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[isl.git] / isl_map_simplify.c
blob04d277197634c52a0a3382bb48b9d848223d4838
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 struct isl_basic_map *isl_basic_map_drop_inputs(
208 struct isl_basic_map *bmap, unsigned first, unsigned n)
209 {
210 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
211 }
212
213 struct isl_map *isl_map_drop(struct isl_map *map,
214 enum isl_dim_type type, unsigned first, unsigned n)
215 {
216 int i;
217
218 if (!map)
219 goto error;
220
221 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
222
223 if (n == 0)
224 return map;
225 map = isl_map_cow(map);
226 if (!map)
227 goto error;
228 map->dim = isl_dim_drop(map->dim, type, first, n);
229 if (!map->dim)
230 goto error;
231
232 for (i = 0; i < map->n; ++i) {
233 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
234 if (!map->p[i])
235 goto error;
236 }
237 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
238
239 return map;
240 error:
241 isl_map_free(map);
242 return NULL;
243 }
244
245 struct isl_map *isl_map_drop_inputs(
246 struct isl_map *map, unsigned first, unsigned n)
247 {
248 return isl_map_drop(map, isl_dim_in, first, n);
249 }
250
251 /*
252 * We don't cow, as the div is assumed to be redundant.
253 */
254 static struct isl_basic_map *isl_basic_map_drop_div(
255 struct isl_basic_map *bmap, unsigned div)
256 {
257 int i;
258 unsigned pos;
259
260 if (!bmap)
261 goto error;
262
263 pos = 1 + isl_dim_total(bmap->dim) + div;
264
265 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
266
267 for (i = 0; i < bmap->n_eq; ++i)
268 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
269
270 for (i = 0; i < bmap->n_ineq; ++i) {
271 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
272 isl_basic_map_drop_inequality(bmap, i);
273 --i;
274 continue;
275 }
276 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
277 }
278
279 for (i = 0; i < bmap->n_div; ++i)
280 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
281
282 if (div != bmap->n_div - 1) {
283 int j;
284 isl_int *t = bmap->div[div];
285
286 for (j = div; j < bmap->n_div - 1; ++j)
287 bmap->div[j] = bmap->div[j+1];
288
289 bmap->div[bmap->n_div - 1] = t;
290 }
291 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
292 isl_basic_map_free_div(bmap, 1);
293
294 return bmap;
295 error:
296 isl_basic_map_free(bmap);
297 return NULL;
298 }
299
300 struct isl_basic_map *isl_basic_map_normalize_constraints(
301 struct isl_basic_map *bmap)
302 {
303 int i;
304 isl_int gcd;
305 unsigned total = isl_basic_map_total_dim(bmap);
306
307 isl_int_init(gcd);
308 for (i = bmap->n_eq - 1; i >= 0; --i) {
309 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
310 if (isl_int_is_zero(gcd)) {
311 if (!isl_int_is_zero(bmap->eq[i][0])) {
312 bmap = isl_basic_map_set_to_empty(bmap);
313 break;
314 }
315 isl_basic_map_drop_equality(bmap, i);
316 continue;
317 }
318 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
319 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
320 if (isl_int_is_one(gcd))
321 continue;
322 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
323 bmap = isl_basic_map_set_to_empty(bmap);
324 break;
325 }
326 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
327 }
328
329 for (i = bmap->n_ineq - 1; i >= 0; --i) {
330 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
331 if (isl_int_is_zero(gcd)) {
332 if (isl_int_is_neg(bmap->ineq[i][0])) {
333 bmap = isl_basic_map_set_to_empty(bmap);
334 break;
335 }
336 isl_basic_map_drop_inequality(bmap, i);
337 continue;
338 }
339 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
340 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
341 if (isl_int_is_one(gcd))
342 continue;
343 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
344 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
345 }
346 isl_int_clear(gcd);
347
348 return bmap;
349 }
350
351 struct isl_basic_set *isl_basic_set_normalize_constraints(
352 struct isl_basic_set *bset)
353 {
354 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
355 (struct isl_basic_map *)bset);
356 }
357
358 /* Assumes divs have been ordered if keep_divs is set.
359 */
360 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
361 unsigned pos, isl_int *eq, int keep_divs, int *progress)
362 {
363 unsigned total;
364 int k;
365 int last_div;
366
367 total = isl_basic_map_total_dim(bmap);
368 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
369 bmap->n_div);
370 for (k = 0; k < bmap->n_eq; ++k) {
371 if (bmap->eq[k] == eq)
372 continue;
373 if (isl_int_is_zero(bmap->eq[k][1+pos]))
374 continue;
375 if (progress)
376 *progress = 1;
377 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
378 }
379
380 for (k = 0; k < bmap->n_ineq; ++k) {
381 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
382 continue;
383 if (progress)
384 *progress = 1;
385 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
386 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
387 }
388
389 for (k = 0; k < bmap->n_div; ++k) {
390 if (isl_int_is_zero(bmap->div[k][0]))
391 continue;
392 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
393 continue;
394 if (progress)
395 *progress = 1;
396 /* We need to be careful about circular definitions,
397 * so for now we just remove the definition of div k
398 * if the equality contains any divs.
399 * If keep_divs is set, then the divs have been ordered
400 * and we can keep the definition as long as the result
401 * is still ordered.
402 */
403 if (last_div == -1 || (keep_divs && last_div < k))
404 isl_seq_elim(bmap->div[k]+1, eq,
405 1+pos, 1+total, &bmap->div[k][0]);
406 else
407 isl_seq_clr(bmap->div[k], 1 + total);
408 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
409 }
410 }
411
412 /* Assumes divs have been ordered if keep_divs is set.
413 */
414 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
415 unsigned div, int keep_divs)
416 {
417 unsigned pos = isl_dim_total(bmap->dim) + div;
418
419 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
420
421 isl_basic_map_drop_div(bmap, div);
422 }
423
424 /* Elimininate divs based on equalities
425 */
426 static struct isl_basic_map *eliminate_divs_eq(
427 struct isl_basic_map *bmap, int *progress)
428 {
429 int d;
430 int i;
431 int modified = 0;
432 unsigned off;
433
434 bmap = isl_basic_map_order_divs(bmap);
435
436 if (!bmap)
437 return NULL;
438
439 off = 1 + isl_dim_total(bmap->dim);
440
441 for (d = bmap->n_div - 1; d >= 0 ; --d) {
442 for (i = 0; i < bmap->n_eq; ++i) {
443 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
444 !isl_int_is_negone(bmap->eq[i][off + d]))
445 continue;
446 modified = 1;
447 *progress = 1;
448 eliminate_div(bmap, bmap->eq[i], d, 1);
449 isl_basic_map_drop_equality(bmap, i);
450 break;
451 }
452 }
453 if (modified)
454 return eliminate_divs_eq(bmap, progress);
455 return bmap;
456 }
457
458 /* Elimininate divs based on inequalities
459 */
460 static struct isl_basic_map *eliminate_divs_ineq(
461 struct isl_basic_map *bmap, int *progress)
462 {
463 int d;
464 int i;
465 unsigned off;
466 struct isl_ctx *ctx;
467
468 if (!bmap)
469 return NULL;
470
471 ctx = bmap->ctx;
472 off = 1 + isl_dim_total(bmap->dim);
473
474 for (d = bmap->n_div - 1; d >= 0 ; --d) {
475 for (i = 0; i < bmap->n_eq; ++i)
476 if (!isl_int_is_zero(bmap->eq[i][off + d]))
477 break;
478 if (i < bmap->n_eq)
479 continue;
480 for (i = 0; i < bmap->n_ineq; ++i)
481 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
482 break;
483 if (i < bmap->n_ineq)
484 continue;
485 *progress = 1;
486 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
487 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
488 break;
489 bmap = isl_basic_map_drop_div(bmap, d);
490 if (!bmap)
491 break;
492 }
493 return bmap;
494 }
495
496 struct isl_basic_map *isl_basic_map_gauss(
497 struct isl_basic_map *bmap, int *progress)
498 {
499 int k;
500 int done;
501 int last_var;
502 unsigned total_var;
503 unsigned total;
504
505 bmap = isl_basic_map_order_divs(bmap);
506
507 if (!bmap)
508 return NULL;
509
510 total = isl_basic_map_total_dim(bmap);
511 total_var = total - bmap->n_div;
512
513 last_var = total - 1;
514 for (done = 0; done < bmap->n_eq; ++done) {
515 for (; last_var >= 0; --last_var) {
516 for (k = done; k < bmap->n_eq; ++k)
517 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
518 break;
519 if (k < bmap->n_eq)
520 break;
521 }
522 if (last_var < 0)
523 break;
524 if (k != done)
525 swap_equality(bmap, k, done);
526 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
527 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
528
529 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
530 progress);
531
532 if (last_var >= total_var &&
533 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
534 unsigned div = last_var - total_var;
535 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
536 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
537 isl_int_set(bmap->div[div][0],
538 bmap->eq[done][1+last_var]);
539 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
540 }
541 }
542 if (done == bmap->n_eq)
543 return bmap;
544 for (k = done; k < bmap->n_eq; ++k) {
545 if (isl_int_is_zero(bmap->eq[k][0]))
546 continue;
547 return isl_basic_map_set_to_empty(bmap);
548 }
549 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
550 return bmap;
551 }
552
553 struct isl_basic_set *isl_basic_set_gauss(
554 struct isl_basic_set *bset, int *progress)
555 {
556 return (struct isl_basic_set*)isl_basic_map_gauss(
557 (struct isl_basic_map *)bset, progress);
558 }
559
560
561 static unsigned int round_up(unsigned int v)
562 {
563 int old_v = v;
564
565 while (v) {
566 old_v = v;
567 v ^= v & -v;
568 }
569 return old_v << 1;
570 }
571
572 static int hash_index(isl_int ***index, unsigned int size, int bits,
573 struct isl_basic_map *bmap, int k)
574 {
575 int h;
576 unsigned total = isl_basic_map_total_dim(bmap);
577 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
578 for (h = hash; index[h]; h = (h+1) % size)
579 if (&bmap->ineq[k] != index[h] &&
580 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
581 break;
582 return h;
583 }
584
585 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
586 struct isl_basic_set *bset, int k)
587 {
588 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
589 }
590
591 /* If we can eliminate more than one div, then we need to make
592 * sure we do it from last div to first div, in order not to
593 * change the position of the other divs that still need to
594 * be removed.
595 */
596 static struct isl_basic_map *remove_duplicate_divs(
597 struct isl_basic_map *bmap, int *progress)
598 {
599 unsigned int size;
600 int *index;
601 int *elim_for;
602 int k, l, h;
603 int bits;
604 struct isl_blk eq;
605 unsigned total_var = isl_dim_total(bmap->dim);
606 unsigned total = total_var + bmap->n_div;
607 struct isl_ctx *ctx;
608
609 if (bmap->n_div <= 1)
610 return bmap;
611
612 ctx = bmap->ctx;
613 for (k = bmap->n_div - 1; k >= 0; --k)
614 if (!isl_int_is_zero(bmap->div[k][0]))
615 break;
616 if (k <= 0)
617 return bmap;
618
619 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
620 size = round_up(4 * bmap->n_div / 3 - 1);
621 bits = ffs(size) - 1;
622 index = isl_calloc_array(ctx, int, size);
623 if (!index)
624 return bmap;
625 eq = isl_blk_alloc(ctx, 1+total);
626 if (isl_blk_is_error(eq))
627 goto out;
628
629 isl_seq_clr(eq.data, 1+total);
630 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
631 for (--k; k >= 0; --k) {
632 uint32_t hash;
633
634 if (isl_int_is_zero(bmap->div[k][0]))
635 continue;
636
637 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
638 for (h = hash; index[h]; h = (h+1) % size)
639 if (isl_seq_eq(bmap->div[k],
640 bmap->div[index[h]-1], 2+total))
641 break;
642 if (index[h]) {
643 *progress = 1;
644 l = index[h] - 1;
645 elim_for[l] = k + 1;
646 }
647 index[h] = k+1;
648 }
649 for (l = bmap->n_div - 1; l >= 0; --l) {
650 if (!elim_for[l])
651 continue;
652 k = elim_for[l] - 1;
653 isl_int_set_si(eq.data[1+total_var+k], -1);
654 isl_int_set_si(eq.data[1+total_var+l], 1);
655 eliminate_div(bmap, eq.data, l, 0);
656 isl_int_set_si(eq.data[1+total_var+k], 0);
657 isl_int_set_si(eq.data[1+total_var+l], 0);
658 }
659
660 isl_blk_free(ctx, eq);
661 out:
662 free(index);
663 free(elim_for);
664 return bmap;
665 }
666
667 static int n_pure_div_eq(struct isl_basic_map *bmap)
668 {
669 int i, j;
670 unsigned total;
671
672 total = isl_dim_total(bmap->dim);
673 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
674 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
675 --j;
676 if (j < 0)
677 break;
678 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
679 return 0;
680 }
681 return i;
682 }
683
684 /* Normalize divs that appear in equalities.
685 *
686 * In particular, we assume that bmap contains some equalities
687 * of the form
688 *
689 * a x = m * e_i
690 *
691 * and we want to replace the set of e_i by a minimal set and
692 * such that the new e_i have a canonical representation in terms
693 * of the vector x.
694 * If any of the equalities involves more than one divs, then
695 * we currently simply bail out.
696 *
697 * Let us first additionally assume that all equalities involve
698 * a div. The equalities then express modulo constraints on the
699 * remaining variables and we can use "parameter compression"
700 * to find a minimal set of constraints. The result is a transformation
701 *
702 * x = T(x') = x_0 + G x'
703 *
704 * with G a lower-triangular matrix with all elements below the diagonal
705 * non-negative and smaller than the diagonal element on the same row.
706 * We first normalize x_0 by making the same property hold in the affine
707 * T matrix.
708 * The rows i of G with a 1 on the diagonal do not impose any modulo
709 * constraint and simply express x_i = x'_i.
710 * For each of the remaining rows i, we introduce a div and a corresponding
711 * equality. In particular
712 *
713 * g_ii e_j = x_i - g_i(x')
714 *
715 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
716 * corresponding div (if g_kk != 1).
717 *
718 * If there are any equalities not involving any div, then we
719 * first apply a variable compression on the variables x:
720 *
721 * x = C x'' x'' = C_2 x
722 *
723 * and perform the above parameter compression on A C instead of on A.
724 * The resulting compression is then of the form
725 *
726 * x'' = T(x') = x_0 + G x'
727 *
728 * and in constructing the new divs and the corresponding equalities,
729 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
730 * by the corresponding row from C_2.
731 */
732 static struct isl_basic_map *normalize_divs(
733 struct isl_basic_map *bmap, int *progress)
734 {
735 int i, j, k;
736 int total;
737 int div_eq;
738 struct isl_mat *B;
739 struct isl_vec *d;
740 struct isl_mat *T = NULL;
741 struct isl_mat *C = NULL;
742 struct isl_mat *C2 = NULL;
743 isl_int v;
744 int *pos;
745 int dropped, needed;
746
747 if (!bmap)
748 return NULL;
749
750 if (bmap->n_div == 0)
751 return bmap;
752
753 if (bmap->n_eq == 0)
754 return bmap;
755
756 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
757 return bmap;
758
759 total = isl_dim_total(bmap->dim);
760 div_eq = n_pure_div_eq(bmap);
761 if (div_eq == 0)
762 return bmap;
763
764 if (div_eq < bmap->n_eq) {
765 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
766 bmap->n_eq - div_eq, 0, 1 + total);
767 C = isl_mat_variable_compression(B, &C2);
768 if (!C || !C2)
769 goto error;
770 if (C->n_col == 0) {
771 bmap = isl_basic_map_set_to_empty(bmap);
772 isl_mat_free(C);
773 isl_mat_free(C2);
774 goto done;
775 }
776 }
777
778 d = isl_vec_alloc(bmap->ctx, div_eq);
779 if (!d)
780 goto error;
781 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
782 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
783 --j;
784 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
785 }
786 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
787
788 if (C) {
789 B = isl_mat_product(B, C);
790 C = NULL;
791 }
792
793 T = isl_mat_parameter_compression(B, d);
794 if (!T)
795 goto error;
796 if (T->n_col == 0) {
797 bmap = isl_basic_map_set_to_empty(bmap);
798 isl_mat_free(C2);
799 isl_mat_free(T);
800 goto done;
801 }
802 isl_int_init(v);
803 for (i = 0; i < T->n_row - 1; ++i) {
804 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
805 if (isl_int_is_zero(v))
806 continue;
807 isl_mat_col_submul(T, 0, v, 1 + i);
808 }
809 isl_int_clear(v);
810 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
811 /* We have to be careful because dropping equalities may reorder them */
812 dropped = 0;
813 for (j = bmap->n_div - 1; j >= 0; --j) {
814 for (i = 0; i < bmap->n_eq; ++i)
815 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
816 break;
817 if (i < bmap->n_eq) {
818 bmap = isl_basic_map_drop_div(bmap, j);
819 isl_basic_map_drop_equality(bmap, i);
820 ++dropped;
821 }
822 }
823 pos[0] = 0;
824 needed = 0;
825 for (i = 1; i < T->n_row; ++i) {
826 if (isl_int_is_one(T->row[i][i]))
827 pos[i] = i;
828 else
829 needed++;
830 }
831 if (needed > dropped) {
832 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
833 needed, needed, 0);
834 if (!bmap)
835 goto error;
836 }
837 for (i = 1; i < T->n_row; ++i) {
838 if (isl_int_is_one(T->row[i][i]))
839 continue;
840 k = isl_basic_map_alloc_div(bmap);
841 pos[i] = 1 + total + k;
842 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
843 isl_int_set(bmap->div[k][0], T->row[i][i]);
844 if (C2)
845 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
846 else
847 isl_int_set_si(bmap->div[k][1 + i], 1);
848 for (j = 0; j < i; ++j) {
849 if (isl_int_is_zero(T->row[i][j]))
850 continue;
851 if (pos[j] < T->n_row && C2)
852 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
853 C2->row[pos[j]], 1 + total);
854 else
855 isl_int_neg(bmap->div[k][1 + pos[j]],
856 T->row[i][j]);
857 }
858 j = isl_basic_map_alloc_equality(bmap);
859 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
860 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
861 }
862 free(pos);
863 isl_mat_free(C2);
864 isl_mat_free(T);
865
866 if (progress)
867 *progress = 1;
868 done:
869 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
870
871 return bmap;
872 error:
873 isl_mat_free(C);
874 isl_mat_free(C2);
875 isl_mat_free(T);
876 return bmap;
877 }
878
879 static struct isl_basic_map *set_div_from_lower_bound(
880 struct isl_basic_map *bmap, int div, int ineq)
881 {
882 unsigned total = 1 + isl_dim_total(bmap->dim);
883
884 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
885 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
886 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
887 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
888 isl_int_set_si(bmap->div[div][1 + total + div], 0);
889
890 return bmap;
891 }
892
893 /* Check whether it is ok to define a div based on an inequality.
894 * To avoid the introduction of circular definitions of divs, we
895 * do not allow such a definition if the resulting expression would refer to
896 * any other undefined divs or if any known div is defined in
897 * terms of the unknown div.
898 */
899 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
900 int div, int ineq)
901 {
902 int j;
903 unsigned total = 1 + isl_dim_total(bmap->dim);
904
905 /* Not defined in terms of unknown divs */
906 for (j = 0; j < bmap->n_div; ++j) {
907 if (div == j)
908 continue;
909 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
910 continue;
911 if (isl_int_is_zero(bmap->div[j][0]))
912 return 0;
913 }
914
915 /* No other div defined in terms of this one => avoid loops */
916 for (j = 0; j < bmap->n_div; ++j) {
917 if (div == j)
918 continue;
919 if (isl_int_is_zero(bmap->div[j][0]))
920 continue;
921 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
922 return 0;
923 }
924
925 return 1;
926 }
927
928 /* Given two constraints "k" and "l" that are opposite to each other,
929 * except for the constant term, check if we can use them
930 * to obtain an expression for one of the hitherto unknown divs.
931 * "sum" is the sum of the constant terms of the constraints.
932 * If this sum is strictly smaller than the coefficient of one
933 * of the divs, then this pair can be used define the div.
934 * To avoid the introduction of circular definitions of divs, we
935 * do not use the pair if the resulting expression would refer to
936 * any other undefined divs or if any known div is defined in
937 * terms of the unknown div.
938 */
939 static struct isl_basic_map *check_for_div_constraints(
940 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
941 {
942 int i;
943 unsigned total = 1 + isl_dim_total(bmap->dim);
944
945 for (i = 0; i < bmap->n_div; ++i) {
946 if (!isl_int_is_zero(bmap->div[i][0]))
947 continue;
948 if (isl_int_is_zero(bmap->ineq[k][total + i]))
949 continue;
950 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
951 continue;
952 if (!ok_to_set_div_from_bound(bmap, i, k))
953 break;
954 if (isl_int_is_pos(bmap->ineq[k][total + i]))
955 bmap = set_div_from_lower_bound(bmap, i, k);
956 else
957 bmap = set_div_from_lower_bound(bmap, i, l);
958 if (progress)
959 *progress = 1;
960 break;
961 }
962 return bmap;
963 }
964
965 static struct isl_basic_map *remove_duplicate_constraints(
966 struct isl_basic_map *bmap, int *progress)
967 {
968 unsigned int size;
969 isl_int ***index;
970 int k, l, h;
971 int bits;
972 unsigned total = isl_basic_map_total_dim(bmap);
973 isl_int sum;
974
975 if (bmap->n_ineq <= 1)
976 return bmap;
977
978 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
979 bits = ffs(size) - 1;
980 index = isl_calloc_array(ctx, isl_int **, size);
981 if (!index)
982 return bmap;
983
984 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
985 for (k = 1; k < bmap->n_ineq; ++k) {
986 h = hash_index(index, size, bits, bmap, k);
987 if (!index[h]) {
988 index[h] = &bmap->ineq[k];
989 continue;
990 }
991 if (progress)
992 *progress = 1;
993 l = index[h] - &bmap->ineq[0];
994 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
995 swap_inequality(bmap, k, l);
996 isl_basic_map_drop_inequality(bmap, k);
997 --k;
998 }
999 isl_int_init(sum);
1000 for (k = 0; k < bmap->n_ineq-1; ++k) {
1001 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1002 h = hash_index(index, size, bits, bmap, k);
1003 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1004 if (!index[h])
1005 continue;
1006 l = index[h] - &bmap->ineq[0];
1007 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1008 if (isl_int_is_pos(sum)) {
1009 bmap = check_for_div_constraints(bmap, k, l, sum,
1010 progress);
1011 continue;
1012 }
1013 if (isl_int_is_zero(sum)) {
1014 /* We need to break out of the loop after these
1015 * changes since the contents of the hash
1016 * will no longer be valid.
1017 * Plus, we probably we want to regauss first.
1018 */
1019 if (progress)
1020 *progress = 1;
1021 isl_basic_map_drop_inequality(bmap, l);
1022 isl_basic_map_inequality_to_equality(bmap, k);
1023 } else
1024 bmap = isl_basic_map_set_to_empty(bmap);
1025 break;
1026 }
1027 isl_int_clear(sum);
1028
1029 free(index);
1030 return bmap;
1031 }
1032
1033
1034 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1035 {
1036 int progress = 1;
1037 if (!bmap)
1038 return NULL;
1039 while (progress) {
1040 progress = 0;
1041 bmap = isl_basic_map_normalize_constraints(bmap);
1042 bmap = remove_duplicate_divs(bmap, &progress);
1043 bmap = eliminate_divs_eq(bmap, &progress);
1044 bmap = eliminate_divs_ineq(bmap, &progress);
1045 bmap = isl_basic_map_gauss(bmap, &progress);
1046 /* requires equalities in normal form */
1047 bmap = normalize_divs(bmap, &progress);
1048 bmap = remove_duplicate_constraints(bmap, &progress);
1049 }
1050 return bmap;
1051 }
1052
1053 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1054 {
1055 return (struct isl_basic_set *)
1056 isl_basic_map_simplify((struct isl_basic_map *)bset);
1057 }
1058
1059
1060 /* If the only constraints a div d=floor(f/m)
1061 * appears in are its two defining constraints
1062 *
1063 * f - m d >=0
1064 * -(f - (m - 1)) + m d >= 0
1065 *
1066 * then it can safely be removed.
1067 */
1068 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1069 {
1070 int i;
1071 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1072
1073 for (i = 0; i < bmap->n_eq; ++i)
1074 if (!isl_int_is_zero(bmap->eq[i][pos]))
1075 return 0;
1076
1077 for (i = 0; i < bmap->n_ineq; ++i) {
1078 if (isl_int_is_zero(bmap->ineq[i][pos]))
1079 continue;
1080 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1081 int neg;
1082 isl_int_sub(bmap->div[div][1],
1083 bmap->div[div][1], bmap->div[div][0]);
1084 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1085 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1086 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1087 isl_int_add(bmap->div[div][1],
1088 bmap->div[div][1], bmap->div[div][0]);
1089 if (!neg)
1090 return 0;
1091 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1092 bmap->n_div-div-1) != -1)
1093 return 0;
1094 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1095 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1096 return 0;
1097 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1098 bmap->n_div-div-1) != -1)
1099 return 0;
1100 } else
1101 return 0;
1102 }
1103
1104 for (i = 0; i < bmap->n_div; ++i)
1105 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1106 return 0;
1107
1108 return 1;
1109 }
1110
1111 /*
1112 * Remove divs that don't occur in any of the constraints or other divs.
1113 * These can arise when dropping some of the variables in a quast
1114 * returned by piplib.
1115 */
1116 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1117 {
1118 int i;
1119
1120 if (!bmap)
1121 return NULL;
1122
1123 for (i = bmap->n_div-1; i >= 0; --i) {
1124 if (!div_is_redundant(bmap, i))
1125 continue;
1126 bmap = isl_basic_map_drop_div(bmap, i);
1127 }
1128 return bmap;
1129 }
1130
1131 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1132 {
1133 bmap = remove_redundant_divs(bmap);
1134 if (!bmap)
1135 return NULL;
1136 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1137 return bmap;
1138 }
1139
1140 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1141 {
1142 return (struct isl_basic_set *)
1143 isl_basic_map_finalize((struct isl_basic_map *)bset);
1144 }
1145
1146 struct isl_set *isl_set_finalize(struct isl_set *set)
1147 {
1148 int i;
1149
1150 if (!set)
1151 return NULL;
1152 for (i = 0; i < set->n; ++i) {
1153 set->p[i] = isl_basic_set_finalize(set->p[i]);
1154 if (!set->p[i])
1155 goto error;
1156 }
1157 return set;
1158 error:
1159 isl_set_free(set);
1160 return NULL;
1161 }
1162
1163 struct isl_map *isl_map_finalize(struct isl_map *map)
1164 {
1165 int i;
1166
1167 if (!map)
1168 return NULL;
1169 for (i = 0; i < map->n; ++i) {
1170 map->p[i] = isl_basic_map_finalize(map->p[i]);
1171 if (!map->p[i])
1172 goto error;
1173 }
1174 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1175 return map;
1176 error:
1177 isl_map_free(map);
1178 return NULL;
1179 }
1180
1181
1182 /* Remove definition of any div that is defined in terms of the given variable.
1183 * The div itself is not removed. Functions such as
1184 * eliminate_divs_ineq depend on the other divs remaining in place.
1185 */
1186 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1187 int pos)
1188 {
1189 int i;
1190
1191 for (i = 0; i < bmap->n_div; ++i) {
1192 if (isl_int_is_zero(bmap->div[i][0]))
1193 continue;
1194 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1195 continue;
1196 isl_int_set_si(bmap->div[i][0], 0);
1197 }
1198 return bmap;
1199 }
1200
1201 /* Eliminate the specified variables from the constraints using
1202 * Fourier-Motzkin. The variables themselves are not removed.
1203 */
1204 struct isl_basic_map *isl_basic_map_eliminate_vars(
1205 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1206 {
1207 int d;
1208 int i, j, k;
1209 unsigned total;
1210
1211 if (n == 0)
1212 return bmap;
1213 if (!bmap)
1214 return NULL;
1215 total = isl_basic_map_total_dim(bmap);
1216
1217 bmap = isl_basic_map_cow(bmap);
1218 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1219 bmap = remove_dependent_vars(bmap, d);
1220
1221 for (d = pos + n - 1;
1222 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1223 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1224 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1225 int n_lower, n_upper;
1226 if (!bmap)
1227 return NULL;
1228 for (i = 0; i < bmap->n_eq; ++i) {
1229 if (isl_int_is_zero(bmap->eq[i][1+d]))
1230 continue;
1231 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1232 isl_basic_map_drop_equality(bmap, i);
1233 break;
1234 }
1235 if (i < bmap->n_eq)
1236 continue;
1237 n_lower = 0;
1238 n_upper = 0;
1239 for (i = 0; i < bmap->n_ineq; ++i) {
1240 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1241 n_lower++;
1242 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1243 n_upper++;
1244 }
1245 bmap = isl_basic_map_extend_constraints(bmap,
1246 0, n_lower * n_upper);
1247 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1248 int last;
1249 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1250 continue;
1251 last = -1;
1252 for (j = 0; j < i; ++j) {
1253 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1254 continue;
1255 last = j;
1256 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1257 isl_int_sgn(bmap->ineq[j][1+d]))
1258 continue;
1259 k = isl_basic_map_alloc_inequality(bmap);
1260 if (k < 0)
1261 goto error;
1262 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1263 1+total);
1264 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1265 1+d, 1+total, NULL);
1266 }
1267 isl_basic_map_drop_inequality(bmap, i);
1268 i = last + 1;
1269 }
1270 if (n_lower > 0 && n_upper > 0) {
1271 bmap = isl_basic_map_normalize_constraints(bmap);
1272 bmap = remove_duplicate_constraints(bmap, NULL);
1273 bmap = isl_basic_map_gauss(bmap, NULL);
1274 bmap = isl_basic_map_convex_hull(bmap);
1275 if (!bmap)
1276 goto error;
1277 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1278 break;
1279 }
1280 }
1281 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1282 return bmap;
1283 error:
1284 isl_basic_map_free(bmap);
1285 return NULL;
1286 }
1287
1288 struct isl_basic_set *isl_basic_set_eliminate_vars(
1289 struct isl_basic_set *bset, unsigned pos, unsigned n)
1290 {
1291 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1292 (struct isl_basic_map *)bset, pos, n);
1293 }
1294
1295 /* Don't assume equalities are in order, because align_divs
1296 * may have changed the order of the divs.
1297 */
1298 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1299 {
1300 int d, i;
1301 unsigned total;
1302
1303 total = isl_dim_total(bmap->dim);
1304 for (d = 0; d < total; ++d)
1305 elim[d] = -1;
1306 for (i = 0; i < bmap->n_eq; ++i) {
1307 for (d = total - 1; d >= 0; --d) {
1308 if (isl_int_is_zero(bmap->eq[i][1+d]))
1309 continue;
1310 elim[d] = i;
1311 break;
1312 }
1313 }
1314 }
1315
1316 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1317 {
1318 compute_elimination_index((struct isl_basic_map *)bset, elim);
1319 }
1320
1321 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1322 struct isl_basic_map *bmap, int *elim)
1323 {
1324 int d;
1325 int copied = 0;
1326 unsigned total;
1327
1328 total = isl_dim_total(bmap->dim);
1329 for (d = total - 1; d >= 0; --d) {
1330 if (isl_int_is_zero(src[1+d]))
1331 continue;
1332 if (elim[d] == -1)
1333 continue;
1334 if (!copied) {
1335 isl_seq_cpy(dst, src, 1 + total);
1336 copied = 1;
1337 }
1338 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1339 }
1340 return copied;
1341 }
1342
1343 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1344 struct isl_basic_set *bset, int *elim)
1345 {
1346 return reduced_using_equalities(dst, src,
1347 (struct isl_basic_map *)bset, elim);
1348 }
1349
1350 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1351 struct isl_basic_set *bset, struct isl_basic_set *context)
1352 {
1353 int i;
1354 int *elim;
1355
1356 if (!bset || !context)
1357 goto error;
1358
1359 bset = isl_basic_set_cow(bset);
1360 if (!bset)
1361 goto error;
1362
1363 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1364 if (!elim)
1365 goto error;
1366 set_compute_elimination_index(context, elim);
1367 for (i = 0; i < bset->n_eq; ++i)
1368 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1369 context, elim);
1370 for (i = 0; i < bset->n_ineq; ++i)
1371 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1372 context, elim);
1373 isl_basic_set_free(context);
1374 free(elim);
1375 bset = isl_basic_set_simplify(bset);
1376 bset = isl_basic_set_finalize(bset);
1377 return bset;
1378 error:
1379 isl_basic_set_free(bset);
1380 isl_basic_set_free(context);
1381 return NULL;
1382 }
1383
1384 static struct isl_basic_set *remove_shifted_constraints(
1385 struct isl_basic_set *bset, struct isl_basic_set *context)
1386 {
1387 unsigned int size;
1388 isl_int ***index;
1389 int bits;
1390 int k, h, l;
1391
1392 if (!bset)
1393 return NULL;
1394
1395 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1396 bits = ffs(size) - 1;
1397 index = isl_calloc_array(ctx, isl_int **, size);
1398 if (!index)
1399 return bset;
1400
1401 for (k = 0; k < context->n_ineq; ++k) {
1402 h = set_hash_index(index, size, bits, context, k);
1403 index[h] = &context->ineq[k];
1404 }
1405 for (k = 0; k < bset->n_ineq; ++k) {
1406 h = set_hash_index(index, size, bits, bset, k);
1407 if (!index[h])
1408 continue;
1409 l = index[h] - &context->ineq[0];
1410 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1411 continue;
1412 bset = isl_basic_set_cow(bset);
1413 if (!bset)
1414 goto error;
1415 isl_basic_set_drop_inequality(bset, k);
1416 --k;
1417 }
1418 free(index);
1419 return bset;
1420 error:
1421 free(index);
1422 return bset;
1423 }
1424
1425 /* Tighten (decrease) the constant terms of the inequalities based
1426 * on the equalities, without removing any integer points.
1427 * For example, if there is an equality
1428 *
1429 * i = 3 * j
1430 *
1431 * and an inequality
1432 *
1433 * i >= 1
1434 *
1435 * then we want to replace the inequality by
1436 *
1437 * i >= 3
1438 *
1439 * We do this by computing a variable compression and translating
1440 * the constraints to the compressed space.
1441 * If any constraint has coefficients (except the contant term)
1442 * with a common factor "f", then we can replace the constant term "c"
1443 * by
1444 *
1445 * f * floor(c/f)
1446 *
1447 * That is, we add
1448 *
1449 * f * floor(c/f) - c = -fract(c/f)
1450 *
1451 * and we can add the same value to the original constraint.
1452 *
1453 * In the example, the compressed space only contains "j",
1454 * and the inequality translates to
1455 *
1456 * 3 * j - 1 >= 0
1457 *
1458 * We add -fract(-1/3) = -2 to the original constraint to obtain
1459 *
1460 * i - 3 >= 0
1461 */
1462 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1463 struct isl_basic_set *bset)
1464 {
1465 int i;
1466 unsigned total;
1467 struct isl_mat *B, *C;
1468 isl_int gcd;
1469
1470 if (!bset)
1471 return NULL;
1472
1473 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1474 return bset;
1475
1476 if (!bset->n_ineq)
1477 return bset;
1478
1479 bset = isl_basic_set_cow(bset);
1480 if (!bset)
1481 return NULL;
1482
1483 total = isl_basic_set_total_dim(bset);
1484 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1485 C = isl_mat_variable_compression(B, NULL);
1486 if (!C)
1487 return bset;
1488 if (C->n_col == 0) {
1489 isl_mat_free(C);
1490 return isl_basic_set_set_to_empty(bset);
1491 }
1492 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1493 0, bset->n_ineq, 0, 1 + total);
1494 C = isl_mat_product(B, C);
1495 if (!C)
1496 return bset;
1497
1498 isl_int_init(gcd);
1499 for (i = 0; i < bset->n_ineq; ++i) {
1500 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1501 if (isl_int_is_one(gcd))
1502 continue;
1503 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1504 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1505 }
1506 isl_int_clear(gcd);
1507
1508 isl_mat_free(C);
1509
1510 return bset;
1511 }
1512
1513 /* Remove all information from bset that is redundant in the context
1514 * of context. In particular, equalities that are linear combinations
1515 * of those in context are removed. Then the inequalities that are
1516 * redundant in the context of the equalities and inequalities of
1517 * context are removed.
1518 *
1519 * We first simplify the constraints of "bset" in the context of the
1520 * equalities of "context".
1521 * Then we simplify the inequalities of the context in the context
1522 * of the equalities of bset and remove the inequalities from "bset"
1523 * that are obviously redundant with respect to some inequality in "context".
1524 *
1525 * If there are any inequalities left, we construct a tableau for
1526 * the context and then add the inequalities of "bset".
1527 * Before adding these equalities, we freeze all constraints such that
1528 * they won't be considered redundant in terms of the constraints of "bset".
1529 * Then we detect all equalities and redundant constraints (among the
1530 * constraints that weren't frozen) and update bset according to the results.
1531 * We have to be careful here because we don't want any of the context
1532 * constraints to remain and because we haven't added the equalities of "bset"
1533 * to the tableau so we temporarily have to pretend that there were no
1534 * equalities.
1535 */
1536 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1537 struct isl_basic_set *context)
1538 {
1539 int i;
1540 struct isl_tab *tab;
1541 unsigned context_ineq;
1542 struct isl_basic_set *combined = NULL;
1543
1544 if (!context || !bset)
1545 goto error;
1546
1547 if (context->n_eq > 0)
1548 bset = isl_basic_set_reduce_using_equalities(bset,
1549 isl_basic_set_copy(context));
1550 if (!bset)
1551 goto error;
1552 if (isl_basic_set_fast_is_empty(bset))
1553 goto done;
1554 if (!bset->n_ineq)
1555 goto done;
1556
1557 if (bset->n_eq > 0) {
1558 struct isl_basic_set *affine_hull;
1559 affine_hull = isl_basic_set_copy(bset);
1560 affine_hull = isl_basic_set_cow(affine_hull);
1561 if (!affine_hull)
1562 goto error;
1563 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1564 context = isl_basic_set_intersect(context, affine_hull);
1565 context = isl_basic_set_gauss(context, NULL);
1566 context = normalize_constraints_in_compressed_space(context);
1567 }
1568 if (!context)
1569 goto error;
1570 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1571 isl_basic_set_free(bset);
1572 return context;
1573 }
1574 if (!context->n_ineq)
1575 goto done;
1576 bset = remove_shifted_constraints(bset, context);
1577 if (!bset->n_ineq)
1578 goto done;
1579 context_ineq = context->n_ineq;
1580 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1581 if (isl_basic_set_free_equality(combined, context->n_eq) < 0)
1582 goto error;
1583 combined = isl_basic_set_extend_constraints(combined,
1584 bset->n_eq, bset->n_ineq);
1585 tab = isl_tab_from_basic_set(combined);
1586 if (!tab)
1587 goto error;
1588 for (i = 0; i < context_ineq; ++i)
1589 if (isl_tab_freeze_constraint(tab, i) < 0)
1590 goto error;
1591 tab = isl_tab_extend(tab, bset->n_ineq);
1592 if (!tab)
1593 goto error;
1594 for (i = 0; i < bset->n_ineq; ++i)
1595 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1596 goto error;
1597 bset = isl_basic_set_add_constraints(combined, bset, 0);
1598 tab = isl_tab_detect_implicit_equalities(tab);
1599 if (isl_tab_detect_redundant(tab) < 0) {
1600 isl_tab_free(tab);
1601 goto error2;
1602 }
1603 for (i = 0; i < context_ineq; ++i) {
1604 tab->con[i].is_zero = 0;
1605 tab->con[i].is_redundant = 1;
1606 }
1607 bset = isl_basic_set_update_from_tab(bset, tab);
1608 isl_tab_free(tab);
1609 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1610 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1611 done:
1612 bset = isl_basic_set_simplify(bset);
1613 bset = isl_basic_set_finalize(bset);
1614 isl_basic_set_free(context);
1615 return bset;
1616 error:
1617 isl_basic_set_free(combined);
1618 error2:
1619 isl_basic_set_free(bset);
1620 isl_basic_set_free(context);
1621 return NULL;
1622 }
1623
1624 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1625 * We simply add the equalities in context to bmap and then do a regular
1626 * div normalizations. Better results can be obtained by normalizing
1627 * only the divs in bmap than do not also appear in context.
1628 * We need to be careful to reduce the divs using the equalities
1629 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1630 * spurious constraints.
1631 */
1632 static struct isl_basic_map *normalize_divs_in_context(
1633 struct isl_basic_map *bmap, struct isl_basic_map *context)
1634 {
1635 int i;
1636 unsigned total_context;
1637 int div_eq;
1638
1639 div_eq = n_pure_div_eq(bmap);
1640 if (div_eq == 0)
1641 return bmap;
1642
1643 if (context->n_div > 0)
1644 bmap = isl_basic_map_align_divs(bmap, context);
1645
1646 total_context = isl_basic_map_total_dim(context);
1647 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1648 for (i = 0; i < context->n_eq; ++i) {
1649 int k;
1650 k = isl_basic_map_alloc_equality(bmap);
1651 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1652 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1653 isl_basic_map_total_dim(bmap) - total_context);
1654 }
1655 bmap = isl_basic_map_gauss(bmap, NULL);
1656 bmap = normalize_divs(bmap, NULL);
1657 bmap = isl_basic_map_gauss(bmap, NULL);
1658 return bmap;
1659 }
1660
1661 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1662 struct isl_basic_map *context)
1663 {
1664 struct isl_basic_set *bset;
1665
1666 if (!bmap || !context)
1667 goto error;
1668
1669 if (isl_basic_map_is_universe(context)) {
1670 isl_basic_map_free(context);
1671 return bmap;
1672 }
1673 if (isl_basic_map_is_universe(bmap)) {
1674 isl_basic_map_free(context);
1675 return bmap;
1676 }
1677 if (isl_basic_map_fast_is_empty(context)) {
1678 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1679 isl_basic_map_free(context);
1680 isl_basic_map_free(bmap);
1681 return isl_basic_map_universe(dim);
1682 }
1683 if (isl_basic_map_fast_is_empty(bmap)) {
1684 isl_basic_map_free(context);
1685 return bmap;
1686 }
1687
1688 bmap = isl_basic_map_convex_hull(bmap);
1689 context = isl_basic_map_convex_hull(context);
1690
1691 if (context->n_eq)
1692 bmap = normalize_divs_in_context(bmap, context);
1693
1694 context = isl_basic_map_align_divs(context, bmap);
1695 bmap = isl_basic_map_align_divs(bmap, context);
1696
1697 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1698 isl_basic_map_underlying_set(context));
1699
1700 return isl_basic_map_overlying_set(bset, bmap);
1701 error:
1702 isl_basic_map_free(bmap);
1703 isl_basic_map_free(context);
1704 return NULL;
1705 }
1706
1707 /*
1708 * Assumes context has no implicit divs.
1709 */
1710 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1711 {
1712 int i;
1713
1714 if (!map || !context)
1715 goto error;;
1716
1717 if (isl_basic_map_is_universe(context)) {
1718 isl_basic_map_free(context);
1719 return map;
1720 }
1721 if (isl_basic_map_fast_is_empty(context)) {
1722 struct isl_dim *dim = isl_dim_copy(map->dim);
1723 isl_basic_map_free(context);
1724 isl_map_free(map);
1725 return isl_map_universe(dim);
1726 }
1727
1728 context = isl_basic_map_convex_hull(context);
1729 map = isl_map_cow(map);
1730 if (!map || !context)
1731 goto error;;
1732 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1733 map = isl_map_compute_divs(map);
1734 for (i = 0; i < map->n; ++i)
1735 context = isl_basic_map_align_divs(context, map->p[i]);
1736 for (i = 0; i < map->n; ++i) {
1737 map->p[i] = isl_basic_map_gist(map->p[i],
1738 isl_basic_map_copy(context));
1739 if (!map->p[i])
1740 goto error;
1741 }
1742 isl_basic_map_free(context);
1743 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1744 return map;
1745 error:
1746 isl_map_free(map);
1747 isl_basic_map_free(context);
1748 return NULL;
1749 }
1750
1751 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1752 struct isl_basic_set *context)
1753 {
1754 return (struct isl_basic_set *)isl_basic_map_gist(
1755 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1756 }
1757
1758 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1759 {
1760 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1761 (struct isl_basic_map *)context);
1762 }
1763
1764 /* Quick check to see if two basic maps are disjoint.
1765 * In particular, we reduce the equalities and inequalities of
1766 * one basic map in the context of the equalities of the other
1767 * basic map and check if we get a contradiction.
1768 */
1769 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1770 struct isl_basic_map *bmap2)
1771 {
1772 struct isl_vec *v = NULL;
1773 int *elim = NULL;
1774 unsigned total;
1775 int i;
1776
1777 if (!bmap1 || !bmap2)
1778 return -1;
1779 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1780 return -1);
1781 if (bmap1->n_div || bmap2->n_div)
1782 return 0;
1783 if (!bmap1->n_eq && !bmap2->n_eq)
1784 return 0;
1785
1786 total = isl_dim_total(bmap1->dim);
1787 if (total == 0)
1788 return 0;
1789 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1790 if (!v)
1791 goto error;
1792 elim = isl_alloc_array(bmap1->ctx, int, total);
1793 if (!elim)
1794 goto error;
1795 compute_elimination_index(bmap1, elim);
1796 for (i = 0; i < bmap2->n_eq; ++i) {
1797 int reduced;
1798 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1799 bmap1, elim);
1800 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1801 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1802 goto disjoint;
1803 }
1804 for (i = 0; i < bmap2->n_ineq; ++i) {
1805 int reduced;
1806 reduced = reduced_using_equalities(v->block.data,
1807 bmap2->ineq[i], bmap1, elim);
1808 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1809 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1810 goto disjoint;
1811 }
1812 compute_elimination_index(bmap2, elim);
1813 for (i = 0; i < bmap1->n_ineq; ++i) {
1814 int reduced;
1815 reduced = reduced_using_equalities(v->block.data,
1816 bmap1->ineq[i], bmap2, elim);
1817 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1818 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1819 goto disjoint;
1820 }
1821 isl_vec_free(v);
1822 free(elim);
1823 return 0;
1824 disjoint:
1825 isl_vec_free(v);
1826 free(elim);
1827 return 1;
1828 error:
1829 isl_vec_free(v);
1830 free(elim);
1831 return -1;
1832 }
1833
1834 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1835 struct isl_basic_set *bset2)
1836 {
1837 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1838 (struct isl_basic_map *)bset2);
1839 }
1840
1841 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1842 {
1843 int i, j;
1844
1845 if (!map1 || !map2)
1846 return -1;
1847
1848 if (isl_map_fast_is_equal(map1, map2))
1849 return 0;
1850
1851 for (i = 0; i < map1->n; ++i) {
1852 for (j = 0; j < map2->n; ++j) {
1853 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1854 map2->p[j]);
1855 if (d != 1)
1856 return d;
1857 }
1858 }
1859 return 1;
1860 }
1861
1862 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1863 {
1864 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1865 (struct isl_map *)set2);
1866 }
1867
1868 /* Check if we can combine a given div with lower bound l and upper
1869 * bound u with some other div and if so return that other div.
1870 * Otherwise return -1.
1871 *
1872 * We first check that
1873 * - the bounds are opposites of each other (except for the constant
1874 * term)
1875 * - the bounds do not reference any other div
1876 * - no div is defined in terms of this div
1877 *
1878 * Let m be the size of the range allowed on the div by the bounds.
1879 * That is, the bounds are of the form
1880 *
1881 * e <= a <= e + m - 1
1882 *
1883 * with e some expression in the other variables.
1884 * We look for another div b such that no third div is defined in terms
1885 * of this second div b and such that in any constraint that contains
1886 * a (except for the given lower and upper bound), also contains b
1887 * with a coefficient that is m times that of b.
1888 * That is, all constraints (execpt for the lower and upper bound)
1889 * are of the form
1890 *
1891 * e + f (a + m b) >= 0
1892 *
1893 * If so, we return b so that "a + m b" can be replaced by
1894 * a single div "c = a + m b".
1895 */
1896 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1897 unsigned div, unsigned l, unsigned u)
1898 {
1899 int i, j;
1900 unsigned dim;
1901 int coalesce = -1;
1902
1903 if (bmap->n_div <= 1)
1904 return -1;
1905 dim = isl_dim_total(bmap->dim);
1906 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1907 return -1;
1908 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1909 bmap->n_div - div - 1) != -1)
1910 return -1;
1911 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1912 dim + bmap->n_div))
1913 return -1;
1914
1915 for (i = 0; i < bmap->n_div; ++i) {
1916 if (isl_int_is_zero(bmap->div[i][0]))
1917 continue;
1918 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1919 return -1;
1920 }
1921
1922 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1923 if (isl_int_is_neg(bmap->ineq[l][0])) {
1924 isl_int_sub(bmap->ineq[l][0],
1925 bmap->ineq[l][0], bmap->ineq[u][0]);
1926 bmap = isl_basic_map_copy(bmap);
1927 bmap = isl_basic_map_set_to_empty(bmap);
1928 isl_basic_map_free(bmap);
1929 return -1;
1930 }
1931 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1932 for (i = 0; i < bmap->n_div; ++i) {
1933 if (i == div)
1934 continue;
1935 if (!pairs[i])
1936 continue;
1937 for (j = 0; j < bmap->n_div; ++j) {
1938 if (isl_int_is_zero(bmap->div[j][0]))
1939 continue;
1940 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1941 break;
1942 }
1943 if (j < bmap->n_div)
1944 continue;
1945 for (j = 0; j < bmap->n_ineq; ++j) {
1946 int valid;
1947 if (j == l || j == u)
1948 continue;
1949 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1950 continue;
1951 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1952 break;
1953 isl_int_mul(bmap->ineq[j][1 + dim + div],
1954 bmap->ineq[j][1 + dim + div],
1955 bmap->ineq[l][0]);
1956 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1957 bmap->ineq[j][1 + dim + i]);
1958 isl_int_divexact(bmap->ineq[j][1 + dim + div],
1959 bmap->ineq[j][1 + dim + div],
1960 bmap->ineq[l][0]);
1961 if (!valid)
1962 break;
1963 }
1964 if (j < bmap->n_ineq)
1965 continue;
1966 coalesce = i;
1967 break;
1968 }
1969 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1970 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1971 return coalesce;
1972 }
1973
1974 /* Given a lower and an upper bound on div i, construct an inequality
1975 * that when nonnegative ensures that this pair of bounds always allows
1976 * for an integer value of the given div.
1977 * The lower bound is inequality l, while the upper bound is inequality u.
1978 * The constructed inequality is stored in ineq.
1979 * g, fl, fu are temporary scalars.
1980 *
1981 * Let the upper bound be
1982 *
1983 * -n_u a + e_u >= 0
1984 *
1985 * and the lower bound
1986 *
1987 * n_l a + e_l >= 0
1988 *
1989 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1990 * We have
1991 *
1992 * - f_u e_l <= f_u f_l g a <= f_l e_u
1993 *
1994 * Since all variables are integer valued, this is equivalent to
1995 *
1996 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1997 *
1998 * If this interval is at least f_u f_l g, then it contains at least
1999 * one integer value for a.
2000 * That is, the test constraint is
2001 *
2002 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2003 */
2004 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2005 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2006 {
2007 unsigned dim;
2008 dim = isl_dim_total(bmap->dim);
2009
2010 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2011 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2012 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2013 isl_int_neg(fu, fu);
2014 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2015 1 + dim + bmap->n_div);
2016 isl_int_add(ineq[0], ineq[0], fl);
2017 isl_int_add(ineq[0], ineq[0], fu);
2018 isl_int_sub_ui(ineq[0], ineq[0], 1);
2019 isl_int_mul(g, g, fl);
2020 isl_int_mul(g, g, fu);
2021 isl_int_sub(ineq[0], ineq[0], g);
2022 }
2023
2024 /* Remove more kinds of divs that are not strictly needed.
2025 * In particular, if all pairs of lower and upper bounds on a div
2026 * are such that they allow at least one integer value of the div,
2027 * the we can eliminate the div using Fourier-Motzkin without
2028 * introducing any spurious solutions.
2029 */
2030 static struct isl_basic_map *drop_more_redundant_divs(
2031 struct isl_basic_map *bmap, int *pairs, int n)
2032 {
2033 struct isl_tab *tab = NULL;
2034 struct isl_vec *vec = NULL;
2035 unsigned dim;
2036 int remove = -1;
2037 isl_int g, fl, fu;
2038
2039 isl_int_init(g);
2040 isl_int_init(fl);
2041 isl_int_init(fu);
2042
2043 if (!bmap)
2044 goto error;
2045
2046 dim = isl_dim_total(bmap->dim);
2047 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2048 if (!vec)
2049 goto error;
2050
2051 tab = isl_tab_from_basic_map(bmap);
2052
2053 while (n > 0) {
2054 int i, l, u;
2055 int best = -1;
2056 enum isl_lp_result res;
2057
2058 for (i = 0; i < bmap->n_div; ++i) {
2059 if (!pairs[i])
2060 continue;
2061 if (best >= 0 && pairs[best] <= pairs[i])
2062 continue;
2063 best = i;
2064 }
2065
2066 i = best;
2067 for (l = 0; l < bmap->n_ineq; ++l) {
2068 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2069 continue;
2070 for (u = 0; u < bmap->n_ineq; ++u) {
2071 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2072 continue;
2073 construct_test_ineq(bmap, i, l, u,
2074 vec->el, g, fl, fu);
2075 res = isl_tab_min(tab, vec->el,
2076 bmap->ctx->one, &g, NULL, 0);
2077 if (res == isl_lp_error)
2078 goto error;
2079 if (res == isl_lp_empty) {
2080 bmap = isl_basic_map_set_to_empty(bmap);
2081 break;
2082 }
2083 if (res != isl_lp_ok || isl_int_is_neg(g))
2084 break;
2085 }
2086 if (u < bmap->n_ineq)
2087 break;
2088 }
2089 if (l == bmap->n_ineq) {
2090 remove = i;
2091 break;
2092 }
2093 pairs[i] = 0;
2094 --n;
2095 }
2096
2097 isl_tab_free(tab);
2098 isl_vec_free(vec);
2099
2100 isl_int_clear(g);
2101 isl_int_clear(fl);
2102 isl_int_clear(fu);
2103
2104 free(pairs);
2105
2106 if (remove < 0)
2107 return bmap;
2108
2109 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2110 return isl_basic_map_drop_redundant_divs(bmap);
2111 error:
2112 free(pairs);
2113 isl_basic_map_free(bmap);
2114 isl_tab_free(tab);
2115 isl_vec_free(vec);
2116 isl_int_clear(g);
2117 isl_int_clear(fl);
2118 isl_int_clear(fu);
2119 return NULL;
2120 }
2121
2122 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2123 * and the upper bound u, div1 always occurs together with div2 in the form
2124 * (div1 + m div2), where m is the constant range on the variable div1
2125 * allowed by l and u, replace the pair div1 and div2 by a single
2126 * div that is equal to div1 + m div2.
2127 *
2128 * The new div will appear in the location that contains div2.
2129 * We need to modify all constraints that contain
2130 * div2 = (div - div1) / m
2131 * (If a constraint does not contain div2, it will also not contain div1.)
2132 * If the constraint also contains div1, then we know they appear
2133 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2134 * i.e., the coefficient of div is f.
2135 *
2136 * Otherwise, we first need to introduce div1 into the constraint.
2137 * Let the l be
2138 *
2139 * div1 + f >=0
2140 *
2141 * and u
2142 *
2143 * -div1 + f' >= 0
2144 *
2145 * A lower bound on div2
2146 *
2147 * n div2 + t >= 0
2148 *
2149 * can be replaced by
2150 *
2151 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2152 *
2153 * with g = gcd(m,n).
2154 * An upper bound
2155 *
2156 * -n div2 + t >= 0
2157 *
2158 * can be replaced by
2159 *
2160 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2161 *
2162 * These constraint are those that we would obtain from eliminating
2163 * div1 using Fourier-Motzkin.
2164 *
2165 * After all constraints have been modified, we drop the lower and upper
2166 * bound and then drop div1.
2167 */
2168 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2169 unsigned div1, unsigned div2, unsigned l, unsigned u)
2170 {
2171 isl_int a;
2172 isl_int b;
2173 isl_int m;
2174 unsigned dim, total;
2175 int i;
2176
2177 dim = isl_dim_total(bmap->dim);
2178 total = 1 + dim + bmap->n_div;
2179
2180 isl_int_init(a);
2181 isl_int_init(b);
2182 isl_int_init(m);
2183 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2184 isl_int_add_ui(m, m, 1);
2185
2186 for (i = 0; i < bmap->n_ineq; ++i) {
2187 if (i == l || i == u)
2188 continue;
2189 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2190 continue;
2191 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2192 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2193 isl_int_divexact(a, m, b);
2194 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2195 if (isl_int_is_pos(b)) {
2196 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2197 b, bmap->ineq[l], total);
2198 } else {
2199 isl_int_neg(b, b);
2200 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2201 b, bmap->ineq[u], total);
2202 }
2203 }
2204 isl_int_set(bmap->ineq[i][1 + dim + div2],
2205 bmap->ineq[i][1 + dim + div1]);
2206 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2207 }
2208
2209 isl_int_clear(a);
2210 isl_int_clear(b);
2211 isl_int_clear(m);
2212 if (l > u) {
2213 isl_basic_map_drop_inequality(bmap, l);
2214 isl_basic_map_drop_inequality(bmap, u);
2215 } else {
2216 isl_basic_map_drop_inequality(bmap, u);
2217 isl_basic_map_drop_inequality(bmap, l);
2218 }
2219 bmap = isl_basic_map_drop_div(bmap, div1);
2220 return bmap;
2221 }
2222
2223 /* First check if we can coalesce any pair of divs and
2224 * then continue with dropping more redundant divs.
2225 *
2226 * We loop over all pairs of lower and upper bounds on a div
2227 * with coefficient 1 and -1, respectively, check if there
2228 * is any other div "c" with which we can coalesce the div
2229 * and if so, perform the coalescing.
2230 */
2231 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2232 struct isl_basic_map *bmap, int *pairs, int n)
2233 {
2234 int i, l, u;
2235 unsigned dim;
2236
2237 dim = isl_dim_total(bmap->dim);
2238
2239 for (i = 0; i < bmap->n_div; ++i) {
2240 if (!pairs[i])
2241 continue;
2242 for (l = 0; l < bmap->n_ineq; ++l) {
2243 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2244 continue;
2245 for (u = 0; u < bmap->n_ineq; ++u) {
2246 int c;
2247
2248 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2249 continue;
2250 c = div_find_coalesce(bmap, pairs, i, l, u);
2251 if (c < 0)
2252 continue;
2253 free(pairs);
2254 bmap = coalesce_divs(bmap, i, c, l, u);
2255 return isl_basic_map_drop_redundant_divs(bmap);
2256 }
2257 }
2258 }
2259
2260 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2261 return bmap;
2262
2263 return drop_more_redundant_divs(bmap, pairs, n);
2264 }
2265
2266 /* Remove divs that are not strictly needed.
2267 * In particular, if a div only occurs positively (or negatively)
2268 * in constraints, then it can simply be dropped.
2269 * Also, if a div occurs only occurs in two constraints and if moreover
2270 * those two constraints are opposite to each other, except for the constant
2271 * term and if the sum of the constant terms is such that for any value
2272 * of the other values, there is always at least one integer value of the
2273 * div, i.e., if one plus this sum is greater than or equal to
2274 * the (absolute value) of the coefficent of the div in the constraints,
2275 * then we can also simply drop the div.
2276 *
2277 * If any divs are left after these simple checks then we move on
2278 * to more complicated cases in drop_more_redundant_divs.
2279 */
2280 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2281 struct isl_basic_map *bmap)
2282 {
2283 int i, j;
2284 unsigned off;
2285 int *pairs = NULL;
2286 int n = 0;
2287
2288 if (!bmap)
2289 goto error;
2290
2291 off = isl_dim_total(bmap->dim);
2292 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2293 if (!pairs)
2294 goto error;
2295
2296 for (i = 0; i < bmap->n_div; ++i) {
2297 int pos, neg;
2298 int last_pos, last_neg;
2299 int redundant;
2300 int defined;
2301
2302 defined = !isl_int_is_zero(bmap->div[i][0]);
2303 for (j = 0; j < bmap->n_eq; ++j)
2304 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2305 break;
2306 if (j < bmap->n_eq)
2307 continue;
2308 ++n;
2309 pos = neg = 0;
2310 for (j = 0; j < bmap->n_ineq; ++j) {
2311 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2312 last_pos = j;
2313 ++pos;
2314 }
2315 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2316 last_neg = j;
2317 ++neg;
2318 }
2319 }
2320 pairs[i] = pos * neg;
2321 if (pairs[i] == 0) {
2322 for (j = bmap->n_ineq - 1; j >= 0; --j)
2323 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2324 isl_basic_map_drop_inequality(bmap, j);
2325 bmap = isl_basic_map_drop_div(bmap, i);
2326 free(pairs);
2327 return isl_basic_map_drop_redundant_divs(bmap);
2328 }
2329 if (pairs[i] != 1)
2330 continue;
2331 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2332 bmap->ineq[last_neg] + 1,
2333 off + bmap->n_div))
2334 continue;
2335
2336 isl_int_add(bmap->ineq[last_pos][0],
2337 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2338 isl_int_add_ui(bmap->ineq[last_pos][0],
2339 bmap->ineq[last_pos][0], 1);
2340 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2341 bmap->ineq[last_pos][1+off+i]);
2342 isl_int_sub_ui(bmap->ineq[last_pos][0],
2343 bmap->ineq[last_pos][0], 1);
2344 isl_int_sub(bmap->ineq[last_pos][0],
2345 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2346 if (!redundant) {
2347 if (defined ||
2348 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2349 pairs[i] = 0;
2350 --n;
2351 continue;
2352 }
2353 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2354 bmap = isl_basic_map_simplify(bmap);
2355 free(pairs);
2356 return isl_basic_map_drop_redundant_divs(bmap);
2357 }
2358 if (last_pos > last_neg) {
2359 isl_basic_map_drop_inequality(bmap, last_pos);
2360 isl_basic_map_drop_inequality(bmap, last_neg);
2361 } else {
2362 isl_basic_map_drop_inequality(bmap, last_neg);
2363 isl_basic_map_drop_inequality(bmap, last_pos);
2364 }
2365 bmap = isl_basic_map_drop_div(bmap, i);
2366 free(pairs);
2367 return isl_basic_map_drop_redundant_divs(bmap);
2368 }
2369
2370 if (n > 0)
2371 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2372
2373 free(pairs);
2374 return bmap;
2375 error:
2376 free(pairs);
2377 isl_basic_map_free(bmap);
2378 return NULL;
2379 }
2380
2381 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2382 struct isl_basic_set *bset)
2383 {
2384 return (struct isl_basic_set *)
2385 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2386 }
2387
2388 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2389 {
2390 int i;
2391
2392 if (!map)
2393 return NULL;
2394 for (i = 0; i < map->n; ++i) {
2395 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2396 if (!map->p[i])
2397 goto error;
2398 }
2399 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2400 return map;
2401 error:
2402 isl_map_free(map);
2403 return NULL;
2404 }
2405
2406 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2407 {
2408 return (struct isl_set *)
2409 isl_map_drop_redundant_divs((struct isl_map *)set);
2410 }
Integer set library