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isl_map_simplify.c: eliminate_divs_ineq: avoid NULL pointer dereference
[isl.git] / isl_map_simplify.c
blob9a0a0560f914790b7d49d19592330744b11a84a8
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 = isl_dim_total(bmap->dim);
649 unsigned total = total_var + bmap->n_div;
650 struct isl_ctx *ctx;
651
652 if (bmap->n_div <= 1)
653 return bmap;
654
655 ctx = bmap->ctx;
656 for (k = bmap->n_div - 1; k >= 0; --k)
657 if (!isl_int_is_zero(bmap->div[k][0]))
658 break;
659 if (k <= 0)
660 return bmap;
661
662 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
663 size = round_up(4 * bmap->n_div / 3 - 1);
664 bits = ffs(size) - 1;
665 index = isl_calloc_array(ctx, int, size);
666 if (!index)
667 return bmap;
668 eq = isl_blk_alloc(ctx, 1+total);
669 if (isl_blk_is_error(eq))
670 goto out;
671
672 isl_seq_clr(eq.data, 1+total);
673 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
674 for (--k; k >= 0; --k) {
675 uint32_t hash;
676
677 if (isl_int_is_zero(bmap->div[k][0]))
678 continue;
679
680 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
681 for (h = hash; index[h]; h = (h+1) % size)
682 if (isl_seq_eq(bmap->div[k],
683 bmap->div[index[h]-1], 2+total))
684 break;
685 if (index[h]) {
686 *progress = 1;
687 l = index[h] - 1;
688 elim_for[l] = k + 1;
689 }
690 index[h] = k+1;
691 }
692 for (l = bmap->n_div - 1; l >= 0; --l) {
693 if (!elim_for[l])
694 continue;
695 k = elim_for[l] - 1;
696 isl_int_set_si(eq.data[1+total_var+k], -1);
697 isl_int_set_si(eq.data[1+total_var+l], 1);
698 eliminate_div(bmap, eq.data, l, 0);
699 isl_int_set_si(eq.data[1+total_var+k], 0);
700 isl_int_set_si(eq.data[1+total_var+l], 0);
701 }
702
703 isl_blk_free(ctx, eq);
704 out:
705 free(index);
706 free(elim_for);
707 return bmap;
708 }
709
710 static int n_pure_div_eq(struct isl_basic_map *bmap)
711 {
712 int i, j;
713 unsigned total;
714
715 total = isl_dim_total(bmap->dim);
716 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
717 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
718 --j;
719 if (j < 0)
720 break;
721 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
722 return 0;
723 }
724 return i;
725 }
726
727 /* Normalize divs that appear in equalities.
728 *
729 * In particular, we assume that bmap contains some equalities
730 * of the form
731 *
732 * a x = m * e_i
733 *
734 * and we want to replace the set of e_i by a minimal set and
735 * such that the new e_i have a canonical representation in terms
736 * of the vector x.
737 * If any of the equalities involves more than one divs, then
738 * we currently simply bail out.
739 *
740 * Let us first additionally assume that all equalities involve
741 * a div. The equalities then express modulo constraints on the
742 * remaining variables and we can use "parameter compression"
743 * to find a minimal set of constraints. The result is a transformation
744 *
745 * x = T(x') = x_0 + G x'
746 *
747 * with G a lower-triangular matrix with all elements below the diagonal
748 * non-negative and smaller than the diagonal element on the same row.
749 * We first normalize x_0 by making the same property hold in the affine
750 * T matrix.
751 * The rows i of G with a 1 on the diagonal do not impose any modulo
752 * constraint and simply express x_i = x'_i.
753 * For each of the remaining rows i, we introduce a div and a corresponding
754 * equality. In particular
755 *
756 * g_ii e_j = x_i - g_i(x')
757 *
758 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
759 * corresponding div (if g_kk != 1).
760 *
761 * If there are any equalities not involving any div, then we
762 * first apply a variable compression on the variables x:
763 *
764 * x = C x'' x'' = C_2 x
765 *
766 * and perform the above parameter compression on A C instead of on A.
767 * The resulting compression is then of the form
768 *
769 * x'' = T(x') = x_0 + G x'
770 *
771 * and in constructing the new divs and the corresponding equalities,
772 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
773 * by the corresponding row from C_2.
774 */
775 static struct isl_basic_map *normalize_divs(
776 struct isl_basic_map *bmap, int *progress)
777 {
778 int i, j, k;
779 int total;
780 int div_eq;
781 struct isl_mat *B;
782 struct isl_vec *d;
783 struct isl_mat *T = NULL;
784 struct isl_mat *C = NULL;
785 struct isl_mat *C2 = NULL;
786 isl_int v;
787 int *pos;
788 int dropped, needed;
789
790 if (!bmap)
791 return NULL;
792
793 if (bmap->n_div == 0)
794 return bmap;
795
796 if (bmap->n_eq == 0)
797 return bmap;
798
799 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
800 return bmap;
801
802 total = isl_dim_total(bmap->dim);
803 div_eq = n_pure_div_eq(bmap);
804 if (div_eq == 0)
805 return bmap;
806
807 if (div_eq < bmap->n_eq) {
808 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
809 bmap->n_eq - div_eq, 0, 1 + total);
810 C = isl_mat_variable_compression(B, &C2);
811 if (!C || !C2)
812 goto error;
813 if (C->n_col == 0) {
814 bmap = isl_basic_map_set_to_empty(bmap);
815 isl_mat_free(C);
816 isl_mat_free(C2);
817 goto done;
818 }
819 }
820
821 d = isl_vec_alloc(bmap->ctx, div_eq);
822 if (!d)
823 goto error;
824 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
825 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
826 --j;
827 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
828 }
829 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
830
831 if (C) {
832 B = isl_mat_product(B, C);
833 C = NULL;
834 }
835
836 T = isl_mat_parameter_compression(B, d);
837 if (!T)
838 goto error;
839 if (T->n_col == 0) {
840 bmap = isl_basic_map_set_to_empty(bmap);
841 isl_mat_free(C2);
842 isl_mat_free(T);
843 goto done;
844 }
845 isl_int_init(v);
846 for (i = 0; i < T->n_row - 1; ++i) {
847 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
848 if (isl_int_is_zero(v))
849 continue;
850 isl_mat_col_submul(T, 0, v, 1 + i);
851 }
852 isl_int_clear(v);
853 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
854 /* We have to be careful because dropping equalities may reorder them */
855 dropped = 0;
856 for (j = bmap->n_div - 1; j >= 0; --j) {
857 for (i = 0; i < bmap->n_eq; ++i)
858 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
859 break;
860 if (i < bmap->n_eq) {
861 bmap = isl_basic_map_drop_div(bmap, j);
862 isl_basic_map_drop_equality(bmap, i);
863 ++dropped;
864 }
865 }
866 pos[0] = 0;
867 needed = 0;
868 for (i = 1; i < T->n_row; ++i) {
869 if (isl_int_is_one(T->row[i][i]))
870 pos[i] = i;
871 else
872 needed++;
873 }
874 if (needed > dropped) {
875 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
876 needed, needed, 0);
877 if (!bmap)
878 goto error;
879 }
880 for (i = 1; i < T->n_row; ++i) {
881 if (isl_int_is_one(T->row[i][i]))
882 continue;
883 k = isl_basic_map_alloc_div(bmap);
884 pos[i] = 1 + total + k;
885 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
886 isl_int_set(bmap->div[k][0], T->row[i][i]);
887 if (C2)
888 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
889 else
890 isl_int_set_si(bmap->div[k][1 + i], 1);
891 for (j = 0; j < i; ++j) {
892 if (isl_int_is_zero(T->row[i][j]))
893 continue;
894 if (pos[j] < T->n_row && C2)
895 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
896 C2->row[pos[j]], 1 + total);
897 else
898 isl_int_neg(bmap->div[k][1 + pos[j]],
899 T->row[i][j]);
900 }
901 j = isl_basic_map_alloc_equality(bmap);
902 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
903 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
904 }
905 free(pos);
906 isl_mat_free(C2);
907 isl_mat_free(T);
908
909 if (progress)
910 *progress = 1;
911 done:
912 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
913
914 return bmap;
915 error:
916 isl_mat_free(C);
917 isl_mat_free(C2);
918 isl_mat_free(T);
919 return bmap;
920 }
921
922 static struct isl_basic_map *set_div_from_lower_bound(
923 struct isl_basic_map *bmap, int div, int ineq)
924 {
925 unsigned total = 1 + isl_dim_total(bmap->dim);
926
927 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
928 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
929 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
930 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
931 isl_int_set_si(bmap->div[div][1 + total + div], 0);
932
933 return bmap;
934 }
935
936 /* Check whether it is ok to define a div based on an inequality.
937 * To avoid the introduction of circular definitions of divs, we
938 * do not allow such a definition if the resulting expression would refer to
939 * any other undefined divs or if any known div is defined in
940 * terms of the unknown div.
941 */
942 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
943 int div, int ineq)
944 {
945 int j;
946 unsigned total = 1 + isl_dim_total(bmap->dim);
947
948 /* Not defined in terms of unknown divs */
949 for (j = 0; j < bmap->n_div; ++j) {
950 if (div == j)
951 continue;
952 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
953 continue;
954 if (isl_int_is_zero(bmap->div[j][0]))
955 return 0;
956 }
957
958 /* No other div defined in terms of this one => avoid loops */
959 for (j = 0; j < bmap->n_div; ++j) {
960 if (div == j)
961 continue;
962 if (isl_int_is_zero(bmap->div[j][0]))
963 continue;
964 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
965 return 0;
966 }
967
968 return 1;
969 }
970
971 /* Given two constraints "k" and "l" that are opposite to each other,
972 * except for the constant term, check if we can use them
973 * to obtain an expression for one of the hitherto unknown divs.
974 * "sum" is the sum of the constant terms of the constraints.
975 * If this sum is strictly smaller than the coefficient of one
976 * of the divs, then this pair can be used define the div.
977 * To avoid the introduction of circular definitions of divs, we
978 * do not use the pair if the resulting expression would refer to
979 * any other undefined divs or if any known div is defined in
980 * terms of the unknown div.
981 */
982 static struct isl_basic_map *check_for_div_constraints(
983 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
984 {
985 int i;
986 unsigned total = 1 + isl_dim_total(bmap->dim);
987
988 for (i = 0; i < bmap->n_div; ++i) {
989 if (!isl_int_is_zero(bmap->div[i][0]))
990 continue;
991 if (isl_int_is_zero(bmap->ineq[k][total + i]))
992 continue;
993 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
994 continue;
995 if (!ok_to_set_div_from_bound(bmap, i, k))
996 break;
997 if (isl_int_is_pos(bmap->ineq[k][total + i]))
998 bmap = set_div_from_lower_bound(bmap, i, k);
999 else
1000 bmap = set_div_from_lower_bound(bmap, i, l);
1001 if (progress)
1002 *progress = 1;
1003 break;
1004 }
1005 return bmap;
1006 }
1007
1008 static struct isl_basic_map *remove_duplicate_constraints(
1009 struct isl_basic_map *bmap, int *progress)
1010 {
1011 unsigned int size;
1012 isl_int ***index;
1013 int k, l, h;
1014 int bits;
1015 unsigned total = isl_basic_map_total_dim(bmap);
1016 isl_int sum;
1017
1018 if (bmap->n_ineq <= 1)
1019 return bmap;
1020
1021 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1022 bits = ffs(size) - 1;
1023 index = isl_calloc_array(ctx, isl_int **, size);
1024 if (!index)
1025 return bmap;
1026
1027 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1028 for (k = 1; k < bmap->n_ineq; ++k) {
1029 h = hash_index(index, size, bits, bmap, k);
1030 if (!index[h]) {
1031 index[h] = &bmap->ineq[k];
1032 continue;
1033 }
1034 if (progress)
1035 *progress = 1;
1036 l = index[h] - &bmap->ineq[0];
1037 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1038 swap_inequality(bmap, k, l);
1039 isl_basic_map_drop_inequality(bmap, k);
1040 --k;
1041 }
1042 isl_int_init(sum);
1043 for (k = 0; k < bmap->n_ineq-1; ++k) {
1044 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1045 h = hash_index(index, size, bits, bmap, k);
1046 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1047 if (!index[h])
1048 continue;
1049 l = index[h] - &bmap->ineq[0];
1050 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1051 if (isl_int_is_pos(sum)) {
1052 bmap = check_for_div_constraints(bmap, k, l, sum,
1053 progress);
1054 continue;
1055 }
1056 if (isl_int_is_zero(sum)) {
1057 /* We need to break out of the loop after these
1058 * changes since the contents of the hash
1059 * will no longer be valid.
1060 * Plus, we probably we want to regauss first.
1061 */
1062 if (progress)
1063 *progress = 1;
1064 isl_basic_map_drop_inequality(bmap, l);
1065 isl_basic_map_inequality_to_equality(bmap, k);
1066 } else
1067 bmap = isl_basic_map_set_to_empty(bmap);
1068 break;
1069 }
1070 isl_int_clear(sum);
1071
1072 free(index);
1073 return bmap;
1074 }
1075
1076
1077 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1078 {
1079 int progress = 1;
1080 if (!bmap)
1081 return NULL;
1082 while (progress) {
1083 progress = 0;
1084 bmap = isl_basic_map_normalize_constraints(bmap);
1085 bmap = remove_duplicate_divs(bmap, &progress);
1086 bmap = eliminate_divs_eq(bmap, &progress);
1087 bmap = eliminate_divs_ineq(bmap, &progress);
1088 bmap = isl_basic_map_gauss(bmap, &progress);
1089 /* requires equalities in normal form */
1090 bmap = normalize_divs(bmap, &progress);
1091 bmap = remove_duplicate_constraints(bmap, &progress);
1092 }
1093 return bmap;
1094 }
1095
1096 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1097 {
1098 return (struct isl_basic_set *)
1099 isl_basic_map_simplify((struct isl_basic_map *)bset);
1100 }
1101
1102
1103 /* If the only constraints a div d=floor(f/m)
1104 * appears in are its two defining constraints
1105 *
1106 * f - m d >=0
1107 * -(f - (m - 1)) + m d >= 0
1108 *
1109 * then it can safely be removed.
1110 */
1111 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1112 {
1113 int i;
1114 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1115
1116 for (i = 0; i < bmap->n_eq; ++i)
1117 if (!isl_int_is_zero(bmap->eq[i][pos]))
1118 return 0;
1119
1120 for (i = 0; i < bmap->n_ineq; ++i) {
1121 if (isl_int_is_zero(bmap->ineq[i][pos]))
1122 continue;
1123 if (isl_int_eq(bmap->ineq[i][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(bmap->ineq[i], 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(bmap->ineq[i]+pos+1,
1135 bmap->n_div-div-1) != -1)
1136 return 0;
1137 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1138 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1139 return 0;
1140 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1141 bmap->n_div-div-1) != -1)
1142 return 0;
1143 } else
1144 return 0;
1145 }
1146
1147 for (i = 0; i < bmap->n_div; ++i)
1148 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1149 return 0;
1150
1151 return 1;
1152 }
1153
1154 /*
1155 * Remove divs that don't occur in any of the constraints or other divs.
1156 * These can arise when dropping some of the variables in a quast
1157 * returned by piplib.
1158 */
1159 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1160 {
1161 int i;
1162
1163 if (!bmap)
1164 return NULL;
1165
1166 for (i = bmap->n_div-1; i >= 0; --i) {
1167 if (!div_is_redundant(bmap, i))
1168 continue;
1169 bmap = isl_basic_map_drop_div(bmap, i);
1170 }
1171 return bmap;
1172 }
1173
1174 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1175 {
1176 bmap = remove_redundant_divs(bmap);
1177 if (!bmap)
1178 return NULL;
1179 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1180 return bmap;
1181 }
1182
1183 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1184 {
1185 return (struct isl_basic_set *)
1186 isl_basic_map_finalize((struct isl_basic_map *)bset);
1187 }
1188
1189 struct isl_set *isl_set_finalize(struct isl_set *set)
1190 {
1191 int i;
1192
1193 if (!set)
1194 return NULL;
1195 for (i = 0; i < set->n; ++i) {
1196 set->p[i] = isl_basic_set_finalize(set->p[i]);
1197 if (!set->p[i])
1198 goto error;
1199 }
1200 return set;
1201 error:
1202 isl_set_free(set);
1203 return NULL;
1204 }
1205
1206 struct isl_map *isl_map_finalize(struct isl_map *map)
1207 {
1208 int i;
1209
1210 if (!map)
1211 return NULL;
1212 for (i = 0; i < map->n; ++i) {
1213 map->p[i] = isl_basic_map_finalize(map->p[i]);
1214 if (!map->p[i])
1215 goto error;
1216 }
1217 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1218 return map;
1219 error:
1220 isl_map_free(map);
1221 return NULL;
1222 }
1223
1224
1225 /* Remove definition of any div that is defined in terms of the given variable.
1226 * The div itself is not removed. Functions such as
1227 * eliminate_divs_ineq depend on the other divs remaining in place.
1228 */
1229 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1230 int pos)
1231 {
1232 int i;
1233
1234 for (i = 0; i < bmap->n_div; ++i) {
1235 if (isl_int_is_zero(bmap->div[i][0]))
1236 continue;
1237 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1238 continue;
1239 isl_int_set_si(bmap->div[i][0], 0);
1240 }
1241 return bmap;
1242 }
1243
1244 /* Eliminate the specified variables from the constraints using
1245 * Fourier-Motzkin. The variables themselves are not removed.
1246 */
1247 struct isl_basic_map *isl_basic_map_eliminate_vars(
1248 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1249 {
1250 int d;
1251 int i, j, k;
1252 unsigned total;
1253
1254 if (n == 0)
1255 return bmap;
1256 if (!bmap)
1257 return NULL;
1258 total = isl_basic_map_total_dim(bmap);
1259
1260 bmap = isl_basic_map_cow(bmap);
1261 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1262 bmap = remove_dependent_vars(bmap, d);
1263
1264 for (d = pos + n - 1;
1265 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1266 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1267 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1268 int n_lower, n_upper;
1269 if (!bmap)
1270 return NULL;
1271 for (i = 0; i < bmap->n_eq; ++i) {
1272 if (isl_int_is_zero(bmap->eq[i][1+d]))
1273 continue;
1274 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1275 isl_basic_map_drop_equality(bmap, i);
1276 break;
1277 }
1278 if (i < bmap->n_eq)
1279 continue;
1280 n_lower = 0;
1281 n_upper = 0;
1282 for (i = 0; i < bmap->n_ineq; ++i) {
1283 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1284 n_lower++;
1285 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1286 n_upper++;
1287 }
1288 bmap = isl_basic_map_extend_constraints(bmap,
1289 0, n_lower * n_upper);
1290 if (!bmap)
1291 goto error;
1292 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1293 int last;
1294 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1295 continue;
1296 last = -1;
1297 for (j = 0; j < i; ++j) {
1298 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1299 continue;
1300 last = j;
1301 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1302 isl_int_sgn(bmap->ineq[j][1+d]))
1303 continue;
1304 k = isl_basic_map_alloc_inequality(bmap);
1305 if (k < 0)
1306 goto error;
1307 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1308 1+total);
1309 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1310 1+d, 1+total, NULL);
1311 }
1312 isl_basic_map_drop_inequality(bmap, i);
1313 i = last + 1;
1314 }
1315 if (n_lower > 0 && n_upper > 0) {
1316 bmap = isl_basic_map_normalize_constraints(bmap);
1317 bmap = remove_duplicate_constraints(bmap, NULL);
1318 bmap = isl_basic_map_gauss(bmap, NULL);
1319 bmap = isl_basic_map_convex_hull(bmap);
1320 if (!bmap)
1321 goto error;
1322 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1323 break;
1324 }
1325 }
1326 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1327 return bmap;
1328 error:
1329 isl_basic_map_free(bmap);
1330 return NULL;
1331 }
1332
1333 struct isl_basic_set *isl_basic_set_eliminate_vars(
1334 struct isl_basic_set *bset, unsigned pos, unsigned n)
1335 {
1336 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1337 (struct isl_basic_map *)bset, pos, n);
1338 }
1339
1340 /* Don't assume equalities are in order, because align_divs
1341 * may have changed the order of the divs.
1342 */
1343 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1344 {
1345 int d, i;
1346 unsigned total;
1347
1348 total = isl_dim_total(bmap->dim);
1349 for (d = 0; d < total; ++d)
1350 elim[d] = -1;
1351 for (i = 0; i < bmap->n_eq; ++i) {
1352 for (d = total - 1; d >= 0; --d) {
1353 if (isl_int_is_zero(bmap->eq[i][1+d]))
1354 continue;
1355 elim[d] = i;
1356 break;
1357 }
1358 }
1359 }
1360
1361 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1362 {
1363 compute_elimination_index((struct isl_basic_map *)bset, elim);
1364 }
1365
1366 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1367 struct isl_basic_map *bmap, int *elim)
1368 {
1369 int d;
1370 int copied = 0;
1371 unsigned total;
1372
1373 total = isl_dim_total(bmap->dim);
1374 for (d = total - 1; d >= 0; --d) {
1375 if (isl_int_is_zero(src[1+d]))
1376 continue;
1377 if (elim[d] == -1)
1378 continue;
1379 if (!copied) {
1380 isl_seq_cpy(dst, src, 1 + total);
1381 copied = 1;
1382 }
1383 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1384 }
1385 return copied;
1386 }
1387
1388 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1389 struct isl_basic_set *bset, int *elim)
1390 {
1391 return reduced_using_equalities(dst, src,
1392 (struct isl_basic_map *)bset, elim);
1393 }
1394
1395 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1396 struct isl_basic_set *bset, struct isl_basic_set *context)
1397 {
1398 int i;
1399 int *elim;
1400
1401 if (!bset || !context)
1402 goto error;
1403
1404 if (context->n_eq == 0) {
1405 isl_basic_set_free(context);
1406 return bset;
1407 }
1408
1409 bset = isl_basic_set_cow(bset);
1410 if (!bset)
1411 goto error;
1412
1413 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1414 if (!elim)
1415 goto error;
1416 set_compute_elimination_index(context, elim);
1417 for (i = 0; i < bset->n_eq; ++i)
1418 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1419 context, elim);
1420 for (i = 0; i < bset->n_ineq; ++i)
1421 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1422 context, elim);
1423 isl_basic_set_free(context);
1424 free(elim);
1425 bset = isl_basic_set_simplify(bset);
1426 bset = isl_basic_set_finalize(bset);
1427 return bset;
1428 error:
1429 isl_basic_set_free(bset);
1430 isl_basic_set_free(context);
1431 return NULL;
1432 }
1433
1434 static struct isl_basic_set *remove_shifted_constraints(
1435 struct isl_basic_set *bset, struct isl_basic_set *context)
1436 {
1437 unsigned int size;
1438 isl_int ***index;
1439 int bits;
1440 int k, h, l;
1441
1442 if (!bset)
1443 return NULL;
1444
1445 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1446 bits = ffs(size) - 1;
1447 index = isl_calloc_array(ctx, isl_int **, size);
1448 if (!index)
1449 return bset;
1450
1451 for (k = 0; k < context->n_ineq; ++k) {
1452 h = set_hash_index(index, size, bits, context, k);
1453 index[h] = &context->ineq[k];
1454 }
1455 for (k = 0; k < bset->n_ineq; ++k) {
1456 h = set_hash_index(index, size, bits, bset, k);
1457 if (!index[h])
1458 continue;
1459 l = index[h] - &context->ineq[0];
1460 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1461 continue;
1462 bset = isl_basic_set_cow(bset);
1463 if (!bset)
1464 goto error;
1465 isl_basic_set_drop_inequality(bset, k);
1466 --k;
1467 }
1468 free(index);
1469 return bset;
1470 error:
1471 free(index);
1472 return bset;
1473 }
1474
1475 /* Tighten (decrease) the constant terms of the inequalities based
1476 * on the equalities, without removing any integer points.
1477 * For example, if there is an equality
1478 *
1479 * i = 3 * j
1480 *
1481 * and an inequality
1482 *
1483 * i >= 1
1484 *
1485 * then we want to replace the inequality by
1486 *
1487 * i >= 3
1488 *
1489 * We do this by computing a variable compression and translating
1490 * the constraints to the compressed space.
1491 * If any constraint has coefficients (except the contant term)
1492 * with a common factor "f", then we can replace the constant term "c"
1493 * by
1494 *
1495 * f * floor(c/f)
1496 *
1497 * That is, we add
1498 *
1499 * f * floor(c/f) - c = -fract(c/f)
1500 *
1501 * and we can add the same value to the original constraint.
1502 *
1503 * In the example, the compressed space only contains "j",
1504 * and the inequality translates to
1505 *
1506 * 3 * j - 1 >= 0
1507 *
1508 * We add -fract(-1/3) = -2 to the original constraint to obtain
1509 *
1510 * i - 3 >= 0
1511 */
1512 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1513 struct isl_basic_set *bset)
1514 {
1515 int i;
1516 unsigned total;
1517 struct isl_mat *B, *C;
1518 isl_int gcd;
1519
1520 if (!bset)
1521 return NULL;
1522
1523 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1524 return bset;
1525
1526 if (!bset->n_ineq)
1527 return bset;
1528
1529 bset = isl_basic_set_cow(bset);
1530 if (!bset)
1531 return NULL;
1532
1533 total = isl_basic_set_total_dim(bset);
1534 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1535 C = isl_mat_variable_compression(B, NULL);
1536 if (!C)
1537 return bset;
1538 if (C->n_col == 0) {
1539 isl_mat_free(C);
1540 return isl_basic_set_set_to_empty(bset);
1541 }
1542 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1543 0, bset->n_ineq, 0, 1 + total);
1544 C = isl_mat_product(B, C);
1545 if (!C)
1546 return bset;
1547
1548 isl_int_init(gcd);
1549 for (i = 0; i < bset->n_ineq; ++i) {
1550 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1551 if (isl_int_is_one(gcd))
1552 continue;
1553 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1554 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1555 }
1556 isl_int_clear(gcd);
1557
1558 isl_mat_free(C);
1559
1560 return bset;
1561 }
1562
1563 /* Remove all information from bset that is redundant in the context
1564 * of context. Both bset and context are assumed to be full-dimensional.
1565 *
1566 * We first * remove the inequalities from "bset"
1567 * that are obviously redundant with respect to some inequality in "context".
1568 *
1569 * If there are any inequalities left, we construct a tableau for
1570 * the context and then add the inequalities of "bset".
1571 * Before adding these inequalities, we freeze all constraints such that
1572 * they won't be considered redundant in terms of the constraints of "bset".
1573 * Then we detect all redundant constraints (among the
1574 * constraints that weren't frozen), first by checking for redundancy in the
1575 * the tableau and then by checking if replacing a constraint by its negation
1576 * would lead to an empty set. This last step is fairly expensive
1577 * and could be optimized by more reuse of the tableau.
1578 * Finally, we update bset according to the results.
1579 */
1580 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1581 __isl_take isl_basic_set *context)
1582 {
1583 int i, k;
1584 isl_basic_set *combined = NULL;
1585 struct isl_tab *tab = NULL;
1586 unsigned context_ineq;
1587 unsigned total;
1588
1589 if (!bset || !context)
1590 goto error;
1591
1592 if (isl_basic_set_is_universe(bset)) {
1593 isl_basic_set_free(context);
1594 return bset;
1595 }
1596
1597 if (isl_basic_set_is_universe(context)) {
1598 isl_basic_set_free(context);
1599 return bset;
1600 }
1601
1602 bset = remove_shifted_constraints(bset, context);
1603 if (!bset)
1604 goto error;
1605 if (bset->n_ineq == 0)
1606 goto done;
1607
1608 context_ineq = context->n_ineq;
1609 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1610 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1611 tab = isl_tab_from_basic_set(combined);
1612 for (i = 0; i < context_ineq; ++i)
1613 if (isl_tab_freeze_constraint(tab, i) < 0)
1614 goto error;
1615 tab = isl_tab_extend(tab, bset->n_ineq);
1616 for (i = 0; i < bset->n_ineq; ++i)
1617 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1618 goto error;
1619 bset = isl_basic_set_add_constraints(combined, bset, 0);
1620 combined = NULL;
1621 if (!bset)
1622 goto error;
1623 if (isl_tab_detect_redundant(tab) < 0)
1624 goto error;
1625 total = isl_basic_set_total_dim(bset);
1626 for (i = context_ineq; i < bset->n_ineq; ++i) {
1627 int is_empty;
1628 if (tab->con[i].is_redundant)
1629 continue;
1630 tab->con[i].is_redundant = 1;
1631 combined = isl_basic_set_dup(bset);
1632 combined = isl_basic_set_update_from_tab(combined, tab);
1633 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1634 k = isl_basic_set_alloc_inequality(combined);
1635 if (k < 0)
1636 goto error;
1637 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1638 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1639 is_empty = isl_basic_set_is_empty(combined);
1640 if (is_empty < 0)
1641 goto error;
1642 isl_basic_set_free(combined);
1643 combined = NULL;
1644 if (!is_empty)
1645 tab->con[i].is_redundant = 0;
1646 }
1647 for (i = 0; i < context_ineq; ++i)
1648 tab->con[i].is_redundant = 1;
1649 bset = isl_basic_set_update_from_tab(bset, tab);
1650 if (bset) {
1651 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1652 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1653 }
1654
1655 isl_tab_free(tab);
1656 done:
1657 bset = isl_basic_set_simplify(bset);
1658 bset = isl_basic_set_finalize(bset);
1659 isl_basic_set_free(context);
1660 return bset;
1661 error:
1662 isl_tab_free(tab);
1663 isl_basic_set_free(combined);
1664 isl_basic_set_free(context);
1665 isl_basic_set_free(bset);
1666 return NULL;
1667 }
1668
1669 /* Remove all information from bset that is redundant in the context
1670 * of context. In particular, equalities that are linear combinations
1671 * of those in context are removed. Then the inequalities that are
1672 * redundant in the context of the equalities and inequalities of
1673 * context are removed.
1674 *
1675 * We first compute the integer affine hull of the intersection,
1676 * compute the gist inside this affine hull and then add back
1677 * those equalities that are not implied by the context.
1678 */
1679 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1680 __isl_take isl_basic_set *context)
1681 {
1682 isl_mat *eq;
1683 isl_mat *T, *T2;
1684 isl_basic_set *aff;
1685 isl_basic_set *aff_context;
1686 unsigned total;
1687
1688 if (!bset || !context)
1689 goto error;
1690
1691 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1692 if (isl_basic_set_fast_is_empty(bset)) {
1693 isl_basic_set_free(context);
1694 return bset;
1695 }
1696 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1697 if (!aff)
1698 goto error;
1699 if (isl_basic_set_fast_is_empty(aff)) {
1700 isl_basic_set_free(aff);
1701 isl_basic_set_free(context);
1702 return bset;
1703 }
1704 if (aff->n_eq == 0) {
1705 isl_basic_set_free(aff);
1706 return uset_gist_full(bset, context);
1707 }
1708 total = isl_basic_set_total_dim(bset);
1709 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1710 eq = isl_mat_cow(eq);
1711 T = isl_mat_variable_compression(eq, &T2);
1712 if (T && T->n_col == 0) {
1713 isl_mat_free(T);
1714 isl_mat_free(T2);
1715 isl_basic_set_free(context);
1716 isl_basic_set_free(aff);
1717 return isl_basic_set_set_to_empty(bset);
1718 }
1719
1720 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1721
1722 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1723 context = isl_basic_set_preimage(context, T);
1724
1725 bset = uset_gist_full(bset, context);
1726 bset = isl_basic_set_preimage(bset, T2);
1727 bset = isl_basic_set_intersect(bset, aff);
1728 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1729
1730 if (bset) {
1731 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1732 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1733 }
1734
1735 return bset;
1736 error:
1737 isl_basic_set_free(bset);
1738 isl_basic_set_free(context);
1739 return NULL;
1740 }
1741
1742 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1743 * We simply add the equalities in context to bmap and then do a regular
1744 * div normalizations. Better results can be obtained by normalizing
1745 * only the divs in bmap than do not also appear in context.
1746 * We need to be careful to reduce the divs using the equalities
1747 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1748 * spurious constraints.
1749 */
1750 static struct isl_basic_map *normalize_divs_in_context(
1751 struct isl_basic_map *bmap, struct isl_basic_map *context)
1752 {
1753 int i;
1754 unsigned total_context;
1755 int div_eq;
1756
1757 div_eq = n_pure_div_eq(bmap);
1758 if (div_eq == 0)
1759 return bmap;
1760
1761 if (context->n_div > 0)
1762 bmap = isl_basic_map_align_divs(bmap, context);
1763
1764 total_context = isl_basic_map_total_dim(context);
1765 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1766 for (i = 0; i < context->n_eq; ++i) {
1767 int k;
1768 k = isl_basic_map_alloc_equality(bmap);
1769 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1770 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1771 isl_basic_map_total_dim(bmap) - total_context);
1772 }
1773 bmap = isl_basic_map_gauss(bmap, NULL);
1774 bmap = normalize_divs(bmap, NULL);
1775 bmap = isl_basic_map_gauss(bmap, NULL);
1776 return bmap;
1777 }
1778
1779 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1780 struct isl_basic_map *context)
1781 {
1782 struct isl_basic_set *bset;
1783
1784 if (!bmap || !context)
1785 goto error;
1786
1787 if (isl_basic_map_is_universe(context)) {
1788 isl_basic_map_free(context);
1789 return bmap;
1790 }
1791 if (isl_basic_map_is_universe(bmap)) {
1792 isl_basic_map_free(context);
1793 return bmap;
1794 }
1795 if (isl_basic_map_fast_is_empty(context)) {
1796 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1797 isl_basic_map_free(context);
1798 isl_basic_map_free(bmap);
1799 return isl_basic_map_universe(dim);
1800 }
1801 if (isl_basic_map_fast_is_empty(bmap)) {
1802 isl_basic_map_free(context);
1803 return bmap;
1804 }
1805
1806 bmap = isl_basic_map_convex_hull(bmap);
1807 context = isl_basic_map_convex_hull(context);
1808
1809 if (context->n_eq)
1810 bmap = normalize_divs_in_context(bmap, context);
1811
1812 context = isl_basic_map_align_divs(context, bmap);
1813 bmap = isl_basic_map_align_divs(bmap, context);
1814
1815 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1816 isl_basic_map_underlying_set(context));
1817
1818 return isl_basic_map_overlying_set(bset, bmap);
1819 error:
1820 isl_basic_map_free(bmap);
1821 isl_basic_map_free(context);
1822 return NULL;
1823 }
1824
1825 /*
1826 * Assumes context has no implicit divs.
1827 */
1828 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1829 __isl_take isl_basic_map *context)
1830 {
1831 int i;
1832
1833 if (!map || !context)
1834 goto error;;
1835
1836 if (isl_basic_map_is_universe(context)) {
1837 isl_basic_map_free(context);
1838 return map;
1839 }
1840 if (isl_basic_map_fast_is_empty(context)) {
1841 struct isl_dim *dim = isl_dim_copy(map->dim);
1842 isl_basic_map_free(context);
1843 isl_map_free(map);
1844 return isl_map_universe(dim);
1845 }
1846
1847 context = isl_basic_map_convex_hull(context);
1848 map = isl_map_cow(map);
1849 if (!map || !context)
1850 goto error;;
1851 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1852 map = isl_map_compute_divs(map);
1853 for (i = 0; i < map->n; ++i)
1854 context = isl_basic_map_align_divs(context, map->p[i]);
1855 for (i = 0; i < map->n; ++i) {
1856 map->p[i] = isl_basic_map_gist(map->p[i],
1857 isl_basic_map_copy(context));
1858 if (!map->p[i])
1859 goto error;
1860 }
1861 isl_basic_map_free(context);
1862 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1863 return map;
1864 error:
1865 isl_map_free(map);
1866 isl_basic_map_free(context);
1867 return NULL;
1868 }
1869
1870 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1871 __isl_take isl_map *context)
1872 {
1873 return isl_map_gist_basic_map(map, isl_map_convex_hull(context));
1874 }
1875
1876 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1877 struct isl_basic_set *context)
1878 {
1879 return (struct isl_basic_set *)isl_basic_map_gist(
1880 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1881 }
1882
1883 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1884 __isl_take isl_basic_set *context)
1885 {
1886 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1887 (struct isl_basic_map *)context);
1888 }
1889
1890 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1891 __isl_take isl_set *context)
1892 {
1893 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1894 (struct isl_map *)context);
1895 }
1896
1897 /* Quick check to see if two basic maps are disjoint.
1898 * In particular, we reduce the equalities and inequalities of
1899 * one basic map in the context of the equalities of the other
1900 * basic map and check if we get a contradiction.
1901 */
1902 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1903 struct isl_basic_map *bmap2)
1904 {
1905 struct isl_vec *v = NULL;
1906 int *elim = NULL;
1907 unsigned total;
1908 int i;
1909
1910 if (!bmap1 || !bmap2)
1911 return -1;
1912 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1913 return -1);
1914 if (bmap1->n_div || bmap2->n_div)
1915 return 0;
1916 if (!bmap1->n_eq && !bmap2->n_eq)
1917 return 0;
1918
1919 total = isl_dim_total(bmap1->dim);
1920 if (total == 0)
1921 return 0;
1922 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1923 if (!v)
1924 goto error;
1925 elim = isl_alloc_array(bmap1->ctx, int, total);
1926 if (!elim)
1927 goto error;
1928 compute_elimination_index(bmap1, elim);
1929 for (i = 0; i < bmap2->n_eq; ++i) {
1930 int reduced;
1931 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1932 bmap1, elim);
1933 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1934 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1935 goto disjoint;
1936 }
1937 for (i = 0; i < bmap2->n_ineq; ++i) {
1938 int reduced;
1939 reduced = reduced_using_equalities(v->block.data,
1940 bmap2->ineq[i], bmap1, elim);
1941 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1942 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1943 goto disjoint;
1944 }
1945 compute_elimination_index(bmap2, elim);
1946 for (i = 0; i < bmap1->n_ineq; ++i) {
1947 int reduced;
1948 reduced = reduced_using_equalities(v->block.data,
1949 bmap1->ineq[i], bmap2, elim);
1950 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1951 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1952 goto disjoint;
1953 }
1954 isl_vec_free(v);
1955 free(elim);
1956 return 0;
1957 disjoint:
1958 isl_vec_free(v);
1959 free(elim);
1960 return 1;
1961 error:
1962 isl_vec_free(v);
1963 free(elim);
1964 return -1;
1965 }
1966
1967 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1968 struct isl_basic_set *bset2)
1969 {
1970 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1971 (struct isl_basic_map *)bset2);
1972 }
1973
1974 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1975 {
1976 int i, j;
1977
1978 if (!map1 || !map2)
1979 return -1;
1980
1981 if (isl_map_fast_is_equal(map1, map2))
1982 return 0;
1983
1984 for (i = 0; i < map1->n; ++i) {
1985 for (j = 0; j < map2->n; ++j) {
1986 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1987 map2->p[j]);
1988 if (d != 1)
1989 return d;
1990 }
1991 }
1992 return 1;
1993 }
1994
1995 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1996 {
1997 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1998 (struct isl_map *)set2);
1999 }
2000
2001 /* Check if we can combine a given div with lower bound l and upper
2002 * bound u with some other div and if so return that other div.
2003 * Otherwise return -1.
2004 *
2005 * We first check that
2006 * - the bounds are opposites of each other (except for the constant
2007 * term)
2008 * - the bounds do not reference any other div
2009 * - no div is defined in terms of this div
2010 *
2011 * Let m be the size of the range allowed on the div by the bounds.
2012 * That is, the bounds are of the form
2013 *
2014 * e <= a <= e + m - 1
2015 *
2016 * with e some expression in the other variables.
2017 * We look for another div b such that no third div is defined in terms
2018 * of this second div b and such that in any constraint that contains
2019 * a (except for the given lower and upper bound), also contains b
2020 * with a coefficient that is m times that of b.
2021 * That is, all constraints (execpt for the lower and upper bound)
2022 * are of the form
2023 *
2024 * e + f (a + m b) >= 0
2025 *
2026 * If so, we return b so that "a + m b" can be replaced by
2027 * a single div "c = a + m b".
2028 */
2029 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2030 unsigned div, unsigned l, unsigned u)
2031 {
2032 int i, j;
2033 unsigned dim;
2034 int coalesce = -1;
2035
2036 if (bmap->n_div <= 1)
2037 return -1;
2038 dim = isl_dim_total(bmap->dim);
2039 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2040 return -1;
2041 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2042 bmap->n_div - div - 1) != -1)
2043 return -1;
2044 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2045 dim + bmap->n_div))
2046 return -1;
2047
2048 for (i = 0; i < bmap->n_div; ++i) {
2049 if (isl_int_is_zero(bmap->div[i][0]))
2050 continue;
2051 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2052 return -1;
2053 }
2054
2055 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2056 if (isl_int_is_neg(bmap->ineq[l][0])) {
2057 isl_int_sub(bmap->ineq[l][0],
2058 bmap->ineq[l][0], bmap->ineq[u][0]);
2059 bmap = isl_basic_map_copy(bmap);
2060 bmap = isl_basic_map_set_to_empty(bmap);
2061 isl_basic_map_free(bmap);
2062 return -1;
2063 }
2064 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2065 for (i = 0; i < bmap->n_div; ++i) {
2066 if (i == div)
2067 continue;
2068 if (!pairs[i])
2069 continue;
2070 for (j = 0; j < bmap->n_div; ++j) {
2071 if (isl_int_is_zero(bmap->div[j][0]))
2072 continue;
2073 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2074 break;
2075 }
2076 if (j < bmap->n_div)
2077 continue;
2078 for (j = 0; j < bmap->n_ineq; ++j) {
2079 int valid;
2080 if (j == l || j == u)
2081 continue;
2082 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2083 continue;
2084 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2085 break;
2086 isl_int_mul(bmap->ineq[j][1 + dim + div],
2087 bmap->ineq[j][1 + dim + div],
2088 bmap->ineq[l][0]);
2089 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2090 bmap->ineq[j][1 + dim + i]);
2091 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2092 bmap->ineq[j][1 + dim + div],
2093 bmap->ineq[l][0]);
2094 if (!valid)
2095 break;
2096 }
2097 if (j < bmap->n_ineq)
2098 continue;
2099 coalesce = i;
2100 break;
2101 }
2102 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2103 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2104 return coalesce;
2105 }
2106
2107 /* Given a lower and an upper bound on div i, construct an inequality
2108 * that when nonnegative ensures that this pair of bounds always allows
2109 * for an integer value of the given div.
2110 * The lower bound is inequality l, while the upper bound is inequality u.
2111 * The constructed inequality is stored in ineq.
2112 * g, fl, fu are temporary scalars.
2113 *
2114 * Let the upper bound be
2115 *
2116 * -n_u a + e_u >= 0
2117 *
2118 * and the lower bound
2119 *
2120 * n_l a + e_l >= 0
2121 *
2122 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2123 * We have
2124 *
2125 * - f_u e_l <= f_u f_l g a <= f_l e_u
2126 *
2127 * Since all variables are integer valued, this is equivalent to
2128 *
2129 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2130 *
2131 * If this interval is at least f_u f_l g, then it contains at least
2132 * one integer value for a.
2133 * That is, the test constraint is
2134 *
2135 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2136 */
2137 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2138 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2139 {
2140 unsigned dim;
2141 dim = isl_dim_total(bmap->dim);
2142
2143 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2144 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2145 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2146 isl_int_neg(fu, fu);
2147 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2148 1 + dim + bmap->n_div);
2149 isl_int_add(ineq[0], ineq[0], fl);
2150 isl_int_add(ineq[0], ineq[0], fu);
2151 isl_int_sub_ui(ineq[0], ineq[0], 1);
2152 isl_int_mul(g, g, fl);
2153 isl_int_mul(g, g, fu);
2154 isl_int_sub(ineq[0], ineq[0], g);
2155 }
2156
2157 /* Remove more kinds of divs that are not strictly needed.
2158 * In particular, if all pairs of lower and upper bounds on a div
2159 * are such that they allow at least one integer value of the div,
2160 * the we can eliminate the div using Fourier-Motzkin without
2161 * introducing any spurious solutions.
2162 */
2163 static struct isl_basic_map *drop_more_redundant_divs(
2164 struct isl_basic_map *bmap, int *pairs, int n)
2165 {
2166 struct isl_tab *tab = NULL;
2167 struct isl_vec *vec = NULL;
2168 unsigned dim;
2169 int remove = -1;
2170 isl_int g, fl, fu;
2171
2172 isl_int_init(g);
2173 isl_int_init(fl);
2174 isl_int_init(fu);
2175
2176 if (!bmap)
2177 goto error;
2178
2179 dim = isl_dim_total(bmap->dim);
2180 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2181 if (!vec)
2182 goto error;
2183
2184 tab = isl_tab_from_basic_map(bmap);
2185
2186 while (n > 0) {
2187 int i, l, u;
2188 int best = -1;
2189 enum isl_lp_result res;
2190
2191 for (i = 0; i < bmap->n_div; ++i) {
2192 if (!pairs[i])
2193 continue;
2194 if (best >= 0 && pairs[best] <= pairs[i])
2195 continue;
2196 best = i;
2197 }
2198
2199 i = best;
2200 for (l = 0; l < bmap->n_ineq; ++l) {
2201 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2202 continue;
2203 for (u = 0; u < bmap->n_ineq; ++u) {
2204 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2205 continue;
2206 construct_test_ineq(bmap, i, l, u,
2207 vec->el, g, fl, fu);
2208 res = isl_tab_min(tab, vec->el,
2209 bmap->ctx->one, &g, NULL, 0);
2210 if (res == isl_lp_error)
2211 goto error;
2212 if (res == isl_lp_empty) {
2213 bmap = isl_basic_map_set_to_empty(bmap);
2214 break;
2215 }
2216 if (res != isl_lp_ok || isl_int_is_neg(g))
2217 break;
2218 }
2219 if (u < bmap->n_ineq)
2220 break;
2221 }
2222 if (l == bmap->n_ineq) {
2223 remove = i;
2224 break;
2225 }
2226 pairs[i] = 0;
2227 --n;
2228 }
2229
2230 isl_tab_free(tab);
2231 isl_vec_free(vec);
2232
2233 isl_int_clear(g);
2234 isl_int_clear(fl);
2235 isl_int_clear(fu);
2236
2237 free(pairs);
2238
2239 if (remove < 0)
2240 return bmap;
2241
2242 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2243 return isl_basic_map_drop_redundant_divs(bmap);
2244 error:
2245 free(pairs);
2246 isl_basic_map_free(bmap);
2247 isl_tab_free(tab);
2248 isl_vec_free(vec);
2249 isl_int_clear(g);
2250 isl_int_clear(fl);
2251 isl_int_clear(fu);
2252 return NULL;
2253 }
2254
2255 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2256 * and the upper bound u, div1 always occurs together with div2 in the form
2257 * (div1 + m div2), where m is the constant range on the variable div1
2258 * allowed by l and u, replace the pair div1 and div2 by a single
2259 * div that is equal to div1 + m div2.
2260 *
2261 * The new div will appear in the location that contains div2.
2262 * We need to modify all constraints that contain
2263 * div2 = (div - div1) / m
2264 * (If a constraint does not contain div2, it will also not contain div1.)
2265 * If the constraint also contains div1, then we know they appear
2266 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2267 * i.e., the coefficient of div is f.
2268 *
2269 * Otherwise, we first need to introduce div1 into the constraint.
2270 * Let the l be
2271 *
2272 * div1 + f >=0
2273 *
2274 * and u
2275 *
2276 * -div1 + f' >= 0
2277 *
2278 * A lower bound on div2
2279 *
2280 * n div2 + t >= 0
2281 *
2282 * can be replaced by
2283 *
2284 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2285 *
2286 * with g = gcd(m,n).
2287 * An upper bound
2288 *
2289 * -n div2 + t >= 0
2290 *
2291 * can be replaced by
2292 *
2293 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2294 *
2295 * These constraint are those that we would obtain from eliminating
2296 * div1 using Fourier-Motzkin.
2297 *
2298 * After all constraints have been modified, we drop the lower and upper
2299 * bound and then drop div1.
2300 */
2301 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2302 unsigned div1, unsigned div2, unsigned l, unsigned u)
2303 {
2304 isl_int a;
2305 isl_int b;
2306 isl_int m;
2307 unsigned dim, total;
2308 int i;
2309
2310 dim = isl_dim_total(bmap->dim);
2311 total = 1 + dim + bmap->n_div;
2312
2313 isl_int_init(a);
2314 isl_int_init(b);
2315 isl_int_init(m);
2316 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2317 isl_int_add_ui(m, m, 1);
2318
2319 for (i = 0; i < bmap->n_ineq; ++i) {
2320 if (i == l || i == u)
2321 continue;
2322 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2323 continue;
2324 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2325 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2326 isl_int_divexact(a, m, b);
2327 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2328 if (isl_int_is_pos(b)) {
2329 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2330 b, bmap->ineq[l], total);
2331 } else {
2332 isl_int_neg(b, b);
2333 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2334 b, bmap->ineq[u], total);
2335 }
2336 }
2337 isl_int_set(bmap->ineq[i][1 + dim + div2],
2338 bmap->ineq[i][1 + dim + div1]);
2339 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2340 }
2341
2342 isl_int_clear(a);
2343 isl_int_clear(b);
2344 isl_int_clear(m);
2345 if (l > u) {
2346 isl_basic_map_drop_inequality(bmap, l);
2347 isl_basic_map_drop_inequality(bmap, u);
2348 } else {
2349 isl_basic_map_drop_inequality(bmap, u);
2350 isl_basic_map_drop_inequality(bmap, l);
2351 }
2352 bmap = isl_basic_map_drop_div(bmap, div1);
2353 return bmap;
2354 }
2355
2356 /* First check if we can coalesce any pair of divs and
2357 * then continue with dropping more redundant divs.
2358 *
2359 * We loop over all pairs of lower and upper bounds on a div
2360 * with coefficient 1 and -1, respectively, check if there
2361 * is any other div "c" with which we can coalesce the div
2362 * and if so, perform the coalescing.
2363 */
2364 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2365 struct isl_basic_map *bmap, int *pairs, int n)
2366 {
2367 int i, l, u;
2368 unsigned dim;
2369
2370 dim = isl_dim_total(bmap->dim);
2371
2372 for (i = 0; i < bmap->n_div; ++i) {
2373 if (!pairs[i])
2374 continue;
2375 for (l = 0; l < bmap->n_ineq; ++l) {
2376 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2377 continue;
2378 for (u = 0; u < bmap->n_ineq; ++u) {
2379 int c;
2380
2381 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2382 continue;
2383 c = div_find_coalesce(bmap, pairs, i, l, u);
2384 if (c < 0)
2385 continue;
2386 free(pairs);
2387 bmap = coalesce_divs(bmap, i, c, l, u);
2388 return isl_basic_map_drop_redundant_divs(bmap);
2389 }
2390 }
2391 }
2392
2393 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2394 return bmap;
2395
2396 return drop_more_redundant_divs(bmap, pairs, n);
2397 }
2398
2399 /* Remove divs that are not strictly needed.
2400 * In particular, if a div only occurs positively (or negatively)
2401 * in constraints, then it can simply be dropped.
2402 * Also, if a div occurs only occurs in two constraints and if moreover
2403 * those two constraints are opposite to each other, except for the constant
2404 * term and if the sum of the constant terms is such that for any value
2405 * of the other values, there is always at least one integer value of the
2406 * div, i.e., if one plus this sum is greater than or equal to
2407 * the (absolute value) of the coefficent of the div in the constraints,
2408 * then we can also simply drop the div.
2409 *
2410 * If any divs are left after these simple checks then we move on
2411 * to more complicated cases in drop_more_redundant_divs.
2412 */
2413 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2414 struct isl_basic_map *bmap)
2415 {
2416 int i, j;
2417 unsigned off;
2418 int *pairs = NULL;
2419 int n = 0;
2420
2421 if (!bmap)
2422 goto error;
2423
2424 off = isl_dim_total(bmap->dim);
2425 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2426 if (!pairs)
2427 goto error;
2428
2429 for (i = 0; i < bmap->n_div; ++i) {
2430 int pos, neg;
2431 int last_pos, last_neg;
2432 int redundant;
2433 int defined;
2434
2435 defined = !isl_int_is_zero(bmap->div[i][0]);
2436 for (j = 0; j < bmap->n_eq; ++j)
2437 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2438 break;
2439 if (j < bmap->n_eq)
2440 continue;
2441 ++n;
2442 pos = neg = 0;
2443 for (j = 0; j < bmap->n_ineq; ++j) {
2444 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2445 last_pos = j;
2446 ++pos;
2447 }
2448 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2449 last_neg = j;
2450 ++neg;
2451 }
2452 }
2453 pairs[i] = pos * neg;
2454 if (pairs[i] == 0) {
2455 for (j = bmap->n_ineq - 1; j >= 0; --j)
2456 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2457 isl_basic_map_drop_inequality(bmap, j);
2458 bmap = isl_basic_map_drop_div(bmap, i);
2459 free(pairs);
2460 return isl_basic_map_drop_redundant_divs(bmap);
2461 }
2462 if (pairs[i] != 1)
2463 continue;
2464 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2465 bmap->ineq[last_neg] + 1,
2466 off + bmap->n_div))
2467 continue;
2468
2469 isl_int_add(bmap->ineq[last_pos][0],
2470 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2471 isl_int_add_ui(bmap->ineq[last_pos][0],
2472 bmap->ineq[last_pos][0], 1);
2473 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2474 bmap->ineq[last_pos][1+off+i]);
2475 isl_int_sub_ui(bmap->ineq[last_pos][0],
2476 bmap->ineq[last_pos][0], 1);
2477 isl_int_sub(bmap->ineq[last_pos][0],
2478 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2479 if (!redundant) {
2480 if (defined ||
2481 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2482 pairs[i] = 0;
2483 --n;
2484 continue;
2485 }
2486 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2487 bmap = isl_basic_map_simplify(bmap);
2488 free(pairs);
2489 return isl_basic_map_drop_redundant_divs(bmap);
2490 }
2491 if (last_pos > last_neg) {
2492 isl_basic_map_drop_inequality(bmap, last_pos);
2493 isl_basic_map_drop_inequality(bmap, last_neg);
2494 } else {
2495 isl_basic_map_drop_inequality(bmap, last_neg);
2496 isl_basic_map_drop_inequality(bmap, last_pos);
2497 }
2498 bmap = isl_basic_map_drop_div(bmap, i);
2499 free(pairs);
2500 return isl_basic_map_drop_redundant_divs(bmap);
2501 }
2502
2503 if (n > 0)
2504 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2505
2506 free(pairs);
2507 return bmap;
2508 error:
2509 free(pairs);
2510 isl_basic_map_free(bmap);
2511 return NULL;
2512 }
2513
2514 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2515 struct isl_basic_set *bset)
2516 {
2517 return (struct isl_basic_set *)
2518 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2519 }
2520
2521 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2522 {
2523 int i;
2524
2525 if (!map)
2526 return NULL;
2527 for (i = 0; i < map->n; ++i) {
2528 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2529 if (!map->p[i])
2530 goto error;
2531 }
2532 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2533 return map;
2534 error:
2535 isl_map_free(map);
2536 return NULL;
2537 }
2538
2539 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2540 {
2541 return (struct isl_set *)
2542 isl_map_drop_redundant_divs((struct isl_map *)set);
2543 }
Integer set library