ++j) {
1989 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1990 map2->p[j]);
1991 if (d != 1)
1992 return d;
1993 }
1994 }
1995 return 1;
1996 }
1997
1998 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1999 {
2000 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2001 (struct isl_map *)set2);
2002 }
2003
2004 /* Check if we can combine a given div with lower bound l and upper
2005 * bound u with some other div and if so return that other div.
2006 * Otherwise return -1.
2007 *
2008 * We first check that
2009 * - the bounds are opposites of each other (except for the constant
2010 * term)
2011 * - the bounds do not reference any other div
2012 * - no div is defined in terms of this div
2013 *
2014 * Let m be the size of the range allowed on the div by the bounds.
2015 * That is, the bounds are of the form
2016 *
2017 * e <= a <= e + m - 1
2018 *
2019 * with e some expression in the other variables.
2020 * We look for another div b such that no third div is defined in terms
2021 * of this second div b and such that in any constraint that contains
2022 * a (except for the given lower and upper bound), also contains b
2023 * with a coefficient that is m times that of b.
2024 * That is, all constraints (execpt for the lower and upper bound)
2025 * are of the form
2026 *
2027 * e + f (a + m b) >= 0
2028 *
2029 * If so, we return b so that "a + m b" can be replaced by
2030 * a single div "c = a + m b".
2031 */
2032 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2033 unsigned div, unsigned l, unsigned u)
2034 {
2035 int i, j;
2036 unsigned dim;
2037 int coalesce = -1;
2038
2039 if (bmap->n_div <= 1)
2040 return -1;
2041 dim = isl_dim_total(bmap->dim);
2042 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2043 return -1;
2044 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2045 bmap->n_div - div - 1) != -1)
2046 return -1;
2047 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2048 dim + bmap->n_div))
2049 return -1;
2050
2051 for (i = 0; i < bmap->n_div; ++i) {
2052 if (isl_int_is_zero(bmap->div[i][0]))
2053 continue;
2054 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2055 return -1;
2056 }
2057
2058 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2059 if (isl_int_is_neg(bmap->ineq[l][0])) {
2060 isl_int_sub(bmap->ineq[l][0],
2061 bmap->ineq[l][0], bmap->ineq[u][0]);
2062 bmap = isl_basic_map_copy(bmap);
2063 bmap = isl_basic_map_set_to_empty(bmap);
2064 isl_basic_map_free(bmap);
2065 return -1;
2066 }
2067 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2068 for (i = 0; i < bmap->n_div; ++i) {
2069 if (i == div)
2070 continue;
2071 if (!pairs[i])
2072 continue;
2073 for (j = 0; j < bmap->n_div; ++j) {
2074 if (isl_int_is_zero(bmap->div[j][0]))
2075 continue;
2076 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2077 break;
2078 }
2079 if (j < bmap->n_div)
2080 continue;
2081 for (j = 0; j < bmap->n_ineq; ++j) {
2082 int valid;
2083 if (j == l || j == u)
2084 continue;
2085 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2086 continue;
2087 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2088 break;
2089 isl_int_mul(bmap->ineq[j][1 + dim + div],
2090 bmap->ineq[j][1 + dim + div],
2091 bmap->ineq[l][0]);
2092 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2093 bmap->ineq[j][1 + dim + i]);
2094 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2095 bmap->ineq[j][1 + dim + div],
2096 bmap->ineq[l][0]);
2097 if (!valid)
2098 break;
2099 }
2100 if (j < bmap->n_ineq)
2101 continue;
2102 coalesce = i;
2103 break;
2104 }
2105 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2106 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2107 return coalesce;
2108 }
2109
2110 /* Given a lower and an upper bound on div i, construct an inequality
2111 * that when nonnegative ensures that this pair of bounds always allows
2112 * for an integer value of the given div.
2113 * The lower bound is inequality l, while the upper bound is inequality u.
2114 * The constructed inequality is stored in ineq.
2115 * g, fl, fu are temporary scalars.
2116 *
2117 * Let the upper bound be
2118 *
2119 * -n_u a + e_u >= 0
2120 *
2121 * and the lower bound
2122 *
2123 * n_l a + e_l >= 0
2124 *
2125 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2126 * We have
2127 *
2128 * - f_u e_l <= f_u f_l g a <= f_l e_u
2129 *
2130 * Since all variables are integer valued, this is equivalent to
2131 *
2132 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2133 *
2134 * If this interval is at least f_u f_l g, then it contains at least
2135 * one integer value for a.
2136 * That is, the test constraint is
2137 *
2138 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2139 */
2140 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2141 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2142 {
2143 unsigned dim;
2144 dim = isl_dim_total(bmap->dim);
2145
2146 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2147 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2148 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2149 isl_int_neg(fu, fu);
2150 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2151 1 + dim + bmap->n_div);
2152 isl_int_add(ineq[0], ineq[0], fl);
2153 isl_int_add(ineq[0], ineq[0], fu);
2154 isl_int_sub_ui(ineq[0], ineq[0], 1);
2155 isl_int_mul(g, g, fl);
2156 isl_int_mul(g, g, fu);
2157 isl_int_sub(ineq[0], ineq[0], g);
2158 }
2159
2160 /* Remove more kinds of divs that are not strictly needed.
2161 * In particular, if all pairs of lower and upper bounds on a div
2162 * are such that they allow at least one integer value of the div,
2163 * the we can eliminate the div using Fourier-Motzkin without
2164 * introducing any spurious solutions.
2165 */
2166 static struct isl_basic_map *drop_more_redundant_divs(
2167 struct isl_basic_map *bmap, int *pairs, int n)
2168 {
2169 struct isl_tab *tab = NULL;
2170 struct isl_vec *vec = NULL;
2171 unsigned dim;
2172 int remove = -1;
2173 isl_int g, fl, fu;
2174
2175 isl_int_init(g);
2176 isl_int_init(fl);
2177 isl_int_init(fu);
2178
2179 if (!bmap)
2180 goto error;
2181
2182 dim = isl_dim_total(bmap->dim);
2183 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2184 if (!vec)
2185 goto error;
2186
2187 tab = isl_tab_from_basic_map(bmap);
2188
2189 while (n > 0) {
2190 int i, l, u;
2191 int best = -1;
2192 enum isl_lp_result res;
2193
2194 for (i = 0; i < bmap->n_div; ++i) {
2195 if (!pairs[i])
2196 continue;
2197 if (best >= 0 && pairs[best] <= pairs[i])
2198 continue;
2199 best = i;
2200 }
2201
2202 i = best;
2203 for (l = 0; l < bmap->n_ineq; ++l) {
2204 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2205 continue;
2206 for (u = 0; u < bmap->n_ineq; ++u) {
2207 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2208 continue;
2209 construct_test_ineq(bmap, i, l, u,
2210 vec->el, g, fl, fu);
2211 res = isl_tab_min(tab, vec->el,
2212 bmap->ctx->one, &g, NULL, 0);
2213 if (res == isl_lp_error)
2214 goto error;
2215 if (res == isl_lp_empty) {
2216 bmap = isl_basic_map_set_to_empty(bmap);
2217 break;
2218 }
2219 if (res != isl_lp_ok || isl_int_is_neg(g))
2220 break;
2221 }
2222 if (u < bmap->n_ineq)
2223 break;
2224 }
2225 if (l == bmap->n_ineq) {
2226 remove = i;
2227 break;
2228 }
2229 pairs[i] = 0;
2230 --n;
2231 }
2232
2233 isl_tab_free(tab);
2234 isl_vec_free(vec);
2235
2236 isl_int_clear(g);
2237 isl_int_clear(fl);
2238 isl_int_clear(fu);
2239
2240 free(pairs);
2241
2242 if (remove < 0)
2243 return bmap;
2244
2245 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2246 return isl_basic_map_drop_redundant_divs(bmap);
2247 error:
2248 free(pairs);
2249 isl_basic_map_free(bmap);
2250 isl_tab_free(tab);
2251 isl_vec_free(vec);
2252 isl_int_clear(g);
2253 isl_int_clear(fl);
2254 isl_int_clear(fu);
2255 return NULL;
2256 }
2257
2258 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2259 * and the upper bound u, div1 always occurs together with div2 in the form
2260 * (div1 + m div2), where m is the constant range on the variable div1
2261 * allowed by l and u, replace the pair div1 and div2 by a single
2262 * div that is equal to div1 + m div2.
2263 *
2264 * The new div will appear in the location that contains div2.
2265 * We need to modify all constraints that contain
2266 * div2 = (div - div1) / m
2267 * (If a constraint does not contain div2, it will also not contain div1.)
2268 * If the constraint also contains div1, then we know they appear
2269 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2270 * i.e., the coefficient of div is f.
2271 *
2272 * Otherwise, we first need to introduce div1 into the constraint.
2273 * Let the l be
2274 *
2275 * div1 + f >=0
2276 *
2277 * and u
2278 *
2279 * -div1 + f' >= 0
2280 *
2281 * A lower bound on div2
2282 *
2283 * n div2 + t >= 0
2284 *
2285 * can be replaced by
2286 *
2287 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2288 *
2289 * with g = gcd(m,n).
2290 * An upper bound
2291 *
2292 * -n div2 + t >= 0
2293 *
2294 * can be replaced by
2295 *
2296 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2297 *
2298 * These constraint are those that we would obtain from eliminating
2299 * div1 using Fourier-Motzkin.
2300 *
2301 * After all constraints have been modified, we drop the lower and upper
2302 * bound and then drop div1.
2303 */
2304 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2305 unsigned div1, unsigned div2, unsigned l, unsigned u)
2306 {
2307 isl_int a;
2308 isl_int b;
2309 isl_int m;
2310 unsigned dim, total;
2311 int i;
2312
2313 dim = isl_dim_total(bmap->dim);
2314 total = 1 + dim + bmap->n_div;
2315
2316 isl_int_init(a);
2317 isl_int_init(b);
2318 isl_int_init(m);
2319 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2320 isl_int_add_ui(m, m, 1);
2321
2322 for (i = 0; i < bmap->n_ineq; ++i) {
2323 if (i == l || i == u)
2324 continue;
2325 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2326 continue;
2327 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2328 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2329 isl_int_divexact(a, m, b);
2330 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2331 if (isl_int_is_pos(b)) {
2332 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2333 b, bmap->ineq[l], total);
2334 } else {
2335 isl_int_neg(b, b);
2336 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2337 b, bmap->ineq[u], total);
2338 }
2339 }
2340 isl_int_set(bmap->ineq[i][1 + dim + div2],
2341 bmap->ineq[i][1 + dim + div1]);
2342 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2343 }
2344
2345 isl_int_clear(a);
2346 isl_int_clear(b);
2347 isl_int_clear(m);
2348 if (l > u) {
2349 isl_basic_map_drop_inequality(bmap, l);
2350 isl_basic_map_drop_inequality(bmap, u);
2351 } else {
2352 isl_basic_map_drop_inequality(bmap, u);
2353 isl_basic_map_drop_inequality(bmap, l);
2354 }
2355 bmap = isl_basic_map_drop_div(bmap, div1);
2356 return bmap;
2357 }
2358
2359 /* First check if we can coalesce any pair of divs and
2360 * then continue with dropping more redundant divs.
2361 *
2362 * We loop over all pairs of lower and upper bounds on a div
2363 * with coefficient 1 and -1, respectively, check if there
2364 * is any other div "c" with which we can coalesce the div
2365 * and if so, perform the coalescing.
2366 */
2367 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2368 struct isl_basic_map *bmap, int *pairs, int n)
2369 {
2370 int i, l, u;
2371 unsigned dim;
2372
2373 dim = isl_dim_total(bmap->dim);
2374
2375 for (i = 0; i < bmap->n_div; ++i) {
2376 if (!pairs[i])
2377 continue;
2378 for (l = 0; l < bmap->n_ineq; ++l) {
2379 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2380 continue;
2381 for (u = 0; u < bmap->n_ineq; ++u) {
2382 int c;
2383
2384 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2385 continue;
2386 c = div_find_coalesce(bmap, pairs, i, l, u);
2387 if (c < 0)
2388 continue;
2389 free(pairs);
2390 bmap = coalesce_divs(bmap, i, c, l, u);
2391 return isl_basic_map_drop_redundant_divs(bmap);
2392 }
2393 }
2394 }
2395
2396 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2397 return bmap;
2398
2399 return drop_more_redundant_divs(bmap, pairs, n);
2400 }
2401
2402 /* Remove divs that are not strictly needed.
2403 * In particular, if a div only occurs positively (or negatively)
2404 * in constraints, then it can simply be dropped.
2405 * Also, if a div occurs only occurs in two constraints and if moreover
2406 * those two constraints are opposite to each other, except for the constant
2407 * term and if the sum of the constant terms is such that for any value
2408 * of the other values, there is always at least one integer value of the
2409 * div, i.e., if one plus this sum is greater than or equal to
2410 * the (absolute value) of the coefficent of the div in the constraints,
2411 * then we can also simply drop the div.
2412 *
2413 * If any divs are left after these simple checks then we move on
2414 * to more complicated cases in drop_more_redundant_divs.
2415 */
2416 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2417 struct isl_basic_map *bmap)
2418 {
2419 int i, j;
2420 unsigned off;
2421 int *pairs = NULL;
2422 int n = 0;
2423
2424 if (!bmap)
2425 goto error;
2426
2427 off = isl_dim_total(bmap->dim);
2428 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2429 if (!pairs)
2430 goto error;
2431
2432 for (i = 0; i < bmap->n_div; ++i) {
2433 int pos, neg;
2434 int last_pos, last_neg;
2435 int redundant;
2436 int defined;
2437
2438 defined = !isl_int_is_zero(bmap->div[i][0]);
2439 for (j = 0; j < bmap->n_eq; ++j)
2440 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2441 break;
2442 if (j < bmap->n_eq)
2443 continue;
2444 ++n;
2445 pos = neg = 0;
2446 for (j = 0; j < bmap->n_ineq; ++j) {
2447 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2448 last_pos = j;
2449 ++pos;
2450 }
2451 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2452 last_neg = j;
2453 ++neg;
2454 }
2455 }
2456 pairs[i] = pos * neg;
2457 if (pairs[i] == 0) {
2458 for (j = bmap->n_ineq - 1; j >= 0; --j)
2459 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2460 isl_basic_map_drop_inequality(bmap, j);
2461 bmap = isl_basic_map_drop_div(bmap, i);
2462 free(pairs);
2463 return isl_basic_map_drop_redundant_divs(bmap);
2464 }
2465 if (pairs[i] != 1)
2466 continue;
2467 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2468 bmap->ineq[last_neg] + 1,
2469 off + bmap->n_div))
2470 continue;
2471
2472 isl_int_add(bmap->ineq[last_pos][0],
2473 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2474 isl_int_add_ui(bmap->ineq[last_pos][0],
2475 bmap->ineq[last_pos][0], 1);
2476 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2477 bmap->ineq[last_pos][1+off+i]);
2478 isl_int_sub_ui(bmap->ineq[last_pos][0],
2479 bmap->ineq[last_pos][0], 1);
2480 isl_int_sub(bmap->ineq[last_pos][0],
2481 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2482 if (!redundant) {
2483 if (defined ||
2484 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2485 pairs[i] = 0;
2486 --n;
2487 continue;
2488 }
2489 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2490 bmap = isl_basic_map_simplify(bmap);
2491 free(pairs);
2492 return isl_basic_map_drop_redundant_divs(bmap);
2493 }
2494 if (last_pos > last_neg) {
2495 isl_basic_map_drop_inequality(bmap, last_pos);
2496 isl_basic_map_drop_inequality(bmap, last_neg);
2497 } else {
2498 isl_basic_map_drop_inequality(bmap, last_neg);
2499 isl_basic_map_drop_inequality(bmap, last_pos);
2500 }
2501 bmap = isl_basic_map_drop_div(bmap, i);
2502 free(pairs);
2503 return isl_basic_map_drop_redundant_divs(bmap);
2504 }
2505
2506 if (n > 0)
2507 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2508
2509 free(pairs);
2510 return bmap;
2511 error:
2512 free(pairs);
2513 isl_basic_map_free(bmap);
2514 return NULL;
2515 }
2516
2517 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2518 struct isl_basic_set *bset)
2519 {
2520 return (struct isl_basic_set *)
2521 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2522 }
2523
2524 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2525 {
2526 int i;
2527
2528 if (!map)
2529 return NULL;
2530 for (i = 0; i < map->n; ++i) {
2531 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2532 if (!map->p[i])
2533 goto error;
2534 }
2535 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2536 return map;
2537 error:
2538 isl_map_free(map);
2539 return NULL;
2540 }
2541
2542 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2543 {
2544 return (struct isl_set *)
2545 isl_map_drop_redundant_divs((struct isl_map *)set);
2546 }
Integer set library